diff --git a/09-Nonlinear-Filtering.ipynb b/09-Nonlinear-Filtering.ipynb index 26958db..9800c5c 100644 --- a/09-Nonlinear-Filtering.ipynb +++ b/09-Nonlinear-Filtering.ipynb @@ -292,7 +292,7 @@ "\n", "$$m\\frac{d^2x}{dt^2} + c\\frac{dx}{dt} +kx = 0$$\n", "\n", - "It is not possible to write a linear equation for this second order differential equation, and therefore we cannot design a Kalman filter using the theory that we have learned.\n", + "There is no linear solution for $x(t)$ for this second order differential equation, and therefore we cannot design a Kalman filter using the theory that we have learned.\n", "\n", "A second source of nonlinearity comes from the measurements. For example, radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n", "\n", @@ -942,7 +942,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.0" + "version": "3.5.1" } }, "nbformat": 4, diff --git a/10-Unscented-Kalman-Filter.ipynb b/10-Unscented-Kalman-Filter.ipynb index a2c82a3..2a1a9e8 100644 --- a/10-Unscented-Kalman-Filter.ipynb +++ b/10-Unscented-Kalman-Filter.ipynb @@ -16,7 +16,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -262,7 +262,7 @@ "" ] }, - "execution_count": 1, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -290,7 +290,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": { "collapsed": false, "scrolled": true @@ -298,9 +298,9 @@ "outputs": [ { "data": { - "image/png": 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JiIgMgaQ91Ybeg3P26jGcvLQf1TW3UFJeiJyCDIho+Ntlb+OICUNmIzQwXI8p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\nREREREQGYlJNRERERGSg/w/lTkwC6Q5XNgAAAABJRU5ErkJggg==\n", 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Yf/ALAEC7Vp0xcchMtHDz0ntWIiKi+jCYpdITEhLkilEvkiQhtyQTKTk3EZd2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\nT7feckcgG8d5sC3I1j8Gaq3Ocj5Hjx7FG2+8gR9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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -351,7 +351,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "metadata": { "collapsed": false, "scrolled": false @@ -359,9 +359,9 @@ "outputs": [ { "data": { - "image/png": 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D7rQT8odu6kS1ziiKgtPtxOPzUPQxc4qyrAHSLw1mz+9dxl3kT5eT4ZNZWrc9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\n0UqOH5+Hy7UR6Kp3WWHg1r2ttQHSw8NhsbGt7vgHg6L/gS3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j9m7Z2+Q8Y6Gv4qvFTM6Y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39GnIjh8+js1hI+gL3vYopclkwuFykOXJYuHH9CnKevaWfmnQL3gboA1gxpQZ\nRpci7kBGtz0sXbqU73//5/j9FUjwFTd2Nz7fWo4dW8KcOc/w6KNz+dnPfijLJYvramxsZPPmzaxd\nu5bVq1dz5swZnE4nzc3N8XBy9QITZrMZj8dDIBCgsLAwHnYnTJggF2DehPr6enYc3UG/Uen5e735\ncjN7t+5l6/qt7Nqyi2gkiqqo8enHbqWVIZHD5UBVVB4qeohFzy/ivrH3pf0FkbdK0zRMZvmepLu0\nDb8nT57k+edfwe9/G8jcfjBxq0zA0/j983jjja+zZs2DLF78O2bPnm10YSJJNDc3s2XLFtatW8eq\nVas4ceIETqeTlpaW+Pyg1wu7w4cPj4fdSZMm4Xa7jXgZKSsajbJx+0a8g7xYbenxJ0xRFKrfq2bn\npp1UrKug9nQtNrstPvfunTCbzdgcNnrl96LkxRKmLZyG2ys/cx2RtofMkB6/Oa4SiURYtOgj+P1f\nAmSJQnE7sgmHf0o4vIhHH/04L730DP/xH9+XU9AZyO/3U1FRwfr161mxYgXV1dW4XK7rhl2TyYTX\n6yUYDDJo0CCKi4uZO3cukydPJjs724iXkTb2HdhHvVrPwF6pvZjFhdoL7Nqyi4q1FRyoPIDZYiYc\nCqNEFeD2R3djnFlONE1j6oKpFD9bzPD7hndG2WlP0zSslrSMRiJBWv4Lf+lL/8wHH+SiKF80uhSR\n8mYRCOzlt7/9O9aufZilS//CfffdZ3RRogsFg0G2bdtGaWkpy5cv5/DhwzidTnw+H4qiB5NIpO3q\nV4lht6CggPnz5zN37lymTp0qi6l0ooaGBrYd2pby7Q7ffuXbvLftPSwWC8FAxyvz3Sqr1YrZYmbg\nXQMpebGEiXMmyqIftygaieLuKSPj6S7twu/KlSv59a9fw+/fBcipC9EZehEIvMEHH/yWhx6axr/9\n27f57Gc/Jb1yaSIcDrNjxw42bNjA8uXL2bdvH06nE7/fTzQajT/mal6vl3A4TJ8+fZg7dy7z5s1j\n2rRp5OXldfdLyAiKolC+tRz3AHfKtztEo1Ei4QgROl5C+Fa43C5MJhNznprDvGfmUTCkoFOOm4mU\niILbJeE33aX2b5Cr1NXV8eyzn8Tvfx2QP0CiM5nQtE/i90/ha197jrfeWsVrr/2WPn36GF2YuEXR\naJSqqirKyspYunQpu3fvxul0EggE4iO61wu7ubm5zJ49m+LiYqZPn05+fn53v4SMdODQAWqjtQzq\nPcjoUu4IJA1gAAAgAElEQVTYrMdncXTv0Tvq6bU5bKDBiDEjKHmxhLFTxqb8m4KkoOjzaov0llb/\nU/7lX75DKPQ0MNnoUkTaugefr4ItW75FYeFo3njjz8yYIVPiJDNFUdizZw9lZWUsW7aMnTt3YrPZ\nCIVC8ZDbXtj1eDwoioLH42HWrFkUFxdTVFRE//5yAW13u3z5MhUHKuh3X+q2OyhRhf2V+ylfWs7W\n9Vtva5qy2BRlTpeT4ueKmf3EbHrly2w0ncmkmCT8ZoC0Cb/vv/8+f/7zXwmFDhldikh7NiKR73H5\n8kwWLnyWH/zgG/z933/a6KJEK1VV2b9/fzzsbtu2DavVSjgcJhTSVwAIBq/ts3S73aiqisvlYsaM\nGSxYsICioiIGDx7c3S9BJNA0jYqdFdjz7djsqbXAx9WBFyAYCKKptxZ8Y1OUfWjKh1j0/CJGjR+V\ncctYdxsFubA5A6RN+P3CF/6FcPgfkBXcRPeZQSDwLl/9agm7d+/nF7/4qay+ZQBN0zh06BDl5eUs\nW7aMiooKQG9vaC/kxmRlZQH6amrTp09n4cKFFBUVMWzYMOnnTiKnTp3i+OXjDByVGrM73ErgNZlN\nHQbh2BRlPXr1YNELiygqKcLbw9ultQvQopqM/GaAtAi/lZWVlJa+g6L8xuhSRMYZjt+/lcWLn+XA\ngbmsWrVEFsXoYpqmUV1dTXl5OcuXL+edd95BURRUVSUQ6LiH0ul0YrFYMJvNTJ48mUWLFlFUVERh\nYaGE3SQViUR4Z9c79BrSK6n/jW4l8LqyXESjUe554B6Ovnc0vnBFjDPLiaqqTJ43mQXPLeCuUXcl\n9WtPO6r0/GaClA+/mqbxmc98hWDwm4BcoSmMkI3fv5Q9e77G/fc/TGnpMpkOrZMdP36csrIyVqxY\nwaZNm+LtC36/v8PnOJ1OrFYrmqYxYcIESkpKKCoqYuTIkRImUsSBQwdotjYzwJt8SxjfTuAtfLCQ\nWU/MYvyM8XiyPXz9pa+zt2IvFqsFi8VCwZACHv34o0yaOwlnlrO7X1LGU1UVk2qSM3gZIOXDb2lp\nKQcPnkPTXjK6FJHRLITDP6S2diTjx0/nb3/7PcXFxUYXlbJOnz5NeXk5K1eupKysDJ/Ph9lsxufz\ndfgch8OB3W4nGo3y0EMPUVJSwowZM3jwwQelPzIFNTc3s/3QdvLvS57ZNDoj8CZ69MVHOX7oOFMX\nTqX4o8UMGJZ8IT+TKFEFp8Mpb44zgEnr4JLTxsbG+P2cnJxuK+hWzZr1GBs2LAReNroUIVpV4HI9\nyXe+8xW++MXPGV1MSqipqaG8vJxVq1ZRWlpKY2MjVquVlpaWDp9jt9txOp2EQiHGjh0bD7tjxozB\nak359/UZr3RTKSeiJ8gfYGz47ezAK5KXv8WP5byFJ4ufNLoUcYdulGFT+i9ETU0NW7ZsAv5sdClC\nJJhIILCVb3xjFs3NLXzrW/9sdEFJp66ujo0bN7J69WrWrVvHxYsXsdvtNDc3d/gcm82Gy+UiGAwy\nevRoFi1axMyZMxk3bpycpkwz58+f58j5Iwx8wJiL3CTwZqZIOEKPrB5GlyG6QUqH39/85veYTE8C\nmfiL5gfAL4GPAE8CowE5VZM8BuP3b+ZHP5qF3x/gBz/4TkafSmtoaGDTpk2sWbOGtWvXUlNTg9Pp\npKmpKf6YWB9vjNVqJSsri2AwyMiRI1m4cCGzZ89m/PjxMhVRGlNVlS07t5A9ILtb/89I4BUBf4De\nvWTGqEyQ0uH317/+C8HgfxtdhgE04CfAeeBHwH8CDuBx4GlgGiAjYcbrh9+/kZ//fDZ+f4Cf/ezf\nMyYANzY2snnzZtauXcvq1as5c+YMTqeT5ubm+OT+Vy8sYTab8Xg8BAIBCgsL42F3woQJuFwuI16G\nMMCJEyeoDdUyqFfXr+QmgVckUoIKPXN6Gl2G6AYpG34PHjxIff0lYKLRpRjgIBDrZ4m0bi3Ab4DF\nQBSYBTwLzAeyDahR6Hrj95fxu9/Nw+//DL/+9X+l5cVXzc3NbNmyhXXr1rFq1SpOnDiB0+mkpaUF\nVVWB64fd4cOHx8PupEmTcLtl5pZMFIlEeGf3O+QN6brl6SXwio6YwiY8Hvn3zQQpG35fe20J0ehT\nQPoFiRvzAgXAOfRWh9jcpioQO428DCgHQsCHgBeAEkCWZu1+ufj9pSxeXEwg8DJ//vOvsFgsRhd1\nR/x+PxUVFaxfv54VK1ZQXV2Ny+XC5/OhKApwbdg1mUx4vV6CwSCDBg2iuLiYuXPnMnnyZLKz5Q2a\n0Kc28zv85HpyO/W4EnjFzdDCmoTfDJGy4ff119cQDn/f6DIMMgj4ADgOLEW/4G8fYEcfAY6JXTy0\nDXgP+DwwGH1E+HFgFNIn3F2y8fvXsGzZozz55PMsWfLHlJqRIBgMsm3bNkpLS1m+fDmHDx/G6XS2\nCbuRSNvJ+hPDbkFBAfPnz2fu3LlMnTqVnj3l1KJoKxAIUHmostOmNpPAK26FElWwYcPplPmVM0FK\nTnUWiURwu3sQidSij4IKaABWAf8DbEQPws3o/cFXs6P3BLvRL5Z7CphMCr8XSiEBXK7HePzxgfzp\nT79K2h7gcDjMjh072LBhA8uXL2ffvn04nU78fj/RaLTD53m9XsLhMH369GHu3LnMmzePadOmkZfX\ndaexRXrYtWcXlTWVFAwruO1jSOAVt6ulqQXXRRePzXvM6FJEJ0jLqc4OHDiA0zmYSESC7xW5wMda\ntyBQht7/uxS9HSKA3gsMEG7dfMAvgD+1PmY+8FFgDpk5g0Z3cBEIvMFbb03jG9/4Dt/5zjeMLgiA\naDRKVVVVPOzu2rULp9NJIBCIj+he3cYA4PF4iEQi5ObmMnv2bIqLi5k+fTr5+cmzMIFIfoFAgJ1H\ndtL7vlu/0l4Cr+gMQX+QQT27/iJLkRxSMvzu3LkTVR1ndBlJzAkUt24qUAm8jh6GL6CPBgdbH6tw\npT3idWAtejAeDzwPLAL6dlfhGcKD37+SH/94AkOHDuKllz7e7RUoisKePXsoKytj2bJl7Ny5E5vN\nRigUiofcjsKuoih4PB5mzpzJggULKCoqon9/6SUXt+/g4YNo2Ro2+83NUiOBV3S2kD9EXl85Q5Up\nUjL8vvPOTnw+Cb83xww83Lr9CKgG3kbvEz5Mx33C7wC7gL8H7gKeAz4MjOiWqtNfX/z+1Xz2s9MY\nMKCAOXPmdOlXU1WV/fv3U1ZWxtKlS9m+fTtWq5VwOByfXzcYDF7zPLfbjaqquFwuZsyYEQ+7gwcP\n7tJ6ReYIBAJUHa264aivBF7RpcJ625bIDCkZfisqdgIvGl1Girob+HLrVg+sQA/C76LPFdyU8Fhf\n6+0B4NvAd4Ee6D3CTwGPAKk9a4GxRhAIvMHjjz/Oli3rGD16dKcdWdM0Dh06RHl5OcuWLaOiogLQ\n2xvaC7kxLpcLk8mEzWZj2rRpLFy4kKKiIoYPH560/ckitR08fBAtp/1RXwm8otuEkZkeMkjKhd9Q\nKMTJkweBB40uJQ30Bj7RuvmBUuA19EBM6z6l9X4oYd9/Ab9t/Xgh+ipzswFZiODWTcbn+3/MnLmQ\n3bsrGDTo9nrONE2jurqa8vJyli9fzjvvvIOiKKiqSiAQ6PB5TqcTi8WC2Wxm8uTJLFq0iKKiIgoL\nCyXsii7n9/vZebRtr68EXtHdVFWFCDK/eAZJufBbX1+PzdaTSCTL6FLSTBb6PMAl6IF3K3oP8N/Q\nF9RQuBKAE/uE/wqsbP3cZPQL7hYC0jt1856ksfE0U6fOZ+/eipueXeX48eOUlZWxYsUKNm3aFG9f\n8Pv9HT7H6XRitVrRNI0JEyZQUlJCUVERI0eOlLArut2BQwcgR1/wZO/WvRJ4hSH8zX7yc/NTfv51\ncfNSLvw2NjZisSTX1Gvpx4IeZCejL6N8GHgLfRq1D9B/bHwJj4+1SmwAtgOvAveiB+HH0HuGxfUo\nyuepra3mIx95iVWrXm83iJ4+fZry8nJWrlxJWVkZPp8Ps9mMz+dr54g6h8OB3W4nGo3y0EMPUVJS\nwowZM3jwwQfTcqU5kTqampr4y1t/Yc++PWzfsB1Iz8AbCoT47Q9/SzQcxe6043A5cDgd2Ow2bA6b\nfhvbbDbsDjtWu7XN/vg+W9t9FquEtc7Q0tRCYd9Co8sQ3Sglw6/ZLKtBdR8TepC9F/gnoAZYjt4n\nvINr+4RjF8/tBY4A30Bvr3gGfU7hcWTmqnw3Fgr9hM2bJ/HjH/8nX/zi56ipqaG8vJxVq1ZRWlpK\nY2MjVquVlpaWDo9ht9txOp2EQiHGjh0bD7tjxoxJqUU1RHqKRqNs2rSJP/3pTyx5fQmqqhIKhdIu\n8CY6d/IcpW+WEgm1XQTGbDFjNpv1W5MZk8mkv+k1EX/zq6GBprc1aZqGpmqoqqpviho/jsVqwWKx\nYLVZ45vNZsNqt2K32+NB2+6wY3foAdzutONwOvT7Dnv8cYnB2+64ap/tyr7E/XaHHavNmrJvqBWf\nQv69Mj1jJkm5v4ZNTU2AjPwapx/wSuvWgj412l+BNeih1oc+vRpcmU7tFPoI8n+jjyo/hh6GZ6CH\nZ6FrxO//OF/5ypf4wQ++R1NTE3a7nebm5g6fYbPZcLlcBINBRo8ezaJFi5g5cybjxo3DZru5aaOE\n6EqJgffNN98EwOfz6X2WV0mXwJsoFkqvDr+q0hpgIx088SYpUQUlqtz4gddhMpmwWCyYzCbMZjMm\ns6lNGI/T9ECuqVeFcUUP5GazGbPVjNVixWKzYLVa2wTyxOBsd9ixOWz6SLjD0WZUvN2Abbe3GQ23\n2tse7+rNYrXcdCuXFtBk1ckMk3Lht7GxEVWV8JscPMATrVsU2AIsad386L/VY3PFRrkyKvxH9DaK\nMDAdfRq1BUCm/fJpADahv3FYiz6q7kRRQtTX1wPE+3hjLBYLbrebYDDIyJEjWbhwIbNnz2b8+PE4\nHPJGQiSHWwm8TpeTaDTKXSPvYkrxFB6Y8AAOlwNVUbl84TIN5xtQFD3gqara5jZ2UacaVVFURb9V\nFFRFv028H7+N6kEtti8ajRKNRFGiin6rKCgRhWi0dV80Gn+cEm09TuvXjh0v9rUTj6sq+v5oONru\nyHYy0TTtuis33ixVVVHDKlGi+rpKtyk+Kp4QxM0mM5j0WhP/PTpkIh6+YyPeX/vZ17j7/rvbPCwU\nCJHtzCYrS64jyiQpGX4VRcJv8rGiB9np6LNB7APeBP6CPvJrQQ/EoC+yEWuVWIMemsPAA1zpE07H\neWQbgc3oQXc1cAZ9QZLEZajbLixhNpvxeDwEAgEKCwvjYXfChAm4XDK7RrLSNC0ejqLRqP6HuvV+\ne/tu9Pk73ReJRAiHw0Sj0WtuI5EIkUgk/rzE+7HnXn28q+/HtmAwSDAYbHeBlHaZ9MVUzBYzxw4d\n49jhY/qII21P/8dH8DoayNOu3MZbBdBHJ68erUQDVVOvfCyShslswmq1YrHqM9BgQv/3Uq+8SQGw\nO+14sj243C5cbhdurxt3tpvsHtl4e3rxZHvI8maR5cnC7XHj8uiPKRh87dLZLU0tDMsf1s2vVBgt\n5cJvU1MTkYj0/CY3E3qQfQD4FnrIW4a+jPIu9FaHxFP5sRHhnehzCn8VKECfQu1JYDQd/9VLZs3o\nwX4dsAo4gR52W7jSGnJ1SDCjj6gHMJlMzJ07i3/4h88xadKkpJuGJxbwujq4dXXAS9xuJuDFRhvj\no45X3VdVFU3T9NEqs7nNbWyL9UYm7ou53qnaWFiL9YAm3tc0Lf61Y/djHyctLeH0v0hpVpseWi1m\nvX0i9oYjPmqvqHqbg9OBM8tJlrs1nGa78fbw4u3hJbtntr6/Nbi6PC7cHjdZniv77A57p9YdbA4y\n4N4BnXpMkfxSLvy6XC4slgCRO+yTEt1pAPDp1q0RfbT3f9DnFbbRNgzGzpUdQ1+R7j/Rw/LjwNPA\ntNbndBcNfWq3aDu3V+9rRg/wFejtDKdaaw/ScdgFfX7kMNALGIW+it4QNK2ODRv+H/ffP4rKysp4\nQEsMdomhLhkDXuLI3TWjeB19x9Mk4MXeHIiuldif2uY+115Apg8oJ/z8tfej2PqjlPizd81IcuIF\naJoa3xc/RZ94yh49CIYCoXa+mPHiI60WvV4g3ssb6ye22qzYnXacLicutyseWj05HrJ7ZOuhNRZQ\nE8Kr2+uOP96Z5UzO6RQDSL9vBkq58JuXl4fNdoHrLFIlbtmtBLyr993OcxRgPlAEHEUfDd6X8PlY\nUIy0bi3Ar4DftdbaB+iPHhZJOH7ilvi1rr6fuKkJt1ffV1u/ngl9RDbxNrZpVx3rah3Puas/P/Zf\n0Il+seA29DmW9a8dDkf54Q9/iMlkkoCXweJh6qo3Fldv0E6rQDvaBDvavrlo741G4huOm2W32/F4\nPHg8Hux2e3y0uyXYgtPtjAcui0W/TQxhsfsWi0W/tbbOZNC632rVL6iKPSbxOBbLtftiMyKYzQm3\nrceO77v68e0cJ/E5bfbHTtO34+L5i7w699Wb/r7drPj3qfVCtdjviFhojUaimC1m7A47ziwnrixX\nPKB6sj14e3rJ7pGttw+0tgW0N9rqzHKm7fy3SlTBErXc9NzqIn2kZPg1my8YXUY7GtD7OG82CEbR\nR/tit7Ggl7g/tkVoP+BdHei6KuDFPiZhH9y4FSGhEe+a+1rC147dVxMe157YBRk1rVt3iQXcrjhu\n7N/9Bo9MwuDb2ZIp4MVqSdxiK+El3iZuVqs+1VMskFit1vh9m80Wv43tj+2z2+3xj2Oft9vtbfZf\nfbyr73fFPoBt27axePFili5dCugLqLR30ZrH4yESifDII4/w0ksvUVJSQo8ePa553Oqy1dTZ6sjt\nk3sHPympxWK1tLkwy2QyxVsEru5rjV3IhUZ8KjJnllMPop4sPDkevDl6e4Anx9PuaGvsY5fb1e6S\n0eKKlqYW+vfun7JTtInbl5LhV9OSMfz+GP00vZ07C3hG6aqAJ9oy0/bNxdVvNNp7c6FgMvnxer3X\nhL3uDniJQe/q28SAF7tNDHixYHcrAe9O9t3ucRLbNTLNrczScLOBN+by5cscrzvOgNGZ1V/pzfEy\n56k5BHwBsntm4+3hjV+ElRhW3d4rF2bZ7LaM/RnsTr4mH6MHjDa6DGGAlAu/vXv3JhpNxvBrQh+x\nvcmrnNPa7QS86/2iV7kyIn6rAd2EPtOE+arNkrA/8b6KvlSzr/U21tpwvTcsltbP29DnQR7cuuWg\nvxmyJWwW9P92sVvrDfbp9+32f2XBgmG88spLnRIOMzngiba6MvAmOlx9GFte5oU6i9XCp775KaPL\nEO3QfBp9evcxugxhgJQLv7169SIYvMCVU/XJwob+7bTTccC7+n4irZ3b9jaVtqPI0DZsJga99gLe\n1VtH4cvKlbBmS9hnT/hc7PZOA96t7FOASvTZE9a3fhyi/VBsBtyt36f5wEeBOeizKdC6fz9QBixF\nX5rZih6yYxentBd6Y8d0oS/UsQC9f7nrpmcLhe7n7bfH8N3vfothw2RaHnFnuivwxgSDQfYd20fe\nyLxOqV+IOxWNRLFFbeTlyc9kJkq58OtwOLDZnIRCjcCt/QLuWp9CvxDr5kbyOm9fYj9upngA+CR6\nAK0EXgcWA7E3RbGrIVWuTKn2OvosEyFgEPosDCfRv3fRhOe0x9X6OBv6bBML0cPucLrvez+IcPiL\n/N3f/QMbNizrpq8p0kl3B95Ex08cJ+qOYrWl3J8ckaYaGxoZVjBM+n0zVEr+Jho0qJDq6gPAJKNL\nSdAb+F9GF5FhzMDDrduPgPeBt4E/A4fQw6ov4fGx+YQ/uMFxnVwZMZ8MLEIPu4UY+UZDUb7Itm33\ns3LlShYsWGBYHSJ1GBl4Y1RVpepQFb0G97rxg4XoJoHLAYY9KGfRMlVKht8pU8ZTXV1JcoVfYby7\n0Jda7gm8gT7XbqyP92aYgIHocwp/HH2EOZlG1R34/f/B3//91yguLs643klxc5Ih8CY6d+4cTTQx\n0D2wU48rxO3SNA18kJ+fb3QpwiApGX6nTh3P4sVr8flu/FiR7k4D5cBK9N5dH3rgvZ0fDg04C/ym\ndVuIvsrcbPTWByOdAg4C06ivh9WrV1NcXGxwTSJZJFvgTbTv6D48vT03fqAQ3aSlsYWC3AKcTqfR\npQiDpGT4HT9+PCbTd4wuQxiiBj3srkJfIa4R/ce45TrPsaO3MoSADwEPApeBjUATVy6agysrtQH8\nFT1Uh9DbHz6GHoiNuEDiefT+5igtLb35xCde4Q9/+DWTJk3C6/UaUI8wWjIH3hifz8eJuhMUPFjQ\n5V9LiJvV1NDEmKFjjC5DGCglw29hYSHRaD1wkSurfIn0VIceUlcD69D/ze1cCajtsaGP1AaB0eg9\nuzOBcbRdGlkDDgNvoS+3/AH6f4nEUeOm1tsN6LNBvArcix6EH0NvtehqCrCDKxflnaOuDp588knC\n4TDDhw+nuLiY2bNnSxhOc6kQeBOdPnMaU7ZJLioSyaUF+vXtZ3QVwkAmrYOloxobG+P3k3Hpv7Fj\nZ7Br1z8C84wuRXSqBvRe3TXAWvSRXidXQmh7LOjTjwWB+9DD7mxgPPqsDjerFliOfsHc9tbndvR1\nnej9wL2BZ4An0cN1V/yRr0Z/XdEOH2E2m/F4PAQCAQnDaSbVAm+iJSuWEM2P4smWtgeRHEKBEMHj\nQZ577Dm5biKN3SjDpmz4/dKXvspPfuJCVb9pdCnijjQCm9GD7mrgDHqwbKbjhSXM6HP1BtBnYFiI\nHnYn0Hm9uS2tNf0VPYjH+ojbu3jOypUZIh5DD8MzuLXgfT0a+gV8sbmN69FHsDtu9ZAwnNpSOfDG\nNDQ0sLh0MQMezKwV3URyqz1TywM5D/DwuIeNLkV0obQNv2vXruWpp75Jc/M2o0sRt6QF2ILewrAS\nOIEeHFvoeFaGxLA7nCthdxL6iG9Xi6LXvAR9vmAfEKH91fxMgLf1c9OB59AXwejZifXUoo+O/wCX\n6wiqqmC322lu7rgVRMJw8kuHwJuoancVVfVV9Bssp5dF8jhz8AyPPfIY/frJz2U6S9vwG4lEyM0t\noKWlEhhidDmiQ36gAn3EcgX6KXwXeoDsaKniWIAMoK+aVgzMRb/oLLuL670RDX1VuDeAv6DPwmBB\nf53t8aAH4Qe40ifcWSvBNeBwDGPXrgr27dvHmjVrWL9+PRcuXJAwnCLSLfDGqKrKn976E+673Dic\nnXUGRIg7o0QV6vfV84knP4HVmpKXPImblLbhF+D551/hf/7nbjTty0aXksFOAv8J5KAHVid6n+4R\noKr18070IHujsBsECtCXIp4LTKVzR0y7whlgGfAnYBd6q0NHodOFHp4L0KdQexL9grzb7ztzu5/i\npz+dxyc/+cn4vtraWjZt2iRhOEmla+BNVFtby1sVbzFgpLQ8iORRX1PPcPtwpk2cZnQpoouldfgt\nLS3l8ce/RnNzpdGlZLB/A/4JPdSZ6LhPtyNW9NHcvugLTOSjB95c9EDsRR899V61xfZlkTwLUTSi\n9wf/BX2kO9aX2147hw09KDvQF9V4Gn3pZFs7j72eJTz88K/Ytm1dh4+QMGy8TAi8iTZXbOb90Pv0\nLuhtdClCxJ05cIbHJkjLQyZI6/AbjUbJzS1o7fuVZQq7RxR9RHcD+swIlXQ8onsnTOhB0MqVpYZB\nD9dqax3R1q/tQB9VdaH3AHvQA3UO0ANjwnQYvS/3b8CbrR+H0HuFrxbraY4Cs4Bn0Ue/b6bFw4/d\n3o8zZ96nd++bCxoShrtHpgXemHA4zB/f+iN5o/KwWC1GlyMEAKFgiJajLbzwxAsy9V4GSOvwC/CJ\nT3yKP/5xMKr6VaNLSVMKsAd99bRlwE70eXaDtH/BV7IyMkwD7EbvE34NONdaT6CDWr1cWZDjBaAE\n6N/hK3O7P8KPfzyDV1555ea+FVeRMNx5MjXwJjpx4gSr965mwAhpeRDJo+ZUDWPzxjJ2zFijSxHd\nIO3D78aNGykp+QLNzbuMLiVNqOgXdJUBS9EXV7BwZeSyI87W59qAu9EXf+iNHiYvoa+o1ow+b66v\ndQu0HjP2vFgwjY28JgbTCF0zwny77iRM29Bf9wX074mF9keE4cr3dQDwUfT2iPtpOzr9FuPG/ReV\nlRs65ZVJGL41EnjbWrVhFRecF+iZl+z9+iKTnHnvDM/MfIbc3FyjSxHdIO3Dr6Io5OcP5eLFN4CH\njC4nBWnAIfQlg5ehz8wAenALdvQkrrQHWNEvTFsEFKFPRXarbQNh9N7Y5tYt8X7ivkb0RTDSMUzf\nKgf66HJPwIPJtI85c2aRn59Pz549yc3Nxev14vV68Xg88ftX78vKyrrhRO8Shq8lgbd9oVCI37/1\ne/o+2FdOLYuk4Wv2Yaox8cyiZ4wuRXSTtA+/AD/+8f/l619/F79/idGlpAANfbqxcvSe3XfQQ6BG\nx9N1wZVFHMzoU47Fwm4hyXPBWYyEaZPJhM1mw2q1YrFY4kFE0zRUVSUajRKNRlEUBYfDgcvlwuVy\n4Xa78Xg8ZGdnk5OTQ48ePa4J04qicOzYMd577z127drF5cuXsdvttLSk96IbEnhv7PTp06zcvZL+\nhR236QjR3c4dO8fUoVO5d8S9RpciuklGhN+Wlhb69RtKS8u7wD1Gl5OEjqO3MaxAvwgr1r5wo7Br\nRQ94E9D7TouAkSRf2O1qtxumm1o/dzthOkzHi350v+uF6Wg0SiQSIRqN0sGvk3aP53A4iEQi5Ofn\nM378eCZOnMiECRPo27dvfHT6Zkamu5IE3luzeetmPgh/QF7fPKNLEQLQf0ed3XOWFxa9gNvdHYsi\niWSQEeEX4J/+6Zv85Cc1BIO/NLqUJHAafWR3JXro9XFled6O2NFPpUeA8ehhdwbwIFf6WUXnuNkw\nfRk9SF9Cv0juFFDH9XuvrzCbzVgsFkwmE4qioCjJMzJ9PSaTCbPZHB+ldjqdtzQyfb1Wj5sJ08ke\neFC4zpYAACAASURBVE+fPk19fT1DhgyhZ8+ehr45SKSqKr9//ff0uLcHNvutTtknRNe4fPEyuf5c\nFsxaYHQpohtlTPi9cOECgwbdQyCwH30RgUxSgx52VwGl6COQVvQA1RE7+uhuCBjLlbA7pvW5InnV\no7+x+RPwLvq/Zfv9t1arFZPJhNPp5J577qF///7Y7XYaGxtpamqiubkZn8+Hz+cjEAgQCoVQVbXN\nKG8sXCW2TEQikaQK03fa5uH1eolEIpw/f57Tp09jMpmIRCLtjmRnZWURjUYZP348L7/8Mo8++mi3\njvCOGDGCM2fOEIlEMJlM9O3bl8GDBzNixAhGjBjBkCFD4luPHj26LRzX19fz+ubXGTBKZnkQyeP0\n4dMUP1jMkCFDjC5FdKOMCb8Ar776v/nd75xEIj80upQuVg9sRA+764CLXC8A6Wzosw0E0VcVWwTM\nBMZx6wsriOThR3/D8xqwmKwsJ6FQqN1garFYyMrSp15btGgRH/nIR5g1axYul6vN48LhMC0tLTQ3\nN8e3qz9ubm6msbGRS5cucenSJS5fvtxumA4Gg2ia1iaYJrZKKIpy060SycBiscSXRY2NpjscDpxO\nJ1lZWd0yMp2fn09dXV27n7Pb7TidTgCCwSBms7lNOC4sLGTIkCEMHTo0Ho47y+69u6k8X0m/wbKA\ngEgO0UiU+v31fPzxj2O3240uR3SjjAq/J06cYMSIDxEKHUOfjzVdNKD36q4B1qKP9F5vGV3Qe0nd\n6GH3PvSwOxu9pcHRlcUKg9hsn+Oll8K4XE4WL15MY2MjiqIQCrXfJpGdnU0oFGLy5Ml87GMfY+HC\nheTldX6v5o3C9NmzZ9m3bx/79+/n2LFjBIPBeKvGzTCbzVit1vgot6IoKT8yfb0w/dprrxEO394c\n2x2F4yFDhnDvvfdyzz33xEeNhw4deku/+xcvXwwFkOXJuvGDhegGdWfruNt5N1MnTjW6FNHNMir8\nAjz11Iu8/fZAotHvGl3KHWgENqMH3dXAGfQWhWY6Xj44tkpYAH0Ghv+/vfsOj+q88/7/npkzTaOO\nJECiGUQXIDqYZoEoomNkwMB6EzuPn+yVTdlkky3Z32+zT+LNZh/vJrvJlsSOUwzYBoyNMRgwSzO2\nARsMiCI6qCGQUJ2iaec8fwySBUgghKQzI31f13WuGY3OaL4jhPSZe+77ey8kFHYnExrxFZ3fBubM\n2cKuXZvRNI38/Hzeeecd1q9fz+XLl1EUBZer6Xnf0dHR+Hw+hg4dytq1a1m6dCnp6ekdXH9Ia1ur\nWa1WfD4fSUlJpKenk5qaisPhoLa2lqtXr1JQUEBFRQWapj10tNlkMmE2mzGZTGEZpttL43Ds8XhQ\nFKXZcNyvX7+Gvw1Op5N129eRlildHkT4KDxVyIqsFe3yol6Ety4XfouKihg8OBO3+zChjRYigRM4\nRGgKw3bgGqGw66T5Ff+Nw+4Avgy7UwiN+Iqu5yLdumVTXn79vs+Ulpaybds21q1bx5EjR7BardTU\n1DT5VWw2GwaDgeTkZFauXElubi7jxo3TrW9ra8OwzWZrmHahKEqz3Sjqg//o0aNZvHgx48aNw2Aw\ntNk0j0iYM91SVqsVqzX0zpHH48FsNtOjRw+6d++OJdHCoFGDSOmVQkpaCt3TussosNBNdUU1jioH\ny3KW6V2K0EGXC78A//iP/8xLLx3A7X6f8G7LpRJaZPYJodFZF833ijUQ2vbWA/QFcoC5wDRCW+8K\n4cdojCIQ8D1w3qjT6WT37t1s2LCBnTt3YjQam+1moCgKNpsNk8nE0qVLWblyJTNnzmwIQHpoTRi+\nl9lsRtM0Jk6cyIsvvtimXRoeZc50RUUFVVVVd4Vpp9OJ2+1uNkyrqvrAnsp6MlvMmC2h763P60NR\nFBKSE0hJS6H3gN6k9UsjJS2l4ZBwLNpL4blCFo5ZSJ8+ffQuReigS4Zfn89HevooCgt/RqiLQbjS\ngERCLa3uVR926wh1r5h355hOaFcvIe5nscRTWnqVhISW/YwEAgEOHTrEpk2b2Lx5My6XC7/f3+Sc\nUoPBQExMDD6fj6eeeoq1a9cyf/78Fj9WewgEArzzzjv86le/4pNPPmnxAjqDwUB0dDR1dXVhv+lG\n4zB98eJFlixZgtv9oB7d4ctoMoJGwwstq91KQlIC3Xt1p/eA3mQ+mcmEmRN0rlJEujp3He4rbtYu\nXYvJZNK7HKGDLhl+Afbs2cOSJS/idp8hvOe8LgW23rkeQ6gHbDKhUd0cYAYg85VEy0RHp3P8+AcM\nHDjwke+raRqnT59my5YtbNiwgevXr2MymZoNWvXTBUaOHNkwT7hv376P+xQe6lH68BoMBjRNa5i7\n25xI2YHu3LlzTJgwoU1Hfk0mU8MivPrDYDA0HI3V/7lQVbVhGkcwGCQQDE0p0VQNoynUX9poMmJS\nQt0x6i8V85eH2WJuuDRbzVgsFkZOGsn81fPb7LmJrqn4cjFT+04lY3iG3qUInXTZ8AuwYMEz7N49\nnEDgR3qX8gA7gD8jFHLnA08BPfQsSESwuLhJfPDBz5k8efJjf62ioiLee+89Xn/9dY4fP47Vam12\naoHdbkfTNFJTU1m1ahW5ublkZma2WY/ZR914wufzMXnyZJ5//nkmTpzIiRMnHnnOcDiG4aKiIoYP\nH47PF5pSYDabG6ZEWCwWLBYLZrMZq9WKxWJp6BxRf1l/2O12oqKisNlsDefV37+p6w/6/PmL5zlZ\neZLe/XtjUkxhs+mG6JqCgSA3T9/kucXP3dfGUXQdXTr8FhYWMmTIaNzuo0B/vcsRot3Fxi5k3br/\nzaJFi9r061ZXV7Nz5042bNjAhx9+iNlsxul0Nhk+68OX1Wrl6aefZsWKFcyYMQOz+dH6ST9O4H3Q\nHN7WLqALxzAcDrbt3kZtXC0x8V37+yDCw82imwyNHsqUiVP0LkXoqEuHX4Af//in/NM/HcDt/oDw\nXvwmxONzOL7Kv//7NJ5//vl2ewyfz8eBAwfYuHEj77zzDl6vF6/Xi9/vv+/c+tAYCATIzs5m9erV\n5OTkEBvb9CLN9gq8DyJhuPWCwSC/3fhbumd2160biBD1NE2j6FQRq7JXkZiYqHc5QkddPvz6/X5G\nj57KuXNrUdVv6l2OEO1KUf6Sl15K4Qc/+EGHPJ6maXzxxRe8/fbbvPnmm5SUlGAwGPB4PE2eHxMT\ng9frZcyYMTz33HMsXryY7t27d3jgfRAJwy13+/ZtNu3fRFqG9PcV+qssryTBlcCiOW37zpeIPF0+\n/AJcunSJUaMm43bvA2QCvOi8LJa/4Kc/7c13v/tdXR7/2rVrbN26lXXr1nHq1CksFkuzi7OsVit+\nv7+hlVcgENAt8D6IhOHmXbhwgb2X9pI2QMKv0F/h2UIWj19Mr1699C5F6EzC7x2vvfZ7vvnNf8Ht\n/ozQBhJCdD4Ox/P84hdP8rWvfU3vUqioqGDHjh2sX7+e/fv3YzabW9yL1263EwwGdQu8DyJh+Ev7\nDu2jQCsgMUXeYhb6cjvd+Av8rF6yWqbgiIdmWKUji9HTV7/6p7z77k4+/PA71NX9t97lCNEuTKaa\nsHmxmpiYyKpVq+jZsydJSUm8/fbbmM3mJucG36t+V7bk5GSio6MfebFce+rRowcrV65k5cqVQMvC\nsKqqDTvq5efnc+HCBV599dWIDsOaplFQWkD0oGi9SxGC20W3mTV8lgRf0SJdZuQXoKamhmHDxlFc\n/PfAGr3LEaLNxcXNZuPG7zNnzhzdamhNH976y6bUb6wxceJE1q5dy6JFi+jRI3zbAXaVkWGn08m6\nHetIGyVTHoS+PC4Pnqse1ixZg6J0mTE98QAy7eEeJ0+e5Mkns3G7DwJD9S5HiDYVFzeBXbt+ycSJ\nEzv0cR+nS0NGRgZ79+5l3bp15OfnN7RRa4rD4SAQCJCens6aNWtYtmwZQ4YMadfn9rg6axguKChg\nx4kdpA2W8Cv0VZhfyKyhsxg8aLDepYgwIeG3Ca+88lu+852Xcbs/QbYKFp1JTMxgjh7d2iGBsD3a\nkpWVlbF9+3bWrVvHoUOHsFqtDdMF7mW1WjGZTMTHx7NixQpyc3OZNGlS2G9n2lnC8NFjRzlVdYru\nvbrr8vhCgIz6iqZJ+G3GN77xXX7/++O43bsAq97lCNEmbLYUrlw5Sc+ePdvl63dkH163282ePXt4\n8803ef/99xtua2qbYpPJRFRUFACLFi1i1apVZGdnR8QOT5Eahjdv30ywR5Co6KgOeTwhmlJ0voiZ\nQ2bKqK+4i4TfZqiqyqJFK9m3T8HjWQ/IJHkR6W5htw/G5apo0y1m9dh44l7BYJDDhw+zefNmNm7c\nSFVVFcFgEK/X2+T5sbGxeL1epk6dytq1a1m4cCFJSUmPXUdHiIQwHAwGeeWtV0gdkyrbGQvduJ1u\nfNd9PLv4WRn1FXeR8PsAdXV1TJ6czZkzT+L3/7Pe5QjxmHYwbty/8tlnex77K4VD4H2Q/Px8tmzZ\nwvr167l8+TKKouByuZo8t76+oUOHsnbtWpYuXUp6enq71teWwjEM19TUsGHXBtJGynxfoZ/C/EKy\nh2UzaOAgvUsRYUbC70Pcvn2bzMwplJR8E1X9ht7lCNFqRuP/4S/+ws3LL/9Tq+4f7oG3OaWlpWzb\nto1169Zx5MiRB84TttlsGAwGkpOTWblyJbm5uYwbNy6i2iOFQxguKSnhvc/eI22IhF+hDxn1FQ8i\n4bcFrl69ypgxU6mq+g9gqd7lCNEqMTGLee2158jNzW3xfSI18DbH6XSye/du3njjDT744AOMRmOz\nz0dRFGw2GyaTiaVLl7Jy5UpmzpyJ1RpZawD0CMPnz59n35V9pPWX8Cv0UZhfyOzhsxmYPlDvUkQY\nkvDbQp9//jkzZuTgdr8HTNa7HCEemd2eyrlzn9K3b98HntfZAm9zAoEAhw4dYtOmTWzevBmXy4Xf\n78fn8913rsFgaOgnnJWVxZo1a5g/fz4JCZHXDaYjwvDHRz7mQt0FknpExjxq0bnU7+b27OJnw767\ni9CHhN9HsGPHDnJzv4rHsw2YoHc5QjyCEqKjR1FTc6vJBUhdJfA2R9M0Tp8+zZYtW9iwYQPXr1/H\nZDLhdrubPL/+ezBy5MiGecIPe1ERrtojDG/ZuQVvNy/RseG1u1tNZQ27Nu7CYrNgtVqx2q1YbdbQ\nx7bQxxar5b7bFbMiC/ciSOG5QmZnyKivaJ6E30e0bds2Vq58AY9nCzBV73KEaKG3mDbtdQ4efL/h\nlq4eeB+kqKiI9957j9dff53jx49jtVqbDYN2ux1N00hNTWXVqlXk5uaSmZkZsWGpLcJw7wG9mbRo\nEsPHDQ+rVmc73tjBKy+9gsFgwGQyYTAaMBqMYAQDBjQ0NFVD0zRUVUUNqqHWeRqYzCbMZjNmS+iw\nWC13hWZblA1blA17lJ2o6CjsDvuDw3UT4dtis0TU/PJw5Kp1ESgMyKiveCAJv62we/duli1bg9v9\nFjBT73KEeCiHI5d/+7cc/vRP/1QC7yOqrq5m586dbNiwgT179qAoCk6ns8nvmdlsDoUaq5Wnn36a\nFStWMGPGDMxmsw6Vt43WhGGDwYDdYcdX56NHnx6MnT6WzCmZDB09tNkw/O5r7/Le6++R/XQ2Ty1+\nitS+qW3+XHZt3MWrP30Vr6fpFnhtzaSYMJqMGI2hw2AwhLbqRgONL0N2fdAOBDGajJjNZhSL8mXI\nvhO0bTYb1igrNrsNu8PecNiibM0G6q42ml1wuoAFYxfQr18/vUsRYUzCbysdOHCA+fNzcbv/COTo\nXY4QD1CF2ZzG8uWL2b59OyCBt7V8Ph8HDx5k48aNbNmyBa/Xi9frxe/333du/WhoIBAgOzub1atX\nk5OTQ2xsrA6Vt53WhGEMYLPb8Hv9JKcmM2zsMAaNGkTfgX1RzArBQJCX//Jlym+UY1JMGDAQmxjL\niIkjGJgxEHu0naA/SCAQIBj48jIYCOL3+RuOgD9AwB/A7/cT8AUaPg4EAgT9QSrKKqgsq8Rb1zHh\nt6MYjKGR7HtHsxtoNARsnzc0p91gMDSMZitmBavNis1hIyo6im/95Fv0GdhHnyfzGCrLKolzxrF4\n7uJOGexF25Hw+xg+/fRT5sxZgtP5a2CZ3uUI0UgAOAC8DryFyeRvGGW6lwTe1tE0jS+++IK3336b\nN998k5KSEgwGAx6Pp8nzY2Ji8Hq9jB07lj/5kz9h8eLFpKWloapqKKwFQqHt3qOp2x/l3Ma314d1\nr9eLz+fD5/Pddd3n8911v/qP6+8fDAYbPg4EAg0f19/W1M/XwxgMBkyKiYA/8MBzjIoRo8GIpn05\nLUFTm/zz1OWZlFCoNZpCCVhVQ6PKAX8Ai81CVHQU0bHRxMTHEJ8UT2JyIgnJCcQmxBITH8PIiSOJ\njguv+doPo6oqxXnFPJP1DMnJyXqXI8KchN/HdOzYMWbOXEBNzS+AVXqXI7q0xoF3y53bXEDnCbyq\nqrY6+LV3UHQ6nVRUVFBZWUldXV3o7e2mf33ep34OauO3xxu/TV4/itXUaFb9Y9SHwoZg2OgyGAy2\nKpgK/SkWBUVRQkH2zghuwB964WGz24iKCQXZuMQ44rvF061HN+IT44mJj2kIs/XXHbGOTjsP9lbR\nLfpb+5M1NUvvUkQEeFiGlc7QDzF27FgOHfqQ6dPnUlNThap+Xe+SRJfS8sDrcDjw+XyMGTOG5cuX\nM2PGDOx2O36/n/Pnz4fdiGJTh6ZpDQEx3INiS4Nv/bmBQPMjn6JpJpMJxaLcFeg07c58Wu78G6t3\n/zubzWZ9pj0YwGwxoygKBqMBtNA20H6fH4PBgC3KhiPGQUxcDLGJsSQkJ9AtpRuxibHEJsQSGx97\nV6CNio6St/bv8Pv8BMoDjF8wXu9SRCchI78tdOnSJWbOXMStW7Pwen8ORO4Cl65JJRQk/U0cbXF7\n49u8jY7GH/saHY3v62v0Neq/jgtwAnUtenYGgwFFuTOC1EZBsfEhOl596L/3hUD97fXnNBeQGv+7\nAs3+29a/4KgfmTaZTCiK0nBZf91sDgU7j9eD0WrEYrFgUkyYzHfOM4cOTdVw1jipKq+ioqwCn9eH\n0WgkGAi26vtgsVnQVI0RE0cwOXsyA0cNxGKxoJgVTMqdWhUTJsXEiY9P8Mu/+yVuZ9Mt7FrKYDRg\nsVgaFrOpqtoQZBVFwe6wh4JsQgxxiXEkJieSmJLYEFwbLuNDwdZqj6yNU8JN8aViJqRNYEzmGL1L\nERFCRn7bSHp6Onl5h1m0aBXHjuXgdm8EEvUuKwzUAcdofXhsHBTrg+GjBMXAPR8Hmzk0QitETIDh\nzvXGl/UHjS4b0xpd1h9qo8vGR8fTNK1h1LUr0iMo1ofFe4OiqqrU1dXhcrlCbbRofpS4/vzk5GQG\nDx7MwIEDSUxMxGq1htpuNXEoitLi21tyrqI8WleA9e+ux/pEqLNASxRfLebPF/55i7/+vXx1oQVc\nXxz6gnPHz2E0GZmxcAazls0iPSP9rtptDlvD97yeSTGFgrLJBAbQVK1hoZzFGpof64h1EBsfS1xS\n3F3zY+8djY2Jj8FskYGPjuR2unF4HYwYPkLvUkQnIuH3EcTFxbFv3/t8+9s/4He/m4jbvQ0YondZ\nOvsX4MeArdFtTQXFpkJiRwdF/cJpONErKDY+6oNi46NxKLNYLCiKgsViafjYarVisVgajvqWY/W3\nt3UobOr2Rw2Kly5d4t1332XdunXk5+djNptxOp0Nn6+fCnHz5k2cTidHjhwhPT2dNWvWsGzZMoYM\nCb/fL+46Nw6zo8XnlxaWYrVbH3s0VtM0PK7QYsOdb+1k77t7sUfZmfX0LLKWZNF7QG/6DuxLv8H9\nsFgtdy30amo0tjPPj+1Myq+Vs2DsgohuJyjCj0x7aKXf/vZ3fPObf4XH80dgnt7l6OhHwD/oXUQ7\nqh8dbnwYGt0Od48a36s++Ndfr59+EaDlQdwMRAHRgIXQa1YVg+EaI0dmEBUVdVdQa0lQbOtQ2NTt\njxoUO7uysjK2b9/OunXrOHToEFarlZqamibPtVqtmEwm4uPjWbFiBbm5uUyaNEn3sBYIBHhl4yv0\nGturxffZ8/Ye/vNH/4nFamloWdaWFEXBqBhJSEpg7oq5zFg4g+RU6QbQGdy+eZskbxILshfI7xLx\nSKTbQzs6dOgQCxc+g9P5A4LB79B8AOrMXgL+P0LBrj2CYuMRY437pzDceyj3HOZ7rlsaXSp3Lq13\nLhtftza6bm50/3uPltxuAE4A7wG77jw/d6Pn2lg0oakdk4HngcXA/V0aoqJy+Zu/Gcvf/d3fNPO9\nFOHM7XazZ88e3nzzTd5///2G2+59yx5Ci76iokIbRyxatIhVq1aRnZ2N3W7v0Joh1D/69e2vkzYq\nrcX30TSNspIyiq8WU3SliCvnrnD1/FVKC0vxerxYbVZUVcXr8T7SIsKmWKyW0G58/VKZu2IuU3Om\nEt8t/LuciPsFA0Fu5N1g1dxVJCQk6F2OiDASftvZ9evXmTVrMcXFmdTV/QqI0bukDnYV+C/uDoqP\nGxYfdnv9vN1w1vIuDS0NvF86TEJCLkVFFxpCkYhcwWCQw4cPs3nzZjZu3EhVVRXBYBCvt+mOBbGx\nsXi9XqZOncratWtZuHAhSUlJHVJrZWUlG/duJDWjbXZnc9W6KLlWQtGVIq5fvM7lM5cpvlpMZVkl\nZqsZo9GIt87bqsVyVrsVNagyYPgA5q6Yy+TZk8NqK2bxYCVXSshMymTi+Il6lyIikITfDuB0Onnx\nxW+zdetB3O71wAS9SxK6aM/AWy+IwzGDX/ziq3ztay88fski7OTn5/POO++wfv16Ll26hKIouFyu\nJs+t7+c8dOhQ1q5dy9KlS0lPT2+32m7evMm7n75L6tC235q4sWAgyM3imxRfCY0WXzp7iesXrnOr\n+FbDQrVgMNjibYxtUTaCgSAZEzKY+8xcxj01DovV0q7PQbSes8ZJoDDAigUrsFqlU4Z4dBJ+O9Dm\nzZt5/vlv4PF8i0DgrwmNUIrOrSMC75cU5SVGjtzF0aP7dJ//KdpfaWkp27ZtY926dRw5cuSB84Rt\nNhsGg4Hk5GRWrlxJbm4u48aNa1jE2BYKCwvZfmI7aYNaPu2hrdVU1lB0tSg0WnzhOlfOXqHkWgnV\nldVYbVYMBgN1njrUYNNz6u0OO8FAkPFZ45m9fDajJo/CpMj/pXChqipFeUUsnbKUtDT9fs5EZJPw\n28GKiopYvvw5zpwJ4HK9DvTVuyTR5jo28H7pILGxKzh79pj8UeiCnE4nu3fv5o033uCDDz7AZDLh\ndDqb7MOsKAp2ux2TycSSJUtYuXIlM2fOfOxRtEuXLrHn4h7S+offz5/f5+dGwQ2KroSC8eUzlym4\nVMCtklsYMKBYFAL+QEPrNAB7lB0MMDVnKrOensWQzCFt+mJBPLob124wJGYI05+crncpIoJJ+NVB\nMBjkZz/7F37yk5fxeP4d2Ra5M9Ar8NYrIypqDJs3/4acnJzH/Foi0gUCAT7++GM2bdrEpk2bcLlc\nDTvr3ctgMBATE4PP5yMrK4s1a9Ywf/78Vi0iyjudxycln5Dat32nPbQlTdOoLKsMheKrjUaLr5fg\nqg1NJ6kfJY5NiCVrSRYzl86k3+B+0mGgg7mdbjxXPaxauAqbzfbwOwjRDAm/Ojp27BhLl67h9u0J\neDy/AmL1Lkk8Er0Dbz2VqKiFvPjiCH7+85+10dcUnYWmaZw+fZotW7awYcMGrl+/jslkwu1uuq9u\n/TzhkSNHNswT7tu3Ze9QHT12lLzqPFLSUtryKejG6/FSfK2Y4qvFFF4u5NLpSxRdLaLiZgW/2v4r\nevTqoXeJXYamaRTmFbJwwsIW/zwK0RwJvzpzuVx84xvfY9Om7bjdPweWE/6dCrqycAm8XzKZ/pmM\njK189tl+afQuHqqoqIht27bxxz/+kePHj2O1WqmtrW3yXLvdHmoNlprKqlWryM3NJTMzs9kRz8Of\nHeas82yn76OrquoDN3oRba+0oJQBtgHMnDZT71JEJyDhN0x89NFHPPfcn1FW1huX65dA+63IFo8q\n/ALvl94mLu7POXXqCH369GnHxxGdUXV1NTt37mTDhg3s2bMHRVGanSdsNpsbNkJ5+umnWbFiBTNm\nzLjrBdcnRz8h351Pcs/OHX5Fx/K4PLiuuFi1YJUu/atF5yPhN4z4/X5efvkX/OQnP8Pn+xaBwA+4\ne1tg0XHCOfDWe5fY2K9z4MBOMjMzO+DxRGfm8/k4ePAgGzduZMuWLXi9XrxeL37//TuuGY1GoqOj\nCQQCZGdns3r1anJycsg7l8dF70W6de+mwzMQnZGmaRSeLmT+2Pk88cQTepcjOgkJv2GooKCA//W/\nvsPHH5/G5foPYLbeJXURkRB4620jJuZr7N//AWPGjOnAxxVdgaZpnDhxgs2bN/Pmm29SUlKCwWDA\n4/E0eX5MTAxer5eBgwYyZvYYZi6dKQFYtIlbRbfoY+pD9oxsmWYi2oyE3zC2fft2Xnjhm9TUjMfj\n+TkQOSuoI0ckBd56O4iO/gp7925n/PjxOjy+6GquXbvG1q1bWbduHXl5eZjNZpxOZ5Pn1m8hnJya\nzIyFM5g8ezJ9B/WV4CIeWZ27juqL1Ty74FkcDofe5YhORMJvmHO73fzDP/yUX/7yv/D7v0Eg8F1A\nvt+PJxIDb71dOBx/wp497zFp0iQd6xBdVWVlJTt27GD9+vXs27cPi8VCbW0tTf2pUMwKJsWEzW7j\nyblPMi1nGkPHDJVNI8RDaZpGwekC5o2eR/oAWQMj2paE3whx9epV/vqv/4Ft23bg8/0lweCfA7IP\nfctFcuANMRheIyrqr9i1612mTJmidzlC4PV62bt3L2+99RZbt27F6wvNE25q9zSj0YjVbkVTNcZM\nH8P0BdMZM3UMtqj71zXs2LCDgzsOMv/Z+UycNRGrTbaw7WpuXL1BuiOdrKlZ8q6BaHMSfiPMoR9N\nmQAAFJlJREFU2bNn+d73/n8OHPiUurofomlfA2QP+qZFfuAN8WKzfYvk5APs2vUOQ4cO1bsgIe6j\nqiqv/eE13t79NscOHKO6sho08Hnv31gDQtsI+/1+Bo8cTNaSLMZnjSchKbSxxlemf4WKWxWhrYaD\nQSZnT2buyrkMGztMdljrAqorqjHeNLI8Z/lj7zooRFMk/EaoY8eO8Z3v/B3Hj+fjdv8IWAvIW4md\nJ/DWK8ThyGXq1DQ2bvw9sbGyEYoIX0c+P8KZ2jMkpyZTcr2Ew3sOs3/bfoqvFGNSTNS565q8n9Vu\nRQ2q9OzTk7EzxrJ9/fa7thk2GA1YbVasNiuzc2eT/XQ2qf1kDURn5Pf5uXX2FrmzcklKStK7HNFJ\nSfiNcAcPHuTb3/4hFy/exuX6EaFNMrpaCO5sgbfePuz21fzwh9/hb//2B/LWnwh7nx//nJNVJ+/b\n4a26oprP93/O/m37OXvsLGaLGbez6R3mzBYzGhoBX6DJzytmBaPRSI8+PZi/ej7TcqYREx/T5s9F\ndDxN0yg4U8DMYTMZNnSY3uWITkzCbyegaRq7du3i+9//P1y5cgOP51to2gt07u2SO2vgBfBjMr2M\nw/FvvP32OrKzs/UuSIgWyTudxycln5Dat/lRWW+dl5OfnOTg9oN8tv+zhtuamif8MDa7jWAwyIgJ\nI8hZncOYqWMwW2SXw0hVer2UJyxPMGvGLHmxL9qVhN9O5siRI/zkJz9nz54PUdXn8Pm+BXSmxuA+\n4OvA5jsfd5bAW+8jHI4/IzMzjQ0bXpFd20REuXz5Mh+e/5C0AWktOj8YDHL+5Hk+2fkJh3YewlXj\nQg2qTW6s8TB2hx00mL5wOnOemUN6RroEqAhSU1mDdkMjNycXm002dxLtS8JvJ1VQUMC//uuvePXV\n19C0GbjdfwFMASL9j0EBoTDfmQIvwC3s9u9jt+/l17/+OcuXL5c/3CLiFBUV8f4X75M2qGXh916b\nf7OZjf+9sdm5wS1hNBkxW8zExMUwb9U8spZkyXbLYc7v81N6ppTcmbmkpKQ8/A5CPKaHZVhZVhuh\n+vTpwy9+8c+Ull7jZz+bSc+eXyU6egKwHvDqXd5j6AM07vkYTajbxQzgP4CbwH7gOSIj+AYxGP4L\nuz2DF15I5tq1s+Tm5krwFRHJarViCLT+Z/f4oeOPFXwB1KCK1+OlvLS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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -399,7 +399,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 19, "metadata": { "collapsed": false, "scrolled": true @@ -409,14 +409,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Difference in mean x=0.087, y=42.362\n" + "Difference in mean x=-0.011, y=42.812\n" ] }, { "data": { - "image/png": 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48typVAqxWAxlZWXw+XyKBDEalMvlEIvF0NzcDJfLhcrKSnV8aQJL0uPxeJBI\nJJDNZhEIBFBWVqYiYz6fzzJnI3VlrDJkexOJhEpl0lpCCuztmi5Jqkj8mFIFtnl/sdJSpi95XgAt\n0pr2z5DH11MRaWhoaGh0BpqAlQjtiXwVqrKTKUG6zEuhPPeVP4wiMXrF31xHskaywuNTayUrCqn3\nisfjSKfT8Hg8FnE8o0ly8u1cLodEIqGIC530SbxI7uhSL4X4rIaUlg4U88vUKicNl8t4vFQqpUxe\nJRGjjoxkiu2wp36LFTPIaFyxqZHaQnsqXzU0NDQ0NDQBKwE6knYkWDHIv7mN0+mE3+9XJMIeKZN2\nCwBUxAiAInCMKEmTQWnnQEJCgbxpmvB6vUqHZRgGDMNQxIrb+Hw+hEIhFfUyDEMRu1wuB5fLpYgW\nU3m0i+Ccjy6XS7WR6yjSl1WVJFckMySOkhDK9KrT6UQgEFBzQVJ4LyOPPLYkdfZoWnvIU1skSxMv\nDQ0NDY22oAlYJ1GMfLVFypgGA7ansejqztSZNFZlBIpO93Lya7rjc35G+3G4HYkGtVySSHg8HkWg\nSJiSySTKyspQXl6uyBGPEYvFYJqmxQeMESrux23tES8uMwwDXq9XbSdtMuxRNO4n9WGAtXKT+8nC\nA14biaQECZmskpQVn22RMA0NDQ0NjR1FSSfj/stf/oJTTjkFgwcPhtPpxLJly1pss3DhQgwaNAiB\nQAATJkzo0ESfvQ07Sr7s62XVo3SgJ2EgweCk2vLlL8X6TAEyHWkYhtpHaruSySQaGxsRiUTU+eTx\nOMci28Hok93clHo1tjOVSsEwDEUs6YRPwsRrIlmMRqMIh8OIRqPI5XJwu93w+/2KCBqGgVgsZrlu\nRsBITn0+HwKBAAKBgIU8URvHa+Pk4Ewt2p395WfBfTU0NDQ0NLoKJSVg8Xgc+++/P+644w74/f4W\nL7dbbrkFS5cuxd133421a9eitrYWEydObPdEn70JrZGvQnYJ9opGkgC7eJ4kJZFIqBSbJGdyHwrr\nGSXzer1K8A5sn+ORREoSO0m0aJBKQhWNRpVgP51Oo7m5GYZhWNznGfkiyTMMA4lEQgntpfkrqyuZ\n2iSpA4BEIoFIJKJMY+Wckjw2r0WK/UkAGf1jlFC67RPSS8wuvJckzG7joaGhoaGh0VUoaQpyypQp\nmDJlCgCgrq7Oss40Tdx+++249tprcdpppwEAli1bhtraWqxcuRJz5swpZVO6FG2RL7sNgRSBF3vJ\nU6vE6A6ZD32AAAAgAElEQVTJBCM1TCsyjZfJZNDY2IhsNouKigqLzonRJpIrEhCm87LZLMrLy+H3\n+9U+jPoYhoFkMqkIdCqVUmSMqUWmAkl6pKaL0TC2g3NAMkXpcrlUtIq+Y6zKZLvj8Tii0ahKtdL2\nwu75xXaTSMqUriRW7bn//Pyk9YQmYRoaGhoaXYWSRsBaw/r167F582ZMmjRJLfP5fDj66KPx1ltv\ndVczOo1CES4u78j2xUBBud/vV0QFgCJfAJRpaiwWU9EsEizqxOjXRdJFbVZzczOamppUJCmZTKrI\nVTgcVutk2ynQp9dXNptV0TlWQbLt2WwWiUQC0WgUkUgE8XhcVS6SyJFkbd68GfF4XE3YHY1G0djY\niFgsZiFVNH4Ftum5vF4vfD5fwSIDqZ2T62RFqPxsZApXbq/Jl4aGhgbwyCOPwOl04uuvv+7ppuxy\n6DYCtmnTJgBA//79Lctra2vVut6OYvqiQi97OZl0a3oj+VtaS5BwMSrGdBxTc4ZhwO12IxQKwel0\nqsgZI0lMuTGiRXG6aW6beigejyMWiykdFlOeJHCGYVgMVzkFENuayWQQiUSQSCRUpIppUpnmlLos\nasIo4qffmZw+iVMg9e3bFxUVFRZfMKYtpZi+UErXruPi/efxpZ1HPB5XETwNDY1dD1u3bsU111yD\ncePGIRgMory8HAcccACuvfZa/Pvf/+7p5pUE3333HRYuXIj33nuvx9pAouZ0OrFmzZqC24wcORJO\npxMTJkzo5tb1TvSKKsidIdrQVoQL2O4vZfexas1JvRAJk5WN0vVe+ny53W4Eg0GVRpRaL0a+XC6X\nqlYMhUItNFY+n0/pyEhcvF4v0uk0otGoaj9Tk6lUSu2fTCYRjUZRVlaGqqoqAFApRBIyWR3JqJJh\nGIpoVlVVqX1pI8HjMwJGcinnj5QmtPQu4/+sErX7exX7DOwVmhoaGqVBW5XE3YF//OMfmDJlCqLR\nKGbOnImf/vSncDqdeO+99/DAAw/gmWeewaefftqjbSwFvvvuO9xwww3Ya6+9cMABB/RoW/x+P1au\nXInx48dblr/99tv48ssv4fP5evx70VvQbQRswIABAIDNmzdj8ODBavnmzZvVut6KQhEuuY6RFqbM\nJJlq63hyGTssSaS4jASB6UG7USj1WNlsVhEeEsFkMqm8ueiaT1sKeRzqtaSwndfEVCLTn8lkUqUP\nmRJ0u91KcE8CyjaTFPI63W43+vbtC6fTiaamJni9XgSDQSXsTyQSyqKCui9G8GRVJSNd0kqC5NPp\ndKrPQ07hRJSVlSEQCFh8wDQ0NEoD4+uv4RsypIUtTHchHA7j1FNPhdPpxDvvvIOxY8da1i9evBi/\n+tWveqRtXYXeEMmfMmUKnnzySdx5552WPnflypUYM2aMymRodGMKcvjw4RgwYABWr16tliWTSaxZ\nswZHHHFEdzWjwyj0hZYv60Iar0Jpx9a0Y6zwI/HhchKMcDiMhoYGFYFiOk0K7nO5nNKFMVrF46XT\naUQiEVXdGAgE4PV6LcSR52J6jxEokjbqurZu3YpNmzYhkUiodGdzczMaGxsRjUbV9EOy4tEwDJWu\nBGBJBXIKJG4Ti8WQTCZV++mQT5NVtoWpyvLyckXOPB4P/H5/i0nHmXLlPZaEkI769iiZ/Lx6Q6em\nobEzwTRN4O9/R+a773qsDffddx82btyI2267rQX5AoCKigosWrTIsuzpp5/GIYccgkAggJqaGsya\nNQvffPONZZu6ujr4/X588803OPnkkxEKhTBo0CDcddddAIAPP/wQxx9/PILBIIYOHYoVK1ZY9meq\n7vXXX8dPfvIT1NTUoKKiAjNmzMCWLVss2w4bNgznn39+i7Yfe+yxKo33+uuv49BDDwUAnH/++SoN\n+Mtf/lJt/9lnn2H69OmoqamB3+/HQQcdhKeffrrFcT/88EMcd9xxCAQCGDJkCG666aYW0+C1hZkz\nZ6KxsRF//OMf1bJcLocnnngCZ511VsF9TNPEXXfdhf322w9+vx/9+/fHBRdcgIaGBst2zz33HH70\nox9hyJAh8Pl8GDZsGK6++mpVLU/wM/ruu+9w6qmnIhQKoba2FldddVWHr6crUXIbinfffRfvvvsu\n8vk8NmzYgHfffRfffPMNHA4HLrvsMtxyyy149tlnsW7dOtTV1SEUCmHWrFmlbEbJ0JaVBCNMjLBQ\nL1VorsJCIDmS1gryXJJEyOmFaJ/ACa4Nw0Bzc7Oyi2CkiuuY9mM6kCk9Eh1qzHhO2mA0Njaivr4e\nzc3NiMfj6jwkg8FgEIFAQIn5ZdUmtWr2ttByhPsAQDAYVOlQ6s6YVmT7GNWTJrSMmlFXBmwnd7xG\nbltojkd7pFLef0nU7KJ+DQ2N1pFtaoLnlltg/utfPdaG5557Dn6/H9OnT2/X9itWrMC0adPgdDqx\nZMkSzJ07Fy+88AKOPPLIFkQgn8/jpJNOwpAhQ/DrX/8ae+21F+bNm4eHH34YkydPxiGHHIJf/epX\nqKioQF1dHb744osW55s3bx7++c9/YuHChZgzZw5WrVqFSZMmWTwIi8kn5PJ99tkHN9xwAwDgoosu\nwooVK7BixQqcfvrpAICPP/4YP/jBD/Dhhx/iZz/7GZYuXYq+ffti2rRpeOyxx9QxN23ahAkTJuD9\n99/HNddcg8svvxzLly/HHXfc0a77RwwePBhHHXUUVq5cqZb96U9/wpYtWzBz5syCfenFF1+MK664\nAocffjjuvPNOzJkzB0899RQmTJhgIVePPPII/H4/5s2bh7vuugvHHXccfvOb37RwXQC2fUaTJ09G\nv379cNttt+GYY47Bbbfdhvvvv79D19OVKGkKcu3atTjuuOMAbPuCLFiwAAsWLEBdXR0eeughXH31\n1TAMA5dccgmamppw2GGHYfXq1SgvLy9lM0qOQtYScp18GGQqkSimP6KmC0DBvDhJU3l5udJn2VOO\njBxFo1Fks1kEg0HLdENlZWXw+/3w+/0qchaNRi2u8vTqIolklSPTmQAsoWSPx2MR1NMOgmaqjN4x\nfelyueD1epFIJJBKpZTJq2maqKqqUmlApirkdEpMq5LcFbo/raUP6Ulmj3SRaEp3/x1FWylnDY1d\nHVnDgClelNkvv4Rv7Vrk1q5F+sADoZ4MpxPu/5vOrKvx0UcfYfTo0S2kB4WQyWRw5ZVXYp999sGb\nb76pJA0TJ07EhAkTsGTJEtx6662W7c8880xcf/31AIAzzzwTe+yxBy644AKsWLECM2fOBACccMIJ\nGDNmDB555BHceOONlnM6HA68/vrrql8bN24cZs+ejUcffRSzZ89utb3yHVNbW4vJkyfjF7/4BQ4/\n/PAWAY158+Zh8ODB+Pvf/66u6+KLL8aJJ56Ia665RkWlbrnlFtTX1+N///d/ccghhwDYFkkaOXJk\nhz4vh8OBWbNmYf78+TAMA36/H4899hgOO+ww7LXXXi22f+utt3D//fdj+fLllgjZ5MmTcdRRR+HR\nRx/FhRdeCAB47LHHlO4ZAC688EKMGjUKP//5z3Hrrbda5E2ZTAbTp0/Hz3/+cwDAnDlzcPDBB+PB\nBx/E3Llz2309XYmSRsCOPfbYFo7n+XweDz30kNpmwYIF+O6772AYBl577TXss88+pWxCt0OmGklm\naOvANFqxyIvUJtnTXwAsFZHSmV5OS8ToGe0gaPXASFEoFEIwGFRO+pxyiKTSMAzE43E0NDSgqakJ\n0WjUYpZKIhQIBJTOixYQ/JyltovH5HU0NDTgu+++QyQSsXiTMXoobTR4zawADQQCKC8vV2lYRsxI\n1CjGl9FC6sUYJWQ0jfeHmrHWolpMIcvjtKbna+t4Ghq7PFIppD/4AI4f/hDOo4+G97TT4ADgWbgQ\nrqOPhvPoo5F74AFku7HiPRKJIBQKtWvbv//979iyZQsuvvhii570mGOOwcEHH4wXX3yxxT4XXHCB\n+ruyshJ77703/H6/Il8AsPfee6Oqqgrr169vsf9FF11kGVSee+65qKqqwgsvvNCuNrcHjY2N+POf\n/4xp06YhGo2ivr5e/Zx44on49ttv8a//i1L+4Q9/wKGHHqrIFwD06dMHZ511Vof7tmnTpiGTyWDV\nqlUwDAOrVq0qmn584oknEAwGMWnSJEv7Ro8ejdraWrz22mtqW5KvfD6PcDiM+vp6HHnkkTBNE//8\n5z9bHJvEjRg/fjy+/PLLDl1LV6JXVEF2F3Y0UmEX3tvXyWPzb1ldZ18PWOeC5AhNelIx5SgjVdR0\nUddEAuT3++H1ehEOhxGJROB2u1V0its2NDSolF04HFYaKs7xmEqllLYqn8+rjosVlPIamMZ0Op2q\nitLv9yMYDFrc8E3TRCQSQVNTE1wulxLZcw5Gt9utwsuSmPF/Xr/8vEjOeBweiz+FolmysIFgRM1O\nfu2fa0eho2EauyPcVVVwHnkkUrffjrLLLoPrgw8AAA7DgPPLL5G67z64pkxBWZ8+3damiooKVc3d\nFjZs2AAAGD16dIt1Y8aMaaGX8ng8LSyVKisrMWjQoILtaGpqarF81KhRlv9dLheGDRum2lIKfP75\n5zBNEwsXLsTChQtbrHc4HNiyZQtGjRqFDRs2KC1Za+1sD6qrq3HiiSdixYoVcDqdMAwDM2bMKLjt\nZ599hlgs1uJ+Elu3blV/r1u3DldffTXeeOMNNdAnwuGw5f9Cn1F1dXXBz6KnsNsQMHsacUdIWFvV\niyRcbrfbYkNRbB/pZ0Vz0nw+D6/XqzRLJBr2aJO0fCAR4jUx7cftOe9iKpVCLpfDpk2bkMlk0L9/\nf+Vwz3NEIhE4HA6EQiGEw2Fl60APMqbsSMJo+MqUaFlZmWWyb6/Xi5qaGktEMJPJoLKyEl6vVxE/\nh8OBQCCAYDCoIlXAthFPRUWFSkfG43H4fD74fD4L0SX58nq9KgVLkglA/U/SJefd7Ey5vCTnmnRp\n7M5wOp3wHXIIjDvugPv731fL09dcg7Izz+z26rexY8fin//8Z0H5QkdRaFBXCMWucUej48XOw9lF\n2gIHnfPnz8dJJ51UcJtx48a1eq4dxaxZs3DuueciEolg4sSJqKmpKdrGvn374ve//33B9dXV1QC2\nEawJEyYgFAph8eLFGDlyJPx+PzZu3Ii6uroW4vqdoT/ebQhYR9HWAyOrFBnNIRGQD2GhyjoASuAt\nfb6YimM0yH4uaf3A1CWn6slkMigvL1ekSKYb7RExl8uFVCqlSBJTwhUVFaoy0OHYPvF1c3OzImgk\nNT6fT3UANIttampS5JNar8rKShU2NgzDojFjlCyXyyEWiynriVwuh3g8rtK7vCckigDUtZEYy6pN\nACoyxo5XkmSmJbkdiWNrHZqMbNmjXDvDg66h0V1wfvIJTIcDmTlz4P7v/4b78ceRmzMHrtrabm3H\n1KlT8de//hVPPvlkm4VeQ4cOBQB88sknOOGEEyzrPvnkEwwbNqzk7fvss88s58pms1i/fr3FpLRY\nxGbDhg0YOXKk+r9YH0TNlcvlUvrsYhg6dCg+++yzgu3cEUydOhVerxdvvfUWli1bVnS7ESNG4E9/\n+hN+8IMftKoHf+2119DQ0IBnnnkGRx11lFr+yiuv7FD7egN6xqClB9CaI70d7SFfUvvDSAohtUbS\nVsJuNcF20DFe6sEK/W0/DnVUJBv5fB6xWAzhcBiGYVhICEX+jFYx/UiSJSfoJomixxdtJljpKHVu\nPAZ1ZI2NjWhoaMCWLVsQDodVNWQ8HgcA5RmWyWRQX1+vUqZ+v1/l9ZPJpGpLKpVCU1OTZTJwElFG\n+kisGA2U90xGyfx+v8Wywp4eLva5y89aeo9pzZeGhhXZWAzOF19E8vnn4bztNqRXr0Z+7FjkP/+8\n29ty0UUXYdCgQbjiiivwySeftFgfjUaViP6QQw5B//79cd9991mq7t5880288847OPnkky37lmLQ\ndd999yntKwA8+uijCIfD+OEPf6iWjRgxAm+//balMvKFF17Axo0bLccicWlsbLQsr62txYQJE/Db\n3/4W3xWwBJHpvZNOOglr167F2rVr1bKGhgasXLlyh67X7/fjnnvuwYIFC3DqqacW3e7MM89EPp9X\nlZwSuVwOzc3NALZHF2WkK5/PY+nSpQWPuzMMjHerCFgpKt3sx5M2B2VlZeplTcE4AGWpwOOQFMko\nk7SxsBuIEoFAAB6PRwnvAagJuenr5XQ64fP5VDqR7eDE1zRVZTucTicqKioQiURUx8OUpiQeJGY0\nR2U6k1MQyeug4J+mr7xOv9+vfMJcLheam5sV0erbt68iVSR+skrTPh9lKpVSc0gybVuo8lR6iUl9\nWFc/nJqcaeyOyG7aBFx7LXz77bdtILTffsj8538iE4vB24lU/46gsrISq1atwkknnYSDDjoIs2bN\nwiGHHAKn04l169bh8ccfR01NDW666SaUlZXh1ltvxbnnnoujjjoKZ511FrZu3Yo777wTgwcPxs9+\n9jPLsVsbrLUXDocDEyZMwJlnnomvvvpK+WCdd955apsLLrgATz31FCZPnoxp06bhiy++wGOPPYYR\nI0ZYzjVixAhUV1fjnnvuQXl5OUKhEPbbbz+MGzcO99xzD4488kjsv//+uPDCC7HXXnthy5Yt+Nvf\n/oaPP/5YifCvvvpqLF++HJMnT8a8efNQXl6O3/72t9hzzz3x/vvvd+TWK5x99tltbnPUUUfhkksu\nwa233or3338fkyZNgtfrxeeff46nn34aN954I84991yMHz8effv2xXnnnYdLL70UbrcbTz31lBrc\n27Ez9MG7FQHbURSrYmQKkGkxu48UAEUSGJWRx2DkyDRNZTTKiBIF+UzTJZNJZfNAbZfD4UAkElH2\nE06nU2moGKEiASGJkulBihiZAjQMQ1U3clJtpg39fr8lzSftGxwOhzqGTBFms1lEo1G1H6NHABAK\nhRAKhZSujLYXkiBls1k1+Ta1dYzUMcLF49nF9G15sBUj1IVg13m1V/O1M3QAGhqlhGevvVrooMr6\n94erX78eac/BBx+MdevW4bbbbsPzzz+Pxx9/HKZpYuTIkbjwwgtx2WWXqW3PPvtsBAIB3Hzzzbjm\nmmtQXl6Ok08+Gbfccgv6iOKB9nhz2ZcXwh133IEnn3wSN9xwA1KpFE499VTcddddlvfEpEmTcNtt\nt2Hp0qW4/PLL8f3vfx8vvvgi5s+fbzluWVkZli9fjmuvvRY/+clPkM1msWDBAowbNw577703/v73\nv+OXv/wlHn30UdTX16O2thYHHHCAxYh2wIABeO2113DppZdiyZIlqKmpwdy5czFw4EBLxWdraA/B\nLrTNXXfdhYMOOgj33nsvfv7zn8PtdmPo0KGYMWOGSp1WV1fjxRdfxBVXXIEFCxYgFArh9NNPx9y5\nc7H//vu3OEdHPqOegsPshW8JWc1QWVnZ7ecvRrj4t306IPv2JEDAtjCsrO4jsaJWi0J8apooxGek\nJxAIwOVyoampCel0Gn6/X6X2/H4/otGoikRRtJ9IJJBIJNRxSJY8Hg/i8Tjq6+sRi8XQ3NwM09w2\nSXY8Hle6q1AopOaEpJaMBIxRs0AggEAgoMhaMplUqU+Hw4Hy8nIleOd+nFxb7ksBvtvthmEYyoE6\nEAggl8tZpjkqKytTUb0+ffqgurpakVtq0uQDxs+GxE7O92ifMso+2bhdD9bRh7ZQJLQnvssaGq0h\nmUzC5/P1dDN2KzzyyCP48Y9/jLfffrtg1aFGz6K1Z6LU3ERHwDoBewWktFBgTl6+uOV0P9yXGiYS\nGfp4pdNpxONxRU6kLxePxUm0AahJuh0OB6LRqBLr03yVonuSkVgshvr6ehXFI0FjupDLWE1JHRWv\nIRaLKdLCKJ2MDhG8LyRa/fr1g8PhQDweV2lOftlZ3cj9OK0Qr0+609snO5cFDpKEScF9sUomki0Z\nuZRkrTeNmDQ0NDQ0dg1oAibQWuRLglovkgKK2klQAOtLXUJWTprmtql2SGCoZ6IrPIkXtVTUecnp\nhPx+v0oBymNLE9FMJoNoNIrGxkaVxnS73cregRo1nq+5uRkul0tVRTJKx+pJVkLKeSMZ2aNGjKlD\nksZ4PI5EIoF0Oq1IYi6XU3YUvKdlZWUqNdqvXz9VBcnqTJrA0iyRVYwksjx3W3ovRua4vlAks9i+\n7QHJqIyAaWhoaGhoEJqAFYGMhthTjcVeylLjJCNBdqd2mqiySk+mCSlqd7lc8Pl86n+el1UhkUgE\n5eXlypKCWjMas7JakOlIEiCSOQrX3W63sq3g1EZNTU0qCkciCKDF1D3SDJXEUBYiUMxP37BsNotI\nJAKfz6ciYvQoowaO95GaMTl1kt/vVwTS5/MhlUohEonA6XSiurraUilayNtL+q/JlKQkaoyodTbq\n1Qsz+xoaGr0EOqquAWgCptDRqha+wOUL264Vk6kxVi5KQkNdE6NCAFR6kiJ0TgtEQkeSxh+7QStJ\nWjqdRiwWU5YRiURCESdOC0RRu6yqZHUjyRirB2VEj+lSXh/PSSLGtlMrx2NkMhk0NDQowlhVVaVS\npNSbeb1epXuT94zGs0yNMtpI0kSRvrSd4DROUgtWSOMliXV7zA3bgiTvGhoaGhJ1dXUFJ4/W2P3Q\n7QRs4cKFLfw+BgwYUNCjpLtQLPVEotRadZy98q6Y8z1/y+mHuD8jMbFYzJKSZDUkyRZJTiAQUGSB\n5MUwDEWeYrGYqo5kpSDnXWRUjOSI2rFgMKgIJe0egO0aKpfLpQiNLB4gIWQ6lqk9LmekjNE2pjC5\njZyEnERUTlnk8XgQDAbVNfBe0hG/T58+6pwkhtwunU6rlGWhz1BGxIAdmyFBQ0NDQ0NjR9AjEbAx\nY8bg9ddfV/939xQV7UV7XsbFXNGlWRzJHMXw0owV2O67xYiP1FxJbRin/QkEAmrKHwrk4/G48tVi\nhSUA9Te3IcmjhoxCfmmV4fP51LFJ9EhqpOmsjNpJewtqsLgNU6rUmVEbRv0Wr48aMBJFj8dj8SHj\n3xT/s/qRqUxG5eQ0TFKAz/Qo769M7ZaSeEkirjVgGhoaGhqF0CMEzOVyobabp6XoCshUk5zyhpEY\nEgqCKTqSKntkjESIuiaK3hnpYjqOpIbzM0ajUTQ0NKChoUFFm3w+H9LpNKLRqCJ8cj5HtgfYFo2j\n5xftHOTk38B2oT23p0aMbeK1JZNJVVlpj9IB2z57WnOwDUwnSsd+kjoK8KkRk9fGqYtIRvk5kIQx\nxSvJsUwz2iNfpSZhGho7AwrpJTU0dkd0t3a3RwjYl19+iUGDBsHr9eIHP/gBFi9ejOHDh3d7O1q7\n2YUqIu0aLwmSExnV4XK7TYKsepSVj3K+Q5qPyqpI6TzPyFYkEsGWLVuUriubzSIWiykdVjweV6SN\npMXpdCpiQ+f6RCIB0zRRXV2tUpwkTowksa0ejweGYSiRPgkQCZ7D4UBlZaXFxkIK45PJJILBoCXF\ny3QjSRPvpdvtRigUUrowauh4HBI4RusYbWMUjvfMHqGURExG6zQ0didwYNVbsxAaGt0Jvm+7C91O\nwA477DAsW7YMY8aMwebNm7Fo0SIcccQR+PDDDy1uwz0B+xyNcrkUcUvPq7KyMkvEi/szZUYSwe2Z\nhgTQwmOLeqzq6mp13FgspgxJmT6LRCJq2p5kMonm5mZlh0HxPDVZnIYHgEp/kkgBUFYYTJXZTeiY\nDiRZY4qTESqek/eJ5BKwCt2Z3rRr5hg9a2pqUtfOlGI+n1fpVpJO2lwEAgH1N3VfdN+nXk0SYYli\n9hSdjQS0VSWrodHbQKsUu3WLhsbuBL4TqRvuLnQ7AZs8ebL6e99998Xhhx+O4cOHY9myZbj88su7\nuzkKdGU3zW3TAtnNOVurhpQvdI4kqbGSVXuSmHDkSTIDQFk8SOE8vxjSJoIeWvxfphjZDpIPkhGS\nJb/fr8xMJXEkcUqn02hsbFRtJfny+XyK8DCixfMyyuR2uxEIBBAKhSwaLxIt+1RGACy+YXwJ0K6C\nurFoNKq25TWzPWwnqyelJ5gkhK2Rq0LVq+2xHbEfQ6aj9YtMY2cAdZTUV/YE2BcAsEzDsytD9i32\n7Aorvtn3sz+S7xeul31rW+cpdF6+RwrN/GHvN+W7blck6/aisO5Aj3/bA4EAxo0bh88//7ynm1KQ\nZMkvofSZKuQfJdOOJDXAdp0TI11k2IZhqJQgdVGsYuQUQOXl5Ypc0U6ChI0kz+PxqHQc20ALCx6T\nDy/d5RnB4rG8Xq/aRwraGbWzP4zUiDHSJCNfkoxIqwgSExI2mXLs168fysvLVcVlKBRSaUZOwcQI\nnPRPS6fTKCsrUxoxtoEpWqkJK1QNaY9s0suMpJVt35GHclfroDR2TbASu6cgp3cJBoM91o7ugn2w\nJgf5TqcTsVgMTU1Nqv/yer0qM8GZRKi5pVRFyiwkZIZFFlsB298RzG7wbxI6v9+vjs3+netloZXG\njqPHCVgymcTHH3+sJtzsDhQiWkxr8W9uZzdj5YNSbModRpZSqZTajv9nMhnFsGXFIY/P8zU1NSGb\nzaJPnz4Wfy1OsE2ywAibrJZk1IvraZDKh9DpdFrIHAkQf0vxO9tG4sKRKgkmiVl5ebnFBiKRSChv\nLt5LRssYoaLYnwSQEStaWVBDBmxL1crPJhQKWYhhJpOBYRjqb0b7GP2To7+uEhzLysdSC/o1NDR2\nXdgrtE3TVObZwWAQyWQSjY2NqKqqUv2gJEPsp2Xfxr6O0g1g27tWBhKo2eW2tDFiERX/p5UP3w2F\nyLqWX+wYup2AXXnllTjllFMwZMgQbNmyBTfeeCMMw8B5553X3U1pATujl1+qYj5ShSAjZHKEw2hU\nMplUIxaZdpNifJki5A8fSimqNwxDmbUCUClBmVaMxWLKTd7hcMAwDITDYWVpwVGnfZREbzAel2RO\nPuRyTkr6h7FjAKDSjTLiRvJlGAbi8Tj8fr8igfQiYyfh9XoRCoVUB8BrYnTK5/OpY0sLjkAgoNKU\ncg4h46wAACAASURBVMTHe26PXkrIz64jZKqYtkxDQ0ODsGdMuIwyGMMwlJTD7/erGUwCgYAaHLNf\nspMhOTiXM7NQ1mI/J/enZIRRMBIyqXMGYMlkyHNq+cWOodsJ2LfffouZM2eivr4e/fr1w+GHH463\n334bQ4YM6e6mKLSm75JRDQCWB8ceDeP2jCaRyJimqbyvDMNQE1nLh4fEicRHfqlpOUE/L0ayGNnK\n5XJIJBIqysaHVLaTDyQA5QMmJwDnuZl+pO8YyRmPz6ICqRljeFw61gOwkEy69vM+sRJTVnnyXvJ+\n8ljyuhnZArbrEEhaSaz4GUirC34WXFaILNk7jtbIV7ERn+58NDQ02gO7KTcANYiUM3t4PB5UV1er\nyD8H31Jywn2lnk4OIuU5OLjlO4rFXMyoAFDvm2AwqPpge1ZDo/PodgL2+OOPd/cp20Rr4dPWXqh2\nGwn5MEgyQjsIOwmQqU6m+Eg2+KVntIoO9ow0SV8uaSxKjZh9Um+p+2LYmn8zksYHlSMnmrdSixWL\nxVSKk6lUdgTAdpG8FIYyqmWfNol2FVJoSuIn07HyeDI0LokWOysem2SMUyAxgsjti0Wq7OnJ1shX\noRGfJl8aGho7Ar47ON8to2H0gWSfzH5NzibC/aX8olAkSg6age39dSwWQ0NDAzKZjNIis++1V7IX\ne0faAxUa7UOPa8C6E8VE9vaXaWupRTm/oaxW5KiCkSd+iRnWZeWez+dTpENWOsooFgAVmWpqakJz\nc7N62PgQkKDV19cjHA4rA9Z8Po94PK4iYyQ+9nkf6d9FXZt0xOeoC9g25U8ul1OTeUv9FttBgsd2\nM80KAD6fT3mHkUyxcwG2h97tZIk6NZ6PJIvbyMpLRhelcz/vk0zztpVKbg/5Kgbd8WhoaLQXkrTw\nvcJMBNezP2Z6sLm5GdFoVJGwiooK+P1+9c6SxU6FolR8B8iBdDqdRjweV/PwcgDO/oxZFRl9K3Y9\nGh3HbkXAOgs7MeMLXVb/yR8pvvd6vfB6vWo7RoEYeTJNE4ZhqBEMo1VerxeVlZWqEiWZTKoUYlNT\nk4pAyZEQyRyJIVOVfOgovOTDTuLCCJLdvJT6M8Mw1MNPHRuF7jKlGolElD6rvLxcnUNGoUgEpR6L\nuoNIJKL2YYQOgPIEoyaB+i4KRz0ej7KmYOSRxIudUqGoFwl4eyvB9IhPQ0Ojs5D9HrBdZ8vMhtfr\nVVXwiUQCkUgEsVgMgUAANTU1Fu0wB6gALNkYeQ4emySL7yb24Rzkc7YRvps44JXyG93vlQa7NQEj\nUZITY7clrJeCbTlKIaTWialGRohIlqQonaJHusuT5JAslZeXK3E7HxopxAyFQurY3D8WiyEWi1mi\nVCRWvF5OGyTnnWSETE6jxOtJJBKW9Kn0o6GYH0ALCwtZwixHViR4TG/Se42mslVVVZZOgdfPzkJG\n8vhZEJJ8ScF+WwSrIxWSugPS0NDoLPjukNOmkfRweSQSQSqVQkVFherTORCWfmGyQMo+zZoU5HMq\nNxIsr9erBrns4/me4ICZchr24cxG6H6wc9jtCZisEin2ArZXjsiIF/+XZb+clFqGgzOZjDI4DQaD\n6ovO6Yfk/Iq5XE6Flu3+XiROiUQC+Xwefr9f2U1w7sf6+nqVUuT1yQm6ZdqRBJAPNUkhCaAkXNRh\n8aGU1TaNjY2W+SxlGDyZTKp9mS4kuZQpTEbDOL8jOyOSw2g0Cp/Ph2AwqKJs/fv3t5Rwcx+pg5DE\nzw5uK/UTOv2ooaHR1ZBRKZIoOWilTUQikUAsFoPf71cDcnvREwua7BXdBPs5DsQZBOC+prndgJzv\nnaamJpXFICFk26hB01WPncNuTcAAq18KgBYRrkLby/04siBh4Rea+iTm2enhRVsGjj4ouqS5HYkX\nSQH1VCRYTAVSiC5DyRT7828+xBTU0wEfgKUik9cUj8fVaAeAOj87BWoEpHu+nFOSTvsU3TPNyggU\n05Fsk9PpRHl5ubrnbrcb5eXl6h5QzyWjZfLes2PivpIkcj9+PiR2hbQRrVU7tgXd+WhoaJQC7Odk\ntoN9PbW97H/lDCfs6zlwleJ8WSDEiJmUf8jZUGhZxD7f5/Op8/G94ff7LdY+Gp3Dbk/A7GBUB7CW\nB3Mdf1M4SRJGkIQwJJxKpRCNRpXbMx3nSRwopKT2KZvNWmwoOMKJx+NqPbDdgoFzPvKHegCPx6Oi\nZSSIjJzJOSjtKVeSJRkNlKFnaWUhKxN9Pp/Sgvl8Pos+jClSRuFIrCjwZ1Um7yejcUyZBoNBRdRI\n1ioqKpDNZtU0RT6fT6VjpQ+afT5MoLB1hNZ0aWhodCckKeIgkTpYRsWAbaTH7/cjHo+r90AikbDY\n+Ng9D4tVK/IccmBL+QvfQdFoFP369UN1dbUlMyMHxcU0tRodw25BwIrpuoDtX0r7HGQkWHxICom3\n+Vvuy+3lxNfUItEewTRN+Hw+NDU1qepIabQaiUQUYWLImFPy8JgU0vPh5WjJ5XIhGAwq8tXc3Kym\n6+FDTdLS1v1iWo8kifo0PoRMNTKlShJDET8A9bCyjX6/HxUVFeqhZrRKTreUzWbRt29fS8ROHsfh\ncCAQCKBPnz4qlB4Oh2GapprMm+AMB3YyXeh7oKGhodGdkNXaHODKiJaUgdCHKxqNqgG6aZpqcGrP\nEBQiY3wHcU7dcDhsSSUySxEIBBAIBNQg2jCMFn2p7jM7j92CgBWDPfJB4iHd61vbV6bZpDkpsN0l\nnqlFfnEZDZKjHYacSY4oSgegRkMMK5PIcDkA5R9G7RYfsGQyiXA4bPGPoQ6so2DYm5otqW+jOJ7p\nRkbRGO1jVIpzUdLRmVE0v9+vCCc7HNkhyRQqyTKrIBkit5uy8m9C+ujojkNDQ6O3QEbCAFh8E5m1\n4LzActYQDmTZD8pp30jAeGxpdUF5DLM97M9lZEtWwZMM2pdrdB47paUtGX4p9reXAsuUot2Vneuk\n6J7+LM3NzSr1RVE8o1YALGSBXl+VlZWoqalR6cJ0Oq3mOqTRaSqVQjwet8wHKefvIrFgeo8TfDP1\nyJQl/V529L7JeSXtujdqBCjIl9WSbJudRFI7xgghP4dAIICKigpFxILBICoqKizL5DyQ1I0xZC47\niFwu12Kqpo5+PzQ0dkf85S9/wSmnnILBgwfD6XRi2bJlLbZZuHAhBg0ahEAggAkTJuCjjz6yrE+l\nUrj00kvRr18/BINBTJ06Fd9++213XcJOBQ4YSbTofciBqZwJJBgMKl8uDvrbE5FiUEH+kHTRxoLv\nPKmNzmQyahtNvkqLnY6AyS9FqV+SMg1G4gRApcLovyVFkozsSO+pSCSi0otyG1YfSqd6lhzzAevX\nrx/69euHdDqNxsZGxONxGIah8v7yummQahiGOi5TmUzllfKBSafTCIfDaG5uRiwWU5WYvDaGrUOh\nkKruJAmlT5is2PF6vfD7/aoTkFU+jKTRCwfYnk6k3oHrgsGgCtfzenlPW5vDrBC68vulobGzIB6P\nY//998cdd9yhimIkbrnlFixduhR333031q5di9raWkycOFFpWwHgsssuwzPPPIPf/e53ePPNNxGJ\nRHDyySd3aDC0O0KSKRkFk7ZB7IspmpdpR/Z1ss/jcgYC2M+xf06lUmhuboZhGAiFQqiqqlL9Nd9N\nmnyVHrt1ClKi0ItXRkJk1IsCe1YQlpeXK1E7KxFJuki2SLToOkwiB0A9WBREMtJlJ4EUk5PEUPdF\nsiJJoKyULDV4PpfLpR5UPuCBQEBdA03+fD6fKnGm0F5aTRiGoYgXKzd5z/mbaV6mbnkfpMUE1/FH\nhtQ7KhhtjXzZo6caGrsapkyZgilTpgAA6urqLOtM08Ttt9+Oa6+9FqeddhoAYNmyZaitrcXKlSsx\nZ84chMNhPPTQQ3jkkUdw/PHHAwCWL1+OoUOH4k9/+hMmTZrUrdezM0B6ddEKgvIKThlEMsR+Xk4d\nJ7VczHzI2V0ymQwMw1DLZQSN085xIMyZXNiH23VlGqXBThcBs3s8tYWORjFIImj2yS8gKwvl9BEk\nABSqMz3JB0FWGlK3xWgaI1Y8J+0qwuGwqpikFoBffubueWxGuhgF4zmkP1dXgaMpgpoF6sCYHiQh\nk/NXygeZk77SByyZTKKhoQGxWMwy1RA1cexYqHuT95MdUTKZVOeXVTxygnJ+hvbvh/x+FVqvI2Qa\nuzvWr1+PzZs3W0iUz+fD0UcfjbfeegsA8M477yCTyVi2GTx4MMaOHau20bC+R9hHMbPBaYdqamoQ\nCARUJIyG2TKzwr6Ix6LmS/qMcb9wOIzGxkaEw2EYhoFkMol4PK6OFY1Gles++1HKRnSfV1r0CAH7\nr//6LwwfPhx+vx+HHHII1qxZ06H92xsOLfZlKabx4TI5KuCXTq7jC1pO+ExiJB3i2U76dwFQYnyS\nOv7tdrthGAYaGxuVOJ3WDtRYkbgw8hWLxdDU1ITGxkY0NTUprQDF+HzoSo1gMIjq6mqLrxbbxvPa\npycCthNKOem4jHLxmphSZXqTegiSO+nzJQmWLEywT0TOe8j17KAKdSr8bmmipaHREps2bQIA9O/f\n37K8trZWrdu0aRNcLhf69u1r2aZ///7YvHlz9zS0l4N9EHW90hScxUYU3Us9K4kU3xPyXcgBObWy\n7JMZSQuFQkqy4ff7UVVVBbfbjWg0ikwmoyJqbBP7WN0Xdg26PQX5+9//HpdddhnuuecejB8/Hv/5\nn/+JKVOm4KOPPsKQIUO6/PyyutEeRZOCfD4A3F4Ky4HtRIyRKX4xGaHhl54EiESAaUFWJPJ/bp/N\nZi1aKUZ5WCFITQDD0xTXS3NUmYIsNaRui/eMZJT3h0Z+TE3y+nif5IPMGQISiQSCwSAqKyvRp08f\nZQJIkkeRKj8HaujYQbC4IRAIqBA6jy8rVpk6ld+DjohLZeVsIVNXDY3dGTpFtWPg+4b9HAfmHJC6\nXC5UVlaq7UmKmHmRUTR+BjLFCGzX0Mr5ctPpNJqbm5FMJtWAlzOiMLvDgasW4Zce3f4GWbp0Kc4/\n/3zMnj0bo0ePxp133omBAwfinnvu6e6mtKiGtIsWZcpR2iHwyw5AmYFKEuTz+VQVI6eHCIVCKhok\nv/wkUsD2yaaZUmQqTUb8GJXjiIn5fhl2JhmRGrJSQFpISPE9KxGZJpSpW5IlGY2jiJ7RMEa2/H4/\nKisrlRi/oqJC2XY4nU4Eg0FF/mRJNDsNWULNdsgqVHYgMk0sU8oSraW67RYXGhq7EwYMGAAALSJZ\nmzdvVusGDBiAXC6HhoYGyzabNm1S2+zu4DumvLzcMoClljiTyajIVHl5udLbSlE8ZyFhVoADUA42\neR5aVwDb32Us7jJNE1VVVeodJft0BgqYedAErLTo1rdIOp3GP/7xjxYCzEmTJpVcF1AsVNrWi9W+\nTEawpA0F/bji8Tiam5tVlYqcOoKmo6zqI6GiFop6Mz5ITDkyvy+rJeXDw5x9PB5XBENWZ0rD1lLB\n4/HA5/OpEZFMN8rpLRilYjqWkT1G+6RnGQWhFRUV2HPPPTF48GBUVVUpAsZQOcmOnAONYlGup06M\n94nnZWdCkiY/U5I2dnb2+6WdnjU0WmL48OEYMGAAVq9erZYlk0msWbMGRxxxBADg4IMPRllZmWWb\njRs34pNPPlHbaGwfzNnfPSRmlZWV6Nu3Lzwej2U6oGAwqAbsUgNGrbLdXgnYPnhn0GDjxo345ptv\nEIvFLDO4hMNhRKNRRcJkwZRGadGtKcj6+nrkcrlWtQOlgNQVAS29vgp5f8nfxZbZ9VR8eXPqnVQq\npYSLck5EeoXRdViGiJlCJKRHFiexBqBSaCQudgNXaQjLY5QKtJhghSIJDSNQTIVSs8AIF7ULTIvS\nkR+A2raqqgo1NTUq7SjvP4/JzofRLmlRIWchkClckiuZOrZ3cq11KLqz0didEY/H8a9//QvAtkHf\nhg0b8O6776Jv374YMmQILrvsMixevBhjxozBqFGjsGjRIoRCIcyaNQvANo/D2bNn4+qrr0ZtbS36\n9OmD+fPn44ADDsAJJ5zQk5fWK8GBotSwUrcFQNkKBYNB1Ycyu0CpC/ssyjLku4aDZAAW01YO/hOJ\nhMU/kX6NzGwwKicJo0bnscvaULSm9WptewrICdodpFIphMNhi2je6XSqLyvtFBjqtU/8zLSlnMNR\n5thJHmKxmCUiI1OQfFBkalLqmaj5KrX2i3osh8OholCVlZUIBAIWt3/eRxJC3n+SRMMw1LyOXq9X\nES+/36+Oz3vtcDiU+J4dk5wWSVpPFPubVZpymUwxy2VyOw2N3R1r167FcccdB2Dbc7FgwQIsWLAA\ndXV1eOihh3D11VfDMAxccsklaGpqwmGHHYbVq1crzz4AuP322+F2uzFjxgwYhoETTjgBK1as0M9Z\nEbBfkt5f7MtJsBjtMgwD9fX1qlhLFjvZZSuSfJHYORwOVFdXw+fzWaQ4LJ6SlZYc1FNiIwX+Gp1D\ntxKwmpoauFyugtqBgQMHdmdTCqJQREx+kaVdBEcCcmTCFz49W1jBB2wLG/MhoOkdy4gpmucoiFEd\nVjwydUdHd0m+CLaj1KDAnaMh6sCqqqqUV4x0qGcHIh9oRvpIOhkl4z3jfeUPr4NGq0wvypQshfbS\n84uRLxnSl0QLaCmcl+F77e+lobENxx57bJs2NiRlxeDxeHDnnXfizjvvLHXzdllwIEpvSPaJFNzH\n43FFqOifyCwBgBZSClntzYEsLS4o3SDhY5YCgCJeLLqiG75GadGtBMzj8eDggw/G6tWrcfrpp6vl\nr7zyCqZNm1aSc9hF9fy7kJ+TBMkPwS8yl5WVlaGiokKNPhgp4xea4m8+OCQFjARRcClHEtIDRnpj\nMcrDSVDp7cVRkKxskZGh7gAF8IWsOWQKkfeMZItRPo/Ho8T23F5W65CwUUzKz8LlcqnRG1OzTMvS\nFV+SrkKpxkKaP3tVpoySFYMmaBoaGqUE+yG+C9h3cm5gWTlP4jV48GD4fD41sXZZWZllyiK7nZLs\nB9l/ejweGIahptNzu93o06cPgsGgZTDLwa3sZzU6j25PQc6fPx/nnHMODj30UBxxxBG49957sWnT\nJsydO7fTxy7m51SMfNn9wBh5kbYS3E6GXzmSYNUJPb9IpkgiOLIggWA0yTRNlVoDgFgshlQqpSoD\nAajRD69DTutDMkPS1ZXeLLLCRs51GY/H1TWQbDJ6xYdWks+ysjJlKFhVVWXRFfB+uVwuVSZN/xue\nj1MXscOQFamcM60QwSo1dMejoaHRFZCV4hTAM1pF4T0jVC6XS70vmpubVYaC0he+cxhYME0T4XBY\nvUscDgfKy8vhdDqVETaLmiorKxEMBuHz+VQ/DGwffLOtgO4PO4tuJ2DTp09HQ0MDFi1ahH//+9/Y\nb7/98Ic//KFbPMDskPNckezwRc6Xvz2lBkD5eVEIzsiMnOw6HA4jEomo6sZgMKhE9NIQlNPzJJNJ\n+Hw+lJeXI51OK2sLOeUQpzGiXozt5UhGzn1YCki9m7R8YJtzuZyquJFpQ46Q6HLvcrlQUVGBmpoa\nBINBRehY3clrpBCfZEz6f0mtGT8Pkj1GwmR72gsZKSW0xYSGhkZ3g5EsKV0BoOQdciCaTCYBQM27\nS8ioF4vAPB4PAoGAqo5nBoF9dSQSQTqdRv/+/VVVvsysSEE/gxbUkWktWOfQIyL8iy++GBdffHFP\nnFqBeXT6m/BHCt+ZIrSnI/lF5peSwnjm6U3TVLYLJESM2FBgTp8ujkJM00Q8HrdYWdALTIr32R4e\nhyOcYDBoyeN3NirGsDMrGRl+pi5AVmDKKYP4sHI0x/tJnQKjZl6vV/nOSJNZVnlS+M+RoKy+IQkj\nMSs0JYc97dha9WN7KyM1NDQ0uhLUbHGOX87P6PF4EA6HkU6nUVFRoeYLzuVyCAaDqKioUINiex9G\nzSwHyl6vF7FYDNFoVEXQEokEKisrVb8qI12MujHToKNfpcMuUwVZjHDI+Rnl/0x/cQohrmMkRzoN\ny/JdEjem1/g3v5gkHnJSatM0EY1GVUULiZS0m6C2iQSKBIfXxnanUilF+Ki78nq9MAxDRYhI8DpC\nwhhxYqpR3hcSKpfLpew12CZWfcrUKUdXbDvJVigUUj5ePD7X08NLPtRMtzIUzhEZz80RHgmgrLyU\nE3e3t6PQHYqGhkZPgZKWbDaLrVu3qor4srIyZXHEgSpJWlNTE/r27as8Gu3yFoIDVw6GZfFXIpFQ\n765oNKqiWhxMM5Px/9v79iC5yjL953T39P0203PNJCZBwWCCZSJCEhUTXGKQcLGwVLJLXFyMKwuE\ngOsKGzcBqWzhUrhrUayiu2tKRKBWf2oJGNyCgMDgcknkEgQxWZOQzL3v3dPTM3N+f8Tnm7dP+jbT\n3ZOZ8D1VU5n0nPP115fzned73+d9Xq/XW7B+azuK2nFKELBSRIO2DQCUS7sUXEsndKbB+DghU1Tc\nDTD6xb/zS8nolaxekbovjsG05MTEBKLRKBKJRIEAX7aB4IUnU5eyBQ9ToNStSQJUDQljuo8XFPVs\njD5NTEyo6BWjUtKFnsczDcjX6Ha7EQgE1Hvv8/kQCATU65S2HuFwGKFQSEXQuEBIwiWjktS/kXzy\ns+CCQhNDaiGsaUa5aMjdXDmypnd9GhoajYRcd91uN9LpNAzDKDBQpdCe2RHp+chqRQBqMypTkrLg\ni9Y/w8PDME1Tud4PDw8DQEFlOUkbi61khEyjNpwSBGwqkOQLmIxG8XdGZqQOjF9cphFl1Cefz6s2\nRLKHo81mU+J6AAWRGRqSkjzwxs8wMYWSjIpRfM/dDefKi4RVgGxPRNsIEqpSJIwXlNwtsQKHhI7u\nyCSUfG5ehLxI+X6QIOXzeeUZFgwGEQqF1OIxPj6OaDQKm82G9vb2gvYZvNj5Q1LLSBnJLgAlQuX7\nxx5mxUgS5wWgwLOMj5XTMnAB47mahGloaNQT1vuNy+WC3+9XG3vKNKh7ZcSLx3F9JlHL5/PKIFz6\ngeVyOUSjUQCTAYhQKASfz6eO5xrMNCcLAGSmQ6M+OKUJGEO6/F2m9IBCfRBJhKyclIJDWR4s9Vj0\nZqFOij4tHo9HXUwkUzLFyUga8/uMbjHqxIsFgCJIHINpQqYvWTU4NjaGTCZTEIUrZsFB8DXJ12jt\nr0iCx6pONtrma5NCfe6W+Nz8nXo2KbznnHjR83WRTEo9HndzvPilz5eVWPn9fnUMUJxYyapW+T3Q\n0NDQOBmwRuWZyWC1ONessbExtLW1IRAIqA1pOBxWLYTYU5dj0OFeVtiz6IsRs3Q6jXg8rvRkXq9X\nacrkJl1HveqPOU/AKqXYihlvEjLyZfXXkmFbWRrMHYZ8nLsRAEq0DkDpwNjzkISHmq1kMgkAyu9K\nkhXOiYQPgBJmMlJHQseUIJ9bVkLyIivXmohpRD6frESkj5dMuZKgMRVIYsULXRI2vpfUlXE3RQJJ\ngszfpes+U5ls8ySJV6nPlZ8hfW8kAbM63vN95JiliJhMYWqypqGh0WhIwsWNMavvTdNEIBAo2Pxy\n4+31euH3+ws21lKc73A4EIlElPUEKyAzmQwcDge6urrUGs4NuI76Nw5zmoBJsgRUvjnKMC+rDgGo\nPofWcfk7008kHdxBjI2NqQo9lg4zEsWwMYmD3+8vaEfEqJkkRw6HQxEz7jhcLldBFabM4cs0INOj\nUncmxfOlImF8jBeZbG3hcDgQDAZVaTIvZHrDUJMgm2Bz1+Z2u5HL5eB2u9Hc3KwifYxuUfQvG25b\nWwzxX1lpyWilJGEkWVLvwDLsYhWOxQhVNd8dDQ0NjUZDVo07HA6EQiFV9c6/M+PCbiw0Zw0GgyoT\nARyXaTDbQhkN13X+f968eYqEJZNJpU/2+XxwOp1q86xRf8z5d1USpGo8SRjpYJ6cY1j9s2R0RDoU\ny5s8v+SMOjGtRWKVzWaRSqUAQLnBp9NpZbUATHqRcQw66fPiAqBIXyaTKSgWkNV/UvvEcDPPsfrI\nyNcoySuJJMkkiRTTiSRyTU1NSrTJCJk0Q2Vq1ev1IhAIFJj6UTcHoMANn6RJpmKl8z8JExcQGZGT\n//J36hvKRbWK/V7pu6OhoaHRKExMTCh7CW5sx8bGVHrR7XYrj8jm5mYEg0HlDyllL7wfcNPLivxk\nMqn0yrQ4amlpUdZGJH6Usfj9fpWh0ag/5jwBmy7oug5ARXcocpfhW6bBGPViepEWCLRbkO2FrD8k\nLtRssaejjGilUqkCImm325FKpZSZK8kI9VK80GRzatkCCYCaq7SVkGatJJPUx7H6hlWEfH9YbcP3\nh9EreXEzbE0iRWdmmtTSioIWGRyDlT6yxRGfd2hoCIZhoKOjAw6HQx3LiFmp6BXf71KahWoipsV0\nghoaGhqNhNS00gKCdhO0i7DZbKrCnBYRLL7iPYFpS1nZTamKtE4CJivvvV4vvF5vweZVpkG17UT9\nMacJWLGKRolyAnTeyIHJKBTJkjUyZo24yPJcXiz8oso2RkznkYSQeDGqlMlkVHSHJJA/iUQCmUxG\npdLYjJrRNVY8cpfD18EfmXaU6TspXCcpY9qQkTKmGCn2l1ouXsTcZXG+mUxGhb95oVKbMDY2pnZZ\nrI4MhUJIJpMq2ifTsyR5sr8lPcesi4C0j6D2i6nRYgtGNZWPU42qamhoaNQKrq8ej0dJUZgpYSpw\naGgIDocD8+fPh8vlUkVfUjtL4b3P51PjElKjTBkMI22BQAC5XA6Dg4MIhUJobm4uyGrw/iDXXI3a\nMGcJWLU3yUokjP9SNM7SW5IuNjmlbwqF8jRo5RyYciRB4RwZoWJqT5IlapQYciaRSSQS6jkYXSKh\noJs8I3YkHSRaskUEq2NI8mR4mq/b7XYXVD3yQubfpS2H9IOR4I6Kx7K0uaWlRbXWYOQLmDRJZbl1\nMBhUc6ElhWEYaG9vV58vo43y/eV7XI2VhIaGhsZshdXqRnoqMrvCjXE+n0csFsPAwABGR0cRZZg8\nGwAAIABJREFUDodV9oHpSJpbM7BAOwtu2sfGxhCLxZDNZpVNkAweSE0ZN9xyPoBeb+uBOUvAaoUU\n8DOKRALGslvJ8vkvw7WyFY/D4SgQqhOMwIyOjsLj8SjdFPt4MVqUSCSUb5fP5yuIqslqQ6lDk9op\nmd4kaZJNVEmeSAj5umSJMaNmbD/kdrtVdSc9y2R6k++Zx+NR2gM2gwUAv9+vmrpKUakU9dN7prm5\nucCAlYSNxExaY5RLCXJOXBhKHVOpotF6jF5kNDQ0Zgpc65iVGB4eRn9/P0ZHR5V0o6+vD+l0Gn6/\nH+3t7aqvI+8ZXAOZMaFFES2CpA6MemhG08LhsMoEyayHXgfrjxklYGvWrMFTTz1V8NjnPvc53H//\n/VMeqxZrAGv1pCQkso0Dfb/4HFbbCu5MSC7sdrtqmj04OAgAynKBOxymEfmTSqVUN3u73a50U6yI\nZJoPgIqScb60i2BfSc6f51N4SWIi+1dSl0XyxAtNEjP+nxcfCZLUgbFXo8fjUSSNuzc+B3B8txQM\nBpVPl0ynSg1YseihtKWQnzf/LVXRWErrJQlpJZG+XnQ0NDQaDXk/432GG252EpGbbUpIgOM6sGAw\nqEyzOZbM7HBTT0kIMy1c39PpNIaHh9U5vG9lMhmVqZBFWJyzRm2YUQJmGAa+8IUvYOfOneqxWios\n6vEFYFpO3nCZ82ZaTz4fCRpJFbVfFEjy4mEEjSQmFoupXl6s9ovH4zh69CgSiYRKsUmrB0n4mFqU\nGi9gsuWE3PEAx6NvUg9F/zFG+SielzoxEi9JpDgvjkE9GnVthDT6CwQCBfNnNE1WZ0oiyQgfU4zy\ndUtRKR8j0SSKie2toXIABX0+qwmj6wVGQ0NjpsD1m/IUbsLtdjva29vhdruRzWZVxaPX61WyDkpN\npF0Eqxq5vns8HqRSqYKuLrQLkpX4qVRKZVj4t3w+r/oAa0PW+mHGU5Aej0dpe042qJ9iayDrzZh/\nBwp9smQaMJvNYnh4GIlEQlUP0mcllUohk8monD7Dw7LXobzYpJ8XrR5I9pgmtEZ3eGFQMM+KFV7M\nTO2R6JKIAZMXPImQTEFyPKfTiUAggKamJoyOjqoLkMJ9RsM4HqsdmW5lqwxJwPj6pfGqfH9kNIwh\nco7PefL9kJ+N9bOtJBQtl17U5EtDQ2MmMT4+jng8jomJCbXmMjrFDIlhGAgEAohEIiqbQNkGiRHJ\nlJSycG1mMZfT6UQ4HEYgEFCifcpjeB/z+XwFWmeSMo36YcYJ2AMPPIAHHngAHR0duPDCC7F9+3b1\nRZoqygnsrbDekPn/Yn/nl5FthpiKlJV2uVxORb9kqwa65bNZquxryC8yKyjtdjuam5vV47JfJKNV\nfD7DMApElMBkZSCAgtY/3A2xjFn2DiPJ4WuWujXOk+cyFE19Af8myV0wGFR9w9iCSYa9SSqtpdEs\nd5ZhbRIzEkD5ecmOAJIclSJeMtpVLFVZSSemoaGhcTLANZ9ZAa6dlHHQIkiu5cwosH+uLOKS6UgA\nGBwcRDweV1owZixk2yK51nMjrR3x648ZJWAbN27EokWLMG/ePLz66qu4+eab8fLLL2P37t3THtMa\nsbL+TtLElCJTafL//CJKk89K4mve5O12O8LhsGoTQRLGCA2Fj5lMRtlKyPJgRr+i0agKGTP6Q1JG\nMkOtFyshZQqQqTu+bkaV+Lu1j6I0eeU8/H6/EtKz+pJVkhRySrJE4iUrNbkA0PmeHQE4rvQiY/SN\nOzhJAAGoAgBpbcH3nX+TVhOykoifvSTpMnSuyZeGhsZsgt1uRygUKtBecQNJY9RwOAyfz6c2sjT3\njsfjcLvdiEQiat1n4Zfb7VayF673yWQS8XgcoVAI8+bNU70lgeNkLhaLqXsCMxc69Vh/1EzAtm3b\nVqDpKoY9e/bgvPPOwxe/+EX12NKlS/Hud78b55xzDvbu3Yvly5fXOhUFq0VFqWOk+N5KymQkDCgU\nZctUGgkEdypWPRO9v1h1Qg8vpiVlCpFz5gXHXQ0jUkwlMnpEEz6CRIVkSTr402JCkh6SIZqoNjc3\nq90QvcoMw1D9x6hxYwshklnguKu9x+NR1ZgejwctLS3IZDJqbryg+fxSt8Dz5PPK952/F/uxgtE6\n/k2Wd2uCpaGhMVvBdVFutqmFpW/X+Pi48pckmerr64Pf74ff71cki+PwPiWjah6PR6U2KZOxFn+F\nQiFVEanXzcagZgK2detWbNq0qewxCxYsKPr4ihUrYLfb8dZbb9WVgFlBIiUNO60pSH5JgUlrB7J+\nWS3JMRjhIsGRjanpWh8MBguq/Eh6UqmUusBYvSijNIwOSUIl029er7cgxSerCDkGH5f6MuluTG0X\nXwfz/owI0tOLFy7nxTQiKx+pn3O5XPD5fOp1cPdF4SY1dgyTM7LG+eRyORVml0UGjCJScybTh8VS\nktbUovUz17ovDQ2N2QreS7h2s9iIa2s0GlX9GsfGxlS1ItfWVCqlzqem1zRNlZJ0u90YGRlBKBSC\nw+FQ3VZ4T7AWj+k1sbGomYBFIhFEIpFpnfvKK69gfHwcXV1dtU6jADJyJR8jJiYmlK5KVjTK9KT1\nPOmWT9KSSCSUCzHJEPsdUgjPXQbNRVlBmMlk1EXFSBDJCkuMWdHCcDR3PXJerFTknLj7ASbbJUnB\nP3c5brcbfr+/wAGf5JDhZ/pzMUJGywrZ0Fw2hKX5q0wb8vhAIKDSqnxvpP2F7BgwMjKiyJYkpCMj\nI+o5ZRWkTDdbw+T8jBkV1OaBGhoasxVcy3w+HwzDQCqVQjweV1pkylhCoZDaHPO+lM/nkUqllJk1\nJSWmaSqS1dTUpNKPXKfZBs/lciEcDitDbJ0xaDxmTAN24MAB3HfffbjooosQiUSwf/9+3HTTTVix\nYgU+/OEP1/35Sgn0pUBbtushGJWi8JwRGWmdwAgXCYTUKgFQBEOmN3mx0IrC5XIhlUoV9IUMBoMF\nPbp4LokUo0XSQoFpPz6fTD9yJ0QCwl0Vo1MUc/J8EjhWYdKQdWxsTOkOSKD4d16oMtIXCoUKPMSk\nxovzkaSQ7x01b3ytfD+bmpqQTqeVtoyfI6sg+X7QPoOfv4yCWR8r9n3R0NDQOFkgiaLhKn0i4/E4\nYrGY2qh6vV5EIhGVWWAggB1IWFnO6BczMyMjI+jt7UUqlVLSFfbn5SaXmRtpK6TROMwYAXM6nXj8\n8cfx7W9/G6lUCgsWLMCGDRuwffv2utz8KlVDyjQi5yNTcwBU1SOF5UCh7oiVkfT8khYKwGTzVH7p\nZR8vGYWRpIMRn3A4jObmZgwPD6uUHwmN2+1WZIOpOpIbl8ulxmQhAHUC2Wy2YI60oPD5fIrUUSfA\nqJvNZkMwGERzczM6OjowNjamdmBMUTJczV1WKBRSnyGJFndPfG8ZcZS9HgEoYsW0qnXnxXOkdQUj\nZSyaYPRR9jmTVavFKiIlNPnS0NCYDeB6JeUtbNcGHF9Hh4eHcfDgQbhcLnR2diISiahMRnNzc0Hn\nFGY9gsGg6kccCoWQSCRUGyKfz4eRkREMDg5iYmIC3d3dSpRvXRv1WllfzBgBmz9/Pvbs2dOQsadK\nvkrdiIHJlJXVfZ3aKGliJ1Ne0tmdz8FUH/9P0pHL5ZSYnw7ETKtRi2VNmTLVyB9GgJhyZNSI8wNQ\nIKYnaWM6Ub4WXujS5T4QCKjqRkYASRzdbrfSU3GXRdJIAkhn/NHRUQwNDanFQlYuWiNSJKpyN0bC\nxhSu1RiXc5BjFYt06apHDQ2N2Qy5nnITz/WXhVnZbBb9/f2IxWJobm5WJtcACrqGAMf7OfKeQl9J\np9Op7j/U3vp8vgJbpVgspohfNX6KGtPHO6oXpLXSESjUgzHCQlJiJTiMpLBfI41WSUjk8dKwNJvN\nFqQkgUmX4tbWVnXRjI2NqSpHeo0BUBEeYJIgsgKSzcGppWKpMckUU4eMgPHCln5ffO0+nw+hUEhF\n29jDkkJPOT/DON7L0e/3I5PJIJVKKZLE9ymXy6kqSFpaSI8v6tr4/PybTOHyMyIhI9GkVYbVWsIq\nwpdROL2b09DQmM2w2WwFHUtM00Q6nVbrumEYyug6HA4DAHp7e+H1etHS0gIAyscrm82qbA4zHbxv\nuFwujIyMYGhoCMDxwrNAIAC3243BwUHYbDZEIhF1L9R6sMbgHUXArCAho+YJmLRykF82a8WkYRgq\nxUeyxbAvrR5Y8gtMCuWdTqfybSGp8nq9cDgcyGQyiMfjKlycz+fV+ByL5cEUxJOMMY3JAgFegBTa\nUxvGFChwPFXo9/vhcDjUBe5wOBAKhTA2NqYas/JYtrJgStPj8Si3Zh7L10/ne2rHWltbi6YWgRP1\nciRMJJQA1M5MpoWBE1sQlYpyaf8aDQ2NuYR8Po+RkRG12aTsIp1OKx0YdcTj4+MqusWNrSy6kpmT\nXC6nPCfz+bzSl3HdZqaHVkfW+yCgN671xJwnYNWkH6X9AG/ujHDxMWq0gML+gHSwZ9SI5MswDEVu\nqLHi30hcuJuRGiWOS7dimrcyVExyI1NxLpdLETISMFnhwkoWaQkhKxWlBYYsM2Y7CrfbjUwmA7/f\nr9z2qTugaSxfA6sVSfwYCZPVjjyHZJYXM1DoyWV9n/l5yfebY8gWSYCOZmloaJy64D0rGAwiEAgg\nlUpheHgYwPENsZS2MHPB9CJlGiRnTG1yY87MBKUmvb29GBkZQXNzs9pkc1NPqyJg0p5JV5LXD3Oa\ngFVDvqwpR5KkeDwO0zRVKx1pPyE9wUjcSKqAyd5a9MFiOrGpqUkJ760NrRn6JYEikaD+irsaPlc6\nnVaeLoywWTVeUiMlbRwYHZPtKZiyY/qU8+AFTPE8Pcra29sRDAbh9/uRz+eRTCYVMeP7Q78uXrRM\nT/I9YmEAy5/5mbAqh0SR74NscM4x+Pqkz1kl8lVpcdCLh4aGxmyD1BxLLTIlMLyPURObTqfV2p7N\nZpFKpWAYBkKhUEH/3nQ6rbIurJhkyziPx4NsNotEIqEMWemIL+81pQzNNWrDnCVg1QrvK0GmraTx\naDabVeSEUTBWCsrqOqYJmbfnOBSkS3EjKxhJJKiholEeyRgbshLcxfh8PkVUEomEIjEyJSdJDS9i\nGV2TOixprgpAWWGwh6VsjC2LEMbGxlQI3NpfURr/yRQpX5sU0vMCtxYzkNzKnpblyFc1NhMaGhoa\ncwFST0w5y/DwMHK5nCps4obYNI874fOeReIFTOpumU3g+ut2u5Wg3+12F2hpGV2jPIV64mL6Wo3a\nMafEMUypVUu++KWxhkzZcysUCikyUOpY/k3e6KWInLsROuCTLFC0LudMTRgJitUeQaYuSYba2toQ\nDofVfLlzkd5atJagfUQoFILP50MgEFDaK+rG5L8kVl6vV7WxaG1tVWXNjKjZbDblas+oVygUKqjQ\n4Q6N75NMqwKTXl0kW3wPMpmMipDxeEbZSPCsujH5GUsdn4aGxsxhx44dBRskm82GefPmnXBMd3c3\nvF4v1q5di/3795+k2c4NyPVsbGwMyWQSsVgMExMTCAaDcLvdGBgYwB//+EccO3ZMOeNz00ozbxIs\nSley2awS3xuGgYGBAQwODmJ8fLzgvtHc3Ayv14tcLqdaHxGafNUfcyYCVm1Ey4piXxgp8JaPkSRQ\nb0RCxEgO040kTxSkA1DVJiRSTB2yKpALlGmaKuRLvRc1X9Q+cQcyMjJSsBNidMgqtGe0jUTJbrer\nc2VrH4aW5Wvi35nGlOXPMtJHHQGJEskfXzfHIqH1+XwF77G1tRLHZXidx8rIWylbCau3V6nPWUND\no7FYsmRJgb2QtIm54447cNddd2HXrl0444wzcNttt+GCCy7AG2+8Ab/ffxJmO/sh9ckTExOqJzCD\nBQMDAzh69Ch6e3vh8/kwf/58BAIBZagKQK3nXFNjsRiy2SxcLhdaWlpU5iObzSoSJivMeY+iNEaa\ng2vUF7OegJX74KdTlSG1XqX6XUmhPAClqQKgdickHFabCorrSZLY85EieBIsGommUimlRWOEibn/\nWCxW0IAVANxut7KnYGWlrHZk1IqFAYxA2Ww2ZSchRZy8GPk6s9msMqMFjoex4/E48vk8IpEIAoGA\nWiTYEDyVSsHv96uomoz4MbolWyXR9kNqu2inYRiG0pHxsyin8eI4U/0eaGho1A673Y729vYTHjdN\nE//6r/+Km2++GZ/61KcAALt27UJ7ezvuv/9+bN68eaanOushnfApeWGnFJvNhv7+fuzfvx/9/f0q\nQ8J1n0VU3MzTS5JFYaOjowCgAgiGYSCXy+HYsWOqDR6tlbixlzITvbY2BrOegJWCJFLyC1KtcRx3\nALzhM+0HTOqKrNYTsgE3j6UHF/PlJFyMBjE6BEw2yQ6FQvD7/UgkEhgeHlbRMJIbPi8jRbJnpM/n\nU5E4l8ulLhLOLZPJKMJHgkPSxagWySPnyXZGsrqRr4ueZBMTE0prQDNXmrxyntK9X342LAAg+eJu\njO8Rd2DyvZY/ElKvx/d0Ot8dvaBoaNSOAwcOoLu7Gy6XC+eeey527tyJxYsX4+DBg+jr68O6devU\nsW63G+eddx6effZZTcDKgNEoZjSooeX6yzWVuq5MJqOIlox8sUK+s7NTifaj0SgOHz6MWCymqunZ\np1feu1i5znuFtvJpDOYsASsGa9VjsZsstV5sO8TzZFqL50qBOSM60qB1YmJCCdZpbMo0HZtyU9OU\nzWYLhO9MEdrtdiQSCRUho6ZK+oAxrchdDC9Aitj5/DyX4n7uaugnQ40VU5ZMk1Jcz/eBFY3BYBBO\npxMtLS3w+XzK74tkzul0IhAIqBQrdWBWvy+ZYgRwgoCf5zOCZu1BVoxc16pH0CRMQ6M2rFy5Ert2\n7cKSJUvQ19eH22+/HatXr8Zrr72G3t5eAEBHR0fBOe3t7Th69OjJmO6sB9doSjtIhvL5PIaGhpDN\nZtHd3Y329nbE43GMjIyoYizKWphx4GbXNE2l+U0kEkpTBgCRSAQAlIE3Mxm81/F8vU42DrOegJVK\nM0qCJI8rdqx8XFbiyVQXyYsUd0vxPSNQ2WwWuVxOpRGz2awSxstIjpwPCQsrGK2pStkiYnR0VJG2\n1tZWla6jDkzOlRcJCR8rXOguz0hdIBBQ5zCaRfNVggUIJGUkXyxtlpWU0muMBQSyulFWNUqiRNJK\n2wo+TsJWSfclo2rT3ZFpM0ENjfpg/fr16vdly5Zh1apVWLx4MXbt2oVzzz235Hn62isNvjeUdnBj\nTQsjejE6nU4VEZP3s3A4DK/XC9M0EY1G1d+57nOzzrWbKUiu7a2trWhvb1f3JMo7NBFrDGY9ASNJ\nKNYKgeRI3pitUSsr5Bhs0UDvLlYzymiYTKfJDvP8Yvr9/gJ7Bim2Z1+tTCajKhKl+SrnQiM9pvFk\niJlEic/JlhIAVCqQZImpRoamSQhlCpCROBltkulHPrfX61UthlwulxLmk7TyvWVU0KrzAlBgY8HX\nxffUWvRgJV/FUOnvlVAqba2hoVE7vF4vli5dirfeeguXXXYZAKCvrw/z589Xx/T19aGzs/NkTXFO\nwTAMJJPJAp1wX18fhoeHCyyJiObmZgSDQeXNiFzuuMzmz2svAwW0oaDGmN1YvF5vgdE2pTnagLVx\nqFti995778XatWsRDodhs9lw6NChE46JRqO48sorEQ6HEQ6HsWnTJsTj8bLjUvQ+HV8v+ZgVJAok\nAdZzZVqSz89+ifQG83g8CIfDqnM8dxEkZ6OjoxgZGUEqlVJpQKYX6RDPtB1F+7K5qiSBbPTNnQgj\nZy0tLUqMSed6r9erSovpZCzbB7W0tKCrqwttbW3KN4apRb/frwxhqQHj6+PcKPTn3KQebnR0tMAo\ndmRkRLVJIgnL5/OquKDUZ2X9l+fqRUBDY3ZiZGQEr7/+Orq6urB48WJ0dnbiscceK/j7008/jdWr\nV5/EWc5+MCJFIT37MWYyGSSTSXVPisfjGBgYUKL6dDqNY8eO4fDhw4jH4wjHYmhNpRCPx5FIJDA4\nOIgjR44gk8kgl8up1ndc82lQ3tfXh8HBQVWVLz0pNeqLukXAstks1q9fj8suuwxbt24teszGjRtx\n5MgR7N69G6Zp4uqrr8aVV16JX/ziFyXHLdVImbBqtUpBRsSonWIPSBIOa8pLkgam2qwaJR5HAsXn\nYKSLWjD+jf28qNUiSWEvRmCScJH0cW68MJn+k1FBr9erBJv0kOGceMFJUT5ToXz/+DujdqyECYVC\naifEqBxTibwwpV2HTDdKx33On1EoRtSonZPnVvp3uqj2u6KhoVEZX/nKV3DJJZdgwYIF6O/vxze+\n8Q1ks1l8/vOfBwDccMMN2LlzJ5YsWYLTTz8dt99+OwKBADZu3HiSZz77wfWSdj7ZbBZvv/228vwa\nHx/H0NAQRkZGMG/ePLS2tmJ8fFy1LBodHUXnsWNoMk0kWluRz+eV7yLvYVK3yzWd9wUGKFioxnuV\nRn1RNwK2ZcsWAMALL7xQ9O+vv/46du/ejWeeeUbpA7773e/iox/9KN58802cccYZRc+rxmJgKl8M\nEgA6/JIASIG3bMFAkiO1YSRjckySENM0C8TykpiNjIwoITt3HNI9Xh4ryQ1FlFJjxdRhNptFJpNR\nRJLnMG0ptVgMJ0sbDVpSsOqRFyFJo9frVSSSZJB+YbyAOba1ipQki5FBLhyMElrF+fKzbNTFrhcR\nDY364O2338YVV1yBwcFBtLW1YdWqVXjuueewYMECAMBXv/pVZLNZ/N3f/R2i0ShWrlyJxx57TPWK\n1SgOrp20oHA6ncjn8wgEAgiFQiqrwI1sLpdT6yrb44V8Pvh//nPAMBDZsgVv9/er9314eFhZDdnt\ndmSzWbXO875BWyW5oeZar1E/zJgGrKenB36/H6tWrVKPrV69Gj6fDz09PSUJWCM+cKbwyPxJZqSd\nBIACckbSxr8xKsT0Hf3AGMkhcWPXeRKbdDqtrCiknYTUs0lrC6sAnhecNDDljoXkiMRIGsPybzQ6\npW6Nrw+AKgpoaWlRDvrScZ+RKnrNMCIHQEXZqCOQBQ9S80VvNQpJ5WfSaPKlBfgaGvXDj3/844rH\nbN++Hdu3b5+B2Zw64L2GG2JKNjweD7q7u9HX14ehoSF1z+rv70fA68W6D30Itj17YDcM4MABuH71\nKwDA+9aswRk2Gwy7Hebatfh/e/ZgMJ9HJpNRRtos8vL7/eoeRzcBufZr1BczRsB6e3vR1tZW8Jhh\nGGhvb1clyzMBpqEYqSI5kl8ukh7qjUzTVM20CUargEkdFEkNLR3Y/oHCR6YDAaiolyQpjJCxagWA\nsqCQonoK8TkuSQ/nwrnTo4sXEOcotWjSoG9kZARutxs+n09VGkozVenzxR0SK2uYvpTGtNb3ne8r\n3z9gUudGsliNfm8qkNpBLcDX0NCY7ZAbeFa6p1IpZdxNN/y+vr6C+0wum8X61lZ03ngj7G+/rcZr\n2boV493d6P/Wt/DIU0/hd6++qjS/AJQ4n9E2qRlmhkYTsMagrAh/27ZtJ/T6sv489dRTMzXXuoEk\nQmq7KPAmUSFBkKBjMC0nKIynpYQkdBRNModOwkbBPCNdVsNURpgYeWK1otSAWS8YuuiT0DHtx+ib\n1+tVOjfO2+FwqP6PgUBAVWK2t7erMma+V6UsPpg+pJAzFAqdEJHjD3dTfD5pGCiPs35OVlgNcsv9\njRHFqRRxaGhoaJws8F4kC7qoW43H4/i///s/JZDnPYwekrmJCTw1Po4D//mfmPhzGhgAJt71Lhy+\n7z4873Jh5M/yEtpasGCLFfU+nw/5P0fH+PyafDUOZSNgW7duxaZNm8oOsEB80OXQ2dmJgYGBgscY\nPj1ZZcmy4pEEgOlEWj3Ivof8QkrBIsX2FNHzwmGVIwCkUinkcjlFlCiWzOfzqnmqdK8nYZP+L6xC\nlB5ayWRSkT1J5JxOJ9LptLKcYHiZJCSTyWBiYgItLS2qlQX9YlwulyKVExMTSnsmjQE5nmxCzjJn\nVs5IS45iXQeIUhq/UuSrVBSrksWEFuBraGjMNcjq9YGBAYyNjSktWCgUUptbrn/JZBIJux3G4CBM\nrq2Dg8ikUhgaGkImk1EdTKSY3+VyoaOjQwUIKIvRa2VjUZaARSIR5ZZbK1atWoVUKoWenh6lA+vp\n6UE6na66LLkWDY9M98nHmDKzpsDkF5t2EqwMZAqTpqXSGoKRM5Iiihzpuu/3+wt2FSQ2nAObcpPI\nkNxQT0aCxfAxz2fUSzZy5TwymYyqiqQpq6yCkfo3vse8ADkmDWKtETBZwchKSYo35XtpjXJZvWXk\nZ1Ovi74U6dKLioaGxmwEiRTXXMpeuB6nUilkMhn4fD6Mj4+rNkRcd8fGxtAWjyO/eDHe/sY34HA4\n0HnzzQj292NoeBhHjx5FOp1GJBJRfX5HRkaUpVIoFFINuNkyzion0agf6qYB6+3tRW9vL958800A\nwGuvvYbh4WEsXLgQzc3NOPPMM7F+/Xp86Utfwr333gvTNPGlL30JF198MU4//fSK49dioimrGqV7\nfrEbNEkHyYiMDjGaIwmLbAsEoKCMF4D6AjMCBEARoaamJmSzWQwMDMBut6uLgq+PFx+N8qLRKJLJ\npIqAMYUaCARUPy9qqujdRaG/3W5Xx7HSUjbilsSNkTCpE5AWGHyM85A/JHZWAsYKHAry5edXrdFf\nuShWtWRLky8NDY3ZDm7omZVhZXoul1PNuGk5RG9K0zTh9/ngb23F/jvuwO+GhuD3+3HGnXdi3sQE\nnMkkMpmMkql4vV6VRZHEi/c3XbTUeNSNgH3nO9/BbbfdBuD4B3bRRRfBMAz813/9l0pj3n///bju\nuuvwiU98AgBw6aWX4u67767XFIpC6oCsui4pCrdqnWRkjKSIUS+mJ4HJFJokZwBUZGl8fFyJ5Lmz\noZaMPljxeLxgt0OtFHVd0nWfVZTUoXFudKNnYQBJz9jYGKLRKPL5vIreAVCtKUiUOBewpDD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VrR39+PxYsX47TTTlM9Iq3Pq9E41I2Afec738Ftt90G4PiHdtFFFwEAfvCDH2DTpk1wuVx46KGH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\nbvS8NTTmO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IMmJS7IZuJQB8bbfbFcGyeq7I98v/M+3I6kaPxwO3220iTxS5M2UnWxzJMcdi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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -428,18 +428,17 @@ "from numpy.random import multivariate_normal\n", "from nonlinear_plots import plot_monte_carlo_mean\n", "\n", - "def f(x,y):\n", - " return x+y, .1*x**2 + y*y\n", - " \n", + "def f_nonlinear_xy(x, y):\n", + " return np.array([x + y, .1*x**2 + y*y])\n", + "\n", "mean = (0, 0)\n", "p = np.array([[32, 15], [15., 40.]])\n", - "\n", "# Compute linearized mean\n", - "mean_fx = f(*mean)\n", + "mean_fx = f_nonlinear_xy(*mean)\n", "\n", "#generate random points\n", "xs, ys = multivariate_normal(mean=mean, cov=p, size=10000).T\n", - "plot_monte_carlo_mean(xs, ys, f, mean_fx, 'Linearized Mean');" + "plot_monte_carlo_mean(xs, ys, f_nonlinear_xy, mean_fx, 'Linearized Mean');" ] }, { @@ -475,7 +474,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 9, "metadata": { "collapsed": false, "scrolled": false @@ -483,9 +482,9 @@ "outputs": [ { "data": { - "image/png": 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sbABiYmJsnImwZ62pn5hMJlJTa3jkEWdAgcrpEklPvk5g+JU5w/0iBvPwoGdw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\nUrjfIvbSR+zJ9WpYm64GI0RrUGOoJvf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CABWVZSSf+I6T5w/Qt80oWjj/ttVyhBCiIanzwt3T0xOVSkVeXp5VPC8vDx8fn1vu6+/v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\nB6lknojakHkibqc+zZGcC6fYnbGdtCO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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -529,7 +528,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 10, "metadata": { "collapsed": false, "scrolled": false @@ -537,9 +536,9 @@ "outputs": [ { "data": { - "image/png": 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iizg3Z+HlqvkeRBeXkizHWhhNl9T5im0z6/Ktpum8MZ9gaQkGfSHZHCq2xW61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\nr7c7Ey57QYLfTbGrZ/vKsu2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A93g8nDlzhlOnTmEYhmzePETSpQKhARgd8HXtTvVyrUG9\nDv3u3us74vBKFfJMHOveFZP9ZL7gt9bOXvXiAH5QSqUSZ8+e5Wtf+xrz83MAHDs2zZNPPsmDDz6I\nz9ed2Zn9lCrlu3an+patpdte7jtyRN/hYhgGyWKeU+Pdu2IC7b5Tr4EzIGUP4mCU6zU0pc5A0CK3\nut2C6Z70Vx9CUnu1I9Vqheeee44vfOG3rwa+APPzc/zO73yBb3zjG1QqlQ628PBpahrZSpGBcHfu\nVN+yVfYgfUcclGy5dHWner+/O8tPdN2gWm/RaEipnTg4iXyO8GA74aKq3Zlw2U8mDH7Nu9ltLyws\nLPLnf/7fbvv6l7/8JRYWFg6wRYdfIp8l2K8zFvZ25U71LeVqg1oP1vyKw2s9l2F4CKaGu/fGu0q9\nSa1mYLdKqZ04GI1Wi1y1QGRQYXKor9PNOZRMF/xulT04enjpdr/ous7rr79+1/e9+uqrVy+/MDtN\n10kWcwwPwfTora+P7ga6blCpt2g2FOk74kAUqhV0tcbQoLWrd6rLpFEctHg+y8CAwfhgdydc9pPp\ngt9rdYvyC7FdhmHc8oa4G83OzmIYxgG06PBLFvN4/RojYVfXLtsCVOtN6nUDm8WKKtkrcQDWcxmG\nhuHocF/XbnSD68uFJPgV+6+laaSKOSJdnnDZb937RNmherNFs4XUXu1Qf//dO9N2b4vrVYZhkMhn\nGR6GY13+EKo3NRoNsFmk34j9V6nXqbbKRMJq1y/b1psazYaMOeJgbBTy9AV1RsNuAt7euIlzP5gu\n+G1pOroGFtnVvW2qqvLud7/rru977LHHZNc87VupHK4mw2EHQ/3dvdu2pelouvQbcTDWcxkiEZgc\nCnTlhTDXa2k6miYniYj9pxsGiUI74SJZ3zszVW+8+hBSTPVt7xlFUTh6dIqHHnrLbd9z3333MzU1\nJRs72NysMwzHRro/E77VdyT43Ru6rqNpGpqmSYnQDerNJvlakUhEYaoH+k6zpaFpYFW7O4gXh1+6\nWMDjbTE04CTc5+l0cw41U63DyAx890KhEP/yX/5Lnn76ab73ve+h6xoAqmrh8ccf58knn2RgYKDD\nrey8XKUM1jqRsJXRge7drLNFVkz2Rr1eZ3FxkXPnznH58iX8fj/vfOe7mJqaYmBgQCaNtDfrhMMG\nExE/Lkf318m2NJ1arYnSKmA3wOv1yhgk9pxhGKznMhyd7o2Ey34zX/Crg0UyvzumKApjY2N86lOf\n4kMf+hCJRByASCTCxMQRHA5Hh1t4OMRzGYZH2kc09cIZi1czv9J3dqxarfK3f/u3/P7v/z6Gce00\nlO985zucPHmKf/tv/y3j4+OmDoCbmka6nOeBqe5ftjUMg5WVFb77vb/jT7/8BqmFLE6LjSeeeIIH\nH3yQqakprFIHLPZIrlLG6mgQGbAxMiAXTd2NqXqeLN3uHYfDwfHjxzl+/Hinm3LoFKtV6nqFyKCF\nI12+WWeLrJrsjmEYXLx4kd/7vd+95eszM5f5sz/7M37xF38Rj8e8y5VbZ2KPhj343N07kTYMg0uX\nLvGpT32KF84ug/VhyAMtjT/7sz9FVS384i/+Iu9+97uxySkQYg+sZtOMTrQ3V5t5An2vTDWSydKt\nOAgrmSRjY+2lJ2sXH9F0vWZLQ9OlbnGnarUq3/jGN+74npdeepHl5eUDatHhU282SRazjI7AifFQ\np5uzKxsbG3z605/mhRdeAEUFLHBdbbeua/yn//SfOH/+vNR8i11LFQuo9hojQ7auvkX0IPXGyHyP\nJPMr9lu6VMSwVBkdtvZU3ZWmG9J3diGdzvDqq6/e9X3xePwAWnM4rWbThAd1Jod9BH3deyY2wLlz\n5/hf/+t/tf/jFsEvgGHo/M3f/A3VavXgGyh6hm4YxDIpJsbh5Hioq8/EPkim+inJ0q3YT1sPofEJ\nODk+0FMPoWZLQ5e+s+/MmgWs1OvkawVGRxVOHwl3ujm7ous6zz333LUP3Cb4hfZtmKursYNrnOg5\niXwWj7/JyKCjq29CPGimGsk0TUfX5agzsT82CjlcngajEQfjg731ENINY7PvSC3ZTgSDQR566KG7\nvm9oaOgAWnP4RNNJRkYNjo304XZ2dw2srutcuXLl2gcUFVDhlvMag0pFMr9iZ5qaRjyfYXwMzkyG\npdZ3G0wVBSqKQvt3w5zZFbF/WprGei7N+Dicnui9I6sURQHFvJnJ3XK73fz4j/+jO77n4YffypEj\nRw6oRYdHvlKmYZQZHbZwfKy7a32h3Vcikci1DxgGdxpz7Hb7/jdK9KT1bJr+kMbEkEfO9d0mUwW/\nqtoOfnUZwMUeW89l6OvXGIu4iXT5bW63oioKqgS/O6YoCvfddz8///P//JavT00d4+d+7udMd9KD\nYRispJOMj8PxsX7stu7fUKmqKj/xEz9x3Uc2g99bzIenpo4xPDx8UE0TPaTebJKu5HqiVKgTTHXU\nmXKvmtwAAB54SURBVMLmCpSM32IP1ZtNUqUc9z/QXnrqRYpCO/Pb6YZ0MbfbzQc/+EGOHz/Oq6++\nyoULF/D7/Tz++ONMTU0RiUR6bsXgblKlAhZHnZEhG0d75FhARVF46KGHOHbsGPPz8+3Mr2LQHoHe\n3IOefPJJAoFAR9oputtKJklkyODoSAC/p3uPBewUUwW/qtrOXknmV+ylWDZFOKIzOeynz+vsdHP2\nhWR+94bT6eTMmTOcOnUKXddRFAVVVU0X9AJous5qJs30CTg10VsbRI8cOcKXvvQlPvrRj7Jeuy7z\ne133+af/9OM89NBDpvx/L3anVKtRahSZHlY5NSE3qu6EqYJfi6qiqqBfd7uSELtRqtUo1Aq85ZTS\n0w8hi6XddzRN+s5eUFXV9CdnxPNZvP4moxFnz+1SVxSFt7/97XzrW9/id7/8Tf78v1+inK0B8Oij\nj/JjP/ZjnD59Gq+390qkxP6LpjcYHYPjY0GcdlOFcXvGVD8169YArssALnbPMAyWknEmJtoPoW7f\npX4nVouKxQJ6U/qO2L1qo0GikOb+++G+ni0VUnjwwQf5uO7DH0wQsgbxOl2EwwM4nS7J+Iod2Sjk\nUGxVxkesXX8FeCeZLvi1WttH0QixW/F8FpurzviIjRM9sEv9TqwWFdUiE0exN5ZTCUZHDabHAoQC\n7k43Z1/ZrVYGBoKM+sbxu3r7exX7q9lqsZpNceoM3H90sGduEO0EU/3krg7gUvYgdqnebLKeTzM5\nCQ8ei/RUveKtWC0qVgl+xR5IFvNoaoWJMaspdqlvrZpI3xG7tZzeIDyoMTnsZTjk63Rzulpvj9g3\nsFn///bu4zfy7Frs+LdyzlUsVmCRLGY22a3pkWZGetJ7C/0fAvQXCDBgwBstBAjaPC8FaG0bMGAY\nfga8k7zSysCD5DCa0GE6MVbO+Ze8qCK71dO5SVb4nQ9AkMNhDw7Yc3/3/M49997xBK5q2rRDEXPu\naaXIckonnwma4nxFh82KzQ6qLmNHfDhF0ziplVlbG7c7LMLRZm/jsMvYER+v0evSU9vkVqwc5pem\nHc7cM1nya8PtsmGx6iiSAIsPVGm3UCxdclnbwvYrvszjcuByjSveQnyoo0qJeEJjLeMjs2Cb3F5H\nxo74WJqu86xSZG0d9lbjeFyLu7/kppgq+QXwyoNIfISRqnJcK5Ffh8P8Ei6T7LT1uSfjRpVxIz5M\nvduhq7ZYzVm5nU++/Q8sCJ/bgVvGjvgIR9UyoYjCatrDemoxzsOeNvMlvxeTuDKadihiDj2rFEkk\nNdbSvoU7nulNXE47bqcVA03ahsR7UzSNp5Ui+TzcWk8s9MkoL5OCi/gYzV6X1rDB6qqFH2wuyykh\nV8R0ya/P7cDtlrdw8f6q7RZDo8Pqio07m8vTDufGed0OXDJ2xAc4qpaIxVVW017WFuQmt3f1vOAi\n40a8H03XeVopsrYG+2tx/B7ntENaGKZLfi/fwmUCF+9hqCgc1Uqsr8PBesKUB4v7ZBIXH6DaadNV\nWuRyVu5smKfd4YLbacftsqAZqpz4IN7L00qRYERhNeNmIx2ZdjgLxXzJ72QCH8gELt6Rbhg8Kp2T\nSmvks35yydC0Q5qKixdHGTviXQ2UEUfVApubcDufwGfCypXFYnle/ZWii3hH5XaTntoiv27lk62U\ntDtcMdMlvz63c7x0KxO4eEcntQoOT5/1VQefbJmv3eGCz+OUjTvinemGwXfFczJZnc2VAKsma3d4\nkfT9ivfRGw05qZXY3II7G0vS7nANTJf8elx2XE4Lqq6iG8a0wxEzrt7tUO/XyOctfLqdwmFf/HNJ\nX0cmcPE+jiol3L4B6zmnKXvkX+TzOMd7TWTsiLfQdJ1HxXOyOZ3tXIiVJXOuNF430yW/FouFgNeJ\n22PQGw6mHY6YYUNF4WmlwMYGHObjRAKeaYc0VQGvE68XujJuxFvUOm2aowYbG+OXRrNfwxrwOPHI\n2BHv4Khawhccks+5OFyXyyyuiymfSNGAh2AAWv3+tEMRM8qY9PkupzTyWR8bmei0Q5o6j8tByO/A\n4dToDYfTDkfMqKGi8KxaZHMDDvMJQn73tEOaumhwPOe0BzLniNertFt0lCb5vJVPt1PYTP7SeJ1M\n+ZuNBT34/dCRB5F4jZNaBbu7T37NwSdbqWmHMzOiQQ8BmcTFa4z7fM9IZzQ2cwHWU7JDHSDgdRHw\n2TCsirQ+iFfqj0Yc14psbo77fANe17RDWmimTH6jQQ+B4HgCN6TvV7yk0etS7Y37fO9upXA6zNvn\n+7JY0DtJfnvTDkXMoONqGadvwHrOYcpjzd5Eqr/idcZ9vmdkV3S2ckHTnih0k0yZ/HpcDkK+8fJt\nfyQ3vYnnhorCk/L5uM93I040aO4+35dJ5Ve8TrXTpjGos5G38OlO2tSbQ18lFvTilxdH8QrPKiU8\nwSHrOSeHJrr6e5pMmfwCxEJeAkFoyYNITKiaxv3zEzJZjY0VH5vS5/s9fo+ToN+OxaoykCvCxUS7\n3+eoVmB7G25vJAhLn+/3XFZ+Za+JeMFZvUpfb7K5YeXT7bTpN4feFNP+li82vUnfr4Bxr+LD4hnh\n+IjNNRef7qSnHdLMerFtSIiBMuK70in5vM7eelj6fF8j5HMR8FtRjRGKqk47HDEDqu0W5W6FnR0L\nP9pJEfRJn+9NMW3yGwt6xktQ8hYugKflInZPj+0NO5/tZeTt+w1iQQ8Bv4wdAYqm8eD8lOyKxvaa\nnwM5mum1LBYLkcC4baglL46m1+73OaqPV0t+sJUgGfVPOyRTMe0M7/M4CQcc2J2qTOImd7HstL1l\n5bPdDB6XY9ohzbR4yEsoDM1+Ry6KMbGLkx0i8RGba27ubssVrG+TCHkJhaDR7Uw7FDFFz1dLDPbz\nEVktmQLTJr8AmXiAWBwqnda0QxFT8vKyk5xJ+nYBr4tE2IXbo9HsdacdjpiSJ+UCdk+PLVkteWfp\neIBoFBr9DpquTzscMQWKpnH/hdWSW2uJaYdkSqZ+WmUTQWIxaPTaUsEyIVl2+nDZRJB4HKry4mhK\np/UqQ6N1uVridtqnHdJc8LgcJKNegiGdWrc97XDEDbtYLYlOVks+ldWSqTF18hvwuliKuKWCZUIX\ny04bGwa3ZNnpvY0rWBZag65UsEym0m5R6VbY3rbw2W5aVkveUzYRJBYdrzoJc3lSKuDw9NjedPDZ\nXkZucJsi0//mM/EA8fj4gS7MYago3D8/uVx22pdlp/c2rmB5CASlgmUm9W6H43qB7R34ZHuJpYhv\n2iHNnVTMTyxmpaf0GcmpD6bxrFJiaJHVklkhyW8iSCxmoTXooGratMMR12yoKNw7P2Y5o7Cd93B3\nS5adPlQ2ESQekwqWWdS7HZ5Wz9jeNjjciLK2HJ52SHPJYbeRivqIRA1pGzKJo0qJrlZnb9fCZ3tp\nOdJsBpg++XU77ZMeLIO67MBdaJeJb1phd8PDF/tZWXb6CKlYgGjUSk/pMVSUaYcjrtGLie/trSh7\nq7Ja8jEyk/0m8uK4+I4qJdpqnb09C1/sZ0iEZbVkFsjMz7iClYhDqdWYdijimoxUlXvnJyynFXY2\n3Hwuu9M/mt1mJRX1EY1Cud2cdjjimjR6XZ5Wz9jaNjjcjEib0BVYCvuIR2xolqFctLTAjqrly8T3\n8720tAnNEJn9gVTUTzJhx7ANaMjGt4UzUlW+PTsmmRqxs+Hmi/0sDrtt2mEthPVUhFQKyu2GtA0t\noGavy5PKKVvbBrc3I9ySSyyuhNVqYXU5TCo1PjlDLJ7japm2UptUfNNymtCMkeQXsNmsbGaipNNw\nWqtMOxxxhUaqyr2zY5aWR+xuSuJ71aJBD9mkj3BEo9CsTzsccYWavS6Py2dsbY0rvpL4Xq18KkJq\n2cpA60r1d8EcV8s0J4nv55L4ziRJfidWkyFSSan+LpKLxDchie+12s7GSKel+rtILhPfbZ2DzbBc\nW3wNnA4b+XREqr8L5qRWoanU2J8kvsuS+M4kSX4npPq7WAbKiG/PjolL4nvtXqz+FqVvfu7Vux0e\nl8/Y3Bonvof55LRDWlhS/V0chmFwVCnRGFbZ3bHw2V5KEt8ZJsnvC6T6uxg6gz7fnh2Rzo7YmyS+\nTockvtfpovpbatWl+jvHCs06z2pnbO/oHG5J4nvdpPq7GDRd57viOT2jzv6+hS9upUjFAtMOS7yB\nJL8vkOrv/Kt12jwsnpDf0Li15eMnByuS+N4Aqf7Ot4uqVblbYm/f4If7CUl8b0g+FWE5KdXfeaVo\nGvfPT7B62tzat/HTw6wkvnNAkt+XXFZ/7QO59W3OFBp1jurnbO/o3N4O85kcZ3ajnld/a3Lu7xx5\nsWp1cGDhx7dSbGai0w7LNJwOGxuZCOn0+GgswzCmHZJ4RwNlxDenRwRjfQ73HPzjnRyxkHfaYYl3\nIJnBS2w2K/trCfLrcFwryfWTc8AwDJ5VSlT6z6tWtzeScnPbDYsGPeQzQZZTOk/KhWmHI97BRdXK\n5mlzcMvGPxxkySSC0w7LdDYzUXJZB1ZnX05NmRPt/qS9bmXEwY6bnx7m8Huc0w5LvCNJfl8hmwiy\nnvGzlNR4Wi5OOxzxBuOq1Rl9o86tW1K1mraD9SXWcnZ0e49iU9ofZll/9LxqdbDn4Ge3pWo1LXab\nldv5JOt5KDSr9EejaYck3qDWafNdadxed7Dl5ye3VnA57dMOS7wHSX5f4/ZGktWcjZGlI+0PM2qk\nqpOqVUeqVjPC6bBxmF9ifR3OGmVpf5hRrX6Pe+dStZolSxEfW9kQmex45UTaH2bTWb3GUf2MnV2d\nOzthfrSbxibtdXNH/sZew+20c5hfkvaHGdXsdfn69BnhhFStZk0qFmAjE5D2hxl1Vq/yqHzCxqZU\nrWbN/lqC1RVpf5hFqqbxsHBKY1Rmfx9+uDfeFCrtdfNJnnhvMG5/aFOvd3haLrKdykw7JNMzDIPT\nepVKt8bGlsHGio9PNpdl8p4xh/kk1Vaf/9MYtz8kQ+Fph2R6iqbxqHiOYe9y6xbcysfYWYnJ5D1D\nHHYbt/NJGu0TvvmqStjrx+OUivy0dQZ9HpXOicQV9tZsfLK1LGf4zjnJGN7i9sZ4Ev+/jQ6FRp3l\ncGTaIZnWSFV5VDrH6uxxcGDhIB9nMxOVyXsGXbQ/NNpn3PumjN/txudyTzss02r1ezwunRNfUsmv\n2bm7vUwi7Jt2WOIVLtofmo0mj87O2MvksFllkXZazhs1Cq0K6+sG6ysePt1O4XE5ph2W+EiS/L6F\n22nnzkaSbv+Mb78p47TbifrlDL+bNr5utUAypZJftXN3KyVtDjMuFQuwnQsx6Dd5+OSUvXQOl0Mm\njZtkGAZnjRqldpX8hkF+xcvd7RRuWSmZaftrCWrtPr3ekO+KZ2wvZ+Ql/4YpmsaTUgHV2mH/Fuyv\nRdnNxbFa5e9hEcgT8B2k4wF+sJVAU8vcv1fAabfjd3umHZYpPG9zqLK5BfkVH3e3UnJxxZy4nU/S\nHyqMRj0enJ+yl17BbpO/u5ugqCqPSgVwdDk8tLC3Jm0O88Jht/H5XpaRcsRX33R5Wimynliedlim\n8WKbw8a6jU82l0lKm8NCkeT3HW1movQGCorS4OGjcRXL7ZBerOs0UEY8LhWwufocHFg43IjLMWZz\nxmq18MOdNEPlmOFwyMPiGTupLFZJwK5VvdvhWaVIPDlZKZE2h7njdTv4fD/DSD3m66+bnNUdpCOx\naYe10HTDoNCoUWxXpc1hwUny+x4O80sMRiqjUYf7J6fsZ3I4pIp15S4fQK0a6YzO6oqdT7fTRINS\nbZ9H4ypWBkU94qtvejwpFdhIpqYd1kIaqSrPKiX6Wpv8FqxnpM1hnoX9bn60m0JVz/j66wpOu4N4\nQI5zvA7tfp+nlSIu75Bbt2BvLcrealxWShaUPBHfg8Vi4dPt1LiKNRrwsHDKTiormxGu0MUDyO0b\nsn8AW9kQe6sJaXOYcx6X44Vl3BZHVTu5WGLaYS2UUqvBab1CIqmxk7WyvxZnbTksk/ecW476+WR7\nCUUtcu/bAnabjbBXqvhXRdU0TmoV6oMGqzlYSTu5vZEkLntKFpokv+/JZrPy2W6GkXLEPa3PN6dH\nbC9nZCPPR1I1jeNahcbkAZTLOLmdT8qmtgUS9Ln4bC+Nop5y/36NRyWV9cSytEB8pN5oOL6J0tFn\ndw/W0n4O80uyVLtA1pbD9AYKmlrj4cNTsuEkiWBo2mHNvVqnzVG1RCiqcmfbwk4uylYmKpdWmIAk\nvx/A5bTzk4MVbLZTHj4e8u3ZEVvLGTnK6QNdPIDCUZUf7FjYWYmylY3JrtoFlAj7+PGtNHb7OQ8e\ntnhwrrKZTMsmuA+gGwZn9SrlTo1MxiCXtXOwvkQqJqfRLKL9tQRWqwW7vcr9BwWGqkI2Gp92WHNp\nqCgcVUsM9A4bW7Ca9nB7I0nA65p2aOKGWIzX3KHYbDYvvw6F5A3zVRRV4y/3z3j4tMfTp1bWYiki\nPtkR+q56oyEn1QpDo8P6OuRS8gAyi2ZnwL/eO+XBdyrNmktWT95TvdvhuFrGGxixugpbK2F2c3Ec\ndnmJWHRHxSZ/vV/kwUMDlxFkfclcqye6rmMYBhaLBet7thxquk6p1aDQrJJc1lnJ2ri1Fmd1WS7h\nWTRvy2Gl8vsRLo6jcTsLOJwtHj44Y6QuyW1WbzFUFE7qFVqDNqmUQTZjY39VHkBmEvK7+elhDqf9\nlIdPh3xzcsRWMoPfLasnb9Lq9zipVdBtfXJ5WEm5uJ1PymZQE8klQ3hcdpyOMx48bHF/snqyyJuv\nDcOg0Wjw7Nkzvv76axqNBolEgv39fVZXVwkE3rzaoRsG5VaT80YVX1Blbx/WMwEO1pdkM6hJSeX3\nijw4rvLldxUePAC/I0wulpCNcC8ZqSqn9SqNfpNk0iCVspBPh9nKROV6YpNSNX2yetLlyWMr2ciS\n9DK+Qrvf56ReQTF6ZLKQTtrZykZZTYalPcikWt3hZPVEoVZxsrGUWsiXR8MwePLkCX/4wx+4f//e\n9/79F1/8mF/84hdkMt+/CMQwDCqdFmf1Kh6fQiYDmaSb3Vxcjv5bcG/LYSX5vUIn5Rb/+0GBJ08M\n2k0n+cQyAY9UZBRN47xepdptkljSSaUsrKeCbK/EZFOOwDAMvnxU5P6zJo8fg8Pws5ZI4rTLC1F3\nOOC0VqWvdUhnIL1sYzMTZX05LJtyBIORyr9+e8rj4wFHzywk/FHSkdhCtUEcHx/zu9/9jtPTk9f+\nzO3bd/jVr35FIvH8BJlqp81prYLTMyKTgXTSxW4uzrJcVmEK0vZwg7KJIEGvi5DvnKOzId89OSbm\nDZOJxk1ZBVY0jWKzTrldJxbXOcjD2iTp9XvkghAxZrFYuLO5TDzkJeAv8eyow9enfbKRhGmrwL3h\nkLNGlfaoTToNu0krm5kI+XRE+nrFJbfTzj8crBAPVQkF6zx5UuWbkw5rieWFqAIbhsFXX331xsQX\n4Msv/x+PHj0iFovR7Pc4rVexOgasbUBqycnOSox0PCDH/olLkvxesaDPxc9ur/IwWsXvr3F8XOdv\nx21WYkvE/ObYhd0dDig2GzT6LSJRg/0DyCX97ObiBH2ymU28WiYRJBby8mWwyJNIh6dPC5TbTdbi\nSbyuxf//xjAM6t0OxVaDodYjmYTNlJWNdJjNTFTOuhavZLNZ2V9LsBz1E/IXODod8t3xESF3iJVo\nfK5PUqnVavzLv/y3t/+gxcL/+NMfscbC+IMWsquQSjrYzsZYWQpK0iu+R5Lfa2C1WtjJxUnFAnwZ\nKXJ83ufp0zNKLS+pcHQhDyjXdJ3GZOJWjD5LS7C6bSGT8LOZiRIJSPuHeDu3085nexky8RbRcJnj\n0z73T54R9gRZDkXxOBdvxUBRVcrtFuV2A6dbYSkDS3Erq8kQG5mobMgR7yQa9PBPd1Z5GK8RjdY4\nOmrwt5M2yWCEpWB4LpPgbrdDsVh8/Q/YbOB2gsvOce0ey5k6u5tJ8umI9MOLN5Kn6jUK+lz89DDH\n0VKTSLhModjjpNDjuOoiFY4S9QfmvjerNxxSbjepdlr4/BqpFUjEbawmQ6wth/G6padXvL9MIkgy\n6uderEI02qBYbHKv0MTn8JMKR+e+l94wDBq9LpV2k9agSzRmsLkNybiTteUwK0sh7NLTK96TzWZl\nNxcnmwjyt3CR42KPwnmFL49rxP0hkqHIXB0paLXasFisGIb+/JsWwOkcJ712FSgBZbwOH/94J8nB\nzrpUesVbyYa3G6JqOs8KDR6f1ymWVc4LMOg6SIbCLAXDc9UT3Bn0afS6NLodNMuQeBziCUhG3awm\nw2TiAdmMI65Mtz/i8XmdZ8UWxaLOeQEceC5XUeZlotN0nVa/R6PXodHt4vKoJJYgHrOQjvtZTYZk\nB7q4UpVmj0enNU5KXYpFKJcthDwBUqHoXLQS9fs9/vmf/z1/+etfwOkApx0cNrA0gDLodRi2YNjk\n3/3bf8Nvf/tbbHNY4RZXT057mDG6bnBaafHorE6hPKRQgGbDRtjrJ+z1EfL6Zi4RfnnSdrhUwmEI\nhyEStpFNBMkthaSfV1yrkaLx5LzO00KDQkmjUABl6CTi8xPx+vG73TOXCI9U9XLctIc9fH6dyGTs\nxMJOckshsomgHPUnrlWrO+TRWY2jYpti0aBYBKfVQ8TnJ+z1z2Q7UW84pN5t87/++hf+43/+D0Bj\n8tEEpQ2DJow6wPjCiz//+c/87Gc/m27QYmZI8jvDSvUu353WOK/0qDegUYdOx4Lf5b1MhqexRKXp\nOr3hkO5oQKvX+/tJOwKRgIPlqJ9k1E804JG+KnGjNE3nqNTk8Vmdck0Zj50GjAY2Ql7f5diZxkuk\noqp0R0O6wwGNboehNiA0SXbDIYiHPSQjPpIRv7wsihvXHyo8PqvzrNikWtdp1Mdjx2o4CfvG4ybg\n9kzlJXKgjOgOh7T7PRq9Lha7QiQMdnuHP/7xv/Lf/8t/glF3nPAa2t/92d///vf88pe/xOv13njc\nYjZJ8jsHOv0RhVqHYq1DpTWg2TCo16HZBIfFhc/txuNw4XY68TicV5oQK5pGfzJZ94bjz4qu4PEY\neLwQCkI4bCEWco8T3ohPrh8WM8EwDGqtPsV6l2K9Q605ojFJhNttCz6nB6/zYtyMP1/lLVhDRaH3\n4tgZDTBQ8frA74NgCMJBK0sRL8nIeOxIhVfMAlXTKU3GTanepd7ULsfOcGAj4Pbimcw3bqcTt8N5\nZS+ThmHQH43ojsbjpjca0hsOsDv0y7ETjkAkaL8cN/qow//805/4zW9+w+PHjy//W3fv3uXXv/41\nP//5z996y5swF0l+58xI0Sg1uhRrHUqNLo2WTq8LgwH0+jDog6ZacU8eSi67A6vFgtVindx1Pv56\n/D0Lmq6j6hqqNv5QJh+qrqFoKjoqXg/4fOD1Xny2TM4rdhENelgKy6QtZl+nP6JY61Csdyk3+7Rb\nBv0+44/B+LPVsF++RNpttvFYsVoux5DVYhmPI4tlPF5eGjsXY2mkqtjsGj4feLzg8zKeuL22y7GT\nCPuIBT3S/y5mmmEY1NuDcQFm8hLZ6YzHy2AyboZDC3arffwS6XBgs9mwMJ5vbBfzjdV6WTEejxd1\nPHb0v597FE3B5TLw+p6PG68HAj4HIZ+LkM/NUsRH2O/+Xpynp6c8ePCAwWCA3+9nd3eXRCIxc+1O\nYvok+Z1jum5Qb/dp90d0+iPavSGd/ohuX72czJUR6DroBuja5Gv9+fdsNrDbwWEHh2P89cWHwwFe\nj3U8Wfvdl5N2wOuSVgYx10aK9sqx0x/ol8mwpj4fK9oL48aYjB3HC2PF7pj88wuf/R77eLL2uy8n\nbTndRMy7bn9EozMYj5vJ+On0R/T7xmVC/HfzzMX8o4/nIHjFeHlh/nE4IeRzXs47F2NHzrEWV0mS\n3wWkqBrt3viBNFRUNN1A03R0w7j8WtMNdMPAZrXgcthxOmw47TacDhuuF752O+3y1ixMoz9ULidz\nRZ2Mmcl40XT9cvwYgMNmnYyX74+fi+8JYQaGYdAdKLR7Q3oDBfU1842mjY8kuxgvLqf9cty8OOfI\nMX7iuknyK4QQQgghTONtOay8fgkhhBBCCNOQ5FcIIYQQQpiGJL9CCCGEEMI0JPkVQgghhBCmIcmv\nEEIIIYQwDUl+hRBCCCGEaUjyK4QQQgghTEOSXyGEEEIIYRqS/AohhBBCCNOQ5FcIIYQQQpiGJL9C\nCCGEEMI0JPkVQgghhBCmIcmvEEIIIYQwDUl+hRBCCCGEaUjyK4QQQgghTEOSXyGEEEIIYRqS/Aoh\nhBBCCNOQ5FcIIYQQQpiGJL9CCCGEEMI07O/yQ81m87rjEEIIIYQQ4tpJ5VcIIYQQQpiGJL9CCCGE\nEMI0LIZhGNMOQgghhBBCiJsglV8hhBBCCGEakvwKIYQQQgjTkORXCCGEEEKYhiS/QgghhBDCNP4/\nM1RyzYxXT78AAAAASUVORK5CYII=\n", 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kkAvxpgvQ/DzQ8nByKCYXoB1SFIWJgUGSBQcXL66BkcbpsDE+KDeLvSJTqHJ2LkVipcnC\nIoTdIR4Yi5r+cIpuc9hsnBgeY24tyYVLJRRlmR95cELq53uEYRgspgpcmE+TWNJJJVVG+gaIRWW/\n550KeDycGplgemmZdruB3bbMO+8blwMxtkmC3x63mMxzfj5NfElnTS5Ae2Io1IeCwvR0Crs9hdtp\nl6NdTU7TdC4svFEeVCs7mYrGCJrk9CgzsKkqR2PDXE0aXLlaxmlf4rEHJqQG2OQqtSavzSSJr9SY\nnwePzc99o4NSHrSL3A4np0bGubC8iNNVw+1c5S3Hh2Vc3wa5yvSotqbz+kySmUSJmZnOBej+sZgs\nytkjsVCYRrvF9JUsDvsKP/LgBEGfZNbNqFRt8Mr0CvOJJom4wmCgn6nxSM+daHgQKIrCVGyYyysJ\nrszVcTqWedd947ILhEktp4v8cCbF3LxOLmvnUGSQfr9szbUXnHY7J4bGuDwfx+Eo4XE5OH042u1m\nmYZEQj2oUK7z6pVV5uJNlhMqhyIxqU/cB+P9A8yutbhytYTTscSPPHgIt2SxTCWxVuCHM2vMzemU\nC05ODo/gdcpNzF6yqSrHh0a5uBLnqquOy7HKmZMjksUykc2ZkunFPDMz4FYDPDAWk/KgPeZ1uZga\nHGHm6jIORxaPy86R4b5uN8sUZGTuMQvJPGdn15idNaiXXZweHZGDKvaJoihMDg5zeaXNldkaTvsS\n77p/HIcJz5u3mramc24uxdV4kZkZ8NlD3Dc2KItB94nDbuf40BiXFuM4HWU8rjUemIx1u1niLpRr\nTV6dXmE+0WBxUWGsb5DBoJzit19CXh/j/TGuTCex29bwuBwM9fu73awDT4LfHtFqa7w+m2ImXmJm\nFkLOMKfHBmWqdp+pitLJYi3Huepq4POkeOuJkW43S9xGsdLg1SsrzMebJBIq4/2DRAOyaHG/eZxO\njsVGuTqbwOHIE/K5mYjJv8NBtlnmMDuvU8w5OTk0IgupuyAaCNFst5m+so7Dscp7HzmETxaP3pYE\nvz2gUK5v1Ci2OmUOA0NEpM6qa+wbK9kvJBYIBkoM9xcZlT2AD6R4qrBRo2hQLbo4OTwsZQ5dFPB4\nmOgfYnZ2Fb9vjWjYi8clC6UOGk3TOT+/xpV4obOmRA1y/1hMZkq6aLQvQj3VJB4v8sNAknfdPy6l\nQ7chwa/JbQ7eM7MGjYqb06PDUuZwALgcDsb7B5mbSxIMrDEQ8soq9gNE1w3OzqW4sljg6lXwO0Kc\nHpUyh4NgIBAkVykRT5R5PZTiHafHut0kcY1ao8VLl5alzOEAOjQwyLlElcWVGsORPJMjUv97K3Kl\nN7HL8XVevJDk7DkDRzvM6dEJCXwPkGgwhE33sRjXODuX6nZzxIZWW+PvLy7x+uUCly6pjASHmRwc\nksD3ADk8EGMtZWNhuUI8VbjzF4h9USjX+ZvX45y/3GAp7uTk0CEJfA8Qu83G4WiMuXm4sLBOpdbs\ndpMOLLnam5CuG/zgyiqvXc5w6ZLCSGCIw9GY1PceQEeiMZKrKvPLZZbTxW43x/Kq9RZ/ey7OhStV\n4gt2TgyNMyA7oRw4Dntnm6y5OTg3t0at0ep2kyxvLVfhb84muHCpTbXg5b7RCanvPYD6fH789iDx\nuM4PZ5Lc4hBfy5Pg12Q2s1bnrhS5Mq1yZGCUaFAWhRxUb5Q/wLn5NRrNdrebZFmFcp0Xzsa5cLlJ\nOuni1MgEPpe7280StxAJBHGrfuIJnddnZeakmxaTef7u3DIXL+qo7SDHh8dkG7MD7NDAIJl1O4sr\nNeZX891uzoEkwa+JXJ+1Ojk8QdgrJ4kddNeWP5yfX+t2cywplS1vZa1qRS+nRsblxCkTuLb8IbEm\n5Q/7zTAMLi2meeliigsXDYKOCFODwzLLeMDZbTYOD7xR/lCty8zJ9ST4NYn8TbJWMuVkHkeiMVZX\nFBZWSxQrjW43x1IWknm+f35FslYm5LDbmYgMsrgIVxIZdF2mcPeLrhu8djXJa5ezW+V1Y/0D3W6W\nuEt9Pj8+e4CVFZ2rS5luN+fAkeDXBFLZMi9I1srUXA4H0UCYZBKmE+vdbo4lbGatXr6Y4sIFyVqZ\nVcQfoN1wsrrWYknq5vdFq63x/11IcPZKkatXVCalvM6UxvoHSCYVFpJFyf5eR4LfA25lvcT3z69w\n4YKOrR2SrJWJDYf7Sa8pJFJlyf7uMcMwODe3xmuXs1y8qDASkqyVWSmKwmhfhOUVuLok2d+91mxp\nfP98ggtXalvldSEprzMlt8NJyBMgmTQk+3sdCX4PsNVMiRcvrnL5skHIGWFycEiyVibmsNuJBsKs\nrsIVuRDtqXNza5yfyXP1qsJUdFRObDO5fn+Adl2yv3ut2epkfC/PNEgnndw3ekjK60xuJByR7O9N\nSPB7QF0b+IZdEcla9YihcD/ptEI8KbW/e+XcXOpNga9krcxPsr97b3MnocuzDdIpJydHxnHa5WAe\ns/M4Jft7MxL8HkDJbJkXL65y6bJByNkvgW8PcdrtRP2S/d0r5+fXJPDtUZL93TudGt8lLs/USSed\nnJLAt6dcm/2VPbM7JPg9YJLZMn9/YYVLlw2Cjn7GI9FuN0nssmuzv6WqZH93y/n5Nc5dzXHlisKk\nBL495/rsr2zevzs2A9/p2TprEvj2JI/TScjdyf7OLGe73ZwDQYLfAySVLfPixRUubwS+ExL49iSn\n3U6/L0Q6DYk1yWDthgvza5ybyXH1aifwlf2ve1O/P0Cr7iCdbZEp1rrdHNPbLHWYnq2TWpXAt5cN\n9/WTWoOldEnKhpDg98BIZcv8/cUVLl0yCNj7JPDtcdFAkPV1WF4vSgZrh7YC3ysKhyMjEvj2MEVR\niPiDZDJI6cMOtdoaL15a3gh8HZwcHpPAt4d5nS4ciptsTiOVK3e7OV0nwe8BkClUefHSNYHvwGC3\nmyT2mN/twdAcZHJtyWDtwJVEhnMznVKHw5ER+nz+bjdJ7LGIP0gm29kGUtP0bjfHlHTd4KVLy1ye\nrZFccXByWPaOt4IBfyfpIjeOEvx2XaXW5MVLK0xPG/hsYQl8LUQyWDuzlC5ydmZdAl+L8TidOBU3\n2ZxOKlfpdnNM6YczSa4u1lhZskvgayH9/gC5nMJqpkKzpXW7OV0lwW8XNVudaaeZWQ217eeQBL6W\nMhDoBL+Swdq+TKHKq9NJpqdhJDQoga/FRPxB1uXG8Z5Mx9eZXiiyOK9yYmhMAl8Lcdrt+JxeslmD\n1Uyp283pKgl+u0TXDV6+vMzVuSaVopup2DCKHGBhKW6HE6fqJiMZrG0pb8yWXLliEHb1EQuFu90k\nsc8i/gD5nMJqVjJY25FYK3BuNtNZGDo4IgdYWNBm0sXqN44S/HaBYRhb006ppJ3jQ6PYVPmnsKJI\nIEhGarDuWrOl8eLFJa7OaNg0v2wFaFEOux2/y0sua7Bi8QzW3VovVPnBldTWbIksDLWmPp+fUlEl\nlatZ+sQ3ibi6YDqR4fL8G9NOssLWuiL+IPm8QjJboS2lD7el6wYvXV5mZr5FreRmclBmS6xsYKNm\n3urTt3ejXGvy0sbakrC7X2ZLLMymqoS9fnJZa/cdCX73WTxV4NxMhpkZhSmZdrI8h82G2+6iXDbI\nlWTXh1sxDIPXrq4ys1BjLemQ2RJB0OOlVIZssS77lt5Go9nmxYtLXJnRsOt+xuXEUMsLeX0Ui5C1\n8Jgjo8c+2pp2ugKj4UE5gUoAEHB7KJUgK1ue3dJ0IsP0QonFBZXjw6M4ZLbE8hx2Ow7FSamsU6jU\nu92cA0nTdF6eXuHqXIu6zJaIDQG3h1IZMsWaZfeZl+B3n9QaLV6+3Fmk0+fuZzAo006iI+DxUiwh\n+/3ewmqmxPnZa2ZLnDJbIjoCHi/lsvSdWzk3v8bMQo10SmZLxBtcDgfodkpljXKt2e3mdIX0hH2g\n6wavXlllbkFD1Xwy7STexO/2UCl3pqBk+vbNKrUmP7iS5OoMDIeiMlsi3iTg9lCUWZObWkoXuRIv\nsLiocnxIZkvEmwXdXkoWTrpI8LsPphPrzC/VyKTtMu0kbuCw2XDaOnW/+bJM327avGmcX9BxEWAo\n1NftJokDJuD2UC51bhytOn17M+Vak9euppi5CuN9g7K2RNwg4LF2uZ0Ev3sslS1zcT7L/JzC0cER\nHDZbt5skDiD/Zt2vhRcgXO/iYpr5RJ181sGRaKzbzREHkMvhQDEcFMsapao1p2+vp2k6r0yvMD+v\n47UFiQZD3W6SOIA2x5xMsdrtpnSFBL97qN5s89pMkplZiAUGCHg83W6SOKCCmxeigjUvRNdbzZS4\nvJBjcbFT52uXm0ZxCwFPJ/tr1UH8eufn11hINCjmnRyWm0ZxC16nC61to1huW3K/Xwl+94hhGLw6\nvcL8goZN8zEclilbcWubC3dyUvZAtd7qTNnOwHAwit/t7naTxAG2uVtKriR9Z3mrzlfhWGxEFriJ\n29rc9cGK22xKz9gj04kM80s10mtS5yvuzGm3o2sqtbpm6eNaO3W+nZtGJ36G5KZR3IHH4aJeh0rd\n2mUPlVqTH850bhrHpM5X3AWP00WjDhXJ/IrdkM5XuDCXYW5OYWpwWOp8xV1x2R00GlBtWO9CtOnS\nRp1vdt3BkehQt5sjTMDl2Og3FhzAN+m6wSvTK8zO63jUoGylKe6Ky+6w7I2jBL+7rNFs8+qVVWZn\nIRaIEPR4u90kYRIuh5O6hQfxtVyFS4s55ucVjsaGpc5X3BWn3U67rVBrapY9IvziYpr5pQbFnNT5\nirtn5RtHCX532bn5NRYTGkrby3C4v9vNESayeSGy4l14q63x+mySuVkYCg7gd8viUHH33A4njbo1\nB/FMocr0Yo7Fhc5No9T5irvlsjs6CRcLzjZKL9lFq5kSc8slVldUjkSHpM5XbMtW2YMFB/CLC2kW\nl9oYLY8sDhXbttl3rHbjqGk6P5xJsrAAsWAEn0sWh4q757Tb0doK1XobzWKzJhL87pJmS+P12RTz\nczDWF+0cHyjENrgdjk72ymJ34el8hauJAstLitw0invituj07eX4OvHlFs2qS2YaxbYpioLD5qDR\ntN64I8HvLjk/v0ZiSUPRvAzKpuLiHrxR9mCdi1Bb0zs3jQudcgeP09ntJgkTcjo2F+5Yp+9kizWm\n4znicYUjg0OoctMo7oFVZxwl+N0Fa7kKc8tFVlZUjkRjkrkS98Rpd9BsKlTrLXTdGke1Xo6vE19q\nodXdUu4g7pnVdkrRdYPXZ5MsLMJgoF/KHcQ925xxtNKNI0jwu2OapnN2rpO5Gg5FcDskcyXujaoo\n2G02Wi1otNrdbs6ey5frXInnSCSk3EHsjMvuoNXqnKppBTPLWRIrTaolJyN9kW43R5iY026n2bTG\nmHMtCX53aDqRYWmlRbvmYigkmSuxMzZFRdPp+S2bdN3g9Zkk8ThE/X2yIb/YEZuqomm932+gc5jF\n5XiGxUU4Eo1JuYPYEZtqs0zfuZYEvztQrDS4ksixuAiHJXMldoFNVdHavX8hml/NkVhtUC46JHMl\ndkxVVdoWGcDPzqVIJAyCrpDsIy92xDAMVEVB06HV7v2+cy17txtgZmfnUsTjBhFfH3631FyJnbNC\nBqvebHMpnmFhAQ4NxGRfUrFjNlVFt8CMyXK6yOJKlcy6jfvHot1ujjAhwzAoFAosLi6STCaptBoo\noTZHRiZ45Jh1kngS/N6j1UyJpWSNfNbOgxMD3W6O6BFWGMQvx9dZXtbx2gOEvb5uN0f0AFVRwFDQ\nNANN07HZeu+GStcNLsXXWYx3ttN0yAmIYpsMw+DSpUv8/u//PrOzM50HHXYIajz7zBL/71P/N//g\nH/wDPJ7eP2So964Q+0DXDS4trpNIwGh/RDJXYteoSif47dXdHoqVBnMrBZJJhfGINW8a2+02CwsL\nnDt3jsuXL1MoFDCM3vz33k+qonT6To9+lvOrOVaSLfSGi4FAsNvNESZjGAbT09P85m/+5huBb+cJ\nQGV9PcOTTz7Js88+i673bvJlk2R+78FiKs9yqkmz5iQ6IHv6il2kdK5FvTl8w8XFNCvLEPGFLbcz\nimEYxONxvvWtb/H888/TbDYAOHbsGB/72Md58MEHcco+x/dMURQMNsbyHtNsaVxZypJIwEQkapmp\nabF76vVMuWi4AAAgAElEQVQaTz/9NNVq5SbPdn6fDMPgX/2rf8UjjzzCsWPH9reB+0xSltvUamtM\nJzIk4jAuFyGxy1RFwTB6M/ObzldIJCtk1lVLLnJbWlriqaee4tln/3or8AW4evUqv/mbv8lLL71o\niYzLXlEUBaNHM79XlzIsr2o4FZ+UCol7Eo8nePHFF298wjDoBL+dWGZ9fZ2zZ8/2/GyUBL/bNLOc\nZWVVw2Z46PP5u90c0XMUdKP3BnDDMLi4kCaxBEOhiOXqFXVd55VXXiGRiN/iFQa/+7u/RzKZ3Nd2\n9RKFTua3124cq/UWsyt5VpaxbKmQ2LlsNsut5xQVuCaRd/ny5X1pUzdJ8LsNtUaLq0s5lpZhIjLY\n7eYIYRrL6yWWUw0qRQexULjbzdl3mUyG//k//+dtX1MqFYnHbxUcC6u6tJhmedkg6A7KSW7inm0n\nk2uFGW0JfrfhcnydlRWDgDMgW5uJPaHrOjYV7D20Wl3TdC7HOwtEx/oHLLlAtF6vk8tl7/i6crm8\nD63pTVoP9p18uc7CaolUSmGsT7K+4t5Fo1FU9SYzbooCaGC8UXJ1+vTp/WtYl/TOVWKPFSsN5leK\npFIK4/2yv6LYG5quY7P11gA+n8yzvNpCb7qI+APdbk5XOJ1OAnexQt/rlUML7pVu9F7fuTC/xvIy\nDAb6cDkc3W6OMLGJiQkee+yxG59QFEDfCn6Hh4d56KGHej772ztXiT3WmXqCAV9YLkJiz2g9NoC3\n2hpXEhkSS9ZeIBqNRvnJn/zJ277G6/UxMTGxTy3qLZqug2JgUxVUtTd+x1LZMstrNfI5G8Ph/m43\nR5ic0+nkwx/+MMHgdTtUXZP5tdvtfOELX+Dw4cPdaOK+6o0Rdo8VynWW1ipkMirDFlylfiu6rlOp\nVKhUKrJKfZf0WuZ3IZknuabjUryELLxKXVVVzpw5w8DArWeNfv7nf56RkZF9bFXv0HUdew/1G+gs\nrl5ehqFQP3aLLRAVu09RFKampvi1X/s13vrWM2zu7tD5Q2Nq8ghf+9rX+MAHPmCJJIXs83sXZldy\nJJMQ9Ycst0r9ZjRNY3Z2ltdff50XXngBgHe/+908/PDDHD16FJt8RvdsM/h19MAgrusG86t5kqsw\nIZkrDh8+zGc+8xmefvppvv/976PrGgCxWIxPfOITPProo6gWrIfeDZqho/ZQ8Jst1lhJ1ygWbByZ\nsN4CUbE3FEXh6NGj/Lt/9+9YXFwklUqRr1fxDLR48h8e4/946ylLBL4gwe8dVest4qkS6bTC/aN9\n3W5O1+m6zg9+8Cqf//zv0Go1tx5fWJjny1/+Mr/yK7/CW9/6VgmA75G+Efz2wvGsibUCqXQbRXdb\nOuu7SVEUJicn+dSnPsVHPvJhisUSdrud0dFRIpGIZQadvdBri91mV7IkkzAYDFtygajYO4qi4PV6\nOXXqFKdOnWIll0F3rzMUs9Y1SHrVHcyuZEmlDMLegNT6AvPz8/zO7zz1psB3U7vd4qmnnmJ+fr4L\nLesNmt7JYJk982sYBrMrOVZWkXrFayiKgsvl4tix4zz66KM89NBDDAwMWGrQ2Qu9VC5UrjVJrJXJ\nZBRiQcn6ir21Oeb0Qt/ZDmv9tNvUbGkspoqkUjKAQyeguXz58ptOp7peq9Xk4sWLUgN8DwzDwEDH\nblNMn/lNZsuk1pu06g765TAYsce2yoXs5p9xmlnOkkpCvy+Ewy6Ts2JvtXvoxnE7rPXTbtP8ao5U\nSsfn8ON1urrdnK7bPKXqTl555ZWePxpxL/TSRWhmOcvqamexjmQ1xV5r6xo2u/n7Tr3ZJp4qsram\nMByWMjux9zRdw94Ds43bZa2fdhs0TWduNc9qUrK+17LfRSbibl4jbtRoNXG6wOM09+e3Xqiyul6n\nVLQxcBd72wqxU41WC5cLvG5zl6bNreRIpQyCbj9uh7PbzREWsNl3PC5z953tkuD3FuJrBdbSGg48\nBDyebjfnQFBVlXe96113fN273/1uWbV+DxqtFm4X+DzmHvRmlrMkVyEW6pPFOmJfbAW/Jh7AW22t\nszVgsjNjIsR+qLdauNzgM/mN43bJyHQTm4t1VmWxzpsoisKxY8fo67v1ZxIKhTl27JhMdd+DeruF\n2+QXoWKlwfJahWxWZVAW64h90mhv3DiauO8spgqk1nTcNi9+t7vbzREW0NY0UDTcThWXyWcct0uC\n35tYy1VIZ1q0m07CskXTm4yOjvKrv/qrRCI3njPf3x/h05/+NOPj411omfnVW01cLvC5zZv5XUjm\nWVuDAdkTW+yjrb5j0lkTwzBYTOZJpmBIEi5in9Q3ZkzMfNN4r6wV6t+l+FqBdBqigZBkMK+jKAon\nTpzgc5/7HAsLC1y4cAHDMDh9+jSTk5MMDw/LZ3aPGhvTT2atW9Q0neX1Eul1ODEYuvMXCLELNF1H\nNzTcLgWXw5w3XJlijfVci3bDQcjj7XZzhEU02uYec3ZCgt/rNFsaK5kK2azCA2OyWOdmFEVhZGSE\n4eFh3vGOd2w9JkHvzmzV/Jr0QpTMlslkNRyKG69LdkfpNsMwKBQKZLNZFEUhEokQCAR6rp82Whvl\nQh6naX+2xFqB9XUYCARN+zMI82m0mhtjjjlnTHZCgt/rLKWLZDMGAZcfp+xacFsS8O4eTddpG23c\nLgW3SWuvEuni1oyJ6K5iscjZs6/zF3/xNHNzswCcOHGSn/qpn+KBBx7A5+udcq7NkgezLnZrazrL\n62XW1+G+Eek7Yv802i38IfMmXHZCan6vk9goeZAtmsR+2sz6elwOU95Q1BotVtcrFPIKEX+g282x\ntEqlwrPPPstTTz21FfgCTE9f5rd+63N861vfol6vd7GFu8vsq9VX1ktkMjoeh1dOERX7qt4jWwTe\nC3OmmPZIoVwnnWtQq9oIR+VUqv1gGAbVapVEIkG5XMblcjE6OkpfX58pg8B79cZiN3NehJbSRTJZ\nCHn92GWhW1fNzs7y5S//+S2f/+M//mNOnjzJqVOn9rFVe6fRbuILmnexW3yj5EFmTMR+q7eaGzeO\n5uw7OyHB7zXiawXS6xDxB1EtFHh1i2EYTE9P86UvfYkf/vC1rcfHxyf42Z/9WR566CGcTmt0ymqz\ngdcLAa/5amUNwyCeKrCehrGgDODdpGkaL7300h1eZXDu3DlOnDjRE/txVxoNol4ImDD4LdeapDI1\nSiWVqQlJuIj902q30Wnj86h4XNYLBa33E9+Crhssr5dYT8NxWal+W4ZhkMvlSKfTNJtNABwOB4OD\ng9vK2F69epXf+I3foFIpv+nxRCLOf/gP/4FPf/rTvO1tb7NEBrhcrzEUhf6g+Q5UyRZrZPItmg07\nQVmpfludRWh5isUirVYbVVVxuVzEYjFsu5Ax13Wd6enpO77u6tWrPXEEuabr1FsNfD6FsN98e+Mm\n1gqsZ6DfF5ADYcS+Kjfq+H0Q9rstMcZeT4LfDclsmfWMhl1Wqt+SpmksLS0xM3OVZ575SxKJ+Jue\nHxsb56Mf/SjHjh1jbGzstoN5q9Xi+eefvyHw3WQYOn/wB7/P5OQk0Wh0V3+Og8YwDCqNOj4/5hzA\nr1noZsWL6N3QNI3l5SVmZmb5y7/8SxYXF7aec7s9fPCDH+TMmTNMTEzg9/vv+XNUVZVw+M6Hi0Qi\nvbGXbLXRwOMxCPlc2GzmCh4NwyCxVmQ9DUf6JeEi9le5XsPvh76A+RIuu0GC3w1L6SLrGVnodiuF\nQoHvfe97fPGLX6Rer930NUtLCf7Tf/p/cLnc/MzP/AyPP/74LQfilZUVvvvd7972e6ZSKRKJRM8H\nv7VWE7tTJ+hzmG6nB03TWU6XyGTg1LD0nZtZX1/nO9/5Dk8//RfUajf2nXq9xjPPPM0zzzzNfffd\nzyc+8QlOnDhxTwGwqqo88cQTvPji39/2dWfOvK0nSh7KDfMO4OuFKplcG0NzEvCYr/3C3MqNOiMx\n6DNhwmU3mP/qtws0TWctXyGf70w/iTfL5XJ8+ctf5g//8A9uGfheq9Go80d/9If8+Z//Odls9qav\nqdfrtNutO75XL61Kv5VKvd4ZwE14EcoUa+SLOg7VjdthvprLvZZKJfmjP/pD/uzP/vtNA9/rXbhw\nnl//9V/n7Nmz91SWoCgKU1NTnDhx8pavectbHuXw4cM9kaUvb/adgPn6TjJbJpdDdkcR+84wDCr1\nOj6fOWcbd4MEv0C6UKVQMHDb3LK373VqtSrPP/88X/vas9v+2uee+zrf/OY3qVarNzzn8XhwOu9c\nXuL19n4NqZmzV8lsmXweOQb8JvL5HF/5ylf527/92219XbVa4bd/+7e5cuXKPQXAg4OD/Nt/+2/5\nkR95D4ryxiVeVW28733v55//839OJBLZ9vseRGbuO6lcZaPvyEI3sb9qzSZOV2e20WWy2cbdYs2f\n+jqpzQHcJxeh683PL/ClL33xnr/+z//8f/DQQw9x3333venxkZERPvCBD/Dss399y68dGxtnYmLi\nnr+3WZTrdQZ95sxepXJl8jmYGpC+cy3DMLh8eZr/9b++dU9fX61W+JM/+RN+9Vd/lUBge5lBRVEY\nGxvjX//rf81P/MRPsLa2hqJALDbExMQErh5Z09BotUBp4/fZ8Jtsp4dipUG+2KLdtOPrkX+Pvabr\nOktLS8Tjcer1On6/n4mJCYaGhnqihGc/mfmmcbdYPvg1DIO1fIVcHo4OSPbqWpqm8corr+z4fV5+\n+WVOnjz5pgVwdrud9773vfzd3/0d2Wzmhq+x2x38wi/8An19fTv+/gdZW9NotBv4/Qohn7mC384A\n3kZr2/HeRRbfSqrVKt/4xjd29B7nz58jHo/fcON4NxRFwePxcOLECU6cOLGjdhxU5YZ5y4VSuU7J\nQ9jn64nyk71WqVR44YUX+OM//qM3lQ8FgyH+5b/8l5w5cwaHHBBy18r1Ov6IORMuu8Xyt0vFSoNc\nsY3etuNzWfcX4WaWl5f4+te/tuP3ee6551haWrrh8cnJST772c/yvve9H5vtjfuwhx9+hF//9V/n\nwQcf7PmBodKo492ou1JVc/2s15Y89Pq/03bF43Fee+0HO36fl19+GU3TdqFFvadSr+EzafYqlauQ\nL0jJw93QdZ2XX36Z//pf/8sNdfPFYoGnnnqK8+fP98TWffvF6js9gGR+OwN4Ti5CN7O0tHxXi3Tu\npF6vkUgkOHTo0Jse31yc88lPfpIPfehDVCqVrRPevF6vJQKqUr1GMGDe7FU+DzHpO29iGAYzMzO7\n8l7PPfcc73//+xkZGdmV9+slxXqNQyPmy141mm3W8zUqJYVgf++vadipdDrNf/tv/+2Wz+u6xle+\n8hWOHj267RIhK2q127SMJj6fQtCEhyrtFssHv5uLDoZ8UvJwvZstVLtXtwuiHQ4Hk5OTu/a9zCRf\nKXNoCAb7zPX71xnA65TLCsciMoBfyzAMUqnUrrxXvV6j0Wjsynv1kma7TUOrEwqqRILm+v1by3ey\nvn63Vw62uAsrKys3LY271oUL51ldXZXg9y7kqxVCQRgM+0w327ibLN3z6s02mUKdakWVk6luQtf1\nXXsvTdNkWuo6jVaLpt4w5QCeylUoFCHo9skAfh3DMHY1YN3Nftgr8tUy4RAM9nlNN4DLLg/b02rd\neUtMgHa7vcct6Q35aplwGGImS7jsNkuPWqlsmUIBAha7A9d1/a6C0d1cQOB0Oi1RxrAd+WqFUNis\nA/hGuZDMmNxAURRCod07sUsW8twoX6lsDODmCiB13WAtV6Eg2wPetWAwCNz++ujxePD7zfW70A26\nYVCsVTt9p9/an5elyx4yxRqFAoQschEql8ssLCxw8eJFcrkcIyMjnDhxgkOHDt10+6P+/t07AnU3\n36tX5KtlBkZgyGQXIcMwyBRrFIswNmyNvrMdiqLcUN9+rw4dOkwwKFO519J0nWK9wmTIfOVC+XKd\nYknHobpwyU3NXTl0aIIzZ87w8ssv3fI1H/rQP2R0dHQfW2VOxVoVj08nEnKb7jTR3Wbpnz5XqlEu\nw9BA7694TKfTfPWrX+Wb33zz9kuqauPnfu7n+NEf/VF812XxDh06xOTkFHNzszv63ocPH+Hw4d0J\nBnqFpuuU61WOhjq1V2ZSqbcoVzQw7DKA34SiKBw5cgSv10e1WtnRe330ox8lFLr5EeFWVaxV8fkM\nBsLmG8Dz5TrlMvjd5lqk101ut4ePfexjzM7O3rT298iRSZ544ok3baUpbi5fkZKHTdaZ679Oo9mm\nWGnRbKh4nObaIH27NE3j29/+9g2BL3RWyv7hH/4Br7/++g1lEKFQiA9/+MM7/v4f+chHZAC/TrFW\nxec3GAh7THfCzuZNo9/VWzeNm7W6xWKRZrO5oxr1kZERfvInf3JH7fF4PExNTUq50HXy1Qp9feYr\neYDe7Tt7aXNXoH//7/89H//4z+DfOA66vz/CP/tnv8Av/dIvMTY21uVWmsNW3zHZbONeMNeou4ty\n5TrlSucOvNcHl6WlJZ555pnbvuYrX/kKp0+fJhx+I0hVFIWjR4/S19dPLpe9p+8dCoU5evRoz3/G\n22XmRQe5Um9lrwzDIJ1OMzMzw/PPP8/6+jpDQ0O8733v4+jRowwMDGz7PVVV5dFHH+WZZ56h0ajf\nU7t+6qeeZHRUBvXr5atlhg+btO9sjDvD0d7oO/tFURQmJyc5fPgwTzzxOM1mC7fbTSQSkdPd7lK1\n0UCxtwgH7IR81t3ibJNlf2vemH7q/TvwZDJJvX77/Xrn5mZJp9dueHx0dJRf/uVfxn0Pn5PT6eJX\nfuVX5K78OoZhmHbBDvRe9mp1dZX//J//M5///G/z2ms/IJGI8/LLL/Fbv/U5vvCFL5BKJe/pfY8e\nPcov//Ivoarbn4597LHHeO973ytTudepNOqo9jbhoJ2QyfbGrm/MNrabKh5Hb8827hVVVYnFhhgf\nHycajUrguw35apm+jYSLJKMsHPxuDuBWONXtbqdvNe3GLZUUReHUqVN89rOfJRAI3vX39PsDfPaz\nn+X06dPS0a5TaTSwOdr0hRwETXYH3tZ0CpUmtZqC9yaLJM2m3W7z/PPP8/rrP7zp83//9/8ff/M3\nL9zTdmOqqvLII2/hM5/5NK5tXGfe//4P8IlP/Ow9ZZx7Xa5SNnXJQ6UMPpdHroli3+U2632l5AGw\naNmDYRjkSnUqFfCHez/47UwN2dD1Wx+TOjAQveWODKqqcv/99/Mbv/EbvPjiizz77LO3XMjj9fr4\n8R//cd7+9rczNTUlF/mbWC8ViERg2IQXoc6MiYHb4e6J7QGXlpb4+te/ftvXPPPMM7zzne+8pxkM\nu93Oo4++lc997nP84Ac/4K/+6q+oVMo3fe1b3vIoP/ZjP8bJkycIh/u2/b16nWEYZMpFjo7AcMR8\nfafXyoWEedSaTZpGnb6wSjRkrj3l94olg99StUm5qmNXHDjsvf8RTExM8Pjjj/Od73z7lq/5R//o\nHxGNRm/5/Gb97+TkJO95z3uYm5vj5ZdfJpPJYBgGkUiEM2fOMDU1xejoqExH3YJuGGQrJe6bhPHB\n3dsLdr/kSrXOTWOPzJhks1mazdsfSFGplMnlcvdcvqOqKsePH+fo0aM89thjzM/PE4/HyefzeDwe\notEoR48eZWJiwjLHet+LUr2GzdEi0mdnwIQD+NbuQr7eKBcS5rFeKjAQgdGBADabjM1g0eC312oW\n78TpdPLRj36URCLO1atXb3j+iSfey5kzZ+5q0FVVlfHxccbGxnjssce2poNVVUVVVRm47yBXKeP1\nawz2uU1X8gBv1MqHe6RW/m5/X3fj91pVVcbGxhgdHcUwDAzDQFGUrf/E7aVLBQYGOjeNZvu8dN0g\nX25QqYCvvzduHIU5GIbBeqnIyQlzJlz2iiWD380B3Ar1vtAZuMfHx/mlX/plrly5wje+8Q3y+TwT\nExP86I/+nxw9eoy+vu1NsyqKgs1mkwU525QuFoiOwPjg3ddPHySbfWdsqDf6TiwWIxAIUioVb/ma\naHSQWCy2a99Tgt3t03SdfLXMxDEYj5qv75RrTSpVHbvqxCHXTLGP8tUKLk+baJ+T/mBvJC12gyWD\n33KtSb0G/X7rrLhVFIWhoSFisRhvf/vbaTQauN1uHA6HDMT7pNFqUWlVOBlRGDPhAN7WdCr1Nq2W\ngsveG4dbDA0N8dM//dP8/u9/4Zav+fjHPy6Lz7osWy4RDOoM9Xvxecx33S7XmtRq4O3xPeXFwbNe\nKhIdlKzv9SxZ/FFttGg0wG3B7WYURcHlchEMBnE6nRL47qNMuUh/P4xE/Djs5sv+VOstmg1w2Xvn\nhklVVd797nfzkY985CbPKnz84z9z1yVBYu+kSwWiUfPOmGyOOb1y0yjMoaVpFOtlIiZNuOwly2V+\nNU2nupG9clpgsZs4ONKlIlPHzXsHXqk3qdd776axv7+ff/yP/wlvf/s7uHjxIuvraWKxIU6dOsWh\nQ4fweGSqsJtqzSYNrUZ/n8pwJNDt5tyTSq1JvQHeHus74mDLlIqE+wyG+n2mOwp8r1nu06g2WjSa\n4Oyh7FU3GIZBsVgkk+mctR6JRAgGg/KZ3kKpVkO1NxnosxMNm2+lOnQyv40GuBy9l73y+XycPn2a\nkydPYhiGLN48QNZLBSIDMBYNYDfpSvVKvUWjDv2+3us74uBaLxWYmISJmDkTLnvJcsHv5kXI3YMD\n+H4pl8ucPXuWr371q8zOzgAwNXWUJ598kgcffJBAwJzZmb1k5pXqmyr11kbmt3f7jmzRd7AYhsF6\nucjJcfPOmMA1ZQ/h3u074mCpNOpoSoNIv82Uh8LsNctd6beyV1J7dU9qtSrPPfccn//8b28FvgCz\nszP8zu98nq9//etUq9UutvDgaWkauUqxE/yauO6qUu9M3fZa2YM4uLKVMi5PmwETr1TXdYNKrUWz\nqeCUcUfsk1QhTzQKY9EgqmrOhMteslzw26t1i/tlbm6eP/uz/37L57/0pS8yNze3jy06+FKFHP0D\nBmODflOuVN8kN45iv63mswwPweSIeU+8qzZaNJvgtNtRTTrrI8yl2W6TrxWJxRSODIW73ZwDyYLB\nb2fqthfrFvearuu89tprd3zdq6++unX4hdVpus5aMc/wEBwdvfnx0Wag6wbVRptmU/qO2B/FWhVd\nqROL2sw9Y7Kx2M1lN++NrzCXZCHHwIDBuMkTLnvJcsFvLy/a2WuGYdz0hLjrXb16FcMw9qFFB1+6\nWCAQ0hiOekw7bQtQa7RoNAwcqkOyV2JfrOSyDA93sr5mPpJV1pmI/dTWNNZLeWJDMGXihMteM+8V\n5R41Wm1aLXDaLLfWb1f099+5M233tLhepRsGyUKO4WFzZ30BGi1ta+pWiL1WbTSoaRUGB1UOm3za\ndmvMkb4j9sFaMU+oT2c06iXs742TOPeCpYJfwzBoazqaBjZZ1b1tqqryrne9846ve+yxx2TVPJ1T\nqVyeFkMDTmJ9vm43Z0famo6mS78R+2M1n2UoBkeGQqY8EOZam2OOXBPFXtMNg1Qhz0gPJFz2mqV6\no6YbW4GvWbeb6iZFUThyZJKHHnr4lq+57777mZyclM8XSOazDI/A1Ei/6T+PVluTm8ZdpOs6mqah\naZqUCF2n0WpRqJeIxRRTL3Tb1NZ02tJ3xD5YLxXwBdrEIi6iYXMnXPaapeZh5A585yKRCP/iX/wL\nnn76ab773e+i6xoAqmrj8ccf58knn2RgYKDLrey+fLUC9gZDUXtPHCup6Qa6DOA71mg0mJ+f59y5\nc1y+fIlgMMg73vFOJicnGRgYMP1N0m5IFnJEowYTsSAel/nrZFttjXqthaqVcBkKfr9fxiCx6wzD\nYDWf48hRyfreDesFvzrYFLnw3CtFURgbG+OTn/wkH/zgB0mlkgDEYjEmJg7hcrm63MKDYXUj6zs5\n3NcTeyxuZX6l79yzWq3G9773PX7v934Pw3hjN5Rvf/vbnDhxkn/zb/4N4+Pjlg6AW5rGernAg5Od\nGRMzMwyDRCLBd7/3t/zpl15nfS6H2+bgiSee4MEHH2RychK71AGLXZKrlHG4mgwNOBgZkIOm7sRS\nPU+mbnePy+Xi2LFjHDt2rNtNOXBKtRpNvcpgVO2ZYyVl1mRnDMPg4sWL/O7v/tebPj89fZk//dM/\n5Rd/8Rfx+aw7XZnMZ+mP6IxGfQR95r2RNgyDS5cu8clPfpIXzi6C/S1QMKCt8ad/+ieoqo1f/MVf\n5F3vehcO2QVC7JBhGKzks4xOdHZHsfIN9N2y1EjW1nS0tgS/Ym/FM2uMjcHUSJ/pF+tskoWiO1Ov\n1/j6179+29e89NKLLC4u7lOLDp5Gq8VaKcfoCBwfj3S7OTuytrbGpz71KV544QVQVMAG19R267rG\nf/yP/5Hz589LzbfYsUy5hOqoMxyzM2HiY8D3k6VGsramo8uKdbGHMuUShr3OyJC9p/ZYlOB3ZzKZ\nLK+++uodX5dMJvehNQfTci5DLGZweDhAX8C8e2IDnDt3jv/9v/93539uEvwCGIbOX//1X1Or1fa/\ngaJn6IbBUnad8XE4OTFg6j2x95OlPqXNVbcydSv2QucilGZiHE6MR7D30EVoK/iVmt89ZdUsYLXR\nIF8rMDqqcHLC3AtmdV3nueeee+MBRQXUG4Jf6JyGuby8tH+NEz0nmc/hC7QYjbl6YnH1frHUSKbp\nBoYOqgzgYg+sFfK4vS1GYs6eqfXdpOkGhiE3jveqr6+Phx566I6vGxoa2ofWHDzxTJrRMZgaCZv+\nOFZd17ly5cobD2wFvzd7tUG1KplfcW9amkaykGV8HE4fjkqt7zZYaiRTFYXO74Y1syti77Q1jZV8\nhokJOH2o9y5CqqqAYt3M5E55vV5+/Mf/4W1f88gjb+HQoUP71KKDo1Ct0DAqjA7bODZm7lpf6OyI\nE4vF3njgDn3G6TR3sC+6ZzWXoT+iMT7kk319t8lawa/aCX51GcDFLlvJZ+nr1xiLeYn1+7vdnF2n\nALSGmawAAB93SURBVKoEv/dMURTuu+9+fv7n/9lNn5+cnOLnfu7nLLfTg2EYJDKdUqFjY/04HeZf\nIKqqKj/xEz9xzSMGoMNNbognJ6cYHh7et7aJ3lFvNVmv5Bkd6yRcxPZYaqszhc71RwZwsZsarRbp\nUo4HHuhMPfWircxvtxtiYl6vlw984AMcO3aMV199lQsXLhAMBnn88ceZnJwkFov13IzBnayXi6iu\nBiNDDo4MhbvdnF2hKAoPPfQQU1NTzM7Objx6857z5JNPEgr1VomU2B9L2XWGhgwmR0Km3hawWywV\n/G5mfiX2FbtpKbdObMjgyEiQsN/d7ebsCVVRJPO7C9xuN6dPn+bkyZPouo6iKKgWPW5d03WWsusc\nO957q9QPHTrEF7/4RT7ykY+wWjdAMTrZl2u6zz/5Jz/NQw89ZMl/e7Ez5XqNUrPE1LD5F4h2i6WC\nX5uqotpAv+Z0JSF2olyvUawXefhkb1+EbDYVVQVNk76zG1RVtfziwWQhRyDYZjTmZrTHTqRSFIW3\nve1tfPOb3+S/fOkbfPF/XKKSqwNw5swZfuzHfoxTp07h9/deiZTYW4ZhEM+kGRuD4+P9uJ2WCuN2\njaU+NbtNxaZ2Mg5C7JRuGCykU0xMwLGxPrzu3j2pyW5TsdlAb0nfETtXazZJFTPcfz/c16Or1BVF\n4cEHH+SntQDBcIoBRx9+t4dodOD/b+9OfuPKrseOf2ue53kkq4rFWZK7ZVvdzq9/Wfj/cOBF1gay\n98Ib/wUGvE4QBAiC/AJkF2flXYzYv8DtbrVmcWZVsVjz/N6rl0WRbLVas0QWWe98AIJUN9U4ovq+\ne+65592L0+layD+zuHwn3TbYhuTSVlYW6Cz5q2a85NcyO4pGiI9VaTWxusbk0jZWF+At9TexWma7\nJrJwFJ/CTr1KOq1TygaIBNzzDudS2a0WYrEQGV8Ov2ux/6zick1UlcNmnfUN2C7EF+os+atmqJ/c\nefKrygQuPtJYUah0Tiksw+1SYqH6FV9Fxo74VE66babmAbmsxRBvqdusFiyycBSfwN5pjVhcYznt\nJRVZrFahq7bYM/ZLbFbz2UNIm3co4obbqVdJpqYUM35DnK9os5ixytgRH0nRNA4aJywvzypXi3C0\n2dtYLWYsVlBl7IiP0Oz36Ktdcjkzt4rxeYdz4xks+bXgdJjBPEXR5EEkPsxJt41Cn3zWwtaCHm32\nMpfDhsMxq3gL8aF261UiMY3ljMcwV7G6nTJ2xMdRNY2depXCMmwuRXE5Fvf9kqtiqOQXwC2TuPgI\nE1XloHFCsQjbhRgOg7xp63HacDhhJONGfKBmv8dA7bKUN3O7mHj7b1gQF3OOKmNHfJj9xgnBsMpS\nxkUhtRjnYc+b4ZJfj8uO0wFjZTLvUMQNtFuvEktoLKc95OLGOZzeYbfitJvBpKHKrol4T8p55aoA\nW8vRhT4Z5WUep+1szpHkV7y/9qBPe9RmecnEnZLxLsK5LIZLfmUVLj7UabfDWO+Rz5q5s5KcdzhX\n7mL7VsaOeE979RqRqMpyxs3ygtzk9q6k7UF8KG065fnJbNG4sRTB55ab3D4VwyW/HqcNp1MmcPF+\nxorCXqNGoQC3inFDHizukUlcfIDTboee2iGfNxuycuW0W3E6TGi6Kic+iPeyU68SCCnk00450/cT\nM1zye74Kl95F8a6mus7T2jGptEYx6yWfME67w4vcDun7Fe9npEzYPa1SXoFbxRgel33eIV05k8mE\n22nDbpeFo3h3J902A7VDoWDms3LScIvGy2a85FdeeBPv6aBRx+ocUliy8VnZeO0O56TtQbyPqa7z\npHJEJjdlJeczXLvDi9wO2XEU724wGbPfqLGyAj9ZiUu7wyUwXPI7O7LJhDJVmOr6vMMR11yz36Mx\naFAqmfi8nMJmXfxzSV/H45SXRcW726vXcHrHFHI2bpeMc7rDq7jP2+2k6CLeQptOeVo9JpefUs77\nDfVi9VUyXPJrNpvwue24XNAfjeYdjrjGxorC85MKKyuwXYwS9rvmHdJc+dx23G7oj8fosnAUb9Do\ndWlPWpRKJn66ljb0ohHA73bgckN/LHOOeLPdeg23f0whZ+eWgY4EvGqGS34Bwj4Xfh90R8N5hyKu\nqfM+32Rao5j1UEqH5h3S3LkcNvxeG1a7xnAi1V/xaiNlwk69wkpp1ucb8DrnHdLchf0ufF7ojAbz\nDkVcY/Vuh57SplgwcXc1jdViyBTtShjyJxvxu/B6oSsPIvEah406FseQ4pKVz8opedngjCwcxZtM\ndZ0n1WMy2SkreR+FlCwaAbwuOz6vBcyqtD6IVxpOJuw1qpTL8JOVBH6P9PleJkMmv2G/C58PeqOR\nbN+KH2kN+tTP+nzvrqax24y9ZfuiyNnYkYWjeJX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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -577,21 +576,21 @@ "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\n", "\n", - "We then compute a new mean and covariance of the transformed sigma points. That mean and covariance becomes the new estimate. The figure below depicts the operation of the unscented transform. The green ellipse on the right represents the computed mean and covariance to the transformed sigma points. " + "I use a calligraphic $\\boldsymbol{\\mathcal{Y}}$ to denote that it consists of a set of sigma points. We then compute a new mean and covariance of the transformed sigma points. That mean and covariance becomes the new estimate. The figure below depicts the operation of the unscented transform. The green ellipse on the right represents the computed mean and covariance to the transformed sigma points. " ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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T5NKlS5PdGb6unOG73/0u+/btmyxnuBP9I+ME4yP4ch+c2fC5JpMxsaiWeVeT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\n8asf/Yr7H71/RvczFcsxMWnQ29DJld2NuByvHZo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nx54MlmVx4cKFse4MtypneOqpp9izZ89YOcOd6B4K4Y8NkZc9c2bDp5t02kJX\n9VlXky7EVCPhV4hJ9si6eRw628Wx7nYqjbopNfv76RDr9frwer2fG0xTqSRtbS0cPvwssdgx4BTQ\nj6rqmGb82kI1DZerkKqq3dTU7KG09EvYbBOzYYJTc48G4PbDfGgESRsf8sdf24jPPTUD8J2UMzz2\n2GN89atf/cxyhjthGCY9/hD++DBLq6fOv7fZJm2Mhl/HLO9IIkSmyW+gEJOsOM/LpmXldHV10t5/\nlfnZKzI9JGA0xLa3t3P06FHC4TAAXq+XdevWUVVVhc12Y/lAJNJFR8cvuXDhXxgaOszoEp7kta/a\nMU2D3NyNLF78TSorH8bnq5m0c3FoTpblbeR89xGOKUH+1nWM//XJDdj0qTHjNjAwMNad4b333rtl\nOcPevXtZu3YtmnZv4x4MRAnGgzgdYLfJ5fZMSaVMmfkVYgqQ8CtEBuzeWM+H57v4qKeTcKo2450f\nLMuivb2dt99++4bPh8Nh3n77bbZt20ZVVRl9fYdoa3uF1tYDxOP9WJaJaSYBG2AChUAtsBGoI5XK\npqpqD17vF5+tvFd21cGSnPWc7nifI85h/sl3mt969L6MtJj6ZDnDs88+S0NDA3BjOcP69et5+umn\n2b17NzU1NeN6/P6RCCPxANk+ecrPpLRhYVN17FPkTZgQs5U8EwqRAQXZbh5cXUtffzNNredZlrsx\no30/w+EwR44c/dRnLaAHuMg77/wF0I6q2j61UM2OaS4FVgALgaPAC8BJYCHh8Br8/lV4vQsm83TG\n2DUHi3PXcbbxEL92dlOY4+HxTZMzlkQiwcGDB3nuued48cUXJ6Sc4U4NjEQJJgLUFMtTfial0xY2\nzYZDZn6FyCh5JhQiQ3ZvnM/RS1309vgZiHdR5KrI2FjC4RCRSPgTn3kfeBFIA2lM00TTRheqFRau\nYc6c/VRWPkw8nserr776ift9soPpWeASb775LxQUrKSu7hvU1OzB653cDT48uo963youXvyIF+wN\nFOV42LikckKOdbtyhoqKihu6M9xrOcOdiMSSDEciJMwYHnfWhB9P3FoyZWLX7DhncA9qIaYD+Q0U\nIkNcDhtPbF5Id/9pLp29RJ6jBF2dKr+SHUAc0IAsYBmrVn2XJUv2oesfL5gKhUJ4vd6xGmHYCmwA\nLgAfAZdRFJ3+/qMMDp7k6NE/xuMpZ+7cp6mt3Ut+/opJmfHOcxRRZSzhwvlz/JP9LAXZbuZX3vsG\nD9fLGQ60HLsKAAAgAElEQVQcOMAzzzzD1atXURRl0soZ7kT/SIRAfIRsr012FcuwWMIky+6c1u33\nhJgJpsorrRCz0obFFRw820ZPzzDtoavM8S3KyDiud3X4OMQ+ymjtbj2Qh9frpa5uzw3Bd/R+owvi\nbqwVdgGrgdV8+csP4HJ10dz8HC0tz2MYMUKhFk6d+gHnzv0lmuaitnYfc+Z8hbKyLbfdzOJelLlr\niIcinDvfzN+8dIw/+fomivO8X/hxksnkDd0ZwuHwTeUMe/bs4atf/SoPPfTQhJYz3ImBkSiBRJDs\nfHm6tyyLZCJJMp4kEU+M/plIkIiN3k4mksxZOIe8orwJOX48YeJ0u/BK+BUioxTLsqzP+kIgEBi7\nnZ0t27AKMVFae0f4j//0PidPKCz2bcJny5n0MViWRXNz000L3q7btm0bc+bM/cyZwzvtEmFZFkND\nZ2hpeYGmpmeIRDqxLAPTTKHrHizLpLx8O3V1T1NVtRO7ffyfdyzL4mLgOLacXu5f6+F/e3rTHQWR\n6+UMzz77LO++++5N5QzFxcVj3RnWrVs3KeUMd8I0LV4/2sCx7hMsrXdPyU4PlmURi8RuHUqvf/7a\n7UQ8QSKeIB6NE4vEiEVixKNx4tE4iVhi7H6pZIpUIkUymSSdSpNOpTHSxi3H4XQ7Kaks4bt/8l2W\nrls67udpmhYnLgRZXbaaXevrUVWZhRdiotwuw0r4FWIK+Pk7F3j2jWbaGryszN+Mpkx+ePqirc4+\nybIs/H4/oVAQAJ8vi7y8vM+9zB4Od9DWdoCGhn9hcPAUiqJiGPFrWxybE1YnbJhpzgx/SGFFgC+v\nz+OPntxw025blmVx8eLFsc0mPl3OYBgGK1euHCtnqK2tHbfxjafhUIw3TlymKXiJZfWZnYG+lWf/\n+7M8+7fPott0FFVBVdXRfzfX/+lYoz8Py7QwTRPTMEkb6dH1mLehqiq6TceyLFKpFC63i8LSQspq\nyqhdUEtpdSmlVaMfvhzfhJaFxOIGV5tTbKhaxbZVcybsOEIICb9CTAuptMEP/r/3eeeDEHq4lrqs\nJRkZx91ucnG3ofm6ZDJAR8cvaWz8KZ2db6EoKul05NoGGSoeT8W41gknjDinh99nzvw4j24q59uP\nrCSVSt3QneGzyhkefvjhse4MWVlTf/FYc/cw71y4QFjpYk7l5G9uYaQNgsNBRvwjBIYCjAyN/ukf\n8NPf1Y+/309HUwfhQPj2D3YLNrsNm92GaZok40k8WR4KywqpnFtJzfwaSqtKKakqoaSyBLc3cxt8\nDAdS9Pfa2FS3kvWLMre4VYjZQMKvENNEe1+A//Tj9zl23GK+az25jsJMD+m27qVc4lYMI0lPz0Ga\nm/91rE44nY6jKKBpznGrEw6nApzqf51s21GSvSe4ePrYZ5Yz7N+/n3379k2pcoY7dfJqD+83nMGb\nG6Yof3x2uItH44wMjYx9BIYCBPwBBroHGOwdZHhgmMBwgEgwQiKWwGa3oekapmlipA0Mw8AyP37Z\nUTV1bGb3VhxOB5pNw0gbpJIpsnOzKa4spqquiqp5VZRWllJaXUpReRF2x9Ssp+0ZSJAKZbNlwXKW\n1BZlejhCzGi3y7CyAkKIKaKqOJu9D9QTDF7mysXT3Gfbgk2dmi/k1312f+CPHT16lOLi4i+0yYWm\n2amo2E5FxXYeeODvbqoTTqWCXL789zQ2/vQL1wlblsXw8EXa2g7Q2PgMgcAVLCwsM4XT6SSVSrFu\n3bopX85wp4ZDMcLJMCXuWz/VG4ZBaCQ0OjPrH2FkcISAP8DwwDD93f34+/yMDI0QGgkRDUcxTRO7\n3Y6iKhiGMRpoP1FLqygKmq6haRpOtxPTMInH4thsNnzZPny5PnILcskvzqewrJDB3kEOvnoQTddQ\nVZVUKoVlWuQW5lJaWUp1fTVKVhar76unpKqEwpJCtGm4SUQ0ZpCly2I3IaYCCb9CTCEPr63jXEsf\nQ0PDNPnPsyD7vkwP6XPd3B/4HPAPjHZ88BAOZ/H++69SWFiPy1WEy1WI0zn64XIV4nDko6q3DjKK\nolBQsIKCghWsWfNnn1kn3N7+Cl1dv8KyDAoKVjJv3jeprt6D1zvay/f6THJLy3O0tLxIOh3GMBJY\nlomuu7GwyKlaw+aHt/P//qc/oLBgYlb6T6ZYLEZHZzcnThzjfMsxei8kCfgDDPYOMtjz8exsOBAm\nHouj23R0XccyrbFAa5rm2OOpmoqmaaN1uYoyuoAskcblcZGTn0NOfg65hbkUlBRQUFpATl4O2fnZ\n5OSP/pmdl33LGdlwMExJRQkFJQWUVJVQWlVKbmHuDVcLfvr2OVZsHP9FaJMpHDUoy/GS63VmeihC\nzHpS9iDEFNM/HOHP/vkghz9KU2W7jyJneaaHdEs9Pd288sorn/jM68ArjK5WMvnkqiRF0VFVHUUZ\nDVCmmcIwkui6C7s9G4cjD5erGLe7FK+3Eper+Kaw7HQWommjIerz6oRBxW7Pxm73EQ53oigahhFD\nUTRUVcfpLGLu3CepqdlHQeEazo58SPmcIPsfrOYbDy6bvG/gHTJNk+HhYfr6+ujv76e/v5++vj56\ne3tpb2+ns7OT/v5+BgcHCQQCpNNpHA4HJgpGOoVpGpiGyfWne0VR0DQNVR8NtaZpkkqk0HQNt89N\nVk4WOQU5o7OzpYXkFuaOBtm8bHIKRv/0ZntR1YntHnGupY9zzf08++vzfG3rEpbOKWJpbfGEHnMi\npA2LMxfDrC5fxSPr5kunByEmmJQ9CDHNFOV6+OrWRfgDZ7lw9hxZtlycWuYW6nyem/sDfxkoB0JA\nGF2PUFrqJJkcJBYbIJkcJpkMYlkGmubAZvNiWQbx+BCxWC/Dw+fHHltRtE8EZg3LSmMYcVTVjt2e\nhcORj9NZiNtdyoIFv0002sXAwHHC4TYgRTzeTzzeP/Z4TmchtbX7Wbr0D8jJqb/hPOqz7+Ns80He\nOtbGsjnFLJs78QErHo8zMDBwU6Dt7Oyko6OD7u5uBgYG8Pv9hMNhbDYbdrt9rHNBOp3GMD4uN9A0\nDV0fncG12+0kEklSqSQOl5OcnGyyc7PJLbo2O1tSQE5BDjl5OWNhNjsvG4drfOqCx8vS2uKxsPv0\ntuk78xuOpPHYPeR6XRJ8hZgCZOZXiCnIsiz+9qVj/PJQH92tXlbkbUKfwA0g7tbdLnhLp6PE46OB\nOB4fGPszGu0lEukkGu0hFusnkRgimQxiGAk0zYGq2rAsE8tKYRgpRmeXv4jRNloeTyXFxespLt6I\n11uNy1XIiBUl7O5n86Y8/uNvfgmf+4sFQcuyGBkZGQux1wPtJ2dne3t7GRoaYmRkhGQyidPpRNM0\nDMMYC7SfnJ29HmZ1Xcc0TRKJBIqikJOTQ35+PkVFRVRUVFBZWUlZWRlFRUUUFRVRXFxMV8Dg7EAr\nBcUp8nOnd53puZa+aTnje11XXxwzkseWBUtZLIvdhJhw0u1BiGkqlkjxfz37Ae9/FCIyUMCSnHWo\nytTbpOBe+wPfSWs1w0gSjw8SCDTQ0fELOjreZGTkAgCmmeJ6U1hFUQEVy0qjqjY0zYFlGRhGEstK\n32IUCqpqR1E0TCuJZZm4XG6KCvPJy8sjLy+P7Oxs3G73WIlALBYjEAjg9/sZHh5meHiYYDCIpmk4\nHA4syyKdTo99XKeqKjabDV3XxxZ3JRIJPB4Pubm5FBQUUFpaSmVlJZWVlRQXF98QaIuKivB4PHf0\nc3nnVAuH204wt0bH7Zp+C8RmkistEYrsNWxftpiygqnZb1mImUTKHoSYplwOG7/3+FpC0UMcOTZI\nY+gc83zLJrQR/92w2ezMmTOXoqLice8PPDqbeonW1pdpanqWkZHLn9gMw4VlGRQWrqWu7mmqq3eT\nlTW6eYBpGiQS/htmlePxAUKhNvr6DuP3nyeZ9F8biYVpJm4YWywapq0tTFtb2x1/HxRFGStJAHA6\nneTm5pKXl0dpaSnV1dXU1tZSW1s7NktbXFxMfn4+uj6+T8WWZRGNp4inEjjs03vWdyaIRA08Hi+5\nPlnsJsRUIOFXiCksP9vN7+1dSyT2IcdPtNMZ9VDpqcv0sO6ZZVm0t7ffVC4RDod5++03WLnSRzx+\nmNbWF0mlQjd0ZwCF2tr9zJ37FSoqdqDrrmslFP10dr5JLNZPLNZPJNJNJNJOJNJNLNZHIuEnmQxe\nW+w1Wm9sGMlrM8ef3WP2+oIu0zQ/3nns2v8D6Lo+NhtsmuZoD9trF9NisRjJZJJgMEhnZycnT54c\nm+l1OBxkZ2eTl5dHUVERZWVlVFRUUFJSQmFhIYWFhRQUFIzddrlcAHzve9/jueeeY+HChaxevZpl\ny5axaNEiFixYgNv9cV14LJEmlkqg66BpU+vN0mwTjRto2PA5XbgcU690SYjZSMoehJgGTl7t4f95\n/jinT8Fc12oKnKWZHtKYuyl7CIVCHDhw4BNt0uLAaeAYcAVQgSQw2vtV173k5i7E4cjHNJPEYn3E\n4wMkEiOk07Fr9cA6lmVimulrgfbjeuDrC+dUdfT9/mgZhIHNloXTmY/LVYimuUmlwgSDjSSSI4zu\nq2uOBc8HH3yQp556ip07d5KVlUUkEmFwcJCBgYEbPnp6eujs7KSnp2dswVogECCVGu0lrOs6hmGM\nlUR8ctHap8siDMMgkUigaRpZWVkEg0GSyeS1c1LweDyoqko0GiU3N5cFCxawZs0aaurqGbYcKMUm\nK5YUjOePW3xBPQMJ4kEfD8xbxsp5U+f3VoiZTGp+hZgh3viokR//8hLnzmgsyd6Iz5aT6SHd8YI3\nyzKJxweJx0dnZbu7L3Pq1HtAAPADLcDQp+6tXtveWME0DSwr9YmvKaiq7ROdIIxrnSAcOBw5OJ0F\nuFwleDzleL3VuN3F11qnFeF0FuF2F2OzZd2yLGMwcIXDl/+a1NCvCfS3oqkq8Xgcp9OJaZqsXLmS\nb37zm+zZs4fKyso7+l7F4/GbwvLg4CB9fX10dHTQ09NDX18ffr+fkZER4vE4drsdu92OaZqfWUP8\nWRRFweV2Y1qQTMTw+DyU15RTt6SOmgU1VM2torKuEo/vzmqHxb253Byh2FHDtqWLKC+c+ltiCzET\nSPgVYoawLIt/efMsB95rp+GygxV5mzLeAu3mGdxe4G1gGAiiKBE0LUE6HUXT7GPdGkwzdYtyAwXQ\nGJ3xta7NzvpwOHJxuYpwu8vweCrxeiuubZrxcaAdnb0dv1ZdreHLxN0NPLBaY5EvwLPPPsOvfvUr\nFEUhGo1is9lQVZXKykqeeuop9u3bx/Lly8etJjudTjM0NHRDWP76179+2/B7pzxZHsqqy6hbUse6\nreu474GpvaHKdGSYFqcvhlhRvJJH1tVjt8nCQyEmgyx4E2KGUBSFr29fylBwtE3YhfaPWJ57f0Zb\noN28w9tx4P2x/7MsDcuyY7N5sCyTdDqKqtqw23NIJOxYlgfIAfKBLMAHZOF2F7Nz51fIy6vK2AK/\nSs88Tgx20tgV46EnNnLgwFMkk0kOHjzIz3/+c1544QVisRjNzc384Ac/4C//8i9xu93s27ePJ598\nki1btmCz3f3PRtd1iouLKS7+uMXXxYsXuXjx4m3v6w/GGAgP43CY2Gyf//0L+oMM9Azc9TjFrQXD\nadw2L/lZHgm+QkwhMvMrxDQTjaf482cOceijMPGhIhbnrM1YQLx5h7cu4ACjgTYP8LF27TbKyxdd\nm6EtRNddd90feLINxntoSx/ngQ12fvBbW3E7Pw6zlmVx5swZXnjhBX7605/S1dU11q/3+uKz7du3\n8/TTT/Pwww9P6vPooXPtfNB8gspK8HlkjiNT2rpi2FJFfGnhEuqrpPZaiMlyuww79ZqGCiE+l9tp\n43v71rF8iR08/TSEznKL97AT7npLs4+VA78LPAXswOt9iLq6vRQWrsbrrULXRxePKYpCVVUV27Zt\nu+H+Xq+Xbdu2UVWVuRnfT8p3lKAn82lpT/L2yeYbvqYoCitWrODP/uzPaGxs5MqVK/zwhz9k3bp1\npNNpTNPkwIED/OZv/iZFRUWsX7+ev/mbv6Gjo2PCx51IpkmZaWx65r+Hs9lIKE2OM5uiXKmvFmIq\nkZlfIaappi4/f/GzI5w+Y+BIVDA/a8WkB8Z7ncG9000uMimQHOJK7EMe2KjzX767DY/r9n1zA4EA\nr7/+Oj/5yU94++23J61O+LrXjzZwtPM4yxd60KXVWUbE4gaXGxOsrVzFjjWZv4ohxGwiC96EmMGu\ntA/y3144xskzafRoGfXZKyd9F7h72eFtujg3fISC6gG+89g8Htu04Avd97PqhOPxODC6EcZ41gkD\nmKbFK4evcKL7OGuWyXN3pnT1xTEiOdw/bykr6koyPRwhZhUJv0LMcE1dfv76uaOcOpuGcDELs1eh\nKpO7uGY6zODei2DSz+XYB2y+38b/+W+33fVmBZZlcfr0aV588cUJqxOOJ9O8dvQyFwbPsHKRtNbK\nlLNXQszJqmfb8gVS9iDEJJPwK8Qs0NY7wl89d5STZ5KkA4UsylmDNskBeKY76/+Q4jlD/O4TC9mx\ndnx22Wtvb+fll1/mJz/5CadOnUK91k/Y5XJhGMZd9RMORhK8fvwizcFLLJnvG5dxii8mGjO42pxk\nbcV9PLh6Lqo6M94ECjFdyII3IWaB6pIc/v1XN7BmpQN7zgAXho+SNsenH6wYVeGpo7sLDp5tG7cF\nhlVVVXzve9/jyJEj9Pf384//+I/s2rULGG11dvToUf7oj/6IefPmMW/ePL7//e9z+vTpzz1+Km2Q\nNg3Z1jiDhkaS5LvyKc33SfAVYgqS8CvEDFFRmMUff20ja1c5cRUMcX7kCGkzdfs7ijuSay8kFXXR\n2h3lcvvguD9+dnY2X/va13jllVcYGRnh5Zdf5rvf/S5ZWVlomjbWT/j++++nqKiI3/7t3+btt98m\nlbrxZ2xd++8MqTiZdizLYnA4RYE7nwrZ0U2IKUnCrxAzSEmelz/+6kbW3efCVzTM2eHDpMxkpoc1\nIyiKQomrmp4eOHimbUKPZbfb2b59Oz/60Y8YGBjg0KFD/Mmf/Am1tbWYpkkgEOBHP/oRe/bsIScn\nh8cee4yf/exnBINBLMtidGJY0m8mhCIGNsVFvjeLXJ8z08MRQnwGqfkVYgbyB2P88F8Pc+x0hKEe\nH0tzNmAfx61/Z6uEEefk8K9YvwH+4ncfJMsz+d/T29UJL122nMUbtlC5poZ1a6smfXyzXVN7FI9V\nwgMLFrNANrYQIiNkwZsQs9RIOM5fP3eEo6dC9Hd6WZq7HofmyvSwpr2LI8fIq+rl9766iAdXz83o\nWD7dT1hVVSKRCJquoygKhaUFbN61mQ0PbqB2Qe2M6b4xVaVSJmevRFhevIIdq+fdsCOgEGLySPgV\nYhYLRROjAfh0kM42J4uy1+Cz5WR6WNPaQLybfu0Eex/O5999ZWOmhzPmej/hf/rxT3jp5RdIJhKk\nU6MlL3a7HYfLwYYHN7Bp5yYWr16MbpNtj8dbd1+cRMjHhrlLWbOgPNPDEWLWkvArxCwXiSX525eP\ncfSsn6tXNOZ6l1PknDkvzLFYPx988Pv4/WeJxwcpLt7IypX/O0VFa25732i0lzfe2M3u3e+j63dW\nn5k2UxwdeoP774e/+l92TLnZvZ6hEG+ePs+Zy+/SfeEM7732HkO9Q5imiZE2cLgcYMHyjcvZsmsL\nqzavwu11Z3rY055pWpy5HKI+bxFbl8+nMEd6+wqRKbfLsNqf/umf/uln3TGRSIzddjqlaF+I6cpu\n01i3sIKkmSCcHqGhp4dU2iLblj/tL4ObpsGLL65h1arvs2HDXxAKtdDY+BOuXv1nKioewuOpuOV9\nk8kQr7/+MCtX/h/k5S2542OqisZIYhDdHaW+JpuygqnVSzcST9HcN4CWrfDlh1ex+5u72frYVorK\niwgOB/H3+0GBjsYOjr97nOf/5/Mcf+84qWSK3MJcPD4JbXdjOJgmHnEwv6iGxbVFmR6OELPa7TKs\nhF8hZgFVVVg2t5jcLDuDsQE6hoYYigTJsxdP+nbI48kwkvh8VVRVPQJAaekWrlz5n6TTYQKBq9TX\n/8Zn3s80U7zxxh7q6r7BvHlf/8LHTZlJQuYAxYUaK+eV3sspjLtEMk1z7xCB1BCFeaNbS3t8HuYv\nm8+Or+xg1zd3UVVXRSqVoq+zD1VT6evs4/SHp3ntJ6/x6xd/TXA4iDfLS05BzrR/gzRZWrtiFLsr\nWFFbQa5PauuFyCQJv0IIYLRVV21pLvMrc+kN9TEUCtLu7yPXXohNtWd6eHdFVXVycxeO/b+m2TGM\nON3d7xCJtFNT8zhud8lN93vnnW+Rn7+c5cv//V0dV1NtdIRayStIs23VnLse/0RIGybNPUP44wMU\n5d/cjcLusFM9v5otu7aw99t7qV9Rj91hp6+zb7SN2nCAC8cv8M5L73Dgxwfoae/B4XRQUFKAqk3f\nN0oTKRoz6Os3mZc/h/vml8nGFkJkmIR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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -606,7 +605,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The mean and covariances are computed using these equations.\n", + "The mean and covariance of the transformed sigma points are computed as:\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\sum_i w^m_i\\boldsymbol{\\mathcal{Y}}_i \\\\\n", @@ -616,14 +615,21 @@ "\n", "These equations should be familar - they are the constraint equations we developed above. \n", "\n", + "In short, the unscented transform estimates the mean and covariance of a Gaussian passed through an arbitrary, nonlinear function. I hope you can envision how we can use this to implement a nonlinear Kalman filter. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "### Unscented Transform Example\n", "\n", - "Earlier we wrote a function that found the mean of a distribution by passing 50,000 points through a nonlinear function. Let's now pass 5 sigma points through the same function, and compute their mean with the unscented transform." + "Let's see how accurate the unscented transform is. Earlier we wrote a function that found the mean of a distribution by passing 50,000 points through a nonlinear function. Let's now pass 5 sigma points through the same function, and compute their mean with the unscented transform." ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 20, "metadata": { "collapsed": false, "scrolled": true @@ -638,9 +644,9 @@ }, { "data": { - "image/png": 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UCiGZTCpNCttBMsNj9GgfN+IEON09ZhZrsKthSLLBLwXsc5lzq6nPtiEquwjZ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sb+/fttDRUSmUKhYLN2SGK4+K3Ftrnbu+iuzbFYLKR3Of7445HL5UZtv1KtPqUetuCoICpRH1Kp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\n9zkTBEHZn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+PZVfz9LTr5+ePaeTO5KybMZrAwMDA4P9H4YYNRByZaHVFXzIS1+PXjPIiVRJ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -652,22 +658,17 @@ "from filterpy.kalman import MerweScaledSigmaPoints as SigmaPoints\n", "import scipy.stats as stats\n", "\n", - "def f_nonlinear_xy(x, y):\n", - " return np.array([x + y, .1*x**2 + y*y])\n", - "\n", "#initial mean and covariance\n", "mean = (0, 0)\n", - "p = np.array([[32., 15],\n", - " [15., 40.]])\n", + "p = np.array([[32., 15], [15., 40.]])\n", "\n", - "### create sigma points - we will learn about this later\n", - "### in the chapter\n", + "# create sigma points - we will learn about this later\n", "points = SigmaPoints(n=2, alpha=.1, beta=2., kappa=1.)\n", "Wm, Wc = points.weights()\n", "sigmas = points.sigma_points(mean, p)\n", "\n", "### pass through nonlinear function\n", - "sigmas_f = np.zeros((5, 2))\n", + "sigmas_f = np.empty((5, 2))\n", "for i in range(5):\n", " sigmas_f[i] = f_nonlinear_xy(sigmas[i, 0], sigmas[i ,1])\n", "\n", @@ -679,10 +680,9 @@ "xs, ys = multivariate_normal(mean=mean, cov=p, size=5000).T\n", "\n", "plot_monte_carlo_mean(xs, ys, f, ukf_mean, 'Unscented Mean')\n", - "plt.xlim(-20, 20)\n", - "plt.ylim(0, 100)\n", + "plt.xlim(-30, 30); plt.ylim(0, 90)\n", "plt.subplot(121)\n", - "plt.scatter(sigmas[:,0], sigmas[:,1], c='r', s=40);" + "plt.scatter(sigmas[:,0], sigmas[:,1], c='r', s=30);" ] }, { @@ -705,7 +705,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can present the entire Unscented Kalman filter algorithm. Assume that there is a function $f(x, dt)$ that performs the state transition for our filter - it predicts the next state given the current state. It is the analogue of the $\\mathbf F$ matrix of the Kalman filter. Also assume there is a measurement function $h(x)$. It takes the current state and computes what measurement that state corresponds to. It is the analogue of the $\\mathbf H$ matrix used by the Kalman filter." + "Now we can present the entire Unscented Kalman filter algorithm. Assume that there is a process model $\\mathbf{\\overline x} = f(\\mathbf x, \\Delta t)$ that performs the state transition for our filter - it predicts the next state given the current state. It is the analogue of the $\\mathbf F$ matrix of the Kalman filter. Also assume there is a measurement function $\\mathbf z = h(\\mathbf{\\overline x})$. It takes the prior and computes a measurement for it. It is the analogue of the $\\mathbf H$ matrix used by the Kalman filter.\n", + "\n", + "The algorithm is straightforward. $f()$ is nonlinear, so we will compute a set of sigma points $\\mathcal{X}$ and weights $W^m, W^c$ from $\\mathbf x$ and $\\mathbf P$. We then pass those sigma points through the unscented transform to find the prior:\n", + "\n", + "$$\\begin{aligned}\n", + "\\mathcal{X}, W^m, W^c &= \\text{sigma-function}(\\mathbf x, \\mathbf P) \\\\ \\\\\n", + "\\boldsymbol{\\mathcal{Y}} &= f(\\boldsymbol{\\chi}) \\\\\n", + "\\mathbf{\\overline x}, \\mathbf{\\overline P} &= \n", + "UT(\\mathcal{Y}, \\boldsymbol{\\bar \\mu}, w_{m,c}, \\mathbf Q)\n", + "\\end{aligned}$$\n", + "\n", + "Now we incorporate the measurement. We need to compute the residual: the difference between the predicted measurement and the actual measurement. In the linear Kalman filter the computation is $\\mathbf y = \\mathbf z - \\mathbf{H\\bar x}$. In the UKF we perform all of our computations on sigma points, not the state. " ] }, { @@ -719,41 +730,51 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "As with the linear Kalman filter, the UKF's predict step computes the mean and covariance of the system for the next evolution using the process model. However, the computation is quite different.\n", - "\n", - "First, we generate sigma points $\\mathcal{X}$ and their corresponding weights $W^m, W^c$\n", + "As with the linear Kalman filter, the UKF's predict step computes the prior. The process model $f()$ is assumed to be nonlinear, so we generate sigma points $\\mathcal{X}$ and their corresponding weights $W^m, W^c$\n", "according to some function:\n", "\n", "$$\\begin{aligned}\n", - "\\mathcal{X} &= \\mathtt{sigma\\_function}(\\bf{\\mu}, \\bf{\\Sigma}) \\\\\n", - "W^m, W^c &= \\mathtt{weight\\_function}(\\mathtt{n, parameters})\\end{aligned}$$\n", + "\\mathcal{X} &= \\text{sigma-function}(\\mathbf x, \\mathbf P) \\\\\n", + "W^m, W^c &= \\text{weight-function}(\\mathtt{n, parameters})\\end{aligned}$$\n", "\n", - "We pass each sigma point through a state transition function $f(\\mathcal{X})$ which you define. This projects the sigma points forward in time according to the process model.\n", + "We pass each sigma point through $f(\\mathbf x, \\Delta t)$. This projects the sigma points forward in time according to the process model, forming the new *prior*.\n", "\n", - "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$" + "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi}, \\Delta t)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now we compute the predicted mean and covariance using the *unscented transform *on the transformed sigma points. I've dropped the subscript $i$ for readability.\n", + "We compute the mean and covariance of the prior using the *unscented transform* on the transformed sigma points. \n", + "\n", + "$$\\mathbf{\\overline x}, \\mathbf{\\overline P} = \n", + "UT(\\mathcal{Y}, w_m, w_c, \\mathbf Q)$$\n", + "\n", + "The unscented transform is computed with the equations below. I've dropped the subscript $i$ for readability.\n", "\n", "$$\\begin{aligned}\n", - "\\mathbf{\\bar{\\mu}} &= \\sum w^m\\boldsymbol{\\mathcal{Y}} \\\\\n", - "\\mathbf{\\bar{\\Sigma}} &= \\sum w^c({\\boldsymbol{\\mathcal{Y}}-\\bf{\\bar{\\mu}})(\\boldsymbol{\\mathcal{Y}}-\\bf{\\bar{\\mu}})^\\mathsf{T}} + \\mathbf Q\n", + "\\mathbf{\\overline x} &= \\sum w^m\\boldsymbol{\\mathcal{Y}} \\\\\n", + "\\mathbf{\\overline P} &= \\sum w^c({\\boldsymbol{\\mathcal{Y}} - \\mathbf{\\overline x})(\\boldsymbol{\\mathcal{Y}}-\\mathbf{\\overline x})^\\mathsf{T}} + \\mathbf Q\n", "\\end{aligned}\n", "$$\n", "\n", - "This table compares the Kalman filter with the Unscented Kalman Filter equations.\n", - "\n", + "This table compares the Kalman filter with the Unscented Kalman Filter equations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "$$\\begin{array}{l|l}\n", - "\\mathrm{Kalman} & \\mathrm{Unscented} \\\\\n", + "\\text{Kalman} & \\text{Unscented} \\\\\n", "\\hline \n", - "\\mathbf{\\overline x} = \\mathbf{Fx} & \\mathbf{\\bar{\\mu}} = \\sum w^m\\boldsymbol{\\mathcal{Y}} \\\\\n", - "\\mathbf{\\overline P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q & \\sum w^c({\\boldsymbol{\\mathcal{Y}}-\\bf{\\bar{\\mu}})(\\boldsymbol{\\mathcal{Y}}-\\bf{\\bar{\\mu}})^\\mathsf{T}}+\\mathbf Q\n", - "\\end{array}$$\n", - "\n" + "& \\boldsymbol{\\mathcal Y} = f(\\boldsymbol\\chi) \\\\\n", + "\\mathbf{\\overline x} = \\mathbf{Fx} & \n", + "\\mathbf{\\overline x} = \\sum w^m\\boldsymbol{\\mathcal Y} \\\\\n", + "\\mathbf{\\overline P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q & \n", + "\\mathbf{\\overline P} = \\sum w^c({\\boldsymbol{\\mathcal Y} - \\mathbf{\\overline x})(\\boldsymbol{\\mathcal Y} - \\mathbf{\\overline x})^\\mathsf T}+\\mathbf Q\n", + "\\end{array}$$" ] }, { @@ -774,20 +795,22 @@ "Now we can compute the mean and covariance of these points using the unscented transform.\n", "\n", "$$\\begin{aligned}\n", - "\\mathbf{\\mu}_z &= \\sum w^m\\boldsymbol{\\mathcal{Z}} \\\\\n", - "\\mathbf P_z &= \\sum w^c{(\\boldsymbol{\\mathcal{Z}}-\\bar{\\mu})(\\boldsymbol{\\mathcal{Z}}-\\bar{\\mu})^\\mathsf{T}} + \\mathbf R\n", + "\\boldsymbol\\mu_z, \\mathbf P_z &= \n", + "UT(\\boldsymbol{\\mathcal Z}, w_m, w_c, \\mathbf R) \\\\\n", + "\\boldsymbol\\mu_z &= \\sum w^m\\boldsymbol{\\mathcal Z} \\\\\n", + "\\mathbf P_z &= \\sum w^c{(\\boldsymbol{\\mathcal Z}-\\boldsymbol{\\mu}_z)(\\boldsymbol{\\mathcal Z}-\\boldsymbol{\\mu}_z)^\\mathsf T} + \\mathbf R\n", "\\end{aligned}\n", "$$\n", "\n", "The $z$ subscript denotes that these are the mean and covariance for the measurements.\n", "\n", - "All that is left is to compute the residual and Kalman gain. The residual of the measurement $\\mathbf{z}$ is trivial to compute:\n", + "All that is left is to compute the residual and Kalman gain. The residual of the measurement $\\mathbf z$ is trivial to compute:\n", "\n", - "$$\\mathbf{y} = \\mathbf{z} - \\boldsymbol{\\mu}_z$$\n", + "$$\\mathbf y = \\mathbf z - \\boldsymbol\\mu_z$$\n", "\n", "To compute the Kalman gain we first compute the [cross covariance](https://en.wikipedia.org/wiki/Cross-covariance) of the state and the measurements, which is defined as: \n", "\n", - "$$\\mathbf P_{xz} =\\sum w^c(\\boldsymbol{\\chi}-\\mu)(\\boldsymbol{\\mathcal{Z}}-\\mathbf{\\mu}_z)^\\mathsf{T}$$\n", + "$$\\mathbf P_{xz} =\\sum w^c(\\boldsymbol\\chi-\\mathbf{\\overline x})(\\boldsymbol{\\mathcal Z}-\\boldsymbol\\mu_z)^\\mathsf T$$\n", "\n", "And then the Kalman gain is defined as\n", "\n", @@ -800,11 +823,11 @@ "\n", "Finally, we compute the new state estimate using the residual and Kalman gain:\n", "\n", - "$$\\mathbf x = \\mathbf{\\overline x} + \\mathbf{Ky}$$\n", + "$$\\mathbf x = \\overline{\\mathbf x} + \\mathbf{Ky}$$\n", "\n", "and the new covariance is computed as:\n", "\n", - "$$ \\mathbf P = \\mathbf{\\bar{\\Sigma}} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}$$\n", + "$$ \\mathbf P = \\mathbf{\\overline P} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}$$\n", "\n", "This step contains a few equations you have to take on faith, but you should be able to see how they relate to the linear Kalman filter equations. We convert the mean and covariance into measurement space, add the measurement error into the measurement covariance, compute the residual and kalman gain, compute the new state estimate as the old estimate plus the residual times the Kalman gain, and adjust the covariance for the information provided by the measurement. The linear algebra is slightly different from the linear Kalman filter, but the algorithm is the same Bayesian algorithm we have been implementing throughout the book. \n", "\n", @@ -818,17 +841,22 @@ "$$\\begin{array}{l|l}\n", "\\textrm{Kalman Filter} & \\textrm{Unscented Kalman Filter} \\\\\n", "\\hline \n", - "\\mathbf{\\overline x} = \\mathbf{Fx} & \\mathbf{\\bar{\\mu}} = \\sum w^m\\boldsymbol{\\mathcal{Y}} \\\\\n", - "\\mathbf{\\overline P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q & \\mathbf{\\overline P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q \\\\\n", + "& \\boldsymbol{\\mathcal Y} = f(\\boldsymbol\\chi) \\\\\n", + "\\mathbf{\\overline x} = \\mathbf{Fx} & \n", + "\\mathbf{\\overline x} = \\sum w^m\\boldsymbol{\\mathcal Y} \\\\\n", + "\\mathbf{\\overline P} = \\mathbf{FPF}^\\mathsf T+\\mathbf Q & \n", + "\\mathbf{\\overline P} = \\sum w^c({\\boldsymbol{\\mathcal Y}-\\overline{\\boldsymbol\\mu})(\\boldsymbol{\\mathcal Y} - \\bar{\\boldsymbol\\mu})^\\mathsf{T}} + \\mathbf Q \\\\\n", "\\hline \n", - "\\mathbf{y} = \\boldsymbol{\\mathbf{z}} - \\mathbf{H\\overline x} &\n", - "\\mathbf{y} = \\mathbf{z} - \\sum w^m h(\\boldsymbol{\\mathcal{Y}})\\\\\n", - "\\mathbf{S} = \\mathbf{H\\overline PH}^\\mathsf{T} + \\mathbf R & \n", - "\\mathbf P_z = \\sum w^c{(\\boldsymbol{\\mathcal{Z}}-\\bar{\\mu})(\\boldsymbol{\\mathcal{Z}}-\\bar{\\mu})^\\mathsf{T}} + \\mathbf R \\\\ \n", - "\\mathbf{K} = \\mathbf{\\overline PH}^\\mathsf{T} \\mathbf{S}^{-1} &\n", - "\\mathbf{K} = \\left[\\sum w^c(\\boldsymbol{\\chi}-\\mu)(\\boldsymbol{\\mathcal{Z}}-\\mathbf{\\mu}_z)^\\mathsf{T}\\right] \\mathbf P_z^{-1}\\\\\n", + "& \\boldsymbol{\\mathcal Z} = h(\\boldsymbol{\\mathcal{Y}}) \\\\\n", + "& \\boldsymbol\\mu_z = \\sum w^m\\boldsymbol{\\mathcal{Z}} \\\\\n", + "\\mathbf y = \\mathbf z - \\mathbf{Hx} &\n", + "\\mathbf y = \\mathbf z - \\boldsymbol\\mu_z \\\\\n", + "\\mathbf S = \\mathbf{H\\overline PH}^\\mathsf{T} + \\mathbf R & \n", + "\\mathbf P_z = \\sum w^c{(\\boldsymbol{\\mathcal Z}-\\boldsymbol\\mu_z)(\\boldsymbol{\\mathcal{Z}}-\\boldsymbol\\mu_z)^\\mathsf{T}} + \\mathbf R \\\\ \n", + "\\mathbf K = \\mathbf{\\overline PH}^\\mathsf T \\mathbf S^{-1} &\n", + "\\mathbf K = \\left[\\sum w^c(\\boldsymbol\\chi-\\overline{\\mathbf x})(\\boldsymbol{\\mathcal{Z}}-\\boldsymbol\\mu_z)^\\mathsf{T}\\right] \\mathbf P_z^{-1} \\\\\n", "\\mathbf x = \\mathbf{\\overline x} + \\mathbf{Ky} & \\mathbf x = \\mathbf{\\overline x} + \\mathbf{Ky}\\\\\n", - "\\mathbf P = (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\overline P} & \\mathbf P = \\mathbf{\\bar{\\Sigma}} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}\n", + "\\mathbf P = (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\overline P} & \\mathbf P = \\overline{\\mathbf P} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}\n", "\\end{array}$$" ] }, @@ -843,23 +871,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "There are several published ways for selecting the sigma points for the unscented Kalman filter, and you are free to invent your own. However, since 2005 or so research and industry have mostly settled on the version published by Rudolph Van der Merwe in his 2004 PhD dissertation [1] because it performs well with a variety of problems and it has a good tradeoff between performance and accuracy. It is a slight reformulation of the *Scaled Unscented Transform* published by Simon J. Julier [2].\n", + "There are several published ways for selecting the sigma points for the unscented Kalman filter. Since 2005 or so research and industry have mostly settled on the version published by Rudolph Van der Merwe in his 2004 PhD dissertation [1] because it performs well with a variety of problems and it has a good tradeoff between performance and accuracy. It is a slight reformulation of the *Scaled Unscented Transform* published by Simon J. Julier [2].\n", "\n", "Van der Merwe's formulation uses 3 parameters to control how the sigma points are distributed and weighted: $\\alpha$, $\\beta$, and $\\kappa$. Before we work through the equations, let's look at an example. I will plot the sigma points on top of a covariance ellipse showing the first and second standard deviations, and size the points based on the weights assigned to them." ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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iqQ7XjF7BNftG1vz67fS52kwrXadzW253Gonv3ttO12mmUMeKFKnHTnDj8NXE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\n73nPexbWQiIichzznYjIeY6sCiJJEu6++27s3LkTl112GS6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cHOXgKw/P9/GVj4/XT7I1+ok2ev//NZ2QESKshQgZJpGQQTRskIyaJCImmqZt97cpxDIS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\nA/2xHNZk4wgbbLCp/THf24ssSZAkGQ7z3TNWzcH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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -938,15 +966,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Lets launch into solving some problems so you can gain confidence in how easy the UKF actually is. All of the equations are implemented in FilterPy. Later we will revisit how the UKF is implemented in Python.\n", + "Lets launch into solving some problems so you can gain confidence in how easy the UKF actually is. We will use FilterPy's UKF implementation. Later we will implement the UKF ourselves.\n", "\n", - "Let's start by solving a problem you already know how to do. Although the UKF was designed for nonlinear problems, it works fine on linear problems. In fact, it is guaranteed to get the same result as the linear Kalman filter for linear problems. We will write a solver for the linear problem of tracking using a constant velocity model in 2D. This will allows us to focus on what is the same (and most is the same!) and what is different with the UKF. \n", + "Let's start by solving a problem you already know how to do. Although the UKF was designed for nonlinear problems, it obtains the same result as the linear Kalman filter for linear problems. We will write a filter for the problem of tracking using a constant velocity model in 2D. This will allows us to focus on what is the same (and most is the same!) and what is different with the UKF. \n", "\n", - "To design a linear Kalman filter you need to design the $\\bf{x}$, $\\bf{F}$, $\\bf{H}$, $\\bf{R}$, and $\\bf{Q}$ matrices. We have done this many times already so let me present a design to you without a lot of comment. We want a constant velocity model, so we can define $\\bf{x}$ to be\n", + "To design a linear Kalman filter you need to design the $\\bf{x}$, $\\bf{F}$, $\\bf{H}$, $\\bf{R}$, and $\\bf{Q}$ matrices. We have done this many times already so let me present a design to you without a lot of comment. We want a constant velocity model, so we define $\\bf{x}$ to be\n", "\n", "$$ \\mathbf x = \\begin{bmatrix}x & \\dot x & y & \\dot y \\end{bmatrix}^\\mathsf{T}$$\n", "\n", - "With this ordering of state variables we can define our state transition model to be\n", + "With this ordering of state variables the state transition matrix is\n", "\n", "$$\\mathbf F = \\begin{bmatrix}1 & \\Delta t & 0 & 0 \\\\\n", "0&1&0&0 \\\\\n", @@ -954,16 +982,17 @@ "0&0&0&1\n", "\\end{bmatrix}$$\n", "\n", - "which implements the Newtonian equation\n", + "which implement the Newtonian equations\n", "\n", - "$$x_k = x_{k-1} + \\dot x_{k-1}\\Delta t$$\n", + "$$x_k = x_{k-1} + \\dot x_{k-1}\\Delta t \\\\\n", + " y_k = y_{k-1} + \\dot y_{k-1}\\Delta t$$\n", "\n", "Our sensors provide position measurements but not velocity, so the measurement function is\n", "\n", "$$\\mathbf H = \\begin{bmatrix}1&0&0&0 \\\\ 0&0&1&0\n", "\\end{bmatrix}$$\n", "\n", - "Let's say our sensor gives positions in meters with an error of $1\\sigma=0.3$ meters in both the *x* and *y* coordinates. This gives us a measurement noise matrix of \n", + "Let's say our sensor gives positions in meters with an error of $\\sigma=0.3$ meters in both the *x* and *y* coordinates. This gives us a measurement noise matrix of \n", "\n", "$$\\mathbf R = \\begin{bmatrix}0.3^2 &0\\\\0 & 0.3^2\\end{bmatrix}$$\n", "\n", @@ -978,7 +1007,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 14, "metadata": { "collapsed": false, "scrolled": false @@ -986,9 +1015,9 @@ "outputs": [ { "data": { - "image/png": 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H3Yb2vnM43/UupiJzL1/JzZKjIE+FArkaBXlq6ApN0Ktmwnledn6SKiciIloc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\nAAAASUVORK5CYII=\n", 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4QO91o6fXDW+fG/2D/useOzEhGboME/QZJuiUWdArs5CpykF6qjyCn4BoYWJwJyIiWgD6\nh3pR23oWF1qqUdt2FoPD/dc9llgkhkKqhlKmhTJdC40iE3qlCbqMLCikKm7PSBQlDO5ERETzlCAI\nOFt/Ch9+8Ue02GoRFIJh9ROLxJClKaFIU0EhVYUC+pVnuVTFHV+IZgGDOxER0TzU7mzE/37/f6HF\nfulrX1ekqZClzYdcOh7OFVI15JeDenqKHGIGc6I5h8GdiIgohgWDAfT0dcPjd8Dd44DH74TN046L\nzZ9CgBBqJ4IIWToLFufciMU5ZTCosrmkhSjGMLgTERHFiGAwgE53KxqtF9Fkuwi7pwPdfteUe6RL\nxHH49g3rcPsNP0B6qmIGqyWiSGNwJyIimqMCwQCsrmY0dl5Ao/Uimm01GBwZCLt/SU4Zfvitn3Kf\ndKJ5gsGdiIhoDggGA3D12GB1NcPa1QJrVzPanA0YHhmctq80WQalXAdVug5KmRYqmRaZ6hwY1bkz\nUDkRzRQGdyIiohk2MjYMu7sdne6WUFC3uVsxMjY8bd/0VAUsmYuRb1yMbF0BVDIdEhOSZ6BqIppt\nDO5ERERRIggC/ANedHa1orOrBZ3u8WdXjw1CmFszytOUyDcuRn7mYuRnlkAt1/OiUqIFisGdiIgo\nAkbHRuDo7oDN3QabuxU2Txs6u1rRN+gLe4z0VAWM6tzLjxyYNHnISNcwqBMRgCgFd4fDgV/84hd4\n66230Nvbi7y8PBw5cgTf+ta3Qm327NmDo0ePwuv1YtWqVaisrERxcXE0yiEiIoqoscAomjpr0Oqo\nuxzU29DVYwv7BkciiKBWGJCpyg6tRTeqc5GeKo9y5UQUyyIe3H0+H1avXo01a9bg7bffhkqlQnNz\nMzQaTajNwYMHcejQIRw7dgwFBQXYu3cvysvLUV9fj9TU1EiXRERE9I0Njwyipu0zfN70MWpaqsPe\n3SUxPgkGVXYopGeqc6BXZiExPinKFRPRfBPx4H7w4EEYDAb89re/DR0zm80T2jzzzDPYsWMH7r77\nbgDAsWPHoNFo8PLLL+Ohhx6KdElERETXxeNzoqb1DC62nkF9x+cYC4xO2lYEEVRyPQzKLBhU2TCo\nzDCosqGUaSEWiWewaiKaryIe3N98802sXbsW9957L06ePAmDwYC/+Zu/wWOPPQYAaGlpgcPhQHl5\neahPUlIS1qxZg6qqKgZ3IiKaNYHgGFz+Drz+weeoaT0Lp9c6adsMqRrFOWUwqXNhUGVDpzTxLDoR\nRVXEg3tzczOef/55bNu2DTt27MC5c+ewadMmiEQiPProo3A4HBCJRNBqtRP6abVa2Gy2Kceurq6O\ndLk0z3CO0HQ4R+jLhkYH4O7thKu3A11+K9x9tinvQqpI0cCkLERWRiEUqdrxi0aHgC6rD13W8C9C\npfmB3yc0FYvFEvExIx7cg8EgVq5cif379wMAli1bhvr6elRWVuLRRx+N9NsRERGFbWi0H7aeFjh6\nWtDVa4Vv0DNle4k4DjpZNjIV+chU5EGapJihSomIrhbx4K7X61FUVDThWFFREQ4fPgwA0Ol0EAQB\nTqcTRqMx1MbpdEKn0005dllZWaTLpXniylkPzhGaDOfIwhQIBtBqr0Nt22e41PYZOlxNECBM2Uea\npMANhbegOHsF8o2LkRCXOEPVUqzg9wmFw+eL/G/hIh7cV69ejbq6ugnH6urqQheo5uTkQKfT4cSJ\nEygtLQUADA0N4dSpU3j66acjXQ4RES0AgWAA3X4X3D4H3D12uH0OuLw2NNlqMDTF7i8ScRyMmlzk\n6BchR78Iva5hpCRKGciIaE6KeHDftm0bVq9ejX/8x3/EX/zFX+Ds2bN49tlnceDAgVCbrVu3oqKi\nAoWFhbBYLNi3bx+kUik2bNgQ6XKIiGieGRoZRLOtBg3WC+h0t8LdY0d3bxeCwcC0fcUiMbJ1hVhk\nXg6LcQlM2rwJZ9SrfVyzTERzV8SDe1lZGd544w3s2LED+/btQ1ZWFvbv349HHnkk1Gb79u0YGhrC\npk2bQjdgOn78OPdwJyKiqwyPDqHZVotG6wU0WC+g3dkQ9o2OAECRpkJR9g1YlHUDCrKWIiUxLYrV\nEhFFT1TunLp27VqsXbt2yja7d+/G7t27o/H2REQU44LBAC61n8efak/ii6ZPMBoYmbaPLDUDKpkO\nKrke6svPBpUZWoVxfPcXIqIYF5XgTkREdD0c3R34U81JfHrpPfj6uydtl6nKRr5xMXINxdAqDFDK\ndNxDnYjmPQZ3IiKaUWOB0csXj3bC6bXB5e0MPfqHer+2jy7DhALTUliMi5GfWYLU5PQZrpqIaPYx\nuBMRUUQFAmPo6fPA43fB2+tCt78L3X4Xunu70N3rgtffFdYadWmyDGWLbsPKou8gU50d/cKJiOY4\nBnciIrpuA0N9aHM2oN3ZgDZHAzq7WtDT3w3hGi4e/bKEuEQUmW/AyuLvoNi8AhIJ/5kiIrqC34hE\nRBQWQRDQ1WNHY+dFNHVeRKujHl09tusaSyFVQ6MwQKvIhEaRCY18/FkuVUIsEke4ciKi+YHBnYiI\nvlZQCMLh6UBT58XLYb0G/gHvtP1EECE9VYGMdA0ypGooLj9npGuQka5GhlSDhHjejZSI6FoxuBMR\nEQRBgNvngLWrGR2uZlhdTWh3NWFgkotFr5CI45CpykaWzgKz1oIsrQUqmQ7xcfEzVDkR0cLB4E5E\ntMCML3mxoc3ZMB7Su5rR6WrG4MjAtH2TE1KQm1mM/MwS5BqKYVTnID4uYQaqJiIiBncionnO39+D\nNmd96ALSNmcDBof7w+qbmpyOfEMx8jJLkG8sgUFphlgsiXLFRET0dRjciYjmkUAwgM6uFjTbatFi\nv4Q2Rz26e7vC6puaJIVRkwuTOg9GTS6M6lyo5DpeLEpENEcwuBMRxbCRsWG02C6hqbMGzfZatDrq\nMTI6NG2/1CQpzFoLTNp8mDR5MKpzoZCqIBKJZqBqIiK6HgzuREQxJBAMoN3ZgPqOL1Df8Tla7Jcw\nFhidsk+8JAEmTV7oAlKzzgJlupYhnYgoxjC4ExHNUYHAGFw9Ntg97bC522DtakaTrQbDI4NT9lOk\nqZBrKEKuoQjZ+kIYlGbeyIiIaB7gNzkR0RzQO9CDdmcjbJ522N1tsHna4PRaEQiMTdtXqzDCYlyM\nvMxi5OiLkJGunoGKiYhopjG4ExHNsKAQhLO7Ey322vGLSG2X0OWzh91fkaZCgWkpCrKWwmJcAnma\nMorVEhHRXMHgTkQURSNjw7C729HpbkVnVws63S3odLdOu9zlCkWaCnqVGQalGXqVGdm6AqhkOq5P\nJyJagBjciYgiKBAMoMV+CRdbPkVN61k4uq0QhOC0/SSSuPHdXVQ5XwrqWUhJTJuBqomIKBYwuBMR\nfUMDQ32obTuLC82forbtMwwM903bJzU5HTn6RcjVL0KuoQgmTR7vQEpERFNicCciukaCIMDa1YLa\n1jOoaTuLVnsdgpOcVRdBBLVcD4M6G5mqHBjVOTCosiFPU3K5CxERXZOoB/eKigrs3LkTmzZtwuHD\nh0PH9+zZg6NHj8Lr9WLVqlWorKxEcXFxtMshIrouA8N9qGs/j5rWs6htOwt/v3fStrI0JRZnl6Ek\npwwW42IkJiTPYKVERDRfRTW4f/zxxzh69CiWLVs24fjBgwdx6NAhHDt2DAUFBdi7dy/Ky8tRX1+P\n1NTUaJZERBSWoBCE1dWM2rbPUBvGWfUsnQWLc8bDeqYqh2fTiYgo4qIW3H0+H/7qr/4Kv/3tb7Fn\nz54Jrz3zzDPYsWMH7r77bgDAsWPHoNFo8PLLL+Ohhx6KVklERFPy9XejvuML1LadxaW2c+gb9E3a\nNiVJiqKs5SjOKcWirBsgTZHNYKVERLQQRS24P/zww7jnnntw2223TTje0tICh8OB8vLy0LGkpCSs\nWbMGVVVVDO5ENCMEQUC334XGzotostWgqbMGXT22KftkafJRnF2KouwVMGvzIRZLZqhaIiKiKAX3\no0ePorm5Ga+88spVrzkcDohEImi12gnHtVotbLap/9Gsrq6OaJ00/3CO0JcJgoCRwBBGxv78ePm/\nz8Dpa4fT346Bkd4p+yfFp8Agz4VBnge9PBfJCeNL+TydvfB0fjYTH4FmCb9LKBycJzQVi8US8TEj\nHtzr6+uxc+dOfPTRRxCLxZEenohoguGxQfT0u+Ad6Lr87MLgSC9GxoYxEhi6prHEIgnU0kzo5bnI\nVOQhI5U3OiIiorkj4sH99OnT8Hg8E3aICQQC+OCDD/DrX/8aFy5cgCAIcDqdMBqNoTZOpxM6nW7K\nscvKyiJdLs0TV856cI7MT8OjQ+jpdcPb64a3zw2XtxN2dxtsnjb09Hmue9zE+CTkGIqQbyhGXmYJ\nsrQWxMfFR7ByijX8LqFwcJ5QOHy+ya+Tul4RD+4//OEPceONN0449sADD6CgoAA7d+5EQUEBdDod\nTpw4gdLSUgDA0NAQTp06haeffjrS5RBRDBkLjKKm9SwutX2G7t6u8bDe58bgcP91j5mYkDx+99GA\nCAlxSdBrjMjWFyI/swSZ6hxIuE6diIhiRMSDe3p6+lX7saempiIjIwNFRUUAgK1bt6KiogKFhYWw\nWCzYt28fpFIpNmzYEOlyiGiOEwQB7c4GfHrpPZypO4X+oanXnX+VRBIHXYYJBqUZBpUZeqUZarke\nKYmpSEpMDQVzniEjIqJYNyN3Tv3qGtHt27djaGgImzZtCt2A6fjx49zDnWiB6B3oQaujHq32Opxv\n+hgub+eU7SXiOMjTlJBLVVCkqZCRrgmFdI1cD4mEN4EmIqL5b0b+tXv33XevOrZ7927s3r17Jt6e\niGbRWGAUnV2taHXUjYd1Rx08Puek7RVpKpQuug3ZOgvkaSrI01RIS0mHWMSL3YmIaGHjaSoiirig\nEESj9QI+vvgOzjedxujYyJTtE+OTsDz/FtxYdDvyjSUM6URERF+DwZ2IIqbb34VPat/FJzXvoNvv\nmrSdRBIHkyYP2bpC5OgXoSS7FAnxiTNYKRERUexhcCeib2RoZBDnG6vwp9r30Gi9AAHCVW0y0jXI\n0RUiW1+IbF0BDKocbrtIRER0jRjcieiajYwNo6mzBp/WvjfpUpiUxDSULboNq4rvgEmTOwtVEhER\nzS8M7kQ0qcHhfji6rXB2W+Ho7gg9d/tdX3tmXSQSo9C0FDeV3IkluSsRH5cwC1UTERHNTwzuRAuQ\nIAgYGOqFf6AHvQM98Pd7L//Zi94BH3p63XB6O+Hr7w5rPL0yCyuLvoOywjWQpWVEuXoiIqKFicGd\naB4LBMbg6rHD7mmDw9MBu6cNdk87PH4XAsGx6x5XJBJDLdOhOKcMK4u+jUxVzlX3ayAiIqLIYnAn\nmieCwQA63W1ottWgxV4Hu6cNLq/tGwV0iSQOWnkmtBlG6DJMl5+NUMszeXEpERHRDGNwJ4pRo2Oj\naHc2oKnzIppstWixX8LQyEDY/ZMTUiBNkUOaqkB6ihzpqQpIk2Whn9VyA5QyLSRiSRQ/BREREYWL\nwZ0oRoyOjaLNWY9G6wU0Wi+gxV6H0cDUNzYCAIVUDX2GCXpVFvRKc+jMeWJ80gxUTURERJHC4E40\nR/UP+tHhakaL/RIaOy+iNYygLkvNQF5mMXINRTBp8qHLMCE5MWWGKiYiIqJoYnAnmgN6B3rQ4WpC\nh6sZHa4mWF1N6O7tmrafWqZHnrEEeYZi5GUWQ5mu5UWiRERE8xSDO9EMCwpB2N3taOy8MH4m3VEP\nX58nrL5quQEWYwnyMhcjP7MECqkqytUSERHRXMHgThRlgiDA5m5FfccXaOy8gCZbLQaGeqftJ5HE\nIVOZDZMmD3mZxcg3LoY8TTkDFRMREdFcxOBOFCW9Az349NL7+KTmHdg97VO2jY9LQKY6ByZ1Hoya\nXGRp8qDLMEEi4V9RIiIiGsdUQBQBQSEYutuoy9uJBusXuNBSjWAw8LXt05JlyM8sQb6xBHmGEuiU\nJm67SERERFNicCe6Rt7eLrQ66mH3tMPltcHptcLl7cTo2OQ7viTEJ6EkuxQW4xLkG0ugVRh5ESkR\nERFdEwZ3oimMjo3C2tWMVnsdWuyX0OKoC/tCUgDI1RdhVckduMGyGkkJyVGslIiIiOY7BneiLxkd\nG0GzrRZOi6ZrAAAUoUlEQVSX2s+hyVYDq6sZY4HRsPqmJcugURigVRihzchESc6N0Coyo1wxERER\nLRQRD+4VFRV4/fXXUVdXh8TERNx0002oqKhASUnJhHZ79uzB0aNH4fV6sWrVKlRWVqK4uDjS5RBN\nSRAEOLqtuNT2GS61n0Nj54Upl7wA48tesrUWGDV50GYYx4O6woDU5PQZqpqIiIgWoogH9w8++ACb\nNm1CWVkZBEHArl27cOedd6K2thZyuRwAcPDgQRw6dAjHjh1DQUEB9u7di/LyctTX1yM1NTXSJRGF\nDA4PXL7RUSPanA1osU+/9EUt0yNbX4hsfSFy9IXQK828kJSIiIhmXMSD+9tvvz3h55deegkymQwf\nffQRvv/97wMAnnnmGezYsQN33303AODYsWPQaDR4+eWX8dBDD0W6JFqAhkYG0e13wdvbBbfPgXZn\nI9qdjXB5OyFAmLKvRm7AIvNyFJiWIUdfCGmKfIaqJiIiIppc1Ne4+/1+BINBKBQKAEBLSwscDgfK\ny8tDbZKSkrBmzRpUVVUxuFPYRkaH4ejugN3TjnOtn8I/2I136n8Hr78LA8N9YY+TnJCCgqxlWJS1\nHIvMy6FM10axaiIiIqLrE/XgvmXLFqxYsQI333wzAMDhcEAkEkGrnRiOtFotbDbblGNVV1dHrU6a\n2wRBgKfPhk5vEzz9DvQMuNA31HPN44gggjxFDWWaASqpHso0AxSpWohFYmAYaKnvQAs6ovAJaK7g\n9wiFg/OEwsF5QlOxWCwRHzOqwf2JJ55AVVUVPvroI+5ZTddseHQQtp4mdHqbYOtpwtDoQNh9xSIJ\nUhPTkZooQ1qiDPJUDVRpBmSk6hAniY9i1URERETREbXgvm3bNvz7v/873nvvPZjN5tBxnU4HQRDg\ndDphNBpDx51OJ3Q63ZRjlpWVRatcmgMGh/vR4WpCi/0SalrPotVRD0EITtpeJBJDLdNBp8wChuMg\nS1GhbPlNyEjXQJoiHz+LTnTZlTNj/B6hqXCeUDg4TygcPp8v4mNGJbhv2bIF//Ef/4H33nvvql8T\n5OTkQKfT4cSJEygtLQUADA0N4dSpU3j66aejUQ7NQYPDA7B72tDmbEC7sxEdzka4eqZeKiVNlqEo\newUKTEuRqcqGRpGJ+LgEAH/+Es3RL4p67URERESzIeLB/bHHHsO//du/4c0334RMJoPT6QQApKWl\nhbZ63Lp1KyoqKlBYWAiLxYJ9+/ZBKpViw4YNkS6HZtmXLyB1dLfD7hn/s7e3a9q+IoiQpbOgOLsU\nJdmlMGpyeRadiIiIFqyIB/cjR45AJBLhjjvumHD8qaeewu7duwEA27dvx9DQEDZt2hS6AdPx48e5\nh3uMGxkbRmdXC9ocDeNn0h0NcPsc026/eIVYJIZeZUaWJh/5xhIsyroB0hRZlKsmIiIiig0RD+7B\n4ORrkr9s9+7doSBPsScoBOHstoZCepuzHjZ3G4LBQFj9xWIJtIpMmDR5yNLmw6TJR6Y6GwlxiVGu\nnIiIiCg2RX07SJo//P09qOs4h9q2z1DXfh69A9Nvx3jlAlK9Mgs6ZRb0lx9quZ67uxARERFdAwZ3\nmpQgCLB2NeOz+o9Q2/4ZOrtapu2jUWTCrLXArLPArLXAoMoOXUBKRERERNePwZ2u4vY5cKbuA1Rf\n+gBOr3XSdqlJUuRlFiNLOx7STdo8pCSmzWClRERERAsHg/sCFwwG4O11w+nthKO7HecbP0aL/dLX\nthWLJcjRL0JR1nIsMt/AXV6IiIiIZhCD+wIxOjYKl7cTNk8bnN1WuLyd448eG8YCo5P2S4hPwtK8\nVViefwssxiVITkyZwaqJiIiI6AoG93kmGAzA7XPA7mmHzdMOu6cNdk87urw2BKe4C+mXiUViFJlX\noGzRGizOXYnE+KQoV01ERERE02Fwnwe6euy41PYZatvPoaHjcwyPDl1Tf2myDBpFJjSXt2dcln8z\n908nIiIimmMY3GPQ8MggGqwXUNv2GS61fYYunz2sfkqZFnqlGboME7SKTGgzjNAoDLyglIiIiCgG\nMLjHgEBgDG3OBtS1n0d9x+docdRNeaOj9BQF9Kos6JVm6JVZMCjN0GUYkZiQPINVExEREVEkMbjP\nIUEhiJ5eD9w+B9w+O9w942vVGzsvTLn8JSEuERbjEiwyL0eReQXUcj1EItEMVk5ERERE0cbgPku8\nvW40WL9Ah6sJ7h7HeFj3OxAIjIXV36A0oyj7BizKugG5hmLEx/EupERERETzGYP7DPH1d6Oh4ws0\ndl5AQ8eFsNelX6GQqlGYtQyFpqWwGJciPVUepUqJiIiIaC5icI+SoBBEq70O5xpPo6b1DFzezrD6\npSXLoJLp/vyQ65CjXwSVTMflL0REREQLGIN7BAWCATR1XsS5xtP4vOlj+Pu9k7aNlyQgx7AIeZkl\n0GWYQkGdNzgiIiIioq/D4H6NgsEAevrGLyDt6rGPr03vsaPLN75OfWSSi0jjJPHI1hfCYlwCi3Ex\nzNoCrksnIiIiorAxuE9jdGwUrY46NFi/QIP1Atoc9RgLjIbVNy1ZhqV5K7Es/xbkZ5YgPi4hytUS\nERER0XzF4P4V43umN44H9Y7P0WKvw2hgJOz+stQMLMu/Ccvyb0auoRgSsSSK1RIRERHRQrEgg7sg\nCPD3e8f3Sr+8xOXKloz27o5Jl7tcIU2WQSnXQS3TQyXXQyXTQS3XQy3TISVJyotIiYiIiCji5nVw\nHxzuh8vbCVePbfzZO/7c1WPHyNhw2OOoZXpYTIthMS6FxbgY6amKKFZNRERERHS1WQ3uzz//PH71\nq1/BbrejpKQE//zP/4xbb731uscLBgP4rOEjnL5wAvbuDvQO9FzXOBnpmtBFpBbjEiikquuuiYiI\niIgoEmYtuL/22mvYunUrfv3rX2P16tWorKzE2rVrUVtbC6PReE1jBYUgzjVU4e1PXoWz2xpWn5TE\ntNA+6SqZDsp0LVRyHdRyA+Rpyuv5SEREREREUTNrwf3QoUP46U9/ip/+9KcAgMOHD+MPf/gDjhw5\ngv3790/b39ffjXZnIzqcTTjfdBp2T/tVbeIk8VDL9dDIDdAoMqFRXH6WG5CanB7xz0REREREFC2z\nEtxHR0dx5swZ/OxnP5tw/Lvf/S6qqqom7ffHP/072p2NaHc1wdfn+do2iQnJuH35D7Cy+HZkSNUQ\nc1cXIiIiIpoHZiW4u91uBAIBaLXaCce1Wi3eeeedSfv939MvT/panDgeRYaVKDbchMT4ZLQ2WNGK\n8JbN0PxRXV092yXQHMc5QuHgPKFwcJ7QVCwWS8THjNldZeLE8chI00GZqocyTQ+DIg9J8SmzXRYR\nERERUVTMSnBXqVSQSCRwOp0TjjudTuh0ukn73bp0LczafJg0+dBmGHlzIwq5ctajrKxsliuhuYpz\nhMLBeULh4DyhcPh8voiPKY74iGGIj49HaWkpTpw4MeH4iRMnsHr16kn73XP7RqwqvgMGlZmhnYiI\niIgWlFlbKvPEE0/gvvvuw4033ojVq1fjyJEjsNvt2Lhx42yVREREREQ0Z81acL/nnnvQ3d2N/fv3\nw263Y/HixXj77bdhMplmqyQ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1028,16 +1057,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This should hold no surprises for you. Now let's implement this filter as an Unscented Kalman filter. Again, this is purely for educational purposes; using a UKF for a linear filter confers no benefit.\n", + "This should hold no surprises for you. Now let's implement this with a UKF. Again, this is purely for educational purposes; using a UKF for a linear filter confers no benefit. `FilterPy` implements the UKF with the class `UnscentedKalmanFilter`. \n", "\n", - "The equations of the UKF are implemented for you with the `FilterPy` class `UnscentedKalmanFilter`; all you have to do is specify the matrices and the nonlinear functions `f(x)` and `h(x)`. `f(x)` implements the state transition function that is implemented by the matrix $\\mathbf F$ in the linear filter, and `h(x)` implements the measurement function implemented with the matrix $\\mathbf H$. In nonlinear problems these functions are nonlinear, so we cannot use matrices to specify them.\n", + "The first thing to do is implement the functions `f(x, dt)` and `h(x)`. `f(x, dt)` implements the state transition function, and `h(x)` implements the measurement function. These correspond to the matrices $\\mathbf F$ and $\\mathbf H$ in the linear filter.\n", "\n", - "For our linear problem we can define these functions to implement the linear equations. The function `f(x)` takes the signature `def f(x,dt)` and `h(x)` takes the signature `def h(x)`. Below is a reasonable implementation of these two functions. Each is expected to return a 1-D NumPy array containing the result." + "Below is a reasonable implementation of these two functions. Each is expected to return a 1D NumPy array containing the result. You may give them more readable names than `f` and `h`." ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 15, "metadata": { "collapsed": false, "scrolled": false @@ -1062,7 +1091,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "You need to tell the filter how to compute the sigma points and weights. We gave the Van der Merwe's scaled unscented transform version above, but there are many different choices. FilterPy uses a class named `SigmaPoints` which must implement two methods:\n", + "Next you specify how to compute the sigma points and weights. We gave the Van der Merwe's scaled unscented transform version above, but there are many different choices. FilterPy uses a class named `SigmaPoints` which must implement two methods:\n", "\n", "```python\n", "def sigma_points(self, x, P)\n", @@ -1076,7 +1105,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "When you create the UKF you will pass in the $f(x)$ and $h(x)$ functions and the sigma point object as in this example:\n", + "When you create the UKF you will pass in the $f()$ and $h()$ functions and the sigma point object as in this example:\n", "\n", "```python\n", "from filterpy.kalman import MerweScaledSigmaPoints\n", @@ -1091,12 +1120,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The rest of the code is the same as for the linear kalman filter. Let's just implement it! I'll use the same measurements as used by the linear Kalman filter, and compute the standard deviation of the difference between the two solutions." + "The rest of the code is the same as for the linear kalman filter. I'll use the same measurements used by the linear Kalman filter, and compute the standard deviation of the difference between the two solutions." ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 16, "metadata": { "collapsed": false, "scrolled": false @@ -1111,9 +1140,9 @@ }, { "data": { - "image/png": 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GEjplDozZ+cjJtiBboYNYLIlT9URERPE3q0H9yJEjlxzbsWMHduzYMZvflojm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\nqBMRERERJSAGdSIiIiKiBPT/Af6EVoG5HOZaAAAAAElFTkSuQmCC\n", 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GciK/O4iIaOGbleD+/vvvX3Fs9+7d2L1792y8PRHNocGRfnQ6m9HubAyF9Z5+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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1148,9 +1177,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This gave me a standard deviation of 0.013 which is quite small. \n", + "This gave me a standard deviation of 0.013, which is quite small. \n", "\n", - "So far implementation of the UKF is not *that* different from the linear Kalman filter. Instead of implementing the state function and measurement function as the matrices $\\mathbf F$ and $\\mathbf H$ you supply functions `f(x)` and `h(x)`. The rest of the theory and implementation remains the same. Of course the `FilterPy` code for the UKF is quite different than the Kalman filter code, but from a designer's point of view the problem formulation and filter design is very similar." + "So far the implementation of the UKF is not *that* different from the linear Kalman filter. Instead of implementing the state function and measurement function as the matrices $\\mathbf F$ and $\\mathbf H$ you supply functions `f()` and `h()`. The rest of the theory and implementation remains the same. Of course the `FilterPy` code for the UKF is quite different than the Kalman filter code, but from a designer's point of view the problem formulation and filter design is very similar." ] }, { @@ -1164,16 +1193,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let's tackle our first nonlinear problem. I will keep the problem formulation very similar to the linear tracking problem above. For this problem we will write a filter to track a flying airplane using a stationary radar as the sensor. To keep the problem as close to the previous one as possible we will track in two dimensions. We will track one dimension on the ground and the altitude of the aircraft. The second dimension on the ground adds no difficulty or different information, so we can do this with no loss of generality.\n", + "Let's tackle our first nonlinear problem. We will write a filter to track a flying airplane using a stationary radar as the sensor. To keep the problem as close to the previous one as possible we will track in two dimensions. We will track one dimension on the ground and the altitude of the aircraft. The second dimension on the ground adds no difficulty or different information, so we can do this with no loss of generality.\n", "\n", - "Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object. We also get the bearing to the target. For this 2D problem that will be the angle above the ground plane.\n", + "Radars work by emitting radio waves or microwaves and scanning for a return bounce. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object. We also get the bearing to the target. For this 2D problem that will be the angle above the ground plane. Radars also provide velocity measurements via the Doppler effect, but we will be ignoring this complication.\n", "\n", - "We want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below." + "We can compute the (x,y) position of the aircraft from the slant distance and angle, as in the diagram below." ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 17, "metadata": { "collapsed": false, "scrolled": false @@ -1181,9 +1210,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1219,7 +1248,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 18, "metadata": { "collapsed": false, "scrolled": false @@ -1240,22 +1269,22 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The next step is to design the measurement function. As in the linear Kalman filter the measurement function converts the filter's state into a measurement. For this problem we need to convert the position and velocity of the aircraft and into the bearing and range from the radar station.\n", + "Next we design the measurement function. As in the linear Kalman filter the measurement function converts the filter's state into a measurement. We need to convert the position and velocity of the aircraft and into the bearing and range from the radar station.\n", "\n", - "To compute the range we use the Pythagorean theorem:\n", + "Range is computed with the Pythagorean theorem:\n", "\n", - "$$\\mathtt{range} = \\sqrt{(x_\\mathtt{ac} - x_\\mathtt{radar})^2 + (z_\\mathtt{ac} - z_\\mathtt{radar})^2}$$\n", + "$$\\text{range} = \\sqrt{(x_\\text{ac} - x_\\text{radar})^2 + (y_\\text{ac} - y_\\mathtt{radar})^2}$$\n", "\n", "To compute the bearing we use the arctangent function.\n", "\n", - "$$\\mathtt{bearing} = \\tan^{-1}{\\frac{z_\\mathtt{ac} - z_\\mathtt{radar}}{x_\\mathtt{ac} - x_\\mathtt{radar}}}$$\n", + "$$\\text{bearing} = \\tan^{-1}{\\frac{y_\\mathtt{ac} - y_\\text{radar}}{x_\\text{ac} - x_\\text{radar}}}$$\n", "\n", "As with the state transition function we need to define a Python function to compute this for the filter. I'll take advantage of the fact that a function can own a variable to store the radar's position. While this isn't necessary for this problem (we could hard code in the value), this gives the function more flexibility without requiring it to use a global variable." ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 19, "metadata": { "collapsed": false, "scrolled": false @@ -1276,14 +1305,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between $359^\\circ$ and $1^\\circ$ is $2^\\circ$, but a subtraction of the two values, as implemented by the filter, yields a value of $358^\\circ$. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem.\n", + "There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between 359° and 1° is 2°, but subtracting two values yields a value of 358°. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem.\n", "\n", "We need to simulate the Radar station and the movement of the aircraft. By now this should be second nature for you, so I will present the code without much discussion." ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 20, "metadata": { "collapsed": false, "scrolled": false @@ -1340,7 +1369,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's put it all together. A military grade radar system can achieve 1 meter RMS range accuracy, and 1 mrad RMS for bearing [1]. We will assume a more modest 5 meter range accuracy, and 0.5$^\\circ$ angular accuracy as this provides a more challenging data set for the filter.\n", + "Now let's put it all together. A military grade radar system can achieve 1 meter RMS range accuracy, and 1 mrad RMS for bearing [1]. We will assume a more modest 5 meter range accuracy, and 0.5° angular accuracy as this provides a more challenging data set for the filter.\n", "\n", "The design of $\\mathbf Q$ requires some discussion. The state $\\mathbf x$ contains $\\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are position (down range distance) and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of Q. The third element of $\\mathbf x$ is altitude, which we are assuming is independent of the down range distance. That leads us to a block design of $\\mathbf Q$ of:\n", "\n", @@ -1351,16 +1380,16 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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48CA++eQTbN68GZ999pm8pKY/nnjiCezYsQN79+5FYmKivF2r1QIArFZrnyv3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\nY6NQqVRi27ZtcozZbBYKhUL885//9F7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6jhSsrXuwru7BurrHT1ejuMqwmvzu7m5s3rwZn3/+OSorKwEASUlJuO222/Dg\ngw86NV5z2bJl2L59O7755hu7P1UAQHJyMuRyOXbv3o3JkycDACwWC/bv34/XXnttOKkTEY0KjS3n\noTMU20ZbNrXWO4yPjYhHumoSNKocqJUTERQQ4qFMiYhoJBrWnPy5c+fihx9+gEwmszXmx44dw86d\nO7F582bs2bPHdvOsI4899hi2bt2KHTt2QCqVwmQyAQBCQkJs4zGXL1+OtWvXIj09HWq1GmvWrEFo\naCgWLlzobOpERCNWS7sZZ6pLoNUXQ6cvwrmmGofxYcF9N8teaOwjQqM9lCkREY0GTjf5K1asQElJ\nCd555x0sWrQIYnHfuk5BELB161b8+te/xsqVK7Fp06ZBj7Vp0yaIRCLMnTvXbvsLL7yAVatWAQCe\nfvppWCwWLF261PYwrF27dnFGPhGNah2dbThTfQI6fTG0hmLUnK90GB/gF4Q05cT+JTiTII9U8v4l\nIiIakNNN/o4dO7B06VIsXrzYbrtIJMKiRYvw/fff44MPPhhSk2+1Wof0matWrbI1/UREo1FXdyfK\na05Ba+i7Un/2XBkEYeB/A30lfkiOy4BGmQ21KgcJsjRIxJIB44mIiH7K6Sa/qakJqampA76fmpqK\npqamy0qKiGi06+ntRpVRC23/lfrK2lLHE3DEEiTJNFCrsqFRZSNJng5fHz8PZkxERGOJ001+Wloa\nduzYgUcfffSiPxULgoBPP/0UaWlpLkuQiGg0sFp7oT9XbrtSX1ZzEt09XQPGiyCCMjYFGlU21Moc\npMZNgL9foAczJiKisczpJv+xxx7Do48+iptuugnLli2DRqMBAJSWluL111/H119/PaSlOkREo5kg\nCDA26G3Tb84YStDR1e5wH0VUAtTKviv1afGcgENERO7jdJP/yCOP4Pz581izZg327Nlj2y4IAvz8\n/PDiiy9iyZIlLk2SiGgkqDeb+ubU64ugNRSjpd3x0sRoqdx2pV6tnIiw4MGnjhEREbnCsObkP/fc\nc3jkkUewZ88eVFVVAQASExORl5eHqKgolyZIROQtzW2NfVfq++fVNzSfcxgvDY6EWpWNdFUO1Mps\nRIbFeihTIiIie8N+4m10dDTuueceV+ZCRORV7Z2tOGPom1Wv1RfB2KB3GB8UEAq1ciI0ymxoEiYh\nNjyOYy2JiGhEGHaTT0Q02nV1d6Ks5mTfrHp9EfR15Q7HWvr5BiAtLhNqVQ40qhzExyRBLBJ7MGMi\nIqKhGbT7E9dRAAAgAElEQVTJF4vFEIvFaG9vh5+fH8Ri8aBXqkQiEXp6Bh4VR0TkDX1jLXW25TeD\njbWUSHyQLE+HWpWD9P5Z9T4SXw9mTERENDyDNvmrVq2CSCSCj4+P3WsiopHOau1F9fnK/gk4xSir\nOYmubsuA8SKRGKrY1L7lN6ocpMRNgJ+vvwczJiIico1Bm/zVq1c7fE1ENFIIggBz+3nUmitx/LM9\n0BlK0N7Z6nAfRVQCNP03yqYpsxDkz7GWREQ0+jm9Jv/FF1/Ev/3bv2HixImXfP/EiRP4+OOPsWrV\nqstOjohoMA3Ndf0TcIqg0xfD3NbgMD4qTAaNKqd/tGU2x1oSEdGY5HSTv3r1aqSlpQ3Y5JeUlKCg\noGDITf7+/fvx6quv4ujRo6ipqcG7776L++67z/b+/fffj8LCQrt9pk6dikOHDjmbOhGNAS3tTdAZ\nSmwPoTpvNjqMDwuKgFqVbVuCEyWVeShTIiIi73H5dJ2Wlhb4+g79xrTW1lZkZ2dj8eLFds39T+Xl\n5WHr1q0QBAEA4Ofn55JciWjk6+hsx5nqEtsEnJr6KofxfpIAyKSJuDr7OmhUkyCPVPI+IiIiGneG\n1OQXFRXhhx9+sL3ev3//JafnNDY2YtOmTcjIyBhyAvPmzcO8efMAAIsXL75kjL+/P2JiYoZ8TCIa\nvbp7ulBRW2q7Un/WpIPVwVhLXx8/pMZl9i/ByYHxbAPEIjFyr8j1YNZEREQjy5Ca/E8++QQFBQUA\n+sZjvvXWW3jrrbcuGRsREYGtW7e6LkMABw4cgEwmQ3h4OGbOnImXX36ZTT/RGGG19kJ/rtzW1JfX\nnEJ3b9eA8WKxBElyja2pT5Rp4Ovz418Pz+mPeCJtIiKiEW1ITf6SJUtw6623QhAEXH311XjxxRdt\nV98vEIlECA4ORmpqqm3cpivMmzcP8+fPR3JyMiorK/Hss89i7ty5OHr0qFPLgohoZBAEAaZGg62p\n1xlK0NHZNmC8CCLExyTbmvrUuAnw9wv0YMZERESjj0i4sNB9iPbt24cJEyYgNjbW5cmEhoZi48aN\nA67NB4Da2lokJiZi27ZtyM/Pt3vPbDbbvtfpdC7Pj4iGp63TjNqmShjNFag1V6Gjq8VhfGhAJBTh\nSVBIkyGTJiLAN8hDmRIREXmeWq22fS+VSl1yTKcvuc+cOdMlHzxcCoUCSqWSTTzRCGbpbofJXIVa\ncwVqmyrRYnE81jLQNwSK8CTIpclQhCch2N81/8ARERGNV4M2+Q888ABEIhHefvttSCQSPPDAA4Me\nVCQS4c9//rNLEvy5uro6VFdXQ6FQOIzLzeVNd65y5EjfGmfW1LXGUl07uzpQVnMS2v4JONV1FRAw\n8B8JA/2C+sZa9i/BkUW4bgLOWKrrSMK6ug9r6x6sq3uwru7x09UorjJok//1119DLBbDarVCIpHg\n66+/HvR/xs78z7qtrQ1nzpyBIAiwWq04e/Ysjh8/jsjISERGRmL16tWYP38+FAoFKioqsHLlSsjl\nctx5551D/gwicq3unm5UmbTQnu1bV19p0sJq7R0w3lfih5S4CbamXhWbArFY4sGMiYiIxpdBm/zK\nykqHry/XkSNHMHv2bNsvBi+88AJeeOEFLF68GG+88QaKi4uxZcsWNDU1QaFQYM6cOdi+fTuCg4Nd\nmgcRDcxq7YWhrgKl+iLo9EUoqzmJ7h4HE3BEYiTI1LamPlmRDl8fPt+CiIjIU1z+MCxnzZw5E1br\nwDOwv/zySw9mQ0SA8xNwACAuOsn2VNnU+CwE+vNmWSIiIm9xusk3mUyoqanBlVdeadt2+vRprF+/\nHk1NTbjnnnu4lIZoFGpoPtd/pb4YWkMRmtsaHcZHS+W2K/Vq5USEBoV7KFMiIiIajNNN/mOPPYZz\n587h22+/BQA0NDRgxowZaGpqQmBgID766CPs2LEDt956q8uTJSLXaWlvgs5QAq3+OLT6Ypw3Gx3G\nhwVH9DX1yhxoVNmIDHP9GF0iIiJyDaeb/MOHD+Oxxx6zvd66dSsaGxvx/fffIz09HXPnzsUf//hH\nNvlEI0xHZxvOVJ/oW36jL0ZNfZXD+ED/YKiVFybgZLt0Ag4RERG5l9NNfn19vd34yr///e+YMWMG\nJk6cCAC45557sGrVKtdlSETD0tXTiYqa033r6g3F0JvOwCoMfP+Ln48/UuIzbevqlTHJnIBDREQ0\nSjnd5EdGRqK2thYA0N7ejoMHD+KFF16wvS8SiWCxWFyXIRENSa+1F2dNOtus+ora0+jp7R4wXiL2\nQZJcY5tXnyjTwNfH14MZExERkbs43eRfe+21eOONNzBhwgR8+eWX6OzsxO233257v7S0FPHx8S5N\nkoguZhWsqD1fZWvqz9ScQGdXx4DxIogQH5uMdFUONKpJSImbAH/fAA9mTERERJ7idJO/du1a3HDD\nDZg/fz4A4Le//S0mTJgAAOjt7cVHH32Em2++2bVZEhEEQcB5sxFafRFK9cehM5SgraPZ4T6yCKVt\nTX2aciKCA0I9lC0RERF5k9NNfmpqKkpLS3Hy5EmEhYUhKSnJ9l57ezs2btyISZMmuTJHonHL3NbQ\nt6b+bN+6+saWOofxEaExtqZeo8yBNCTSQ5kSERHRSDKsh2H5+PggJyfnou2hoaG44447LjspovGq\nvbMVZwwl/Vfri2BqMDiMDwmUQqPKtk3BiZbKOQGHiIiIhtfkd3d3Y/Pmzfj8889RWVkJAEhKSsJt\nt92GBx98EL6+vHmPaCh6ertxuuoH25Nl9XXlEBxMwPH3C0RafBY0qhykq3Igj0qAWCT2YMZEREQ0\nGjjd5Dc2NmLu3Ln44YcfIJPJoFarAQDHjh3Dzp07sXnzZuzZswcREREuT5ZotPtxAk4Rjpw4iLoW\nA6xC74DxEokPkhUZ/TfL5iBBpoaEYy2JiIhoEE43+StWrEBJSQneeecdLFq0CGJx31VEQRCwdetW\n/PrXv8bKlSuxadMmlydLNNoIgoDa+iqU9l+pP1M9+AQcVWxq/7r6HKTETYCfr78HMyYiIqKxwOkm\nf8eOHVi6dCkWL15st10kEmHRokX4/vvv8cEHHwy5yd+/fz9effVVHD16FDU1NXj33Xdx33332cWs\nXr0amzdvRmNjI6ZMmYKNGzciMzPT2dSJ3O7CBBydobh/CU4xWjvMDveRRSqRrsqBWpkDtXIiggJC\nPJQtERERjVVON/lNTU1ITU0d8P3U1FQ0NTUN+Xitra3Izs7G4sWLL2ruAWDdunVYv349CgsLodFo\nUFBQgLy8PGi1WgQHBzubPpHL9U3AKYau/2p9w2ATcEKioVHlwLcnFHJpEmZMn+2hTImIiGi8cLrJ\nT0tLw44dO/Doo49eNMVDEAR8+umnSEtLG/Lx5s2bh3nz5gHARX8dAIANGzZgxYoVyM/PBwAUFhYi\nNjYW77//Ph566CFn0ye6bO2WVpypHvoEnKCAUGj6p99oVDmICVdAJBLhyJEjHsqYiIiIxhunm/zH\nHnsMjz76KG666SYsW7YMGo0GQN+Tbl9//XV8/fXXLluPX1FRAaPRiLy8PNu2gIAAzJgxA4cOHWKT\nTx7R1d2JspqT0PU/WXawCTh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kcShuLa+N+0hnkPujntd8ZS7HLuzmUPQ2kjNvVDtWBQrsbB1oYOtIAxvH8t+2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\nMkREpCy87IeIaAh75JFHZK91Oh0AwM/Pr8vtDQ0NAIDy8nI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67WnToCuhNZuavFJFp9dx9spxjpzdxbEL+5TFCP/O3zOIvu0epXm9Dhw6dAiw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\nICKyQf31V+6AgAAIIeDp6Sl7GlFHgoODAQA1NTUYO3Zsu+U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XqSrb4+zgBqW7L7zc/ODp7gdPNz94uvves0tQT7zR6qirkbciAI9NfAYhfoZ1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\nIgLA5oCIiIiIiJ5ic0BERERERACA/wOpVqxoWgurXQAAAABJRU5ErkJggg==\n", 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42jvrJRPF5SWwtbZHaaUfHO1dYGdj3+WCizqdFjV11S03/61JQEsiUIHq2qq2xKC2Epo6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\nTmwWiIiIiIhIJzYLRERERESkE5sFIiIiIiLS6X9KeS5Fb8D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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1430,7 +1459,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This may or may not impress you, but it impresses me! In the Extended Kalman filter chapter we will solve the same problem, but it will take significant amounts of mathematics to handle the same problem. " + "This may or may not impress you, but it impresses me! In the Extended Kalman filter chapter we will solve the same problem, but it will take a significant amount of mathematics. " ] }, { @@ -1444,12 +1473,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The previous example produced extremely good results, but it also relied on an assumption of an aircraft flying at a constant speed with no change in altitude. I will relax that assumption by allowing the aircraft to change altitude. Here are the results if the aircraft starts climbing after one minute." + "The previous example produced good results, but it also relied on an assumption of an aircraft flying at a constant speed with no change in altitude. I will relax that assumption by allowing the aircraft to change altitude. Here are the results if the aircraft starts climbing after one minute." ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 22, "metadata": { "collapsed": false, "scrolled": true @@ -1465,9 +1494,9 @@ }, { "data": { - "image/png": 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gt0eM1q9fb/E+OTkZV1dXMjIyCAsLw9XVlQ0bNljELFy4kO7du3PkyBG6d+9OUVERixYt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\nIBARERERkYwdBCIiIiIikv1/r18vltYnBbIAAAAASUVORK5CYII=\n", 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srCyr9xkZGXh5ebFjxw4iIyPx9PQkOzvbKiY1NZV+/fpRVFREv379qKqqIi0tjfT0dMaN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\n1vzXENk/orLzI0FCxT/0c9/+O9zcXCvOmEoSfrp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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1522,7 +1551,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 23, "metadata": { "collapsed": true }, @@ -1552,7 +1581,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 24, "metadata": { "collapsed": false, "scrolled": false @@ -1568,9 +1597,9 @@ }, { "data": { - "image/png": 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h5+FYqqor1XJzcwuCfUcS1vdpbK0Nh/6UlJSQm5t7ywVIRo0axenTp9W5BD16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\n5RME8afb/RvfeA9bGat01tonCN7e3ri7u7Nx40Y1QSgoKGDnzp28//7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tLa0YN3gKYf6PYmdjOjzo2rVrlJSU0KNHj0btTZ06lVOnTqlzDwYMGCArAgnR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\nCA6uWAysW7du5Ofns3fvXv17C4mJiRQWFtK9e/c7tiHkkcdr7HocbZ3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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1626,7 +1655,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 25, "metadata": { "collapsed": false, "scrolled": false @@ -1634,9 +1663,9 @@ "outputs": [ { "data": { - "image/png": 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H1q5dy/PPP18rQYv648d9X3Po1A62Hv2Wuct/z/oDy0yuZ0oI8WCZeRc5nrpT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\nfhohISGIjIwEwD6rKzfnFWCfvV1ZWVmIjIxEY2MjbG1t8cUXXyAwMFA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EEzUXf/EIq/b8wL6Tm5izfCpfrHiPU0kx900+hRB1h7qinF1nV5BboJ0kwsrC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\nF/G3v/0NEydOxPHjx2FsbIzi4mLWawe88MILCA0NRXh4OAC22a7y23o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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1679,14 +1708,14 @@ "source": [ "To include the doppler we need to add the velocity in $x$ and $y$ into the measurement. The `ACSim` class stores the velocity in the data member `vel`. To perform the Kalman filter update we just need to call `update` with a list containing the bearing, distance, and velocity in $x$ and $y$:\n", "\n", - "$$z = [slant\\_range, bearing, \\dot x, \\dot y]$$\n", + "$$z = [\\text{slant_range}, \\text{bearing}, \\dot x, \\dot y]$$\n", "\n", "The measurement contains four values so the measurement function also needs to return four values. The slant range and bearing will be computed as before, but we do not need to compute the velocity in $x$ and $y$ as they are provided in the state estimate." ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 26, "metadata": { "collapsed": true }, @@ -1709,7 +1738,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 27, "metadata": { "collapsed": false, "scrolled": false @@ -1717,9 +1746,9 @@ "outputs": [ { "data": { - "image/png": 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NDebMmYOGhgZ2m6amJsyfPx///ve/5flSNMbdknS0trcAAKzN7GFpYg0AaGyu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\ncOrUqSrtOGYfT136lWP28a1atQrPPvssrK2tYW1tDX9//yplvzlWH19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OxrqNR5h/NNs+FP8t2tpbNXoOQgghZLDoWDHIyc5N7WOEB8xm5+EJq4txrzhdo30k6tF7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\nRERERKRdejVHoKGWL18OlUoFpVIJX19fJCUl6TokvRIREQG5XK7x5+j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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1784,21 +1813,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The last sensor fusion problem was a toy example. Let's tackle a problem that is not so toy-like. Before GPS ships and aircraft navigated via various range and bearing systems such as VOR, LORAN, TACAN, DME, and so on. I do not intend to cover the intricacies of these systems - Wikipedia will fill in the basics if you are interested. In general these systems are beacons that allow you to extract the range and/or bearing to the beacon. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays what is called the \"radial\" - the direction from the VOR station on the ground to the aircraft. Using a chart they can extend these two radials - the intersection point is the position of the aircraft.\n", + "The last sensor fusion problem was a toy example. Let's tackle a problem that is not so toy-like. Before GPS ships and aircraft navigated via various range and bearing systems such as VOR, LORAN, TACAN, DME, and so on. I do not intend to cover the intricacies of these systems - Wikipedia will fill in the basics if you are interested. In general these systems are beacons that allow you to extract the range and/or bearing to the beacon. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays what is called the *radial* - the direction from the VOR station on the ground to the aircraft. The pilot uses a chart to find the intersection point of the radials, which identifies the location of the aircraft.\n", "\n", - "That is a very manual approach with low accuracy. We can use a Kalman filter to filter the data and produce far more accurate position estimates. Let's work through that." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. The width of the circle is proportional to the amount of sensor noise." + "That is a very manual approach with low accuracy. We can use a Kalman filter to produce far more accurate position estimates. The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. The width of the circle is proportional to the amount of sensor noise." ] }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 28, "metadata": { "collapsed": false, "scrolled": false @@ -1806,9 +1828,9 @@ "outputs": [ { "data": { - "image/png": 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f/lbJYYgGlZ1FyifVV+ZnQq3y646ag15fyz3O5yw7DFmSOrSJkWZoR3kvSjsr\nd2Qc9FpVp4/3RVOLAyXlddAkpyHxmTdguuqG9sdYDhJa9Lneb7icpYe87iMiUh7/qhKFMJvDhX1H\naxTtUyUK3Jfaz/pT7nE+X7PUupwJEFSdJ816jQp5I5XfInHHoXIAgKDRImbJ/7AcJERpR4+DoOq4\nB4FktcBdpfy6DCLqiEk1UQjbU1oNl1vZGaZpOSmINxsV7ZPO6U+5x/lkjxvOsiKvdm322G6fO90P\nJSAXfmJivHQOy0FCkKjTQzPc+9h6Z7H3GzQiUhaTaqIQ5o/Sj7l5nKX2ByXKPc7nOn4EssPeoU3Q\n6aHJ6P7nNzTGgNHpys5Wn6xtRlWdpUMby0FCk683Xr4+9SAiZTGpJgpRsixjV1Glon0atGpMGJmo\naJ+kXLnH+XwlQdrM0V4f7XfmohzlF6IWFnvfjywHCT1aHwfBuGsq4WmoC0I0RIMHk2qiEFXT0ILm\nVoeifU7JToJGrewitsFOqXKP88myDGfxAa/2rhYoXig/R5kTFs9XUt55UnauHGRUexvLQYJDZY6G\nOsn7TZWz9JCPq4lIKUyqiUJUWUV99xf1Uv5o5ROtwUrpco/zeepq4WnquDe5IIrQZvb8FMPUIVFI\njjP1OQZfursnNclpSPzzGzBddX17G8tBgsNnCUgZ39wQ+ROTaqIQdUThpFoUBOTxSHJF+KPc43zu\nCu+dGtSpGRANPV9gKgiC4m+iKs5YYHO4urxG0OoQs+R/WQ4SZNqsMV5t7opTfGND5EdMqolCVFml\nskl1zrB4REXoFO1zMPJHuceFfG1/pk4d1ut+pil8wI8so8ene7IcJLjUQ5O9t9ZrtUJqbgpSREQD\nH5NqohAkyzLKKpQ9mnxKVpKi/Q02/iz3uJC70jup1iSl9bqfnPR4GLQ9W9jYU735BIXlIMEjqNRQ\nDfX+ZIr7VRP5D5NqohBU29ACq82paJ/ZacofCDJY+Lvc43yyJMFd7b2Vojq590m1SiViRHKMEmG1\n6+0nKCwHCR71UO9PKny9YSMiZTCpJgpB/likOFLh5GqwCES5x/k8dbWQXR3fUAl6PcSYvr0pykyJ\nVSKsdn29N1kOEngaH2/EOFNN5D9MqolCUE/rVnsqMSYCkUbWU/dGIMs9zueuLPdq0ySlQRCEPvWn\n9JupnixW7AzLQQLL17Z67spy/ncm8hMm1UQhqLaxRdH+lJ6tHOgCWe5xIXe1d1Kt8pEc9VRWqrJl\nP7IM1DUE3wQ/AAAgAElEQVTb+vx8loMEjiphKBcrEgUQk2qiENRg6XvS4guT6p4LdLnHhSQfp96p\nh/Z9a7zkuEjFFyvW9yOpPovlIP4nqNRQJQz1apcaebIikT8wqSYKQfUKJ9UjklhP3Z1glXtcyGNt\n9mpTRUX3uT9RFDA8qe/P90WpN30sB/E/Mcrs1SZZLUGIhGjgY1JNFILqm+2K9jckuueHhgxGwSz3\nuJBk8U6qxUjvxKg3hkRH9Ov5F1LyTR/LQfxLNPlIqpsbgxAJ0cDHpJooxNidbrT2cSFYZ2IjDYr2\nN5AEu9zjfLIkQfYxUy2aIvvVb4xJ36/nX0iJ8o8LsRzEP1SRUV5tnKkm8g8m1UQhRul6ap1GBaM+\ncDOt4SJUyj06xGRrhSxJHdoEnR6Ctn87t8RGKfumqsGq7CcpZ7EcRHmCyVdS7f3GjYj6T9nVK0TU\nb/3ZWcGX2EhDn7djG6gsrQ7c88zHHWanTQYt/v7gVQGfnT6fZPHelUH0MdPYW0p/UuGPmeqzzpaD\n6Mblov65P0C2tbSXgzj2f43YB34LMcLkt/EHGl/3j6/7jIj6T/GZ6pdffhnDhw+HwWBAXl4eNm/e\nrPQQRAOa0jPVMZHKfvQf7kKp3ONCPuupfcw09laM0km1wveoLywHUYbKRz0+yz+I/EPRpHr58uX4\n2c9+hkceeQR79+5FQUEB5s+fj1OneIITUU/ZnW5F+4uLGtyLFO+66y6IooilS5eGXLnHhaRW7/3J\nlZiVjVO4/EPpe7QznZWDvHjDVRBFsf2fWq1GamoqbrzxRpSUlAQktnAh+KjH5+JPIv9QNKl+9tln\ncccdd+CHP/whRo0aheeffx5JSUl45ZVXlByGaEDzSMrWjQ7memqbzYYVK1YAAP72+lv48bMfBX13\njy5J3smqoNH2u1ul7wGl79Gu+NwdRPIAsow3broaW9evw6ZNm/DEE09gz549mD17NpqbWTN81oWH\nvwBo++9HRIpTLKl2Op3YvXs35s6d26F97ty52Lp1q1LDEA14bo/U/UW9oFYN3vXIq1atgsVigTF5\nDOzWRqC+DEDolHtcSPb1s1egHl7pe0Dpe7QnfJWDZFYeQfqyvyA3PhqLFy/GK6+8goqKCmzbti3g\n8YUsUeXVdOFiWCJShmILFc+cOQOPx4PExMQO7QkJCaiurvb5nMLCQqWGD5hwjJlC3/n3VXFxNRob\nldtH9uTJkxist+3zzz8PY0QkWjMWAFUlQPVeXLtgDh68ZgwstcdRWHs82CF2oC0phvGCn31teQVs\nffgBnn9P2ZxuRe8pe6sqeK+FN90Hx8k6YN8JAG3lIEVf74SzqQXl5W1HvB86dAhxccoezx623G5E\nX/Czl1VqHO/nPUWklHC7r7Kysjp9bPBOYRHRgHb69Gns2rUL86+ci7sWToYqMQfqxjLcPy8Deo33\n7N1ApvTuL0Hd2k6jgX3iNEAQ4FJr0VgwF9b0LBw7dgwvvfQSYmNjkZubG7z4wgK3JiTyB8VmquPj\n46FSqVBTU9OhvaamBklJST6fk5eXp9Twfnf2nVQ4xUyhz9d9Ve0qQXSJcqvz09PTB+V9+9RTT0GS\nJPziF79AXt5UTM/Q4ge3XI+SkhLcc889wQ7PJxucsJbu69CmT09DZC9+fr7uKUurA9EfHVUmSLTV\nowfznjpwoG3nltlf7gG+3APgTwCA5ORkfPbZZ0yqzyM57Kj7rOMx9YJGi6x+3lNE/RWu91VTU+db\nUio2U63VapGbm4u1a9d2aP/8889RUFCg1DBEA56o8KyiFMBFZaHk7bffRnZ2NqZNmwaVSsStN16L\n5ORkvP3228EOrVOCr9pnBepflV5YqPQ92lerVq1CYWEhdu3ahVWrVmHMmDGYP38+ioqKgh1a6PD1\nqcIgXmdB5E+K/mY9+OCDeOutt/CPf/wDhw8fxgMPPIDq6mr8+Mc/VnIYogFNJSqbsARq+7NQUlhY\niMOHD+Paa69FY2MjGhsb0dzcjGuvvRbbt29HaWlpsEP0TfDxkuzp/8/PofA9oPQ92lfjxo3DlClT\nkJubi6uvvhoffvghZFnGo48+GuzQQofbx44yPhYvElH/KXqi4g033IC6ujo89thjqKqqwvjx47F6\n9WqkpaUpOQzRgKZVuN63wer/gzpCzdnZ6CeffBJPPvmk1+PLli3DH/7wh0CH1S1B772ftK+9q3tL\n6WPFNerQnOnU6/UYPnw49u/fH+xQQoav+0fQ8UAoIn9Q/JjyJUuWYMmSJUp3SzRoRJuU/YPXYFE2\noQp1TqcT7733Hi666CL86U9/6vCYLMtYunQp/vnPf4ZkUi36OqjDxymLvaX0seJKn9ColNbWVhw5\ncgTjx4fWVonBJFn9c0onEXlTPKkmov6JVThhqVM4oQp1n3zyCerr67FkyRLMmDHD6/F77rkHS5Ys\nwYYNGzBr1qzAB9gF0eeR0v1PqhsUPlY8JjI0Zjr37NmD2tpayLKMqqoqvPjii2hsbMT9998f7NBC\nhq83ZUyqifwjND/DIxrEYhU+Utpqc8LpGjwnqC1btgxRUVG4/vrrfT5+0003wWAwYNmyZQGOrHs+\nZ6pbrJD7WVddr3BSHRdlVLS/3jq7ReD111+PgoICTJ8+HUuWLIEoilizZg2++93vBjW+UCJZvXcq\nECOZVBP5A2eqiUKMyaCFRi3C5Vbu1LMGiw2JsSbF+gtlK1eu7PLxqKgotLT0v07ZHwSVGqIxwqsO\nVrJaoTJHd/Ks7ile/qFwiVJv3X777bj99tuDGkO4kKze23MyqSbyD85UE4UYQRAUT1oGWwlIOPNH\nCYjSM9VKf5pC/iNZfM1Ue99jRNR/TKqJQpDSScuJGuWOqCb/8lXv2t/FiidqOj+soC+Urvsn/5Ga\nfSTVrKkm8gsm1UQhSOmkpayiXtH+yH/EKO9ZRM/p6j7312CxKf5JRaju/kEdybIMz5kar3Zf9xgR\n9R+TaqIQpPRCsCOVDYr2R/6jHpri1eauOtXn/vzxhiqO5R9hQWqsh2Rr7dAmaDRQxQ4JUkREAxuT\naqIQNCxR2ZmkEzVNcLkHzw4g4Uw9NNWrzV3Z96Ra6TdUMSY9oiJ0ivZJ/uHrzZg6MQWCiicqEvkD\nk2qiEJSZEqtof26PhOPVrKsOB+qkFEDoeAy4p6kBUqu1T/0pPVOdmRLbvqUdhTZ3ZblXmzrJ+5MQ\nIlIGk2qiEDRsaLTiR0Gzrjo8CBot1EMSvdp9JUg94Y+kmsKDu8pHUp2cHoRIiAYHJtVEIUitEhUv\nAdl/tFbR/sh/1ElpXm19qauuON2s+CLFkckxivZH/iHLsu/yjyTv8iIiUgaTaqIQlZUSp2h/X5dU\nwe1R7kAZ8h91so+kug911TuLKpQIpwPOVIeHThcpxnt/CkJEymBSTRSilJ4RbHW4cOAYZ6vDga/F\nis7jpb0+rnzHYWWT6hiTnge/hAnnkWKvNi5SJPIvJtVEIcofM4I7DvWtLpcCS52cBkHbcYcN2W6H\n6+SxHvfR3OLA4RNnFI2LixTDh7PkgFebJmNkECIhGjyYVBOFKH8sVtxZVAFZlhXtk5QnqNXQjhzt\n1e4sOdjjPgqLKyEp/LNm6Ud4kJ0OuI6WerVrR40LQjREgweTaqIQpVaJGJeRoGiftY2t3FovTPhK\ngJzFB3r8psgf9dSTs4Yq3icpz3m0xKtUSIwwcecPIj9jUk0UwvJzlN9TdsPe44r3ScrTZuV471fd\nUAfPae9jpy/UYndjV1GlovFEGXUYlRavaJ/kH85i79IPbfZYCCL/5BP5E3/DiEJY/mjlk+rPC4/C\n6eLpiqFONEZAkzbcq91XwnShnaVn4FT4BM2po5MhiqynDnWyJMFZcsirXZvN0g8if2NSTRTCEmIi\nMHxotKJ9WmxObNp3QtE+yT98lYA4ivZ1+RxJkrG1WPldXvzxBo+U5z51zOv0TUGthnZEVpAiIho8\nFEuqGxoacP/99yMnJwdGoxHp6em49957UV/PU9yI+mOaH0pAVu/wXsREoUebPdarzV15yudJeWeV\nVjXjTLND0Tg0apH11GHCvnubV5tmxCiv3WSISHmKJdWVlZWorKzE008/jQMHDuCdd97Bxo0bcdNN\nNyk1BNGg5I+66pLyepSW1yneLylLHZ8A9VDvn7+tcEunz9lSpPws9cSRiTDoNIr3S8qSWqxwHPzG\nq103ZlIQoiEafBRLqseOHYsPPvgAV111FUaMGIEZM2bg6aefxhdffAGr1dp9B0Tk08jkWMRGKn/g\nxurtnK0OB/rcAq82x/6vIdm9jx8/3diCgyebFI9h6iiWfoQD+94d3rt+GCOgGzMxSBERDS5+ralu\namqCTqeD0Wj05zBEA5ooCn4pAVm/9ziq6iyK90vK0o2fAkGn79Amu1xwfLPL69rl6w8qvjc14J9P\nS0hZsiTBXrjVq10/aRoEDT9lIAoEQfbTSRCNjY2YOnUqFi5ciL/+9a/t7U1N52ZRSks5U0bUEydP\nt+AvH3mv6O+vKSNisXgWT1kLdYbCTdAVd1yg6ImKgeWqm9q33attsuOplQfgkZR9Sc9JNePuudmK\n9knKU1cch2nDJx0bBQHNi26BFGkOTlBEA1BW1rlFv2Zzx9+tbmeqH3nkEYii2OW/jRs3dniO1WrF\nokWLkJaWhqeeekqhb4No8EofEoH0+AjF+919tB7lda2K90vKcmR5L1hUNTdAXXPugJfVX5crnlAD\nwPTRyh5ARP6h83EsuSspnQk1UQCpu7tg6dKluO2227q8Ji0trf3/W61WLFiwAKIo4uOPP4ZWq+30\neXl5eb0INbgKCwsBhFfMFPp6c1/dIcTiuQ92KB7DN9USvjOP93Woaywvhet4WYe2IfWVMF/1HZSW\n1+FEYymio6PR2Nh2YmZ0dP+3YhxiNmLxd2Zzf+oQ564qR0NrE3DBzzzqmuuh87GDTG/x7x/5Q7je\nV+dXXFyo26Q6Li4OcXFxPRrIYrFg/vz5EAQBn376KWupiRR06fh0/GP1HlhtTkX7LSyuwoFjtRg3\nnDOSocww9RKvpNp5rBSOI0V4e4OypyeeNX9aJhPqMNCy7hOvNlV0LLSZOUGIhmjwUmyhosViwdy5\nc9HY2Ig333wTFosF1dXVqK6uhsvlUmoYokFLp1VjzhTvE/aU8MbqPfB4JL/0TcrQjhoLVaz3MeHH\n3l+OfWXVio+nVom4Io/19qHOebwMzrIir3bDxbN4LDlRgCn2G/f1119jx44dOHz4MLKzs5GcnIzk\n5GSkpKRg2zbvzeiJqPfmT/PPqWilFfVYtdn7DzOFDkGlRsRlCzq0eTwSTh0owoiWik6e1XfTx6Uh\n2qTv/kIKGlmW0frFx17tqpg46HMvDkJERIObYkn1rFmzIEkSPB4PJElq/+fxeDBjxgylhiEa1JLj\nIzE50z8n27375X6cqlV+j2NSjnbMRKiTUtu/PlnbBJfbg/yGwxBlZT9pWHgRj7UOdc6i/XBVnPBq\nN866EoKq2+pOIlIYPxsiCjPXTB/ll35dbgl/fX87y0BCmCCKiJh9FQCgyWrHmaa2nVui3VaMtngn\nV32VmRKD0enepSYUOmSPBy3rVnu1qxOToRs3JQgRERGTaqIwMyU7CWMzhvil75JyloGEOs2IbCBt\nBI5VN3Zon9pYBJ1HmUWst8+bBEHgAsVQZv96KzxnarzaI2YvZC01UZDwN48ozAiCgNvn+e/Y4Xe/\n3I8TFyRsFFpWyelwuT0d2oweO6bX7+vkGT03cWQiJvmpxIiU4ak/g5YvPvJq1wwbCQ13/CAKGibV\nRGEoZ9gQvxxdDrSVgfzxnU2wtDr80j/1z6c7yvDhkVYcMSZ7PTbKegojHbX96t+fb9io/2RJguWj\n5ZB97KoVcflCfsJAFERMqonC1G1zJ8Jffz+r6q146l9bWF8dYvYdqcGrH38NANgSNwEOUeN1zVzL\nYeilvpWBTB+XhqzUnp1LQMFhL9zqtV85AOhzC6BJ98+Wm0TUM0yqicJUeqIZl0/23x/RvWU1eOPT\nPX7rn3qnut6KJ9/b0n4UeYvagC2x472ui5AcuNxa3Ov+VaKAxVdM6Hec5D9tZR8ferWrzNGImLMo\nCBER0fmYVBOFsZtnj4dG7b9f4w+3luDzwiN+6596xuZw4bF/bkTzBSU5xaZ0nDAkel0/xl6FjJaq\nXo0xJ3cEUoZE9StO8p+uyj5Mi74PUc89xYmCjUk1URhLiInAQj8dCHPWy/8txMFj/avTpb6TJBnP\n/nsbTtT42ENcEPBV/GSfZSCzzuyByd3aozF0GhVuunxcf0MlP7Jt+bLTsg/tSP9ss0lEvcOkmijM\n3TxnPIbGRvitf7dHwv9bthGl5XV+G4N8kyQZz32wHdsPdX5iYmdlIAbJgfk126GW3N2O84MrJyHO\nbOxXrOQ/jqIDPvekZtkHUWhhUk0U5gw6DX563TS/jtHqcOG3b27AsaoGv45D50iSjFf+uwvr9hzv\n9trOykDinU247MxuQJY7fe744QlY4OdPO6jv3LXVsKx8x+djLPsgCi1MqokGgPEjEv1+rLTV5sTD\nr6/DkYp6v45DbQn1y//dhTW7eljPLghYHz8FVpXB66HMlgpMaSrx+TSdRoWffncaRJHbsIUiqbUF\nzf96HbLTe3tLY8HlLPsgCjFMqokGiNvnTfRrGQgAWGxOPPyPdSg+ecav4wxmHo+E5z7Yjs96mlB/\ny6bWY03iNLgFlddj0xoO+Vy4+IMrJ2ForKnPsZL/yB43LO+/DU+Dd9mVNisHxtkLgxAVEXWFSTXR\nABGIMhAAaLG78Mgb67Ht4Cm/jzXYtNpd+OM7m3pU8uHLaV0M1kSO8fnY7NOFiHOcW+zIso/QJcsy\nWj5bBeexUq/HVPEJiLxuMY8iJwpB/K0kGkDGj0jEVX4uAwEAu9ONx9/djH+tOwC5i3pd6rnKMxb8\n4pW12FVc2a9+ivRJ2GH03r9cK7uxqHoLop0Wln2EuNb1n8K2a4tXu6g3wPz9H0HUe5f5EFHwMakm\nGmBumzcRyXGB+Uj/3S/246l/bYHd2f0OE9S5vWXV+Pkra3HqdLMi/W2OyMRx41CvdoPkwNXVm3HP\npRks+whRrRvXonXT594PCAIiv3c7VHFDAh8UEfUIk2qiAcag0+CRxTNg1HnvXewPm/efwv/+/XOc\nbmwJyHgDiSzL+GhrMR59awOstr4dLe6zX0HAF0Py0KCJ9HoswyRiyv7V8NSzLj7UtG76HC3rP/X5\nmOmKq7kwkSjEMakmGoDSEsz4xY0XQwjQp/tHqxrxsxc/w9YDrLPuqeYWB57+11a8+vHu9qPHleQS\nNfh4aAEs6nP7T5sMWgwbGg2puQmNb70A9+lqxcel3pNlGS3rP/W5FzUAGAoug/6imQGOioh6i0k1\n0QA1dXQKbp87MWDjNbc68MT/bcZT721Bk9UesHHD0baDp/CT51Zj0/6Tfh3Hqjbiw6HTYVUZoFWr\nkJkSC+Hbd1qSpRlNb70Ed1W5X2OgrsmShJYvPkLrxrU+HzfkX4qIOYvaf25EFLqYVBMNYNfNyMHM\nicMCOuam/Sfxk+dWc9bah7bZ6S14/N3NaAzQG49mjQmfpc1AZvYwaNQdt9uTWq1ofPMFOA59E5BY\nqCPJYYfl32/BtnW9z8f1Uy5CxLzvMKEmChOKJ9WyLGP+/PkQRREffPCB0t0TUS8IgoCfXjcNWSmx\nAR23qeXcrHV9sy2gY4ciWZax+ds3Gxv3+Xd22pcf3DQHqUsehBhp9o7N5UTzv99Cy4Y1kCUp4LEN\nVp6GOjS98TwcRft9Pm7Imw7Twuu5dR5RGFH8t/WZZ56BStU2G8J310TBp9Wo8PCtlyLGFPjjjDft\nP4m7n/kIyz77Bi0KLsQLJ/uP1uCXf/scT763JWCz0+e7YdYYXDphGNTxCYj+wX1QmWN8Xtf61Wew\nvL8MkoOlO/7mPF6Gxtf/Anet94E8AGC4aCYiFnyXCTVRmFH0N3bXrl14/vnn8eabbyrZLRH1U5zZ\niN/fMQsmgzbgYztcHvz7q0P40Z8/wspNh+F0eQIeQzAcrWzAo29twEOvr0PxKe9T8QLhitwRuGXO\nhPavVbHxMN9xP9QJ3tvtAYDj8DdoevMFn6f4kTJshVvQ/M9XILX63i3HOHMeIuZew0kpojCkWFJt\nsVhw880347XXXsOQIdxHkyjUDE+Kwf+7Y1bAttq7kNXmxBuf7sU9z36Mz3aWDdjk+mRNE/68fCse\neHENvi7xPRMZCDMnDsN91+Z7HfCiMsfAfOcD0I4a6/N57ppKNL7+FzgO7Q1EmIOGZGuFZeW7sH7y\nvs8yG0GjQdT3bkfErCuZUBOFKUFW6Di0W265BfHx8XjuuecAAKIo4v3338d1113X4bqmpnPH5JaW\neh/BSkT+dazGgr+vLYHDFdz62QidGvlZ8SgYPQTxUYEvTVGS2yPhwMlGbCmqRVmVJdjhYGJGDBbP\nGglVVycmShL0+3dBf6Cw00ucwzJhy5sBmSf49Yu64jiMOzdA7GR2WoqIRMuM+fDEckKKKNRlZZ07\ntdhs7rhORd3VEx955BE8/vjjXXa+fv16nDx5Evv27UNhYduL89k8nccXE4We4YmRuHtuNl77vBR2\nZ/Bmi1scbqw/UI31B6oxOsWM6TlDMCY1OqyOzm5scWJ7yWlsKzqNZpsr2OEAaEuob505ouuEGgBE\nEfaJ0+CJjoVx+zoIbu9TMbUnyqCuqYBt6ky40kf6KeKBS3DYYdi9BdqjRZ1e4x6ShJZLr4RsMHZ6\nDRGFhy5nquvq6lBX13VtXVpaGu69914sW7YM4nmLKjweD0RRREFBATZu3Njefv5M9YUZfig7+4Yh\nLy8vyJHQQBLM+6rkVB1+p/BJfv0VG2nAtJwU5OekYMKIRGg1qu6fFGDV9VbsOFSOnUUVOHj8tF8O\nbumrWZOG4ZIMDVSi0Kt7yl1Vjubl/4CnqbHTa3RjJ8E0/7sQI3i8eU84Sg7C+vG/IVmaOr1GP3ka\nTAu/B0HV5fxW0PHvH/lDuN5XXeWxipR/VFZWorHx3IuxLMsYP348/vKXv+Caa65BRkZGj4IJZeH6\nw6fQFuz76mhlA37zxno0tzqCMn5X9Fo1JmcOxbScFOSOSkZ0EHYvAQCPR0JZRT12HK7AzqIKnKjp\nPEkKpityR+C+a/Oxe/fXAHp/T0lWC6wfr4Cj+ECn14jGCBgvvQL6vOkQ1KGdCAaL+0wtWtethuNw\n53t/Czo9TPOugW7StLConw726xQNTOF6X3WVxyryqpicnIzk5GSv9rS0tA4JNRGFlhHJMXjqnjl4\n7J2NKD8d/Frg89mdbmw7VI5th9pO/EuINiIzJbbDv0ijTtExPR4J5aebUVZRjyOVDSitqMOxqkY4\nQnxR5U2Xj8P3Lx/Xr9IZ0RSJyBvvhHb/12j59D+Q7N77i0utLbB+tgq2HRthnDUfuvFTuO3btzxN\njWj9ag0c3+zqcr9v7cjRMC26ESpzdACjI6JA4FQD0SCXMiQKf/7xXPx5xVYUFgdvt4ru1Da2orax\nFVsPnjtWe4jZiMTYCMSYDIiLMiAm0oDYKANiIw0wGbRQiQJUKhECAI8kQ5JlOF0eNFhsqLfY0GCx\no665FQ0WO+otNpSfbg75BPp8Oo0KD15/MQrGpSnSnyAI0E/Ig3Z4Nqyf/LvTWWtPYz0sq96Fbes6\nGGcvhDZrTFjMuPqD1NqC1i1fwr5zE2QfdelnhdvsNBH1nt+SaokncxGFjQiDFr9ZPBPL1n6DDzYe\nDnY4PXa6qRWnm1qDHUZQJEQb8cjiGRie5Pswl/4QI6O6nbUGAHdtFZrfex2atOEwXDIb2sycQTNz\nLVmaYd+9DbbtX3X63+cszk4TDQ6cqSYiAIAoCvjBlZMwLNGMF1buhMvNN8ahatzwIfjVTZfA7Mc6\n8/NnrVu++BD2fV93eq3r1DG43nsdKnMM9HkF0E+aBtEU6bfYgkWWZbhOHIG9cAuch/d1e6y7GBmF\niMsWQDcpn7PTRIMAk2oi6uCyycOREh+FP76zCfWWrmfgKPDm52fi7kW5UKsCMyMsRkYh8tpbYbj4\nMrSs+wTO0s4/yfA0NaDly0/QuuEzaMdMhCFvOtRpGWGfUEp2Oxz7C2Ev3AJ3bXW314t6AwyXzIYh\n/1IImsCfYkpEwcGkmoi8ZKfF4S8/mYfn/7MjqKcC0jlGnQZ3XTUFc3JHBGV89dAUmG++G87jZWj9\n8hO4yo93eq3sccOx/2s49n8N9ZCh0I4eB232WKiT08OmPESytcJZdhjO4gNwlh6G7Ox+hxxBrYZh\n2kwYpl8OkftOEw06TKqJyKfYKAN+d/tMfLn7GF77eDdaHaFxuMlgNCVrKO6/bhrizcFP1LQZmdDc\n+VM4iw+idd0ncJ/ueubWfboa7tPVaN30BURTJLRZY6DNHgftyOyQm8X11J+Bs/gAHCUH4T55tNvy\njrMEUYRuUj6MM+dBFcW6aaLBikk1EXVKEATMyR2BSZlD8eLKnZy1DjCjToMfLZyMObkjQqqEQhAE\n6EaPgzZ7DFxHimEr3AJnycFunydZLbDv2QH7nh0Q1Gpo0kdAnZQGdVIq1MlpEKNjA/Z9yi4X3DUV\ncFeegruqHK7y4/Ccqe1VH2KECfopF0OfezFUZuUXjBJReGFSTUTdijcbOWsdYKE0O90ZQRShzcqB\nNisHnoY62L/eBvue7ZBaW7p9rux2w3m0BM6jJe1tot4AdXIa1ElpUMUnQIw0Q4yMgmiKgmAw9jrh\nlj1uSFYLJEsTJEszpOZGuKvbEmnPmZoez0RfSJM+Avqp06HLmRDypyESUeDw1YCIeuT8WeuXVu0M\n6T2tw1mozk53RxUTh4g5V8E4cx4ch76BvXBLl3XXvkh2m1eifZagUp9LsI0RbbXZogiIKkCWAEkG\nJA9klwtSy7eJdA+S+54SdHrox+dCn1cAdaL3YWdEREyqiahX4s1G/Pa2mdhdUoVla7/B0arGYIc0\nIERS/kIAAAr1SURBVGjUIhZOy8L1s8YiKkLZkyIDSdBooJ+YB/3EPHiaGuEsPQhnyUG4jpZC9nR+\nOEp3ZI8bnsZ6eBrrFYy2aypzDLSjxkKbPQ6ajJGclSaiLvEVgoh6TRAE5I5KxuSsJGzefxL//Pwb\nVNcrNys4mIiCgMsnZ+DmOeMxJDoi2OEoSmWOhiFvOgx50yE57HAdLYGzpC3JVnIWWUnqlHTossdC\nO2ocVAlJYfVpAREFF5NqIuozURQwY+IwFIxLw2c7y/Cv9QfRaLUHO6ywcdGYFCy+YiLSE83BDsXv\nRJ0eupwJ0OVMgCxJ8Jyp+XaR4Cm4K8vhrqmA7Apsrb7KHA310NT2Om51chrECFNAYyCigYNJNRH1\nm1olYuHF2bh8ynB8uKUYq7YUw2pzBjuskDV+eAIWz52AnGFDgh1KUAiiCHVCEtQJScCkfACA7PHA\nU1fblmjXVJ5bXGhthmRp6nPCLUaYIJqi2uqxI81QRce27zgyEE99JKLgYVJNRIox6DS48fJx+M4l\no7Fp/0ms3l6K0orA1cCGMoNWjVmTMrDgoixkDOVexhcSVKpzifYFZFmG7HBAsrYl2rLDAUgeQJbb\n6rRF8duFiypAFL9NpM0QTSbWQRNRwPDVhogUp9OqMSd3BObkjkBpeR1Wby/Fxn0n4XR7gh1awA1L\nNGPBtCzMmpQBo14T7HDCkiAIEPR6iHo9EJ8Y7HCIiHxiUk1EfpWVGocHvheHOxdMxpe7j+HTHaWo\nrLMGOyy/UqtEXDwmFQsuysLYjCFc7EZENAgwqSaigIg06vCdS0bjmumjcLy6ETsOV2Dn4YoBUx5i\nMmiRm52EaTkpmJKVhAhDaB3BTURE/sWkmogCShAEDE+KwfCkGHz/8nGob7ZhZ1Fbgr33SDVc7r6d\nchcMQ2MjcFFOKvJzUpAzbAjUKjHYIRERUZAwqSaioIqNMuDK/ExcmZ8Ju9ONb8qqUXyqDmUV9ThS\n2YDmVkewQwTQtp90WkIUMlNikZkSiwkjEpGWEMXSDiIiAsCkmohCiF6rxrQxqZg2JhVA264PtQ0t\nOFLZgLKK+oAl2hcm0COT22bW9Vq+ZBIRkW+K/oXYuXMnHn74YWzfvh2CIGD8+PH48MMPERcXp+Qw\nRDRICIKAxFgTEmNNKBiX1t5uc7jQYLGj3mJDfbMN9RYbGiy29q9bHS54PDI8kgSPJEOSZKhUAlSi\nCLWq7V+0SY/YSANiItv+NzbK8O3XBkSb9BBFzkATEVHPKZZU79ixA1deeSX+53/+B8899xy0Wi0O\nHDgAjYZbSBGRsgw6DQw6DZLjeXgHERGFBsWS6qVLl+K+++7Dr3/96/a2zMxMpbonIiIiIgpZiixV\nr62txfbt2zF06FBccsklSExMxIwZM7Bu3ToluiciIiIiCmmKJNVHjx4FAPzud7/Dj370I6xduxaX\nXnop5s2bh3379ikxBBERERFRyBJkWZY7e/CRRx7B448/3mUHGzZsgFqtxiWXXIKHHnoIjz32WPtj\nBQUFmDRpEl5++eX2tqamJgXCJiIiIiIKHrPZ3OHrLmuqly5dittuu63LDtPS0lBdXQ0AGDNmTIfH\ncnJycPLkyb7ESUREREQUNrpMquPi4nq0HV5GRgaSk5NRVFTUob2kpAQTJ07sX4RERERERCFOkd0/\nBEHAL3/5S/zud7/DhAkTMGnSJKxYsQI7d+7sUPoBeE+VExERERGFO8W21HvggQfgcDjw85//HHV1\ndRg3bhw+/fRTjB8/XqkhiIiIiIhCUpcLFYmIiIiIqHuKbKk3kDU0NOD+++9HTk4OjEYj0tPTce+9\n96K+vt7rusWLFyM6OhrR0dG47bbbuNMJderVV1/FZZddhujoaIii6HNBL+8p6ouXX34Zw4cPh8Fg\nQF5eHjZv3hzskChMbNy4EVdffTVSU1MhiiLefvttr2seffRRpKSkwGg04rLLLsOhQ4eCECmFiyee\neAJTp06F2WxGQkICrr76ahw8eNDruoFyXzGp7kZlZSUqKyvx9NNP48CBA3jnnXewceNG3HTTTR2u\nu/nmm7F371589tlnWLNmDXbv3o3FixcHKWoKdTabDVdeeSV+//vfd3oN7ynqreXLl+NnP/sZHnnk\nEezduxcFBQWYP38+Tp06FezQKAy0tLRgwoQJeO6552AwGCAIQofHn3zySTz77LN48cUXsWvXLiQk\nJOCKK66A1WoNUsQU6r766ivcd9992LZtG9atWwe1Wo05c+agoaGh/ZoBdV/J1GurV6+WRVGULRaL\nLMuyfOjQIVkQBHnr1q3t12zevFkWBEEuLi4OVpgUBnbt2iULgiCfOHGiQzvvKeqL/Px8+e677+7Q\nlpWVJf/6178OUkQUrkwmk/z222+3fy1Jkjx06FD58ccfb2+z2WxyZGSk/Pe//z0YIVIYslqtskql\nkj/++GNZlgfefcWZ6j5oamqCTqeD0WgE/n979w+SzB/HAfz9PcE/FEqQpWFgS00NYkM6REtCQVO0\n1dBSg4PkXGjQENHcEETQEJHUFAQ2SCUeLW1FQ9DQ4lVQ6QlR2P2GB4/fPTw8T6ZwZu8XHML3vsJH\neXP34e64LwBZltHa2opQKKTPCYfDaGlpgSzLZpVJ3xgzRdV6e3vDxcUFIpGIYTwSiSCXy5lUFTWL\n29tbKIpiyJfdbsfQ0BDzRZ9WKBTw8fGBtrY2AM2XKzbVVXp+fsbi4iJmZ2chSb/+vnw+D7fbbZgn\nhEBHR4e+MA5RNZgpqtbj4yPK5TI6OzsN48wM1UMlQ8wX1SIWiyEQCOgXjJotVz+2qV5YWIAkSX/d\nTk9PDd9RVRXj4+Po7u7G6uqqSZVTo/pKpoiIvrvfn70m+pN4PI5cLof9/f1PZeY75qpu76n+bj67\nBHuFqqoYGxuDJEk4PDyE1WrV93k8Hjw8PBi+q2ka7u/v4fF46ls4NaxqM/U3zBRVq729HRaLBYqi\nGMYVRYHX6zWpKmoWleOOoijw+Xz6uKIoPCbRP83Pz2Nvbw+ZTAZ+v18fb7Zc/dim+rNLsANAsVjE\n6OgohBA4OjrSn6WuCIVCUFUVsizrtzRkWUapVEI4HK577dSYqsnUvzBTVC2r1YpgMIh0Oo2JiQl9\n/Pj4GJOTkyZWRs2gp6cHHo8H6XQawWAQAPD6+opsNou1tTWTq6NGFovFkEqlkMlk0Nvba9jXbLmy\nJJPJpNlFNLJisYhIJIJCoYDd3V0Av65aq6oKm80Gi8UCt9uN8/Nz7OzsIBAI4O7uDnNzcxgcHEQ0\nGjX5F1AjyufzuLm5wfX1NQ4ODjAyMoJSqQSbzQaHw8FM0Zc4nU4kEgl0dXXB4XBgeXkZ2WwWW1tb\ncLlcZpdHDa5UKuHq6gr5fB6bm5vo7++Hy+XC+/s7XC4XyuUyVlZW0NfXh3K5jHg8DkVRsLGxYbh7\nS1QRjUaxvb2NVCoFn8+n909CCFitVgghmitXZr9+pNFlMhlNCKFJkqQJIfRNkiTt5OREn/f09KRN\nTU1pTqdTczqd2vT0tPby8mJi5dTIEomEIUuVz/+/woqZoq9YX1/X/H6/ZrPZtIGBAe3s7Mzskuib\nqJzvfj/nzczM6HOSyaTm9Xo1u92uDQ8Pa5eXlyZWTI3uT/2TEEJbWloyzGuWXHGZciIiIiKiGv3Y\nt38QEREREdULm2oiIiIiohqxqSYiIiIiqhGbaiIiIiKiGrGpJiIiIiKqEZtqIiIiIqIasakmIiIi\nIqoRm2oiIiIiohqxqSYiIiIiqtF/sFYSLbMZL+AAAAAASUVORK5CYII=\n", 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zx0v/5qnoeE3nLLVh7iIkvfQvloyEIIXe0OV1ueDSxY9EJA8m2ERhwOnyYH9F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\nRqPR5/E+vT1+8skn8fTTT3f7uCAI2LJ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1823,26 +1845,98 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can compute the bearing between a sensor and the target as follows:\n", - "\n", - "```python\n", - "def bearing(sensor, target):\n", - " return math.atan2(target[1] - sensor[1], target[0] - sensor[0])\n", - "```\n", - "\n", - "The filter receives a vector of 2 measurements during each update, one for each sensor. We can implement that as:\n", - "\n", - "```python\n", - "def measurement(A_pos, B_pos, pos):\n", - " angle_a = bearing(A_pos, pos)\n", - " angle_b = bearing(B_pos, pos)\n", - " return [angle_a, angle_b]\n", - "```" + "We can compute the bearing between a sensor and the target as follows:" ] }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def bearing(sensor, target_pos):\n", + " return math.atan2(target_pos[1] - sensor[1], \n", + " target_pos[0] - sensor[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filter receives a vector of 2 measurements during each update, one for each sensor. We can implement that as:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def measurement(A_pos, B_pos, pos):\n", + " angle_a = bearing(A_pos, pos)\n", + " angle_b = bearing(B_pos, pos)\n", + " return [angle_a, angle_b]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I will assume a constant velocity model for the aircraft. For a change of pace I compute the new positions directly rather than using matrix math:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def fx_VOR(x, dt):\n", + " x[0] += x[1] * dt\n", + " x[2] += x[3] * dt\n", + " return x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we need to implement the measurement function, which converts the state $\\mathbf x$ to an array containing the measurement to station A and B. I'm not a fan of global variables, but I put the position of the stations in the global variables `sa_pos` and `sb_pos` just to illustrate this technique of using external data in the $h()$ function:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sa_pos = [-400, 0]\n", + "sb_pos = [400, 0]\n", + "\n", + "def hx_VOR(x):\n", + " # measurement to A\n", + " pos = (x[0], x[2])\n", + " return measurement(sa_pos, sb_pos, pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The rest of the filter consists of boilerplate code to construct the filter, run it, and plot the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, "metadata": { "collapsed": false, "scrolled": true @@ -1850,9 +1944,9 @@ "outputs": [ { "data": { - "image/png": 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ndYqIyEW5pDXoLpeLV199lZ6eHmbMmAGAn58fu3fvJj4+nsjISGbPns2Pf/xj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\n", 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KrVYr6enpFBYWKqyLyLDX19/Hqdoj7Dn9IdUtJbR1tNDe1IXZGu6u8fXxY0Ts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\nnIiIiFw8JQeR/6G3r5e2M00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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1860,31 +1954,6 @@ } ], "source": [ - "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", - "from filterpy.common import Q_discrete_white_noise\n", - "\n", - "sa_pos = [-400, 0]\n", - "sb_pos = [400, 0]\n", - "\n", - "def bearing(sensor, target_pos):\n", - " return math.atan2(target_pos[1] - sensor[1], \n", - " target_pos[0] - sensor[0])\n", - "\n", - "def measurement(A_pos, B_pos, pos):\n", - " angle_a = bearing(A_pos, pos)\n", - " angle_b = bearing(B_pos, pos)\n", - " return [angle_a, angle_b]\n", - "\n", - "def fx_VOR(x, dt):\n", - " x[0] += x[1] * dt\n", - " x[2] += x[3] * dt\n", - " return x\n", - "\n", - "def hx_VOR(x):\n", - " # measurement to A\n", - " pos = (x[0], x[2])\n", - " return measurement(sa_pos, sb_pos, pos)\n", - "\n", "def moving_target_filter(pos, std_noise, Q, dt=0.1, kappa=0.0):\n", " points = SigmaPoints(n=4, alpha=.1, beta=2., kappa=kappa)\n", " f = UKF(dim_x=4, dim_z=2, dt=dt, \n", @@ -1899,9 +1968,7 @@ " return f\n", "\n", "def plot_straight_line_target(f, std_noise):\n", - " xs = []\n", - " txs = []\n", - "\n", + " xs, txs = [], []\n", " for i in range(300):\n", " target_pos[0] += 1 + randn()*0.0001\n", " target_pos[1] += 1 + randn()*0.0001\n", @@ -1936,7 +2003,7 @@ "source": [ "This looks quite good to me. There is a very large error at the beginning of the track, but the filter is able to settle down and start producing good data.\n", "\n", - "Let's revisit the nonlinearity of the angles. I will position the target between the two sensors with the same y-coordinate. This will cause a nonlinearity in the computation of the sigma means and the residuals because the mean angle will be near zero. As the angle goes below 0 the measurement function will compute a large positive angle of nearly $2\\pi$. The residual between the prediction and measurement will thus be very large, nearly $2\\pi$ instead of nearly 0. This makes it impossible for the filter to perform accurately, as seen in the example below." + "Let's revisit the nonlinearity of the angles. I will position the target between the two sensors at (0,0). This will cause a nonlinearity in the computation of the sigma means and the residuals because the mean angle will be near zero. As the angle goes below 0 the measurement function will compute a large positive angle of nearly $2\\pi$. The residual between the prediction and measurement will thus be very large, nearly $2\\pi$ instead of nearly 0. This makes it impossible for the filter to perform accurately, as seen in the example below." ] }, { @@ -1968,9 +2035,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This is unacceptable performance. `FilterPy`'s UKF code allows you to specify a function which computes the residuals in cases of nonlinear behavior like this,. The final example in this chapter explains how to handle this problem.\n", - "\n", - "Finally, let's discuss the sensor fusion method that we used. We used the measurement from each bearing and had the Kalman filter's equations compute the world position from the measurements. This is equivalent to doing a weighted least squares solution. In the *Kalman Filter Math* chapter we discussed the limited accuracy of such a scheme and introduced an *Iterative Least Squares* (ILS) algorithm to produce greater accuracy. If you wanted to use that scheme you would write an ILS algorithm to solve the geometry of your problem, and pass the result of that calculation into the `update()` method as the measurement to be filtered. This imposes on you the need to compute the correct noise matrix for this computed positions, which may not be trivial. For example, the ILS is probably the most common algorithm used to turn GPS pseudoranges into a position, but the literature discusses a number of alternatives." + "This is unacceptable performance. `FilterPy`'s UKF code allows you to specify a function which computes the residuals in cases of nonlinear behavior like this,. The final example in this chapter explains how to handle this problem." ] }, { @@ -1984,7 +2049,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The geometry of the sensors relative to the tracked object imposes a physical limitation that can be extremely difficult to deal with when designing filters. If the radials of the VOR stations are nearly parallel to each other than a very small angular error translates into a very large distance error. What is worse, this behavior is nonlinear - the error in the *x-axis* vs the *y-axis* will vary depending on the actual bearing. For example, here is a scatter plot that shows the error distribution for a $1^\\circ$ standard deviation in the bearing measurement for a $30^\\circ$ bearing." + "The geometry of the sensors relative to the tracked object imposes a physical limitation that can be extremely difficult to deal with when designing filters. If the radials of the VOR stations are nearly parallel to each other than a very small angular error translates into a very large distance error. What is worse, this behavior is nonlinear - the error in the *x-axis* vs the *y-axis* will vary depending on the actual bearing. For example, here is a scatter plot that shows the error distribution for a 1° standard deviation in the bearing measurement for a 30° bearing." ] }, { @@ -2035,7 +2100,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This is **very** important to understand. Try very hard to answer this before reading the answer below. If you cannot answer this you really need to revisit some of the earlier Kalman filter material in the **Multidimensional Kalman Filter** chapter.\n", + "This is very important to understand. Try very hard to answer this before reading the answer below. If you cannot answer this you may need to revisit some of the earlier Kalman filter material in the **Multidimensional Kalman Filter** chapter.\n", "\n", "There are several factors contributing to our success. First, let's consider the case of having only one sensor. Any single measurement has an extreme range of possible positions. But, our target is moving, and the UKF is taking that into account. Let's plot the results of several measurements taken in a row for a moving target to form an intuition." ] @@ -2067,21 +2132,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Each individual measurement has a very large position error. However, a plot of successive measurements shows a clear trend - the target is obviously moving towards the upper right. When a Kalman filter computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately $45^\\circ$ degree line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will be taking that into account. The end result is the track can be computed even with this type of noise distribution. This graph makes it look easy because we have plotted 100 possible measurements for each position update. This makes the aircraft's movement obvious. In contrast, the Kalman filter only gets one measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", + "Each individual measurement has a very large position error. However, a plot of successive measurements shows a clear trend - the target is obviously moving towards the upper right. When a Kalman filter computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately 45° line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will be taking that into account. The end result is the track can be computed even with this type of noise distribution. This graph makes it look easy because we have plotted 100 possible measurements for each position update. This makes the aircraft's movement obvious. In contrast, the Kalman filter only gets one measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", "\n", - "The next interaction we must think about is the fact that the bearing gives us no distance information. Suppose we set the intial position to be 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf P$ very small. At that distance a $1^\\circ$ error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements." + "The next interaction we must think about is the fact that the bearing gives us no distance information. Suppose we set the intial position to be 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf P$ very small. At that distance a 1° error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's consider the effect of adding a second sensor. Again, I will start by plotting the measurements so we can form an intuition about the problem." + "Now let's consider the effect of adding a second sensor. Here are two plots showing the effects of different sensor placements. I used a square and a triangle as a symbol for the two sensors, and drew a distribution of the errors due to each sensor using the same symbol shape and color. I then computed the $(x, y)$ coordinate corresponding to the two noisy bearing measurements and plotted them with red dots to show the distribution of the noisy measurements in $x$ and $y$." ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 61, "metadata": { "collapsed": false, "scrolled": false @@ -2089,9 +2154,9 @@ "outputs": [ { "data": { - "image/png": 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vfow1a0pbHAD331/alZWREWFfg4Hc0CDC986MEXFIa1uJxLi8vBDZ2V7GjCnh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\niz6hpKTkLFRV80TjvauJdJ0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L5rPPqmjZMkRubkLN6xMnTqxZD9y/f382bNhQ817nzp3Jy8urp9HHtogF4ddffx3LsujS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\nublhKioM2mXtxB8qo6AgFPGaatMY/+z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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2107,33 +2172,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "I placed the sensors nearly orthogonal to the target's initial position so we get these lovely 'x' shape intersections. I then computed the $(x, y)$ coordinate corresponding to the two noisy bearing measurements and plotted them with red dots to show the distribution of the noisy measurements in $x$ and $y$. We can see how the errors in $x$ and $y$ change as the target moves by the shape the scattered red dots make - as the target gets further away from the sensors, but nearer the $y$ coordinate of sensor B the shape becomes strongly elliptical.\n", + "In the first plot I placed the sensors nearly orthogonal to the target's initial position so we get these lovely 'x' shape intersections. We can see how the errors in $x$ and $y$ change as the target moves by the shape the scattered red dots make - as the target gets further away from the sensors, but nearer the $y$ coordinate of sensor B the shape becomes strongly elliptical.\n", "\n", - "Next I will alter the sensor positions and rerun the simulation. Here the shape of the errors in $x$ and $y$ changes radically as the target position changes relative to the two sensors. " - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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YbDZsNhtr165lzpw52O12/H5/g3SiKZR4WnPPHzrSr1+Q6dOdFBfrFBfrTJgQ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\nIUxKwiuESf1/4xYgcGjoQRkAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "with figsize(y=4.):\n", - " ukf_internal.plot_iscts_two_sensors_changed_sensors()" + "In the second plot the airplane starts very near one sensor, and then flies past the second sensor. The intersections of the errors are very non-orthogonal, and the resulting positions errors become very spread out." ] }, { @@ -2147,7 +2188,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's implement the UKF equations with Python. As you have seen FilterPy already implements this code for you, but it is instructive to learn how to go from equations to code. Plus, if you encounter a problem and need to debug your code you will likely need to step through the FilterPy code with the debugger.\n", + "Now let's implement the UKF equations with Python. FilterPy implements this for you, but it is instructive to learn how to go from equations to code. Plus, if you encounter a problem and need to debug your code you will likely need to step through the FilterPy code with the debugger.\n", "\n", "Implementing the UKF is quite straightforward. First, let's write the code to compute the mean and covariance given the sigma points. \n", "\n", diff --git a/code/nonlinear_plots.py b/code/nonlinear_plots.py index 43494fc..b724cfa 100644 --- a/code/nonlinear_plots.py +++ b/code/nonlinear_plots.py @@ -246,7 +246,7 @@ def plot_monte_carlo_mean(xs, ys, f, mean_fx, label, plot_colormap=True): plt.scatter(mean_fx[0], mean_fx[1], marker='v', s=300, c='r', label=label) plt.scatter(computed_mean_x, computed_mean_y, - marker='*',s=120, c='r', label='Computed Mean') + marker='*',s=120, c='b', label='Computed Mean') plot_bivariate_colormap(fxs, fys) plt.ylim([-10, 200]) diff --git a/code/ukf_internal.py b/code/ukf_internal.py index fe4aee7..393490a 100644 --- a/code/ukf_internal.py +++ b/code/ukf_internal.py @@ -279,7 +279,7 @@ def plot_radar(xs, t, plot_x=True, plot_vel=True, plot_alt=True): plt.ylabel('altitude') plt.show() - + def plot_altitude(xs, t, track): xs = np.asarray(xs) @@ -289,7 +289,7 @@ def plot_altitude(xs, t, track): plt.ylabel('altitude') plt.legend(loc=4) - + def print_sigmas(n=1, mean=5, cov=3, alpha=.1, beta=2., kappa=2): points = MerweScaledSigmaPoints(n, alpha, beta, kappa) print('sigmas: ', points.sigma_points(mean, cov).T[0]) @@ -404,20 +404,24 @@ def _plot_iscts(pos, sa, sb, N=4): xs_b.append(db*math.cos(a_b) + sb[0]) ys_b.append(db*math.sin(a_b) + sb[1]) - plt.scatter(xs, ys, c='r', marker='.') - plt.scatter(xs_a, ys_a) - plt.scatter(xs_b, ys_b) + plt.scatter(xs, ys, c='r', marker='.', alpha=0.5) + plt.scatter(xs_a, ys_a, c='k', edgecolor='k') + plt.scatter(xs_b, ys_b, marker='v', edgecolor=None) plt.gca().set_aspect('equal') def plot_iscts_two_sensors(): + plt.subplot(121) pos = np.array([4., 4,]) sa = [0., 2.] sb = [8., 2.] - plt.scatter(*sa, s=100) - plt.scatter(*sb, s=100) + plt.scatter(*sa, s=200, c='k', marker='v') + plt.scatter(*sb, s=200, marker='s') _plot_iscts(pos, sa, sb, N=4) + plt.subplot(122) + plot_iscts_two_sensors_changed_sensors() + def plot_iscts_two_sensors_changed_sensors(): @@ -425,8 +429,8 @@ def plot_iscts_two_sensors_changed_sensors(): sb = [3, 7] pos= np.array([3., 3.]) - plt.scatter(*sa, s=100) - plt.scatter(*sb, s=100) + plt.scatter(*sa, s=200, c='k', marker='v') + plt.scatter(*sb, s=200, marker='s') _plot_iscts(pos, sa, sb, N=5) plt.ylim(3.8, 8.5)