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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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      "#format the book\n",
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      "It has probably struck you by now that the performance of the Kalman filter is not optimal when you consider future data. For example, suppose we are tracking an aircraft, and the latest measurement is far from the current track, like so (I'll only consider 1 dimension for simplicity):\n",
      "\n",
      "   10.1 10.2 9.8 10.1 10.2 10.3 10.1 9.9 10.2 10.0 9.9 12.4"
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      "plt.plot(data)\n",
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bB/05derU6F4JAAAAMAw2m02VbBXsdoZMTNrb2zV37ly99NJLCgoKkslkcjjf0dGh5cuX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\n/9MKXbf+NFZj1OjE6bKfli6+fHXlyLGDksWioYl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       "text": [
        "<matplotlib.figure.Figure at 0x7f63a4064e10>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "After a long period of near steady state, we have a very large change. Assume that change is larger than the aircraft's manuevering envelope. Nonetheless the Kalman filter incorporates that new measurement into the filter based on the current Kalman gain. It cannot reject the noise because the measurement could reflect the initiation of a turn. Granted it is unlikely that we are turning so abruptly, but it is impossible to say whether \n",
      "    \n",
      "* The aircraft started a turn awhile ago, but the previous measurements were noisy and didn't show the change.\n",
      "      \n",
      "* The aircraft is turning, and this measurement is very noisy\n",
      "    \n",
      "* The measurement is very noisy and the aircraft has not turned\n",
      "\n",
      "\n",
      "Now, suppose the following measurements are:\n",
      "\n",
      "   11.3 12.1 13.3 13.9 14.5 15.2\n",
      "   "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data2 = [11.3, 12.1, 13.3, 13.9, 14.5, 15.2]\n",
      "plt.plot(data + data2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cQ23mhIVasuiHsujs2oC6xmq9su53sjvsPd1ir7Jm+2sqqSg01L52w7cVGhRu\nUkdA70XIAADAJHvzjFOlhsWNVmRotEYOTtHCqfcaxo4U7tVnme/0ZHu9yrHiw1q/+z1DbdqYeZow\nfKpJHQG9GyEDAACTnL8eY2LSDOfPF027V0mDxhnGP972T+UVHeyR3nqTlrZm/WPdCjnOuRLUL7S/\n7rz+myZ2BfRuhAwAAExQ01Cp/GLjjeAmJk13/txq9dGSRT9SyDlTeewOu1atfUYNTbU91mdv8MGX\nr6i8psRQe2D+9xQUEGJSR0DvR8gAAMAE+3K3yyGH83hIbJKiwwcYHhMZGq2HF/zAUKuur9Crnz4n\nh8MhdO7oiX3avPcjQ21WSrpGDZloUkdA30DIAADABOff5fvcqVLnGps4WTdMvt1Qy87P1MasD7qt\nt96iqaVR//j0D4Za/4iBum3mEpM6AvoOQgYAAD2srrFGuUXZhtrFQoYk3TLjISUOHGWord7ysgpO\n5VzkGZCkd7/4u6rqyp3HFln04PzvK8A/yMSugL6BkAEAQA/bf2yHYRFyfP9ExfaLv+jjfXx8tTT9\nR4Y1BDZ7u15a87SaWhq6tVdvlZ2fqe3Znxlqc1Nv04hBY03qCOhbCBkAAPSw86dKTbrEVYyvRIcP\n0AM3ftdQq6gt1WvrV7I+4zx1jdV67bOVhtqAqATdPOMBkzoC+h5CBgAAPaixuV5HT+wz1CYmXXtZ\nz52YNEOzJ95kqGXlbNXWA+vc1p+3q22o1h/f+S/VNlY5a1aLVQ8veFx+vv4mdgb0LZ2GjM2bN2vx\n4sVKSEiQ1WrVqlWrnGPt7e362c9+pokTJyo0NFTx8fF68MEHdeLEiW5tGgAAb7X/2E7Z7Tbn8YCo\nBMVFD77s5982a5kSYoYbam9v+quKyo+7q0WvVdNQqT+8/aTLXb3nT7lbQwYkmdQV0Dd1GjIaGhqU\nkpKiFStWKCgoSBaLxTC2Z88ePfnkk9qzZ4/ef/99nThxQosWLZLNZrvEqwIA0Ddl5W41HF/OVKlz\n+fn6a1n6EwrwC3TW2m1tenHNb9XS2uSWHr1RdX2F/vDWkyqtOmmojx4ySQun3mNSV0Df1WnISE9P\n11NPPaW77rpLVqvx4REREVq3bp3uueceJScna8qUKXr++ed16NAhHT58+CKvCABA39TU0qjDhVmG\n2qTLnCp1rth+8bpv3rcMtbKqIr258YUu9eetKmvL9dxb/6my6mJDfezQVD1y63/I18fPpM6Avsvt\nazJqamqyHP6iAAAgAElEQVQkSf369XP3SwMA4NWy8zNks7U7j/tHDFR8/8Sreq200ddr+rgbDbWd\nhzZox8HPu9Ki16moLdVzb/+nTtecMtTHD5uib97yc9ZhACaxOK5gS4qwsDCtXLlSS5Zc+CY2ra2t\nmjt3rmJiYvTee+8Zxr4KH5KUk8O+3gCAvmfj4bdUWHH2Sv+4QddqcuK8q369dlubPtr7N9U0nXbW\nfK1+unniNxUR3L9LvXqDuuYqrTvwihpaag31IVGjdN2oO+Vj9TGpM8D7JScnO38eERFxxc9325WM\n9vZ2PfTQQ6qtrdWLL77orpcFAKBXaLO1qqgq11AbGj26S6/p6+On60ffJR+rr7PWbm/TpiPvqN3W\n1qXX9nS1TZX6ZP/LLgFjaPQYzSZgAKbz7fwhnWtvb9f999+v7Oxsbdy4sdOpUmlpae542z4rMzNT\nEufRXTif7sO5dC/Op/t4wrnck7NVNvvZqVL9wmK0cM6thg1VrlZIlK9eW3/2vhDVjWUqqM/SfTd8\n6xLPunpmn8/SqiL94e2VamytM9Qnj7xODy183KsChtnnsrfhfLrPubOQrkaXr2S0tbXpvvvu04ED\nB7RhwwbFxsZ29SUBAOh19p63q9TEpBluCRiSNH3cjZo8arah9uWBT7T76Ba3vL4nKak4oefe+k/V\nNlQZ6lNGz9HDXhYwgN6s0ysZDQ0NzjUUdrtdBQUFysrKUnR0tOLj43XPPfcoMzNTH3zwgRwOh06d\n6lh4FRkZqcDAwEu9NAAAfUJre4uy8zMNtavZVepiLBaL7pv3LRWeylF5TYmz/q/1f9Lg2BGKiYxz\n23uZqfj0cf3xneWqbzJ+wzpt7A26/4Zvy0rAADxGp1cyMjIylJqaqtTUVDU3N2v58uVKTU3V8uXL\ndfLkSa1evVolJSWaPHmy4uPjnf+98cYbPdE/AAAe73BBllramp3HESFRSowb6db3CPQP0rKbnpCP\nz9nvD5tbG7VqzTO9Yn3GyfJj+sPbv3AJGNeOn6/7b/wOAQPwMJ1eyZgzZ47sdvtFxy81BgAApL25\n2wzHE5Omy2px+y7yGhw7Qndc93W9tfEvzlphWa5Wf/mK7pz9Dbe/X08pLM3Vn979pRpb6g31WRMW\n6e65j3bLuQTQNfytBACgG7Xb2nTg2E5DbeIV3uX7SlyXcpNSRkw31DbuWa395/XgLQpOHdXKd/7L\nJWBcP+kW3TP3MQIG4KH4mwkAQDc6emKfmlobncehQREaET+2297PYrHogRu/q6iwGEP9H+ueU2Vt\nebe9b3fILzmsle/+0nD+JGle6m26c/Y33bZwHoD7ETIAAOhGWTnGXaVSRkzr9vUDwYGhWpr+hOF9\nGlvq9fLaZ2Wz27r1vd0lryhbf3r3l2o+L2DcmHaXbpu1jIABeDhCBgAA3cRma9e+86YpuXNXqUsZ\nFjdKt177kKF2rOSQ1mx/rUfevytyTu7Xn9/7lWGxvCQtnHqvbr32IQIG4AUIGQAAdJPcomw1Np+9\nYVxwQKiSE8b32PvPTb1NY4emGmqfZrytQwV7eqyHK3WkcK/+9/3/q9b2FkM9ffr9unnGAwQMwEsQ\nMgAA6CZZ5+0qNWHENMMWs93NarHqwQU/UERIlLPmkEOvfvJ71TRU9lgfl+tQwR69sPrXamtvNdRv\nmfGg0qfdZ1JXAK4GIQMAgG5gt9u0L2+7oTapG3eVupiw4AgtWfQjWc7ZhamuqUavrP2d7B60PiM7\nP1MvfPBrtdmMAeO2WUu1YOo9JnUF4GoRMgAA6AbHSg6rrrHaeRzoH6yRgyea0ktywngtOu9KwNGT\n+/Vp5tum9HO+/cd26q8f/j/ZbO2G+h3XfUM3TL7DpK4AdAUhAwCAbnD+DfjGD5siP18/k7qRFk65\nW8kJEwy1j7f/S7lF2SZ11GFv7jb97aPfyGY3Boy75zyiuamLTeoKQFcRMgAAcDO7w+6yHqM7b8B3\nOaxWHy1Z+EOFBkU4aw6HXavWPKO6xhpTetp9dIte/Pi3LtO27pv3Lc2eeLMpPQFwD0IGAABuVnAq\nRzX1Fc5jf79AjUm8xsSOOkSERunhhY8bajUNlfrHp8/J7rD3aC+Zhzdp1dpnDe9rkUX33/AdzZyw\nsEd7AeB+hAwAANxsb67xBnxjE1Pl7xtgUjdGY4ZeoxvT7jLUDh7fpY17VvdYDzsPbdAr61bIcV7A\neGD+9zRj/Pwe6wNA9yFkAADgRg6Hw2WqVE/dgO9y3Tz9fiXGjTLUVn/5io6fOtrt770t+zP9Y91z\nxoBhserhhY9r2th53f7+AHoGIQMAADc6UZanytoy57Gfj7/GJU42sSNXPj6+WrboxwoOCHXW7Hab\nXvr4t2psru+29/1y/yd67bM/yiGHs2a1WLV00Y+UNvr6bntfAD2PkAEAgBudv6vUmMRrFOAfZFI3\nFxcVHqsH5n/PUKusK+8IAQ7HRZ519Tbv/Vivf/5nQ81q9dGy9CeUOnKW298PgLkIGQAAuMmFpkqZ\nvavUpaSMmKbrJ91iqO3N264t+9a49X027Fmttza+YKj5WH31jZt+qknJnjWVDIB7EDIAAHCTkooC\nlVcXO499rL4aP2yKiR11bvHMpUqIHW6ovfPF33Wy/JhbXn/9rnf17ua/G2o+Pr765s0/U8qIaW55\nDwCeh5ABAICbZOUYr2KMGjJRQQEhJnVzefx8/fT19J8YpnTZbO168eOn1dza1KXXXpfxlt7fsspQ\n8/Xx0yO3/IfGD/fs8AWgawgZAAC4yd48z95V6mJiIuP0tXnfNtTKq4v1xuf/e9XrM9bseF0fbn3V\nUPPz9ddji5/U2MTUq+4VgHcgZAAA4AallSdVUlHoPLZarJrgRd/WTx51na497x4VmUc2acfBz6/o\ndRwOhz7a9k+t2f6aoe7vG6B/v+0XGjVkYpd7BeD5CBkAALjB+Qu+kwdPUEhQuEndXJ07Z/+b4qKH\nGGpvbnxeJRUnLuv5DodDH2x9VZ/sfMNQD/AL1Ldu/y8lJ0xwW68APBshAwAAN8g67y7f3jJV6lz+\nfgFalv4Tw93J29pb9dKa36q1reWSz3U4HHp/y0v6LPNtQz3AP0jfuv2XGjFoXLf0DMAzETIAAOii\n8uoSFZXnO48tFqsmDPfOnZPiogfrnrmPGmolFYV6Z/NfL/och8Ohdzb/TZ/vft9QD/IP1nfu+P80\nPH50t/QKwHMRMgAA6KLzb8A3In6MwkMiTeqm66aOmedyB+6tBz7VriObXR5rd9j15sYXtCnrQ0M9\nOCBU37nzV0ocOLJbewXgmQgZAAB00fkhw9tvMGexWHTv3H9XbGS8of6v9X9SWdXZ+4DYHXa98fmf\nXW7eFxIYpu/c+SsNGZDUI/0C8DyEDAAAuqCytlwFpTmGWsqI6SZ14z6B/kFadtMT8vXxc9Za2pr1\n0tqnZbO3y+6w67XPVmrrgU8NzwsJCtd37/y/GnzeDf4A9C2+ZjcAAIA3O//eGMPiRisyNNqkbtwr\nIWa47pj9Db254Xln7WTZMWVaP1ObrUXHyvcbHh8WHKnv3vkrlx2qAPQ9XMkAAKAL9p53l++JSTNM\n6qR7zJqwyOXXdORUpkvACA/pp+/f9RQBA4AkQgYAAFetpr5S+SWHDbVJvSxkWCwW3X/jdxQVHnvR\nx0SERuv7d/1aA6ISerAzAJ6MkAEAwFXam7ddDjmcx0Niky75YdxbBQeE6uvpT8hq9XEZ6xcWo+/f\n9ZRi+8Vf4JkA+ipCBgAAV+n8XaUmevmuUpcydOBILZ75sKEWFR6r79/9lGIi40zqCoCnYuE3AABX\noa6xRrlF2YZab5sqdb451yxWU0uDNu9Zo34hsXr0jp8rKjzG7LYAeCBCBgAAV2H/sR1yOOzO40H9\nE3v9N/pWi1U3z3hQA/xGSRIBA8BFMV0KAICrkJWz1XDc23aVAoCuIGQAAHCFGprrdPSkcQtXb7/L\nNwC4EyEDAIArdODYTtntNufxgKgEDYwabGJHAOBZCBkAAFyhrPN2lertC74B4EoRMgAAuAJNLY06\nXJhlqE1KYqoUAJyLkAEAwBXIzs+QzdbuPO4fMVDx/RPNawgAPBAhAwCAK3D+DfgmJV0ri8ViUjcA\n4Jk6DRmbN2/W4sWLlZCQIKvVqlWrVhnG33nnHS1cuFCxsbGyWq3atGlTtzULAICZWtqadbBgt6HG\n1rUA4KrTkNHQ0KCUlBStWLFCQUFBLt/WNDY2atasWXr22WcliW9zAAC91sHju9XW3uo87hcWoyED\nkkzsCAA8U6d3/E5PT1d6erokadmyZS7jDz30kCTp9OnT7u0MAAAPszfX9QZ8fLkGAK5YkwEAwGVo\nbW9Rdn6mocauUgBwYZ1eyegOmZmZnT8IneI8uhfn0304l+7F+XSfrpzLwoojamlrdh4H+YepoqhO\nlcV99/eHP5vuw7l0L85n1yUnJ3fp+VzJAADgMhRWHDYcD4kexVQpALgIU65kpKWlmfG2vcZX6Zzz\n6B6cT/fhXLoX59N9unou221tejPjWUNtwbW3KTlhQpd780b82XQfzqV7cT7dp6ampkvP50oGAACd\nOHpin5paG53HoUERGhE/1sSOAMCzdXolo6GhQTk5OZIku92ugoICZWVlKTo6WoMHD1ZVVZUKCgpU\nXV0tScrJyVF4eLji4uI0YMCA7u0eAIAekJVj3FUqZcQ0Wa0+JnUDAJ6v0ysZGRkZSk1NVWpqqpqb\nm7V8+XKlpqZq+fLlkqT3339fqampmjdvniwWix555BGlpqbq+eef7/bmAQDobjZbu/Yd22mosasU\nAFxap1cy5syZI7vdftHxZcuWXfD+GQAA9Aa5RdlqbK5zHgcHhCo5YbyJHQGA52NNBgAAl5CVu81w\nPGHENPn4mLJvCgB4DUIGAAAXYbfbtO+8kDEpaYZJ3QCA9yBkAABwEcdKDquu6ew2joH+wRo5eKKJ\nHQGAdyBkAABwEefvKjV+2BT5+fqZ1A0AeA9CBgAAF2B32LU3b7uhNimZqVIAcDkIGQAAXEDBqaOq\nqa9wHvv7BWr00GtM7AgAvAchAwCAC9h73oLvcYmT5e8bYFI3AOBdCBkAAJzH4XC4rMeYyK5SAHDZ\nCBkAAJznRFmeKuvKncd+Pv4alzjZxI4AwLsQMgAAOM/5N+Abk3iNAvyDTOoGALwPIQMAgHM4HA7t\ndZkqda1J3QCAdyJkAABwjuLTBSqvKXEe+1h9NX5YmokdAYD3IWQAAHCO83eVGjVkooICQkzqBgC8\nEyEDAIBzZOUap0pNYqoUAFwxQgYAAGecqjyhU5UnnMdWi1UThk8xsSMA8E6EDAAAzjh/qlTy4AkK\nCQo3qRsA8F6EDAAAzjh/61qmSgHA1SFkAAAgqby6REXl+c5ji8WqCcOnmdgRAHgvQgYAAHKdKjUi\nfozCQyJN6gYAvBshAwAAuYaMSclMlQKAq0XIAAD0eZW15SoozTHUUkZMN6kbAPB+hAwAQJ+3N894\nFWNY3GhFhkab1A0AeD9CBgCgz9ubYwwZE5NmmNQJAPQOhAwAQJ9WU1+p/JLDhtokQgYAdAkhAwDQ\np+3N2y6HHM7jIbFJigqPNbEjAPB+hAwAQJ92/q5SE9lVCgC6jJABAOiz6hprlFuUbagxVQoAuo6Q\nAQDos/Yf2yGHw+48HtQ/UTGRcSZ2BAC9g6/ZDQA4y+FwqK6xRlV1ZaqoLVNVXXnHj7Xlamlv1qD+\niUoaNE7D48cqLDjC7HYBr5eVs9VwzK5SAOAehAygB9ntNtU0VJ0THspUWVeuyjM/VtWWq83WetHn\n5548oE1ZH0qSBkYNVtKgcUpKGK8Rg8YqIiSqp34ZQK/Q0Fynoyf3G2rc5RsA3IOQAbiRzdau6voK\nVdaVqbL2bHjo+LFM1XUVstnb3fJepypP6FTlCW3Zv1aSFBMZfyZ0jFPSoHHqFxbjlvcBeqsDx3bK\nbrc5jwdEJWhg1GATOwKA3oOQAVyBtvZWVdWVdwSIc8JD5ZkpTdUNlYb53T2pvLpY5dXF2pb9qSQp\nKjy2I3QMGq+khHGKDh8gi8ViSm+AJ8o6b1epSUlcxQAAdyFkAOdoaWs+cwWi1BkinKGitky1jVXd\n3kOgf7CiwmMVFRbT8WN4jKLCYmWxWHWs+KByi7J1sjy/0zBTWVumnbVl2nlogyQpMjRaSYM6plYl\nJYxXbGQ8oQN9VlNLow4XZhlq7CoFAO7TZ0OG3WFXXWO1KmvLDfPjZbFo9JBJGj98iqwWNt/qbRpb\n6lVVW+5cVF1ZW6a8wqNqaK7R27tWqKG5rtt7CAkMOy9ExKpfWIyiw2PVLzxGwQGhF33uxKTpkqSm\nlgYdKz6k3KJs5RUdVGFZrmHax4VU11co88gmZR7ZJEkKD+6nEYPGasSgjulVA6MH82feQzS1NCgr\nZ6t25+2Qv2+gQmN8NSx+tAL8As1urdfIzs+QzXZ26mJMRJzi+yea1xAA9DK9NmTY7TZV11eqqu6c\nOfHnzJGvqitXu63tgs/dsm+N4vsnauHUezQxaQYfvLyEw+FQfVPt2dB43rqIqtoyNbU2dnsf4cH9\nnFcg+n0VJMJiFBU+QFFh/RXgH9Tl9wgKCNG4YWkaNyxNktTS2qT8kiPKLcpWbtEBFZTmGD5AXUht\nY5X25HypPTlfSuoIP18FjhGDxmlQ/6GyWn263Csuj81u05HCvco4tEH78nYYNgDYf3KLrFYfDYlN\nOvP7M1bD48cqKCDYxI692/lTpSYmzeDKHgC4kdeGjHZbW8cCW0N4OBsoqusrOv1m91KKTx/Xix//\nVgOjBmvh1Ht0TfJMPnCZzO6wq66h+qKLqqtqy9Xa3tKtPVgsVkWGRKlf+Ffh4ex0pq9ChZ+vf7f2\ncCEB/kEaPXSSRg+dJElqbW9Rwamjyj2ZrdyibB0vOXLJXaukjp129uVt17687ZKkIP9gDR80tmNN\nx6CxSogdIR/+DrhdUflxZRzeoMzDmy85Hc9ut+n4qSM6fuqIPtv1jiwWqxJihjlD4YhBYxUSGNaD\nnXuvltYmHTq+21BjVykAcC+PDRmt7S2qqjt9JkQY7xdQUVem2vpKOeTo9j5OVZ7QqrXPas32f2nB\n1Hs0edRsPmh1E5vdppr6SudC6nO3da2sLVNlfXmn3853ldXqo35h/TtCw7lrIs4EisjQaPn4eOxf\nGyd/3wAlJ0xQcsIESVJbe5sKS3OUV9QROo6VHFZrW/MlX6OptVHZ+ZnKzs+UJAX4BWpY/Jgzi8nH\naciAJPn6+HX7r6U3qm2o1q4jm7Xz0OcqOn38ql7D4bDrRFmeTpTlacOe1bLIorj+Q52hI2nQWIUF\nR7q38V7iYMFuQ+iOCovR4NgRJnYEAL2PaZ+WmlubjB8kv7r52JkPlHVNNd3eQ9CZBbb9nNNZYlRY\nmqs9R790CTBl1cV6dd0KrdnxLy1Iu1tTxszhA9YVare1nQ2OX4WHcwJFdX2F7N28M5Ovj5/Lgurq\n0/UKCYzQtVNmKyKkX6+8YuXn63dm/cVYLdA9stnadaL8mHJPHlBe0UHlFR9UcydTyVramnW4YI8O\nF+w585r+GjZwlEYkjFfSoHFKHDiyJ34pXqu1vUUHjmVo56ENOlywp9M/61FhMYoLT1ZLW6NqWstU\nXl18ycc75FDx6eMqPn1cm/d+JKljS9aOK1EdWxtzL5UOe5kqBQDdzpSQ8X+ef1iNPbHANihc0WEd\ni2nPXWQbFRZzyQW2i6bdp3U739Kuo1+47OBTUVOq19av1Cc739CNaXdp2tgb5OdL2DiXw+HQyfJ8\n7c/bofLq4o4pTXXlPXL1KcAv0HnVwfX3PVZhwREuHyYyMzu+qe8X1r9be/MkPj6+Shw4UokDR+rG\ntDtlt9tUdPr4melVB5RXfKjTv6Nt7a06enK/82ZmPj6+ig6J04DwoQqL9VNi3Kg+v1DZ4XDoWPEh\nZRzeoD1Hv+x0TVCAf5CuSbpWU8bM1YhBY7V7V8eUnrS0NNXUV55Zc9Pxe1RaebLT9y+tPKnSypP6\n8qt7qUTEacSZ+6gkDRqvqPC+dy+V1vYWHThzde4rE9m6FgDczpSQ4a6AER7S78xceOPUln5n5sdf\n7QecgVGDtWTRD7Vo2n36NOMtZRze6PKtY2Vdud7Y8L/6JONNzU+7UzPGzTdlLr4nqamvVOaRTdp5\naINKKgq75T2CA0KN4eGr3/8zteDAML6RvApWq48Gx47Q4NgRmpu6WHaHXacqCjs+0J5Z11HfydVF\nm61dZbUnVFZ7wmWhclLCOA2LG9NnFiqfrjmlnYc2KOPwRlXUlF7ysRaLVaOHTNLUMXM0Yfg0+fsF\nXPBxEaFRmjzqOk0edZ0kqa6xWnlFB53Bo+R0QachvrymROU1Jdqe/ZmkjqslHXeM7wge/SMG9vq/\nP4cLsgxTBSNCopQYx1U4AHA3j51cbrFYFRka7RIeos9s99kvrH+3f6iP7RevBxd8Xwun3avPMt/W\njoMbXO7WXFNfobc2/kXrdr6lGybfoZkTFl70Q0Jv1NrWon1527Xz8EYdKdzb5RvRhQZFXCA0ntne\nNSy2z3xINZvVYlV8/0TF90/U7Ik3y+FwqLTqZMeH2pMHlFuUrZqGyku+xoUWKg+OGa6khDMLlePH\nKjjw4tv1epvGlnpl5WzVzkMbdKz4UKePj4seoqlj5ilt1GxFhF75NKaw4EhNSr7WuWC5obmuY1vj\nM78/l3Uvlbpy7Ty0wXkvlYjQaCXFd9xHJWnQOMX2G9TrQkdW7lbD8cSk6ewgCADd4JIhY/PmzXr6\n6ae1e/duFRcX68UXX9TSpUsNj/nlL3+pv/zlL6qqqtK0adO0cuVKjR07ttM39rH6nllgG9OxJuK8\nD5aRIZ6zwLZ/xEB97YbvaMGUe/XZrne0LftTlwXItY1VeveLv+uzzLc1N/U2XZeS7patSj2R3WFX\nXtFB7Ty0QVm5W9XS2nRZz7PI0nH1yTll7Wxo/OrHvhTQvInFYtHAqMEaGDVYMycslMPh0OmaUx1r\nOoo7gkdlXfklX8PhsKuwLFeFZbn6fPf7ssii+P5DnR9oRwwap9Cg8B76FbmHzW7T4YI92nlog/Yf\n23nRbbG/EhYUocmjZmvq2Lka1H+YWz/AhwSGacLwqZowfKqks/dS+epqx+XcS6WmvkK7jn6hXUe/\n6Og3OLLj5o3Oe6kM8eoP5DZ7u7KPZRhqE7kBHwB0i0t+im9oaFBKSoqWLl2qJUuWuPwP8Te/+Y2e\nffZZrVq1SiNHjtSvfvUrzZ8/X0eOHFFo6MW/ofzVN/+m8OBIr1tgGxUeo3vnPqYFU+7W+l3vauv+\ndS7bgtY11Wj1ly9r/a53NeeaxZo98SYFBYSY1LF7lVUVKePwRmUc2tjpB0qrxaoxiamaMHyqosMH\nKCo8VpGh/Vm/0ktYLBbFRMYpJjJOM8bPl9Rxh/FPt3yo0poCVbeU6nTNqUu+hkMOFZ0+rqLTx7Up\n60NJHVMVO6ZXdQSP8JB+3f5ruRony49p56GN2nV4U6ebVPj6+GnC8KmaOmauRg+Z1GNfnlzqXip5\nRdk6Xnq0093a6hqrlZWzVVk5Hd/+d9xL5ewNHAf1T/Sqf8dLqo8b1sWEBkVoRHznX4oBAK7cJf9v\nl56ervT0dEnSsmXLDGMOh0O///3v9fOf/1x33HGHJGnVqlWKjY3VP//5Tz366KMXfd3I0Ogutm2u\nyNBo3XX9v2l+2l36fPf72rJvjcv9GRqa6/TRtn/o893vac6kW3X9pFu8cmpIQ3Oddh/dooxDG3X8\n1JFOH58QM1xTxszR5JGzFR7C9pl9SVR4rEbEpmhEbIrS0tJUXV/RsWXumTUdpVWdL1Q+VXlCpypP\naMuZhcqxkfEdH2jPLFbuF2beQuWahsoz285uVPFlbDs7PG6Mpo6dq0nJ117yLu49xX33UtmhfXk7\nJJ25l0p8x65lA6ISnFejPfWLlcIK4zS2lBHTvCokAYA3ueqv1PLz81VaWqoFCxY4a4GBgZo9e7a2\nbt16yZDRW4SH9NPt1y3TDZPv0IY9q/XF3o/Uct69B5paGrRmx7+0Yc9qzZ54s+Zec6tCPHxKiM3W\nroMFu7Xz0AYdyM/o9NvO8OB+Sht9vaaOmaP4/ok90yQ8XmRotCaPmq3Jo2ZL6vhWPLfooPKKDij3\nZLaKKwo6fY2y6mKVVRdrW/ankqTo8AHOheQjBo1TdPiAbl0z0NrWov3HdmjnoY06XJjV6RqH6PAB\nmjJmjqaMnqOYyLhu68sdLnQvlRNluc41HZd9L5Xjmco+btyt6dztwb+aCnnuTm8hJmzQYLfbVFh5\n1FCbxK5SANBtLA6H47L2FA0LC9PKlSu1ZMkSSdLWrVs1a9YsFRYWKiEhwfm4b3zjGyouLtbatWsN\nz6+pOTulICcnxx29e5yWtiYdKt6hQyUZarNd+M7TvlY/jYpL09j46Qry95xv+xwOhyobTimvbJ/y\ny7PV0n7prTZ9rL4aEjVKw2NTFBc5zKvnacMczW2NKqs9odLaQpXWFKiqofSKtzgO9g/TgIihGhA+\nRAMjhiosMKrLH14dDofKaguVV7ZfBRUHO/12388nQEP7j9GImBTFhg/uNQul7XabKhtO6VRNoUpr\nC1RWe+Ki/65dKV+rn0ICIhQaGKGQgEiFBkQ4j0MDIhXoF+L281hcfUyfZf/TeezvG6h7p/yQKxkA\ncBHJycnOn0dERFzx87tlcnBv+Z/slQrwC9KkoXM0dtB0HS7J0MHiHWptN34T2G5vU3bRNh0uydDI\ngZM1btB0BfuHmdSx1NBSq/zyA8or26eaptOdPn5A+BANj03R0Ogx8vdlkTauXqBfsIZEj9KQ6FGS\npNb25nNCR6Eq6os7DR2NrXXKLz+g/PIDkqQgv1DFhg/RgIiO0BER1P+y/z2qbarUsbJ9Ola+X/Ut\nl15nYZFF8f1GaHjMBA2OGtkrb8xptfqof9gg9Q8bpPGaIbvDrqqGMpXWFqi0plCltYVqbb+8TR/O\n19YmznYAABMySURBVG5vU03T6Yv+m2O1+JwTQjqCx7lBJMg/7Iq/2CisOGw4Hhw1ioABAN3oqkPG\nwIEDJUmlpaWGKxmlpaXOsYtJS0u72rf1GtdqlppaGrVl3xp9vud9NTTVGsZt9nYdKt6hnNLdunb8\nfN0w+c7LvhncVzePu9rz2NLWrL2525RxaKOOntjX6Qe5mMh4TR0zR2mjr1d0+ICrek9P1tXzibPc\neS5bWpt0rORwx7qOomwVnMpx2UL6fE1t9SqoOKiCioOSOm7ImRQ/1rmuI75/ouHDaWNzvfbkfKmd\nhzYov+TwxV7WaVD/RE0ZM1dpo2b3yKJ0T/6zee69VIrKj6uyrkyVteWqqivvdJetzl/bprrmStU1\nX3ibZKvVR/1C+6tfeMw5N1w9e8+cfqH9DQvs7Xab3tj5O8Nr3Dj9VueieFw5T/6z6W04l+7F+XSf\nc2chXY2rDhnDhg3TwIEDtW7dOk2ePFmS1NzcrC1btujpp5/uUlO9RVBAsOZPuUuzJ92sL/ev1fpd\n76musdrwmHZbmzbv/VhfHlin6WNv1Py0OxUVHuv2XuwOu3JPHjiz7ey2TudaBwWEKHXkdZo6Zo4S\nB47qs1enYJ4A/yCNGXqNxgy9RlLHQuXjJUc77khedPDyFio31Wpv3nbtzdsuqePP9Yj4sRoWN1on\nyvK0P39np2uOwoIjNWX09Zoyeo4GxQxzzy+uFzj3XirnsjvsqmusVmVtuSpry1RZV/7/t3fvQVHV\nfx/A37vLZZdLhJflIuhydbkIqbAleAFTxC6O9SQOakmX0UZzQC0vqYPNCGhmRSLlOFOZziQ+PaVp\nzk80AeFBE4p1AgTsES/8UkhDkQ0v7J7nD5XaHwKKBw8H368ZRz179uzH76z73Tfne0FjU0Pbn/9s\nami3UMb9sljMuNRUj0tN9fjtLo8rFEq4/GOzVlsbO1y7aWp7XG3ngEDv8AeqgYiIOtflErZ35k9Y\nLBacOXMGRqMR/fv3h7e3N1JSUpCeng69Xo+AgACsWbMGzs7OmDFjxkMpXi7sbdUYP2IqRg+bjOLy\nXPz483ftNjIzm1vxv7/+C0cqDsAQFIuJEf8lysTR+j/r2padbWzufDiUUqlC8JARMATFIsQn4pHf\nwZx6FzsbewR6D0Og998Tlc/Wn7y943U5as9Xdz1R+boJ5bUlKK8t6fQ8W5Udhvk9CUNQDIYOfgIq\nDqu5Z0qFEi6O/eDi2A8+HkPbPS4IAkzXrt4KHXdCyNU/cKmpoS2M/HOZ2e4QBAsuN1/C5eZLOHW+\n/caIoT6RXE6biKiHdRoySkpKMH78eAC35lmkpqYiNTUVSUlJ+Pzzz7FkyRK0tLRg/vz5aGxsxFNP\nPYXc3Fw4OvaeCc29iZ2tPWKGP4/oYZNwtOIgDpZ+2+6Lv8VixtGKgzhWeQgR+nGYGPkS3FwH3dfr\nmFqa8HNNEUpO5OFMfdeT7L21fjAExWJE4Gg4O3DZWZIHWxvb23s2BGMSpsFsbsW5P079vTrS7ydw\n7T6/rPoNCoFBH4MnAqJ67TKscqdQKOCkeQxOmscw2M3/rue0XDfduhNytcE6jDT9gUtXG9oNP71f\nTwRwAz4iop7WaciIiYmBxdL5ko13ggfdO1sbO4wJfwajQifi2Ik8HCj5H1xqqrc6xyJYcOxEHkqq\nCjAiIBpxhgR49Pfu8Jqt5puoPP0zjp3IQ0Xtz12OXXdx7Hd72dlYePQfLMq/i0hKKpUNdO6B0LkH\nYkLEi7BYzPj3xdO394G4NcTqr+vN7Z43wMUdkUGxiNSPwwCXzueT0cOhsXfEoIGOGDRQd9fHr9+8\ndnv+R4PVsKxbvzegydTY4bUHPu4J/e0heERE1HMeztazdFc2KltEhcbhyaDxKK0uQO6xb/DHlfNW\n5wiCBT/XFOKXmiKEB4zCpMiEfzwm4Gz9yVs7D9cU4q9rVzt9PTsbe4T5PwWDPhaB3sO4sgr1aUql\nCt5aP3hr/RA7YorVROW6hlPQ2Dsi3H8UfDz0nHMkM/a2anj09+7wBy83W2+g8erFv4dhXW3Aydoq\nqG0d8eKEl7kyHhHRQ8CQ0QuoVDZ4MvhpROhj8EtNEXKP/Xe73ZEFCDCeLIbxZDG8+wWiv5MH9ld+\neU+7KAd4DYMhKAbh/lFQ22l66p9B1Kt1NFGZ+h5bGztoXT2hdfVsO1Zqe2vFGe19Dj8lIqLuYcjo\nRVRKFSL14zAycDSMvx3B/mM7cf7S2XbnnfuzBuf+Y+fa/6R93BOGoFhE6Mf1yGpVREREREQdYcjo\nhZRKFUYEjsYTAVH49f9+wr+O7cS//6jt8nkO9k4YMXQMDEGxGOIWwCEgRERERCQJhoxeTKlQItx/\nFML8nkJ5bQn2/7QTZxusV4VXKlUI0Y2EIWg8gnUjuSwjEREREUmOIUMGFAoFhvkaEOoTiRNnyrD3\n8NcwW1oRPXwCRgSOgZPmMalLJCIiIiJqw5AhIwqFAsG6Efjr4q1lhSPCIySuiIiIiIioPaXUBRAR\nERERUd/CkEFERERERKJiyCAiIiIiIlExZBARERERkagYMoiIiIiISFQMGUREREREJCqGDCIiIiIi\nEhVDBhERERERiYohg4iIiIiIRMWQQUREREREomLIICIiIiIiUTFkEBERERGRqBgyiIiIiIhIVAwZ\nREREREQkKoYMIiIiIiISFUMGERERERGJiiGDiIiIiIhExZBBRERERESiYsggIiIiIiJRMWQQERER\nEZGoGDKIiIiIiEhUDBlERERERCQqhgwiIiIiIhIVQwYREREREYmKIYOIiIiIiETFkEFERERERKJi\nyCAiIiIiIlExZBARERERkagYMoiIiIiISFQMGUREREREJCqGDCIiIiIiEhVDBhERERERiYohg4iI\niIiIRCVKyLh69SpSUlKg0+ng4OCA6OholJaWinFpIiIiIiKSGVFCxhtvvIEDBw7gq6++Qnl5OeLi\n4jBhwgT8/vvvYlyeiIiIiIhk5IFDRktLC7799lusXbsWY8eOha+vL1JTU+Hv749PP/1UjBqJiIiI\niEhGHjhktLa2wmw2w97e3uq4Wq1GUVHRg16eiIiIiIhkRiEIgvCgF4mOjoZKpcKOHTvg5uaGr7/+\nGklJSQgICMCJEycAAFeuXHngYomIiIiI6OFycXG57+eIMidj27ZtUCqV8PLyglqtRlZWFhITE6FQ\nKMS4PBERERERyYgoIcPX1xf5+fkwmUyoq6vD0aNHcePGDfj5+YlxeSIiIiIikhEbMS+m0Wig0WjQ\n2NiI3NxcrF+/vu2x7txmISIiIiIi+RFlTkZubi7MZjP0ej1+++03vPPOO3BwcEBhYSFUKpUYdRIR\nERERkUyIcifjypUrWL58Oerq6tCvXz+89NJLSEtLY8AgIiIiInoEiXIng4iIiIiI6A5RJn53JTs7\nGz4+PtBoNIiIiOD+Gd2UkZGByMhIuLi4QKvVYsqUKaioqJC6rD4hIyMDSqUSCxYskLoU2Tp//jxm\nz54NrVYLjUaDkJAQHD58WOqyZKe1tRXvvvsufH19odFo4Ovri1WrVsFsNktdmiwcPnwYU6ZMgZeX\nF5RKJbZu3drunNWrV2PQoEFwcHBAbGwsKisrJai09+usLVtbW7F06VKEh4fDyckJnp6emDlzJs6d\nOydhxb3bvbw375g7dy6USiU2bNjwECuUj3tpy5qaGrz44otwdXWFo6MjRo4ciaqqKgmq7f26as+m\npibMmzcP3t7ecHBwgF6vx8cff9zldXs8ZOTk5CAlJQUrV66E0WhEVFQUJk+ezA+ibigoKMBbb72F\nI0eO4NChQ7CxscGECRPQ2NgodWmydvToUWzZsgVhYWFcdrmbLl++jOjoaCgUCuzbtw9VVVXIysqC\nVquVujTZSU9Px+bNm7Fx40ZUV1cjMzMT2dnZyMjIkLo0WTCZTAgLC0NmZiY0Gk27/9Pr1q3Dhx9+\niKysLJSUlECr1WLixIlobm6WqOLeq7O2NJlMKCsrw8qVK1FWVobdu3fj3LlziI+PZyDuQFfvzTu+\n+eYblJSUwNPTk31SB7pqy9raWkRHR8PPzw95eXmoqKhAWloanJycJKq4d+uqPVNSUrB//35s374d\nVVVVWLFiBZYtW4bt27d3fmGhhxkMBmHOnDlWxwICAoTly5f39Ev3ec3NzYJKpRL27t0rdSmydfny\nZcHPz0/Iz88XYmJihAULFkhdkiwtX75cGD16tNRl9AnPPfeckJSUZHXslVdeEZ5//nmJKpIvJycn\nYevWrW1/t1gsgru7u5Cent52rKWlRXB2dhY2b94sRYmy8Z9teTeVlZWCQqEQysvLH1JV8tVRe54+\nfVoYNGiQUFVVJeh0OmHDhg0SVCcvd2vLxMREYdasWRJVJG93a8/Q0FBh9erVVsfGjRvX5XemHr2T\ncePGDfzyyy+Ii4uzOh4XF4fi4uKefOlHQlNTEywWC1xdXaUuRbbmzJmDadOmYdy4cRA4Panbdu3a\nBYPBgOnTp8PNzQ3Dhw/Hpk2bpC5LliZPnoxDhw6huroaAFBZWYm8vDw888wzElcmf7W1taivr7fq\nk9RqNcaOHcs+SQRXrlwBAPZJ3dTa2orExESsWrUKQ4cOlboc2bJYLNi7dy+CgoIQHx8PrVYLg8GA\nnTt3Sl2abE2ePBnff/896urqAADFxcUwGo2Ij4/v9Hk9GjIuXrwIs9kMNzc3q+NarRYXLlzoyZd+\nJCQnJ2P48OEYNWqU1KXI0pYtW3Dq1CmsWbMGAHhb+gGcOnUK2dnZ8Pf3R25uLpKTk7Fs2TIGjW6Y\nN28eZs6ciaCgINjZ2SE0NBRJSUl48803pS5N9u70O+yTxHfjxg0sXrwYU6ZMgaenp9TlyFJqaiq0\nWi3mzp0rdSmy1tDQgObmZqSnpyM+Ph4HDx5EYmIiZs6ciX379kldniytW7cOwcHBGDx4MOzs7BAT\nE4P333+/yx9+iboZHz08ixYtQnFxMYqKivjluBuqq6uxYsUKFBUVtS21LAgC72Z0k8VigcFgQFpa\nGgAgPDwcJ0+exKZNmzB//nyJq5OXTz75BF988QV27NiBkJAQlJWVITk5GTqdDq+99prU5fVZ/Bzt\nvtbWVsyaNQtNTU3Yu3ev1OXIUn5+PrZu3Qqj0Wh1nH3S/bNYLACAqVOnIiUlBQAQFhaG0tJSZGVl\n8a5wN7z99tv46aefsGfPHgwZMgQFBQVYvHgxhgwZgkmTJnX4vB4NGQMGDIBKpUJ9fb3V8fr6enh4\nePTkS/dpCxcuxM6dO5GXlwedTid1ObJ05MgRXLx4ESEhIW3HzGYzCgsLsXnzZphMJtja2kpYobx4\nenoiODjY6pher8fZs2clqki+0tLSsHLlSiQkJAAAQkJCcObMGWRkZDBkPCB3d3cAt/ogLy+vtuP1\n9fVtj9H9uTPEp6KiAvn5+Rwq1U0FBQU4f/681Xcjs9mMpUuXIjMzk5+l92HAgAGwsbG5a5+Uk5Mj\nUVXyZTKZkJmZie+++w7PPvssACA0NBRGoxEffPBBpyGjR4dL2dnZYeTIkcjNzbU6fuDAAURFRfXk\nS/dZycnJyMnJwaFDhxAYGCh1ObL1wgsvoLy8HMePH8fx48dhNBoRERGBxMREGI1GBoz7FB0d3W5p\nwJqaGobgbhAEAUql9UezUqnkTzRF4OPjA3d3d6s+6dq1aygqKmKf1A03b97E9OnTUV5ejry8PK4m\n9wDmzZuHX3/91apP8vT0xKJFi/Djjz9KXZ6s2NnZITIykn2SSO6M8uhOv9Tjw6UWLVqEl19+GQaD\nAVFRUfjss89w4cIFji/uhvnz52P79u3YtWsXXFxc2sYQOzs7w9HRUeLq5MXFxQUuLi5WxxwcHODq\n6trupx/UtYULFyIqKgrp6elISEhAWVkZNm7cyGVXu2Hq1KlYu3YtfHx8EBwcjLKyMnz00UeYPXu2\n1KXJgslkwsmTJwHcGjZx5swZGI1G9O/fH97e3khJSUF6ejr0ej0CAgKwZs0aODs7Y8aMGRJX3vt0\n1paenp6YNm0aSktLsWfPHgiC0NYnPf7441Cr1VKW3it19d4cOHCg1fm2trZwd3dHQECAFOX2al21\n5ZIlS5CQkIAxY8YgNjYWeXl5yMnJwe7duyWuvHfqqj2ffvppLFu2DE5OThg8eDAKCgqwbds2rF+/\nvvMLi7TiVaeys7MFnU4n2NvbCxEREUJhYeHDeNk+R6FQCEqlUlAoFFa/3nvvPalL6xO4hO2D+eGH\nH4Tw8HBBrVYLQ4cOFTZu3Ch1SbLU3NwsLF68WNDpdIJGoxF8fX2FFStWCNevX5e6NFnIy8tr+2z8\n5+flq6++2nbO6tWrBQ8PD0GtVgsxMTFCRUWFhBX3Xp215enTpzvsk7pa6vZRdS/vzX/iErYdu5e2\n/PLLL4XAwEBBo9EI4eHhwo4dOySsuHfrqj0bGhqE119/XfDy8hI0Go0QFBR0T+9NhSDwHjwRERER\nEYmnx3f8JiIiIiKiRwtDBhERERERiYohg4iIiIiIRMWQQUREREREomLIICIiIiIiUTFkEBERERGR\nqBgyiIiIiIhIVAwZREREREQkqv8H7py/LgS1uxgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f63a3d97080>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "   \n",
      "Given these future measurements we can infer that yes, the aircraft initiated a turn. \n",
      "\n",
      "On the other hand, suppose these are the following measurements.\n",
      "\n",
      "   9.8 10.2 9.9 10.1 10.0 10.3 9.9 10.1\n",
      "    \n",
      "In this case we are led to conclude that the aircraft did not turn and that the outlying measurement was merely very noisy. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data3 = [9.8, 10.2, 9.9, 10.1, 10.0, 10.3, 9.9, 10.1]\n",
      "plt.plot(data + data3)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Afq+yztj1PVACk5ioWMVExTmPrVaL6ptqfDgjAPBfBCYAAL/nlmMSIIGJJLfq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\nIiIiItH9f/idwfYZ2JklAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f63a3ce79b0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since this type of smoothing requires knowing data from \"the future\", there are some applications for the Kalman filter where these observations are not helpful. For example, if we are using a Kalman filter as our navigation filter for an aircraft we have little interest in where we have been. While we could use a smoother to create a smooth history for the plane, we probably are not interested in it. However if we can afford a bit of latency some smoothers only require a few measurements into the future prode better results. And, of course any problem where we can batch collect the data and then run the Kalman filter on the data will be able to take maximum advantage of this type of algorithm."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Types of Smoothers"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are three broad classes of Kalman smoothers that produce better tracking in these situations.\n",
      "\n",
      "* Fixed Point Smoothing\n",
      "\n",
      "Fixed point smoothers start out as a normal Kalman filter. But once they get to measurement 4 (say) it then looks backwards and revises the filter output for the previous measurement(s). So, at step 5 the filter will produce a result for 5, and update the result for measurement 4 taking measurement 5 into account. When measurement 6 comes in the filter produces the result for 6, and then goes back and revises 4 using the measurements from 5 and 6. It will revise the output for measurement 5 as well. This process continues, with all previous outputs being revised each time a new input comes in.\n",
      "\n",
      "* Fixed Lag Smoothing\n",
      "\n",
      "Fixed lag smoothers introduce latency into the output. Suppose we choose a lag of 4 steps. The filter will injest the first 3 measurements but not ouput a filtered result. Then, when the 4th measurement comes in the filter will produce the output for measurement 1, taking measurments 1 through 4 into account. When the 5th measurment comes in, the filter will produce the result for measurement 2, taking measurements 2 through 5 into account.\n",
      "\n",
      "\n",
      "* Fixed Interval Smoothing\n",
      "\n",
      "This is a batch processing based filter. It requires all measurements for the track before it attempts to filter the data. Having the full history and future of the data allows it to find the optimal answer, at the cost of not being able to run in real time. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters a it will provide much better results than the recursive forms of the filter from the previous chapters.\n",
      "\n",
      "\n",
      "The choice of these filters depends on your needs and how much memory and processing time you can spare. Fixed point smoothing requires storage of all measurements, and is very costly to compute because the output is for every time step is recomputed for every measurement. On the other hand, the filter does produce a decent output for the current measurement, so this filter can be used for real time applications.\n",
      "\n",
      "Fixed lag smoothing only requires you to store a window of data, and processing requirements are modest because only that window is processed for each new measurement. The drawback is that the filter's output always lags the input, and the smoothing is not as pronounced as is possible with fixed interval smoothing.\n",
      "\n",
      "Fixed interval smoothing produces the most smoothed output at the cost of having to be batch processed. Most algorithms use some sort of forwards/backwards algorithm that is only twice as slow as a recursive Kalamn filter. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fixed Point Smoothing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "not done"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fixed Lag Smoothing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "not done"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fixed Interval Smoothing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are several fixed lag smoothers available in the literature. I have chosen to implement the smoother invented by Rauch, Tung, and Striebel because of its ease of implementation and efficiency of computation. This smoother is commonly known as an RTS smoother, and that is what we will call it\n",
      "\n",
      "Derivation of the RTS smoother runs to several pages of densely packed math, and to be honest I have never read it through. I'm certainly not going to inflict it on you. I don't think anyone but thesis writers really need to understand the derivation. Instead I will briefly present the algorithm, equations, and then move directly to implementation and demonstration of the smoother.\n",
      "\n",
      "The RTS smoother works by first running the Kalman filter in a batch mode, computing the filter output for each step. Given the filter output for each measurement along with the covariance matrix corresponding to each output the RTS runs over the data backwards, incorporating it's knowledge of the future into the past measurements. When it reaches the first measurement it is done, and the filtered output incorporates all of the information in a maximally optimal form.\n",
      "\n",
      "The equations for the RTS smoother are very straightforward and easy to implement. This derivation is for the linear Kalman filter. Similar derivations exist for the EKF and UKF. These steps are performed on the output of the batch processing, going backwards from the most recent in time back to the first estimate. Each iteration incorporates the knowledge of the future into the state estimate. Since the state estimate already incorporates all of the past measurements the result will be that each estimate will contain knowledge of all measurements in the past and future.\n",
      "\n",
      "    Predict Step\n",
      "$$\\begin{aligned}\n",
      "\\mathbf{P} &= \\mathbf{FP}_k\\mathbf{F}^\\mathsf{T} + \\mathbf{Q }\n",
      "\\end{aligned}$$\n",
      "\n",
      "    Update Step\n",
      "$$\\begin{aligned}\n",
      "\\mathbf{K}_k &= \\mathbf{P}_k\\mathbf{F} \\hspace{2 mm}\\mathbf{P}^{-1} \\\\\n",
      "\\mathbf{x}_k &= \\mathbf{x}_k + \\mathbf{K}_k(\\mathbf{x}_{x+1} - \\mathbf{FX}_k) \\\\\n",
      "\\mathbf{P}_k &= \\mathbf{P}_k + \\mathbf{K}_k(\\mathbf{P}_{K+1} - \\mathbf{P})\\mathbf{K}_k^\\mathsf{T}\n",
      "\\end{aligned}$$\n",
      "\n",
      "As always, the hardest part of the implementation is correctly accounting for the subscripts. A basic implementation without comments or error checking would be:\n",
      "\n",
      "    def rts_smoother(Xs, Ps, F, Q):\n",
      "        n, dim_x, _ = Xs.shape\n",
      "        \n",
      "        # smoother gain\n",
      "        K = zeros((n,dim_x, dim_x))\n",
      "        x, P = Xs.copy(), Ps.copy()\n",
      "\n",
      "        for k in range(n-2,-1,-1):\n",
      "            P_pred = dot(F, P[k]).dot(F.T) + Q\n",
      "\n",
      "            K[k]  = dot(P[k], F.T).dot(inv(P_pred))\n",
      "            x[k] += dot(K[k], x[k+1] - dot(F, x[k]))\n",
      "            P[k] += dot(K[k], P[k+1] - P_pred).dot(K[k].T)\n",
      "        return (x, P, K)\n",
      "        \n",
      "This implementation mirrors the implementation provided in FilterPy. It assumes that the Kalman filter is being run externally in batch mode, and the results of the state and covariances are passed in via the `Xs` and `Ps` variable.\n",
      "\n",
      "Let's just look at an example. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from numpy import random\n",
      "import matplotlib.pyplot as plt\n",
      "from filterpy.kalman import KalmanFilter\n",
      "import book_plots as bp\n",
      "\n",
      "def plot_rts(noise):\n",
      "    random.seed(123)\n",
      "    fk = KalmanFilter(dim_x=2, dim_z=1)\n",
      "\n",
      "    fk.x = np.array([0., 1.])      # initial state (location and velocity)\n",
      "\n",
      "    fk.F = np.array([[1., 1.],\n",
      "                     [0., 1.]])    # state transition matrix\n",
      "\n",
      "    fk.H = np.array([[1., 0.]])    # Measurement function\n",
      "    fk.P = 10.                     # covariance matrix\n",
      "    fk.R = noise                   # state uncertainty\n",
      "    fk.Q = 0.001                   # process uncertainty\n",
      "\n",
      "    # create noisy data\n",
      "    zs = np.asarray([t + random.randn()*noise for t in range (40)])\n",
      "\n",
      "    # filter data with Kalman filter, than run smoother on it\n",
      "    mu, cov, _, _ = fk.batch_filter(zs)\n",
      "    M,P,C = fk.rts_smoother(mu, cov)\n",
      "\n",
      "    # plot data\n",
      "    bp.plot_measurements(zs, lw=1)\n",
      "    plt.plot(M[:, 0], c='b', label='RTS')\n",
      "    plt.plot(mu[:, 0], c='g', linestyle='--', label='KF output')\n",
      "    plt.plot([0, len(zs)], [0, len(zs)], 'k', linewidth=2, label='track') \n",
      "    plt.legend(loc=4)\n",
      "\n",
      "    plt.show()\n",
      "    \n",
      "plot_rts(7.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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16qiJzJAQNTNSUdsfvN288a/lz4bEDQXGa7rXLNQQUVQukpQIIUR5ZGaqXZxN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QAAAg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\nIYQQQgiTkqRECCGEEEIIYVL/D4J6QC6A1QuFAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f63a3c7d710>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I've injected a lot of noise into the signal to allow you to visually distinguish the RTS output from the ideal output. In the graph above we can see that the Kalman filter, drawn as the green dotted line, is reasonably smooth compared to the input, but it still wanders from from the ideal line when several measurements in a row are biased towards one side of the line. In contrast, the RTS output is both extremely smooth and very close to the ideal output.\n",
      "\n",
      "With a perhaps more reasonable amount of noise we can see that the RTS output nearly lies on the ideal output. The Kalman filter output, while much better, still varies by a far greater amount."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_rts(noise=1.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZEoBZs2bh4+PD3Llz6datW+b0WkRERCQH2Lt3L8HBwcyfPx+z2QxAxYovEh09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\nf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       "text": [
        "<matplotlib.figure.Figure at 0x7f63a3ca4780>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[1] H. Rauch, F. Tung, and C. Striebel. \"Maximum likelihood estimates of linear dynamic systems,\" *AIAA Journal*, **3**(8), pp. 1445-1450 (August 1965).\n",
      "\n",
      "http://arc.aiaa.org/doi/abs/10.2514/3.3166"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}