diff --git a/01_g-h_filter.ipynb b/01_g-h_filter.ipynb index f1ba7ec..56e8d15 100644 --- a/01_g-h_filter.ipynb +++ b/01_g-h_filter.ipynb @@ -1026,7 +1026,27 @@ "\n", "Now consider trying to track a child's balloon in a hurricane. We have no legitimate model that would allow us to predict the balloon's behavior except over very brief time scales (we know the balloon cannot go 10 miles in 1 second, for example). In this case we would design a filter that emphasized the measurements over the predictions.\n", "\n", - "Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution. In this chapter we will merely be assigning different values to *g* and *h* in a more intuitive, and thus less optimal way. But the fundamental idea is just to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself." + "Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution. In this chapter we will merely be assigning different values to *g* and *h* in a more intuitive, and thus less optimal way. But the fundamental idea is just to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself.\n", + "\n", + "We can express this as an algorithm:\n", + "\n", + "**Initialization**\n", + "\n", + " 1. Initialize the state of the filter\n", + " 2. Initialize our belief in the state - how accurate do we think it is\n", + " \n", + "**Predict**\n", + "\n", + " 1. Based on the system behavior, predict state at the next time step\n", + " 2. Adjust belief in that state to account for the uncertainty in prediction\n", + " \n", + "**Update**\n", + "\n", + " 1. Get a measurement and associated belief about its accuracy\n", + " 2. Compute difference (residual) between our estimated state and measurement\n", + " 3. Update state based on predicted state plus some proportion of the residual\n", + " \n", + "We will use this same algorithm throughout the book, albeit with some modifications. " ] }, { @@ -2322,7 +2342,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.4.3" + "version": "3.4.1" } }, "nbformat": 4, diff --git a/02_Discrete_Bayes.ipynb b/02_Discrete_Bayes.ipynb index 7113577..483f7f9 100644 --- a/02_Discrete_Bayes.ipynb +++ b/02_Discrete_Bayes.ipynb @@ -351,7 +351,7 @@ "data": { "image/png": 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UKH17cnIyRo8ebXIfPz8/zJ07F6Wlpfp518nJyWjfvj1cXFwM+j54G52IiIiI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\n", 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EAmzfvh01NTVYunQpsrOz25w3orMoAbBROTk5OHr0KLfs7OyMxMREm3vamC1g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\n0wdz5syBQqEwKNdoNNi3bx+ysrKg1+t5io5YG5Z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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1170,7 +1170,27 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This filter is just a form of the g-h filter. Here we are using the percentages for the errors to implicitly compute the *g* and *h* parameters. We could express the discrete Bayes algorithm as a g-h filter, but that would obscure the logic of this filter." + "This filter is just a form of the g-h filter. Here we are using the percentages for the errors to implicitly compute the *g* and *h* parameters. We could express the discrete Bayes algorithm as a g-h filter, but that would obscure the logic of this filter.\n", + "\n", + "We can express this in pseudocode. I am going to u that won't immediately strike you as being identical to what we have done in this chapter.\n", + "\n", + "**Initialization**\n", + "\n", + " 1. Initialize our belief in the state\n", + " \n", + "**Predict**\n", + "\n", + " 1. Based on the system behavior, predict state at the next time step\n", + " 2. Adjust belief in that state to account for the uncertainty in prediction\n", + " \n", + "**Update**\n", + "\n", + " 1. Get a measurement and associated belief about its accuracy\n", + " 2. Compute difference (residual) between our estimated state and measurement\n", + " 3. Determine whether whether the measurement matches each state\n", + " 4. Update state belief if it matches the measurement\n", + "\n", + "When we cover the Kalman filter we will use this exact same algorithm; just the details of the computation will differ. " ] }, { @@ -1215,7 +1235,7 @@ "data": { "image/png": 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sc11RUYG6ujp4enqajGs0GhgMhibnlJSU4NKlS0hPT8dHH32EHTt2oKioCM8++yyEENKt\nnIiIHhjznYjIMlp0+fPWqK+vx61bt7Bjxw707t0bALBjxw707dsX+fn5GDJkSJPz8vPzW1yjNdta\ngpL1rbW20vVZ2/rqS1G7T58+Eqyk/XjY852vd+urrXR9a62tdH1L53uze667du0KGxsblJeXm4yX\nl5fD29u7yTne3t6wtbU1Bi8A9O7dGzY2Nrh8+XJr1k1ERBbCfCcisoxm91zb29tj8ODByMzMxKRJ\nk4zjWVlZmDJlSpNzQkNDcfv2bZSUlCAgIADAnbcS6+rq0LNnz/vW0mq1Zhfb8JdGS7a1BCXrW2tt\npeuzNn/nbVFVVdXm+7AU5nv7qK10fWutrXR9a62tdH258t3sea4XLlyIbdu2YevWrTh37hzmz58P\ng8GA2bNnAwDi4uIQERFh3D4iIgJBQUF46aWXUFhYiOPHj+Oll17C8OHDFftFEhFRY8x3IiLpmT3m\nOioqCpWVlUhMTERZWRkGDhyIjIwM4zlQDQYDSkpKjNurVCp8+eWXeP311xEWFgYnJyfodDokJSVZ\n7lEQEVGrMd+JiKTXog80xsTEICYmpsnbUlNTG415eXkhPT29bSsjIiKLY74TEUmrRZc/JyIiIiIi\n89hcExERERFJhM01EREREZFE2FwTEREREUmEzTURERERkUTYXBMRERERSaRFzXVycjL8/f3h5OQE\nrVaL3NzcFt15cXExXF1d4erq2qZFEhGRZTDfiYikZba5TktLQ2xsLBYvXozCwkIEBwcjMjISV65c\naXZebW0tpk2bhlGjRkGlUkm2YCIikgbznYhIemab66SkJOj1esycORN9+/bFmjVr4O3tjZSUlGbn\nvfXWW3jiiScwZcoUCCEkWzAREUmD+U5EJL1mm+va2loUFBRAp9OZjOt0Ohw9evS+8/bu3Yu9e/di\n7dq1DF4ionaI+U5EZBnNXv68oqICdXV18PT0NBnXaDQwGAxNziktLcWsWbOwe/dudOrUqcULyc/P\nt8i2lqBkfWutrXR91ra++lLU7tOnjwQrsQzme/uqrXR9a62tdH1rra10fUvnu+RnC3nhhRcQExOD\nIUOGSH3XRESkIOY7EZF5ze657tq1K2xsbFBeXm4yXl5eDm9v7ybnHDx4EDk5OVi+fDkAQAiB+vp6\n2NnZISUlBS+//HKT87RardnFNvyl0ZJtLUHJ+tZaW+n6rM3feVtUVVW1+T4shfnePmorXd9aaytd\n31prK11frnxvtrm2t7fH4MGDkZmZiUmTJhnHs7KyMGXKlCbnnD592uTn3bt347333kNeXh58fHxa\ns24iIrIQ5jsRkWU021wDwMKFC/HCCy9g6NChCA4OxoYNG2AwGDB79mwAQFxcHPLy8nDgwAEAQP/+\n/U3mf//991Cr1Y3GiYhIWcx3IiLpmW2uo6KiUFlZicTERJSVlWHgwIHIyMiAr68vAMBgMKCkpKTZ\n++B5UImI2h/mOxGR9Mw21wAQExODmJiYJm9LTU1tdm50dDSio6NbvTAiIrI85jsRkbQkP1sIERER\nEZG1YnNNRERERCQRNtdERERERBJhc01EREREJBE210REREREEmlxc52cnAx/f384OTlBq9UiNzf3\nvtseOnQIzz33HHx8fODs7IzAwECznzonIiJlMN+JiKTTouY6LS0NsbGxWLx4MQoLCxEcHIzIyEhc\nuXKlye2PHTuGwMBAfPbZZzhz5gxiYmIwa9YsfPLJJ5IunoiI2ob5TkQkrRad5zopKQl6vR4zZ84E\nAKxZswb79u1DSkoKVqxY0Wj7uLg4k59nz56NgwcP4rPPPsP06dMlWDYREUmB+U5EJC2ze65ra2tR\nUFAAnU5nMq7T6XD06NEWF6qqqoKHh0frV0hERBbBfCcikp7ZPdcVFRWoq6uDp6enybhGo4HBYGhR\nkS+//BLZ2dmtCmsiIrIs5jsRkfRUQgjR3AalpaXo0aMHcnJyEBoaahxPSEjAzp07UVRU1GyBb775\nBmPHjsWqVavw6quvmtxWVVVl/L64uPhB1k9E1G716dPH+L27u7uCK2ka852I6ME0l+9mDwvp2rUr\nbGxsUF5ebjJeXl4Ob2/vZufm5uZi7NixePfddxsFLxERKYv5TkQkPbOHhdjb22Pw4MHIzMzEpEmT\njONZWVmYMmXKfefl5ORg3LhxSEhIwOuvv252IVqt1uw2+fn5Ld7WEpSsb621la7P2vydt8Xde2/b\nI+a78rUtUb+k4jeU3rzdom1/++03AICrq2uravg42yKga+vm3Othe96ttXZrXm/Ag73mpHi9AfLl\ne4vOFrJw4UK88MILGDp0KIKDg7FhwwYYDAbMnj0bwJ1Pj+fl5eHAgQMA7pwH9ZlnnsHcuXMxffp0\n47F7NjY26NatW1sfDxERSYT5/vApvXkb83IqWjnrVqu2XhvWFQFdW1mCHkoP9noDWvOa62ivtxY1\n11FRUaisrERiYiLKysowcOBAZGRkwNfXFwBgMBhQUlJi3H779u2oqanBBx98gA8++MA47ufnZ7Id\nEREpi/lORCStFjXXABATE4OYmJgmb7v36lypqam8YpcZrX4bxVEDAMi9dK3Fc6R6G4UeDq16q/gB\nXm8AX3Md1cOY73y9k5zk+H86wNdcR9Hi5pqkxbdRSG58q5isCV/vJCc5/p8O8DXXUbSb5rolf73x\nLz1qK75jQERERJbUbprr1v3Fx7/06MHwHQMiIiKyJLPnuSYiIiIiopZpN3uulcBDBEhu/JAVERHR\nw61FzXVycjI++OADGAwGPPbYY/jwww9NLpV7r1OnTmHu3LnIy8uDh4cHXn31VSxZskSyRUuFhwgo\nw5r/qOGHrJTBP2ru72HNdyVZc8aRMphx7YvZ5jotLQ2xsbFISUlBaGgo1q9fj8jISJw9e9Z4HtS7\n3bhxA6NHj0Z4eDjy8/Nx7tw56PV6ODs7Y+HChRZ5ENR6Sv5D5B811kfpZoN/1DSN+W4ZzDiSGzOu\nfTHbXCclJUGv12PmzJkAgDVr1mDfvn1ISUnBihUrGm3/8ccfo6amBtu3b4eDgwP69++PoqIiJCUl\nMXzbEf5DJDmx2Wif5Mp3ng3Keii540bpP+JJfu31/OLNNte1tbUoKCjAm2++aTKu0+lw9OjRJucc\nO3YMI0eOhIODg8n2S5YswaVLl9CzZ88WL46IiCxDznzn2aCsh5I7bvhHvPVpr+cXb/ZsIRUVFair\nq4Onp6fJuEajgcFgaHKOwWBotH3Dz/ebQ0RE8mK+ExFZhkoIIe53Y2lpKXr06IGcnByTD7gkJCRg\n586dKCoqajRnzJgx8PX1xZYtW4xjly9fhp+fH44dO4Zhw4YZx6uqqqR6HERE7Zq7u7vSSzDBfCci\nksa9+d7snuuuXbvCxsYG5eXlJuPl5eXw9vZuco6Xl1ejPRgN8728vFq9YCIikh7znYjIMpptru3t\n7TF48GBkZmaajGdlZSE4OLjJOSNGjMCRI0dw69Ytk+27d+/O462JiNoJ5jsRkYUIM9LS0oS9vb3Y\nsmWLOHv2rHj99deFq6uruHz5shBCiLfffls8/fTTxu2rqqqEl5eXmDZtmjh9+rT47LPPhJubm0hK\nSjJXioiIZMR8JyKSntlT8UVFRaGyshKJiYkoKyvDwIEDkZGRYTwHqsFgQElJiXF7Nzc3ZGVl4bXX\nXoNWq4WHhwcWLVqEBQsWWO4vBCIiajXmOxGR9Jr9QCMREREREbVcs8dctzfJycnw9/eHk5MTtFot\ncnNzZambk5OD8ePHo0ePHlCr1di+fbssdQFg5cqVGDJkCNzd3aHRaDB+/HicOXNGltrr169HYGAg\n3N3d4e7ujuDgYGRkZMhS+14rV66EWq3GvHnzZKm3bNkyqNVqky8fHx9ZagNAWVkZXnzxRWg0Gjg5\nOeGxxx5DTk6Oxev6+fk1etxqtRrjxo2zeO3bt2/jnXfeQUBAAJycnBAQEIAlS5agrq7O4rUb/Pbb\nb4iNjYWfnx86deqEkJAQ5Ofny1bfmimR79aa7YD15rvS2Q4w35XId7mzvcM01w2X6V28eDEKCwsR\nHByMyMhIXLlyxeK1b968iccffxyrV6+Gk5MTVCqVxWs2OHz4MObOnYtjx44hOzsbtra2iIiIwLVr\nrbu60IPw9fXFqlWrcPz4cfzwww946qmnMGHCBJw4ccLite/27bffYvPmzXj88cdlfe779esHg8Fg\n/Dp16pQsda9fv46QkBCoVCpkZGSgqKgI69atg0ajsXjtH374weQxFxQUQKVSYerUqRavvWLFCmzc\nuBFr167F+fPnsXr1aiQnJ2PlypUWr93g5ZdfRlZWFj766COcPn0aOp0OERERKC0tlW0N1kipfLfW\nbAesO9+VynaA+a5Uvsue7Uof9N1SQ4cOFbNmzTIZ69Onj4iLi5N1HS4uLmL79u2y1rxbdXW1sLGx\nEV9++aUi9T08PMSmTZtkq3f9+nXRq1cvcejQIREeHi7mzZsnS934+HgxYMAAWWrdKy4uToSGhipS\n+16JiYmiS5cuoqamxuK1xo0bJ6Kjo03G/uu//ks8++yzFq8thBC///67sLW1FZ9//rnJ+ODBg8Xi\nxYtlWYO1ag/5bu3ZLoR15LuS2S4E8/1ucuW7EtneIfZcN1ymV6fTmYw3d5neh9WNGzdQX1+PLl26\nyFq3rq4On376KWpqahAWFiZb3VmzZmHKlCkYNWoUhMwfDygpKUH37t0REBCA6dOn4+LFi7LU3b17\nN4YOHYqpU6fC09MTgwYNwvr162WpfTchBLZu3YoZM2aYXO7aUiIjI5GdnY3z588DAM6ePYuDBw9i\n7NixFq8N3Hnbsq6urtFjdXR0lO0QNGvEfL9DqWwHrC/flcp2gPmuRL4rku0WadkldvXqVaFSqcSR\nI0dMxpcvXy769u0r61qU3rsxZcoUERQUJOrr62Wpd/LkSeHs7CxsbW2Fq6urrHtVNm3aJLRarbh9\n+7YQQsi65/qrr74S//rXv8SpU6fEgQMHRHh4uPDy8hKVlZUWr+3g4CAcHR3FO++8IwoLC0Vqaqpw\ncXER69ats3jtu+3fv1+oVCpx8uRJ2WrGxcUJlUol7OzshEqlEkuWLJGtthBCBAcHi5EjR4qrV6+K\n27dvix07dggbGxvRr18/WddhTdpLvltbtgthnfmuZLYLwXxXKt/lznY2162kZAAvWLBAdO/eXVy8\neFG2mrW1teLChQuioKBAxMXFCRcXF5GXl2fxukVFRaJbt27i/PnzxrFRo0aJuXPnWrx2U27evCk0\nGo0s5/O1s7MTISEhJmPvvPOO+OMf/2jx2nebPHmyGDZsmGz1Vq9eLby8vERaWpo4ffq02LFjh/Dw\n8BBbt26VbQ0XLlwQo0aNEiqVStja2ophw4aJGTNmyP7cW5P2ku/Wlu1CMN+FkDfbhWC+K5Xvcmd7\nh2iub926JWxtbcWuXbtMxufMmSPCw8NlXYtSARwbGyt8fHxMwkgJERERjY6bsoTU1FTjP4KGL5VK\nJdRqtbCzsxO1tbUWX8O9nnzySTFnzhyL1+nZs6d45ZVXTMY++ugj4ezsbPHaDcrLy40XF5GLRqMR\na9asMRlLTEwUvXv3lm0NDX7//XdhMBiEEEJERUWJcePGyb4Ga9Fe8t3as10I6813ubJdCOb73ZTI\nd7myvUMcc/0gl+l9mMyfPx9paWnIzs7Go48+quha6urqUF9fb/E6f/7zn3H69GmcOHECJ06cQGFh\nIbRaLaZPn47CwkLY2dlZfA13q6mpwblz5+Dt7W3xWiEhISgqKjIZ+/HHH+Hn52fx2g22bdsGR0dH\nTJ8+XbaaQgio1aaRpFarZT/WHgCcnJzg6emJa9euITMzE88995zsa7AW1pzv7SnbAevMdzmzHWC+\n302JfJct2y3SsluAucv0WlJ1dbU4fvy4OH78uOjUqZNISEgQx48fl6X2nDlzhJubm8jOzhZlZWXG\nr+rqaovXfuutt8SRI0fExYsXxcmTJ8Xbb78t1Gq1yMzMtHjtpsj5tuEbb7whDh8+LEpKSsS3334r\nnnnmGeHu7i7L7zwvL0/Y2dmJ9957TxQXF4v09HTh7u4ukpOTLV5bCCHq6+tFnz59Gp29wdJeeeUV\n0aNHD7ESR7kSAAAgAElEQVR3715x8eJF8e9//1t069ZNLFq0SLY17N+/X2RkZIiSkhKRmZkpAgMD\nxYgRI4zHhZJlKJXv1prtQlhvviuZ7UIw35XKd7mzvcM010IIkZycLPz8/ISDg4PQarWNjtGzlIMH\nDwqVSmV826rhe71eb/Ha99Zs+Fq+fLnFa0dHR4uePXsKBwcHodFoxOjRoxULXiHk/UDjtGnThI+P\nj7C3txfdu3cXkydPFufOnZOlthBC7N27VwQGBgpHR0fRt29fsXbtWtlqZ2dnC7VaLcuxl3errq4W\nb7zxhvDz8xNOTk4iICBA/PWvfxW3bt2SbQ3p6emiV69ewsHBQXh7e4t58+aJGzduyFbfmimR79aa\n7UJYb74rne1CMN+VyHe5s52XPyciIiIikkiHOOaaiIiIiKgjYHNNRERERCQRNtdERERERBJhc01E\nREREJBE210REREREEmFzTUREREQkETbX1GGEh4dDrVbj8uXLiq3hypUrmDNnDoYNGwYvLy84OjrC\nx8cHISEh2LBhA2pqahRbGxFRR9Ue8r0p7777LtRqNdRqNfbv36/0cqiDYHNNHYpKpVK0/oULF7Bz\n50506dIFEydOxKJFizB+/Hj8/PPPmDNnDsLCwthgExE9AKXz/V55eXlISEiAi4sLVCpVu1sftV+2\nSi+AqDXEnauKKlY/JCQE169fbzR++/Zt6HQ6HDp0CJ988gn0er0CqyMi6riUzve7/f7775gxYwZG\njBgBf39/7NixQ+klUQfCPdfULnzxxReIiIiAj4+P8VCL0NBQrFy5EgCgVquRk5MDAPD39ze+Tefv\n729yP1VVVVi6dCkGDBgAZ2dnuLm5YeTIkdi1a1ejmocOHYJarYZer8fZs2cxfvx4eHh4wMXFBWFh\nYfj6668bzbGzs2ty/ba2tnjuuecAAGVlZW16LoiIHiYdJd/vtmjRIpSVlWHbtm3cY02txj3XpLhN\nmzZh9uzZ8PLywrhx46DRaFBRUYEzZ85g48aNiIuLQ3x8PLZt24ZLly4hNjYWnTt3BgDjfwHg6tWr\nePLJJ/HTTz8hLCwMY8aMQXV1Nfbu3YuoqCjEx8cjPj6+Uf2LFy8iJCQETzzxBGJiYvDzzz8jPT0d\nY8aMQXp6OiZOnGj2MdTV1SEjIwMqlQrh4eGSPTdERB1ZR8z3r776Chs2bMD69esREBBguSeHHl6C\nSGFBQUHC0dFR/Oc//2l0W2VlpfH7UaNGCZVKJS5dutTk/Tz99NPCxsZGfPrppybjN27cEEFBQUKt\nVosTJ04Yxw8ePChUKpVQqVTizTffNJnz3XffCVtbW/HII4+I6urqRrUqKipEfHy8WLp0qYiJiRG9\ne/cWbm5uYv369a167ERED7OOlu+//PKL8PLyEqNHjzaOvfjii0KlUon9+/e3/IGTVeNhIdQu2NjY\nwNa28RspHh4eLZp/6tQpZGdnY8KECZg6darJba6urli2bBmEEPj4448bze3cuTOWLl1qMjZ06FBE\nRUXh119/xZ49exrN+eWXX5CQkIDExERs2LABFy5cwIQJE6DT6Vq0XiIia9GR8n3WrFmoqanB//zP\n/7RobURN4WEhpLgZM2bgjTfeQP/+/TF16lSMHDkSwcHB8Pb2bvF9fPPNNwDuHJO3bNmyRrf/8ssv\nAIBz5841ui0oKAjOzs6NxsPCwvDJJ5+gsLAQzz//vMlt/fr1Q319PYQQ+Pnnn7Fnzx4sWbIEX3zx\nBY4cOYLHHnusxWsnInpYdaR8T01Nxe7du5GamooePXq0eH1E92JzTYpbsGABNBoNUlJSsH79eqxZ\nswYAMHz4cKxcuRKjRo0yex+VlZUAgK+//vq+H1RRqVS4efNmo3FPT88mt28Yr6qqum9dlUoFX19f\nzJ07FxqNBtOmTUN8fHyTH7AhIrI2HSXfr169ivnz52P8+PF48cUXm5wj2smZTKj942Eh1C785S9/\nQW5uLq5du4b9+/fjtddeQ0FBASIjI1FcXGx2vru7OwAgKSkJ9fX1TX7V1dU1Gczl5eVN3mfDeMN9\nmzNmzBgAwIkTJ1q0PRGRNegI+V5cXIzq6mp8/vnnxrOVNHx99NFHAIDIyEio1WqsXr36gZ4Hsh7c\nc03tiouLC0aPHo3Ro0fDzc0NK1euxL59+9CnTx/Y2NgAuHNmjnsFBwcDAHJychAbG9uqmgUFBaiu\nroaLi4vJ+OHDhwEAgwYNatH9XL16FQDg5ubWqvpERNagPee7j48PZs6c2eRp9w4fPozi4mL86U9/\nQo8ePTBw4MBWrYGsD/dck+Kys7ObHG84X3SnTp0AAI888ggA4NKlS422DQoKwqhRo7Bnzx5s2bKl\nyfv78ccfceXKlUbj169fR0JCgsnYd999h/T0dHh4eBjPXw0Ax48fR319faP7qK6uxvz58wEAf/7z\nn5usT0RkbTpKvj/66KPYvHkzNm3a1OhrxIgRAIDY2Fhs2rQJTz31VEseOlkx7rkmxU2cOBEuLi4Y\nPnw4evbsCZVKhe+//x65ubno3bs3oqKiAAA6nQ67du3CK6+8gokTJ8LV1RVdunTBa6+9BgDYuXMn\nnn76acyaNQtr167FsGHD4OHhgatXr+LMmTMoLCzE7t274evra1J/5MiR2Lx5M77//nsEBwfj6tWr\nSEtLg0qlwqZNm4zhDwDLly/H0aNHERwcDF9fX3Tq1AlXrlzBV199haqqKjz99NP47//+b/mePCKi\ndqwj5TuRZMydq+/w4cPi2WefFd27dxcqlUps27bN7Pn9Tp48KcLCwoSTk5Po3r27SEhIaPM5A+nh\ntWHDBjFx4kTRq1cv4ezsLDp37iwCAwPF8uXLxa+//mrcrr6+XixdulT07t1b2NvbC5VKJfz9/U3u\n6+bNm+L9998XQ4YMEa6ursLR0VH4+/uLMWPGiHXr1olr164Zt204D6perxfnzp0T48ePF126dBHO\nzs4iLCxMfP31143WunfvXjFjxgzx6KOPCnd3d2FnZye8vLzEmDFjxPbt2y33JBFZAPOdLK0j5fv9\nREdHC7VazfNcU4uZba4zMjLEX//6V7Fr1y7RqVMnsw1EVVWV8PT0FFOnThVnzpwRu3btEq6uruIf\n//iHZIsmksLd4UtkjZjv9LBivpOSzB4WEhkZicjISABAdHS02T3hH3/8MWpqarB9+3Y4ODigf//+\nKCoqQlJSEhYuXNjmPe1ERCQN5jsRkfQk/0DjsWPHMHLkSDg4OBjHdDodSktLm/ygAhERdQzMdyIi\n8yRvrg0GQ6OTtjf8bDAYpC5HREQyYb4TEZkn+dlCmjpH5P00d+U7IksbNGgQrl27BoCvRbK8ll6M\nqD1jvlNHwXwnOd2b75Lvufby8mq0B6PhSkheXl5SlyMiIpkw34mIzJO8uR4xYgSOHDmCW7duGcey\nsrLQvXt39OzZU+pyREQkE+Y7EZF5Zg8LuXnzJoqLiwEA9fX1uHTpEgoLC/HII4/A19cXcXFxyMvL\nw4EDBwAAzz//PJYvX47o6GgsXrwY58+fx/vvv49ly5Y1W6clb5nm5+cDALRardltLUHJ+tZaW+n6\nrM3feVu097ejme/K11a6vrXWVrq+tdZWur5c+W52z3VeXh6CgoIQFBSEmpoaxMfHIygoCPHx8QDu\nfIilpKTEuL2bmxuysrJQWloKrVaLefPmYdGiRViwYEGbHwgREUmH+U5EJD2ze67Dw8NRX19/39tT\nU1MbjQ0YMACHDx9u28qIiMiimO9ERNKT/JhrIiIiIiJrxeaaiIiIiEgibK6JiIiIiCTC5pqIiIiI\nSCJsromIiIiIJMLmmoiIiIhIIi1qrpOTk+Hv7w8nJydotVrk5uY2u31GRgaGDx8ONzc3dOvWDRMm\nTDBeqICIiNoP5jsRkbTMNtdpaWmIjY3F4sWLUVhYiODgYERGRuLKlStNbv/TTz9hwoQJCA8PR2Fh\nIQ4cOICamhqMHTtW8sUTEdGDY74TEUnPbHOdlJQEvV6PmTNnom/fvlizZg28vb2RkpLS5PaFhYWo\nr6/HypUrERAQgMDAQLz11lu4cOECfv31V8kfABERPRjmOxGR9Jptrmtra1FQUACdTmcyrtPpcPTo\n0SbnhISEwMXFBZs3b0ZdXR1+++03bNu2DUOHDoWHh4d0KyciogfGfCcisoxmm+uKigrU1dXB09PT\nZFyj0cBgMDQ5x9vbGxkZGVi8eDEcHR3RuXNnnDlzBl988YV0qyYiojZhvhMRWYZKCCHud2NpaSl6\n9OiBnJwchIaGGscTEhKwc+dOFBUVNZpTUlKC4cOHQ6/X4/nnn8eNGzewdOlSAEB2djZUKpVx26qq\nKuP3/EAMET1s+vTpY/ze3d1dwZU0xnwnInpwzeW7bXMTu3btChsbG5SXl5uMl5eXw9vbu8k5Gzdu\nhK+vL95//33j2D//+U/4+vri2LFjCA4ObvUDICIiaTHfiYgso9nm2t7eHoMHD0ZmZiYmTZpkHM/K\nysKUKVOanCOEgFpterRJw8/19fX3raXVas0uNj8/v8XbWoKS9a21ttL1WZu/87a4e+9te8N8bx+1\nla5vrbWVrm+ttZWuL1e+mz1byMKFC7Ft2zZs3boV586dw/z582EwGDB79mwAQFxcHCIiIozbjx8/\nHgUFBXj33XdRXFyMgoIC6PV6/OEPf8DgwYPb/GCIiEgazHciIuk1u+caAKKiolBZWYnExESUlZVh\n4MCByMjIgK+vLwDAYDCgpKTEuH1oaCjS0tLwt7/9DatWrUKnTp0wYsQI7Nu3D05OTpZ7JERE1CrM\ndyIi6ZltrgEgJiYGMTExTd6WmpraaGzy5MmYPHly21ZGREQWx3wnIpJWiy5/TkRERERE5rG5JiIi\nIiKSCJtrIiIiIiKJsLkmIiIiIpIIm2siIiIiIom0qLlOTk6Gv78/nJycoNVqkZuba3bOhx9+iH79\n+sHR0RE+Pj6Ii4tr82KJiEhazHciImmZPRVfWloaYmNjkZKSgtDQUKxfvx6RkZE4e/as8Vyo91q4\ncCH27t2Lv//97xg4cCCqqqpQVlYm+eKJiOjBMd+JiKRntrlOSkqCXq/HzJkzAQBr1qzBvn37kJKS\nghUrVjTa/vz581i3bh1OnTqFvn37GscDAwMlXDYREbUV852ISHrNHhZSW1uLgoIC6HQ6k3GdToej\nR482OWfPnj0ICAhARkYGAgIC4O/vj+joaPzyyy/SrZqIiNqE+U5EZBnNNtcVFRWoq6uDp6enybhG\no4HBYGhyTklJCS5duoT09HR89NFH2LFjB4qKivDss89CCCHdyomI6IEx34mILKNFlz9vjfr6ety6\ndQs7duxA7969AQA7duxA3759kZ+fjyFDhjQ5Lz8/v8U1WrOtJShZ31prK12fta2vvhS1+/TpI8FK\n2o+HPd/5ere+2krXt9baSte3dL43u+e6a9eusLGxQXl5ucl4eXk5vL29m5zj7e0NW1tbY/ACQO/e\nvWFjY4PLly+3Zt1ERGQhzHciIstods+1vb09Bg8ejMzMTEyaNMk4npWVhSlTpjQ5JzQ0FLdv30ZJ\nSQkCAgIA3Hkrsa6uDj179rxvLa1Wa3axDX9ptGRbS1CyvrXWVro+a/N33hZVVVVtvg9LYb63j9pK\n17fW2krXt9baSteXK9/Nnud64cKF2LZtG7Zu3Ypz585h/vz5MBgMmD17NgAgLi4OERERxu0jIiIQ\nFBSEl156CYWFhTh+/DheeuklDB8+XLFfJBERNcZ8JyKSntljrqOiolBZWYnExESUlZVh4MCByMjI\nMJ4D1WAwoKSkxLi9SqXCl19+iddffx1hYWFwcnKCTqdDUlKS5R4FERG1GvOdiEh6LfpAY0xMDGJi\nYpq8LTU1tdGYl5cX0tPT27YyIiKyOOY7EZG0WnT5cyIiIiIiMo/NNRERERGRRNhcExERERFJhM01\nEREREZFE2FwTEREREUmEzTURERERkURa1FwnJyfD398fTk5O0Gq1yM3NbdGdFxcXw9XVFa6urm1a\nJBERWQbznYhIWmab67S0NMTGxmLx4sUoLCxEcHAwIiMjceXKlWbn1dbWYtq0aRg1ahRUKpVkCyYi\nImkw34mIpGe2uU5KSoJer8fMmTPRt29frFmzBt7e3khJSWl23ltvvYUnnngCU6ZMgRBCsgUTEZE0\nmO9ERNJrtrmura1FQUEBdDqdybhOp8PRo0fvO2/v3r3Yu3cv1q5dy+AlImqHmO9ERJbR7OXPKyoq\nUFdXB09PT5NxjUYDg8HQ5JzS0lLMmjULu3fvRqdOnaRbKRERSYb5TkRkGc021w/ihRdeQExMDIYM\nGdKqefn5+RbZ1hKUrG+ttZWuz9rWV1+K2n369JFgJe3Hw57vfL1bX22l61trbaXrWzrfmz0spGvX\nrrCxsUF5ebnJeHl5Oby9vZucc/DgQSxfvhx2dnaws7PDyy+/jJs3b8LOzg5btmx5gOUTEZHUmO9E\nRJbR7J5re3t7DB48GJmZmZg0aZJxPCsrC1OmTGlyzunTp01+3r17N9577z3k5eXBx8fnvrW0Wq3Z\nxTb8pdGSbS1ByfrWWlvp+qzN33lbVFVVtfk+LIX53j5qK13fWmsrXd9aaytdX658N3tYyMKFC/HC\nCy9g6NChCA4OxoYNG2AwGDB79mwAQFxcHPLy8nDgwAEAQP/+/U3mf//991Cr1Y3GiYhIWcx3IiLp\nmW2uo6KiUFlZicTERJSVlWHgwIHIyMiAr68vAMBgMKCkpKTZ++B5UImI2h/mOxGR9Fr0gcaYmBjE\nxMQ0eVtqamqzc6OjoxEdHd3qhRERkeUx34mIpNWiy58TEREREZF5bK6JiIiIiCTC5pqIiIiISCJs\nromIiIiIJMLmmoiIiIhIIi1urpOTk+Hv7w8nJydotVrk5ubed9tDhw7hueeeg4+PD5ydnREYGGj2\nU+dERKQM5jsRkXRa1FynpaUhNjYWixcvRmFhIYKDgxEZGYkrV640uf2xY8cQGBiIzz77DGfOnEFM\nTAxmzZqFTz75RNLFExFR2zDfiYik1aLzXCclJUGv12PmzJkAgDVr1mDfvn1ISUnBihUrGm0fFxdn\n8vPs2bNx8OBBfPbZZ5g+fboEyyYiIikw34mIpGV2z3VtbS0KCgqg0+lMxnU6HY4ePdriQlVVVfDw\n8Gj9ComIyCKY70RE0jO757qiogJ1dXXw9PQ0GddoNDAYDC0q8uWXXyI7O7tVYU1ERJbFfCcikp5K\nCCGa26C0tBQ9evRATk4OQkNDjeMJCQnYuXMnioqKmi3wzTffYOzYsVi1ahVeffVVk9uqqqqM3xcX\nFz/I+omI2q0+ffoYv3d3d1dwJU1jvhMRPZjm8t3sYSFdu3aFjY0NysvLTcbLy8vh7e3d7Nzc3FyM\nHTsW7777bqPgJSIiZTHfiYikZ/awEHt7ewwePBiZmZmYNGmScTwrKwtTpky577ycnByMGzcOCQkJ\neP31180uRKvVmt0mPz+/xdtagpL1rbW20vVZm7/ztrh77217xHxXvrYl6pdU/IbSm7dbtO1vv/0G\nAHB1dW1VDR9nWwR0bd2cez1sz7u11m7N6w14sNecFK83QL58b9HZQhYuXIgXXngBQ4cORXBwMDZs\n2ACDwYDZs2cDuPPp8by8PBw4cADAnfOgPvPMM5g7dy6mT59uPHbPxsYG3bp1a+vjoQ6u1f8QHTUA\ngNxL11o8R6p/iPRwaFWz8QCvN6DjvuaY7w+f0pu3MS+nopWzbrVq67VhXRHQtZUl6KH0YK83oDWv\nuY72emtRcx0VFYXKykokJiairKwMAwcOREZGBnx9fQEABoMBJSUlxu23b9+OmpoafPDBB/jggw+M\n435+fibbkXXiP0SSG5uN+2O+ExFJq0XNNQDExMQgJiamydvuvTpXamoqr9hFRNRBMN+JiKTT4uaa\npMVDI0huPDSCiIjI8thcK4SHRpDceGgEERGR5Zk9FR8REREREbUM91wTEdFDh4dBkZzkONQT4Guu\no2BzTUREFtWSBkLqZoOHQVkfJT/LJMehngBfcx0Fm2siIrKo1jUdbDbowfCzTNRetKi5Tk5Oxgcf\nfACDwYDHHnsMH374IUJDQ++7/alTpzB37lzk5eXBw8MDr776KpYsWdJsDSX2bFgza33LlGdpUQaf\n9/ZLjnwnIrImZpvrtLQ0xMbGIiUlBaGhoVi/fj0iIyNx9uxZ40UG7nbjxg2MHj0a4eHhyM/Px7lz\n56DX6+Hs7IyFCxfetw73bMjLWt8y5Z4NZfB5b5/kyndrY81/TFrrjhulWevz3l6PdTfbXCclJUGv\n12PmzJkAgDVr1mDfvn1ISUnBihUrGm3/8ccfo6amBtu3b4eDgwP69++PoqIiJCUltbvwteYAJGVY\nawBS+/Qw57uSrPmPSWvdcaM0a33e2+ux7s0217W1tSgoKMCbb75pMq7T6XD06NEm5xw7dgwjR46E\ng4ODyfZLlizBpUuX0LNnz5avzsKsOQBJGdYagNT+POz5TkSklGbPc11RUYG6ujp4enqajGs0GhgM\nhibnGAyGRts3/Hy/OUREJC/mOxGRZaiEEOJ+N5aWlqJHjx7Iyckx+YBLQkICdu7ciaKiokZzxowZ\nA19fX2zZssU4dvnyZfj5+eHYsWMYNmyYcbyqqkqqx0FE1K65u7srvQQTzHciImncm+/N7rnu2rUr\nbGxsUF5ebjJeXl4Ob2/vJud4eXk12oPRMN/Ly6vVCyYiIukx34mILKPZ5tre3h6DBw9GZmamyXhW\nVhaCg4ObnDNixAgcOXIEt27dMtm+e/fuPB6PiKidYL4TEVmIMCMtLU3Y29uLLVu2iLNnz4rXX39d\nuLq6isuXLwshhHj77bfF008/bdy+qqpKeHl5iWnTponTp0+Lzz77TLi5uYmkpCRzpYiISEbMdyIi\n6Zk9FV9UVBQqKyuRmJiIsrIyDBw4EBkZGcZzoBoMBpSUlBi3d3NzQ1ZWFl577TVotVp4eHhg0aJF\nWLBggeX+QiAiolZjvhMRSa/ZDzQSEREREVHLNXvMdXuTnJwMf39/ODk5QavVIjc3V5a6OTk5GD9+\nPHr06AG1Wo3t27fLUhcAVq5ciSFDhsDd3R0ajQbjx4/HmTNnZKm9fv16BAYGwt3dHe7u7ggODkZG\nRoYste+1cuVKqNVqzJs3T5Z6y5Ytg1qtNvny8fGRpTYAlJWV4cUXX4RGo4GTkxMee+wx5OTkWLyu\nn59fo8etVqsxbtw4i9e+ffs23nnnHQQEBMDJyQkBAQFYsmQJ6urqLF67wW+//YbY2Fj4+fmhU6dO\nCAkJQX5+vmz1rZkS+W6t2Q5Yb74rne0A812JfJc72ztMc91wmd7FixejsLAQwcHBiIyMxJUrVyxe\n++bNm3j88cexevVqODk5QaVSWbxmg8OHD2Pu3Lk4duwYsrOzYWtri4iICFy71rqr9j0IX19frFq1\nCsePH8cPP/yAp556ChMmTMCJEycsXvtu3377LTZv3ozHH39c1ue+X79+MBgMxq9Tp07JUvf69esI\nCQmBSqVCRkYGioqKsG7dOmg0GovX/uGHH0wec0FBAVQqFaZOnWrx2itWrMDGjRuxdu1anD9/HqtX\nr0ZycjJWrlxp8doNXn75ZWRlZeGjjz7C6dOnodPpEBERgdLSUtnWYI2UyndrzXbAuvNdqWwHmO9K\n5bvs2a70Qd8tNXToUDFr1iyTsT59+oi4uDhZ1+Hi4iK2b98ua827VVdXCxsbG/Hll18qUt/Dw0Ns\n2rRJtnrXr18XvXr1EocOHRLh4eFi3rx5stSNj48XAwYMkKXWveLi4kRoaKgite+VmJgounTpImpq\naixea9y4cSI6Otpk7L/+67/Es88+a/HaQgjx+++/C1tbW/H555+bjA8ePFgsXrxYljVYq/aQ79ae\n7UJYR74rme1CMN/vJle+K5HtHWLPdcNlenU6ncl4c5fpfVjduHED9fX16NKli6x16+rq8Omnn6Km\npgZhYWGy1Z01axamTJmCUaNGQcj88YCSkhJ0794dAQEBmD59Oi5evChL3d27d2Po0KGYOnUqPD09\nMWjQIKxfv16W2ncTQmDr1q2YMWOGyeWuLSUyMhLZ2dk4f/48AODs2bM4ePAgxo4da/HawJ23Levq\n6ho9VkdHR9kOQbNGzPc7lMp2wPryXalsB5jvSuS7ItlukZZdYlevXhUqlUocOXLEZHz58uWib9++\nsq5F6b0bU6ZMEUFBQaK+vl6WeidPnhTOzs7C1tZWuLq6yrpXZdOmTUKr1Yrbt28LIYSse66/+uor\n8a9//UucOnVKHDhwQISHhwsvLy9RWVlp8doODg7C0dFRvPPOO6KwsFCkpqYKFxcXsW7dOovXvtv+\n/fuFSqUSJ0+elK1mXFycUKlUws7OTqhUKrFkyRLZagshRHBwsBg5cqS4evWquH37ttixY4ewsbER\n/fr1k3Ud1qS95Lu1ZbsQ1pnvSma7EMx3pfJd7mxnc91KSgbwggULRPfu3cXFixdlq1lbWysuXLgg\nCgoKRFxcnHBxcRF5eXkWr1tUVCS6desmzp8/bxwbNWqUmDt3rsVrN+XmzZtCo9HIcj5fOzs7ERIS\nYjL2zjvviD/+8Y8Wr323yZMni2HDhslWb/Xq1cLLy0ukpaWJ06dPix07dggPDw+xdetW2dZw4cIF\nMWrUKKFSqYStra0YNmyYmDFjhuzPvTVpL/lubdkuBPNdCHmzXQjmu1L5Lne2d4jm+tatW8LW1lbs\n2rXLZHzOnDkiPDxc1rUoFcCxsbHCx8fHJIyUEBER0ei4KUtITU01/iNo+FKpVEKtVgs7OztRW1tr\n8TXc68knnxRz5syxeJ2ePXuKV155xWTso48+Es7Ozhav3aC8vNx4cRG5aDQasWbNGpOxxMRE0bt3\nb9nW0OD3338XBoNBCCFEVFSUGDdunOxrsBbtJd+tPduFsN58lyvbhWC+302JfJcr2zvEMdcPcpne\nh0M22hwAACAASURBVMn8+fORlpaG7OxsPProo4qupa6uDvX19Rav8+c//xmnT5/GiRMncOLECRQW\nFkKr1WL69OkoLCyEnZ2dxddwt5qaGpw7dw7e3t4WrxUSEoKioiKTsR9//BF+fn4Wr91g27ZtcHR0\nxPTp02WrKYSAWm0aSWq1WvZj7QHAyckJnp6euHbtGjIzM/Hcc8/JvgZrYc353p6yHbDOfJcz2wHm\n+92UyHfZst0iLbsFmLtMryVVV1eL48ePi+PHj4tOnTqJhIQEcfz4cVlqz5kzR7i5uYns7GxRVlZm\n/KqurrZ47bfeekscOXJEXLx4UZw8eVK8/fbbQq1Wi8zMTIvXboqcbxu+8cYb4vDhw6KkpER8++23\n4plnnhHu7u6y/M7z8vKEnZ2deO+990RxcbFIT08X7u7uIjk52eK1hRCivr5e9OnTp9HZGyztlVde\nET169BB79+4VFy9eFP/+979Ft27dxKJFi2Rbw/79+0VGRoYoKSkRmZmZIjAwUIwYMcJ4XChZhlL5\nbq3ZLoT15ruS2S4E812pfJc72ztMcy2EEMnJycLPz084ODgIrVbb6Bg9Szl48KBQqVTGt60avtfr\n9RavfW/Nhq/ly5dbvHZ0dLTo2bOncHBwEBqNRowePVqx4BVC3g80Tps2Tfj4+Ah7e3vRvXt3MXny\nZHHu3DlZagshxN69e0VgYKBwdHQUffv2FWvXrpWtdnZ2tlCr1bIce3m36upq8cYbbwg/Pz/h5OQk\nAgICxF//+ldx69Yt2daQnp4uevXqJRwcHIS3t7eYN2+euHHjhmz1rZkS+W6t2S6E9ea70tkuBPNd\niXyXO9t5+XMiIiIiIol0iGOuiYiIiIg6AjbXREREREQSYXNNRERERCQRNtdERERERBJhc01ERERE\nJBE210REREREEmFzTR1GeHg41Go1Ll++rNga/u///g9qtfq+X3Je8YqI6GHRHvK9QV1dHbZs2YKw\nsDB06dIFnTp1Qq9evTBt2jQUFxcrvTzqAGyVXgBRa6hUKqWXAADw8/NDdHR0o/EBAwbIvxgioodA\ne8j36upqPPfcczh48CAGDRoEvV4PR0dH/Pzzz8jNzUVxcTH69Omj9DKpnWNzTR2KuHNVUaWXAT8/\nPyxdulTpZRARPTTaQ76/+uqrOHjwIDZu3IhXXnml0e23b99WYFXU0fCwEGoXvvjiC0RERMDHxweO\njo7w8fFBaGgoVq5cCQBQq9XIyckBAPj7+xsPw/D39ze5n6qqKixduhQDBgyAs7Mz3NzcMHLkSOza\ntatRzUOHDkGtVkOv1+Ps2bMYP348PDw84OLigrCwMHz99deWf+BERA+5jpLvBQUF+OSTTzBt2rQm\nG2sAsLXlPkkyj68SUtymTZswe/ZseHl5Ydy4cdBoNKioqMCZM2ewceNGxMXFIT4+Htu2bcOlS5cQ\nGxuLzp07A4DxvwBw9epVPPnkk/jpp58QFhaGMWPGoLq6Gnv37kVUVBTi4+MRHx/fqP7FixcREhKC\nJ554AjExMfj555+Rnp6OMWPGID09HRMnTmw059q1a/+/vXuPirrO/wf+HO6IiCJyleWirmYpheNt\nxEtpdEgzN+9lu5Jl4qUQPRWmlZd0y122UKGLHjU3C9f22K6yBoappBmEeAWz8GseYShJMe0gP+H1\n+8PDHEeQGeRzAeb5OIdz4D3v97zeM3x8+uYznws2bNiA8vJydOzYEYMGDUJ0dLR6bxIRUSvUmvJ9\n69atAICpU6fi8uXL2LlzJ86fP4/OnTtj5MiR6Natm8rvFrUZQqSz6Oho8fDwkJ9//rneYxUVFZbv\nhw8fLgaDQc6dO9fg84wcOVKcnZ3l008/tWq/cuWKREdHi5OTkxw9etTSvnfvXjEYDGIwGOSll16y\nGnP48GFxcXGRzp07y9WrVy3tZ8+etYy5/WvIkCFy9uzZu3kLiIjapNaU78OGDRODwSCpqani6+tr\nle9OTk4yZ84cqampuav3gRwLDwuhFsHZ2bnBj9t8fX3tGn/8+HHk5ORg3LhxmDx5stVj3t7eeOON\nNyAi+Pjjj+uN7dixY73jpwcMGIBJkybh119/xeeff25p9/LywmuvvYaCggJcvnwZly9fxr59+/Dg\ngw/i4MGDGDlyJK5du2bXnImIHEFryfeff/4ZAJCUlISRI0eiuLgYV69exZ49e9CtWzekpaVh+fLl\nds2ZHBsPCyHdTZs2DQsWLEDv3r0xefJkDB06FCaTCUFBQXY/x9dffw3g5jF5b7zxRr3Hf/nlFwBA\nUVFRvceio6Ph5eVVr33YsGH45JNPUFhYiCeffBIA0KVLl3rPP3ToUGRlZSEmJgaHDx/Ghx9+iMTE\nRLvnTkTUVrWmfK+trQUA3HPPPcjIyLBcveShhx7C9u3bER0djZSUFCxatAiurq52z58cDxfXpLv5\n8+fD398f6enpWLduHVJTUwEAgwYNwqpVqzB8+HCbz1FRUQEA+PLLL+94IqLBYGhwr3JAQECD/eva\nKysrbdZ3dnbGs88+i8OHD+Prr7/m4pqICK0r3+uO8X7sscfqXRawb9++CA8Px9mzZ1FUVIS+ffva\nnDc5Lh4WQi3CU089hdzcXFy6dAlffPEF5syZg4KCAsTFxdl10X4fHx8AQEpKCmpraxv8qqmpaTCY\ny8vLG3zOuva657bFz88PAHhYCBHRLVpLvvfq1QuA9YmUt+rUqRNEBFVVVTbnTI6Ni2tqUdq3b4+H\nH34Ya9aswYIFC1BVVYXdu3cDuLl3GLh596zbmUwmALBczqkpCgoKcPXq1Xrt+/btAwA88MADdj3P\nN998AwCIjIxs8hyIiNq6lp7vo0aNAnDzGO/bXb9+HWfOnIHBYEB4eHiT50GOhYtr0l1OTk6D7WVl\nZQCAdu3aAQA6d+4MADh37ly9vtHR0Rg+fDg+//xzrF+/vsHn+/7773H+/Pl67ZcvX8ayZcus2g4f\nPoxt27bB19cXjz/+uKW9oKCgwZscfPnll/jHP/4Bg8GAadOmNVifiMjRtKZ8Hz9+PIKDg5GRkYG8\nvDyrMcuXL8eVK1fw4IMPwt/f/04vlwgAYJCGVgpEGurYsSPat2+PQYMGISwsDAaDAd9++y1yc3PR\nvXt3fPfdd/D29sb69esxc+ZMdOvWDU888QS8vb3RqVMnzJkzB8DNsK47w7tPnz4YOHAgfH19ceHC\nBZw8eRKFhYXYsWMHxo4dC+DmTQYeeughDB06FMeOHUNUVBRMJhMuXLiAjIwM1NTUICMjw+o6qCNG\njMAPP/wAk8mEkJAQAMCxY8ewd+9eGAwGLF++HIsWLdL+TSQiaoFaU74DwJ49ezBmzBgAwBNPPIHg\n4GDLuTQBAQHIzc3l9a7JNlvX6tu3b5889thjEhISIgaDQTZt2mTz+n7Hjh2TYcOGiaenp4SEhMiy\nZcuaecVAasvee+89eeKJJ6Rbt27i5eUlHTt2lKioKFm6dKn8+uuvln61tbXy2muvSffu3cXNzU0M\nBoNERERYPde1a9fkrbfekv79+4u3t7d4eHhIRESEPPLII7J27Vq5dOmSpW/ddVDj4+OlqKhIxo4d\nK506dRIvLy8ZNmyYfPnll/XmumHDBhk9erSEh4dL+/btxd3dXcLCwmTKlCmSm5ur3ptEpALmO6mt\nNeV7naNHj8qECROkS5cu4ubmJmFhYTJ79mwpKytT/g2iNsnm4jozM1NeffVV2b59u7Rr1042b97c\naP/KykoJCAiQyZMny8mTJ2X79u3i7e0tf//73xWbNJESbg1fIkfEfKe2ivlOerJ5Kb64uDjExcUB\nAKZPn25zT/jHH3+MqqoqbN68Ge7u7ujduzeKi4uRkpKCpKSkZu9pJyIiZTDfiYiUp/gJjYcOHcLQ\noUPh7u5uaYuNjUVpaWmDJyoQEVHrwHwnIrJN8cW12Wyud9H2up/NZrPS5YiISCPMdyIi2xS/Q+Pt\ndzVqjD13viNSywMPPIBLly4B4LZI6rP3ZkQtGfOdWgvmO2np9nxXfM91YGBgvT0YdXdCCgwMVLoc\nERFphPlORGSb4ovrwYMH48CBA7h+/bqlLTs7GyEhIQgLC1O6HBERaYT5TkRkm83DQq5du4YzZ84A\nAGpra3Hu3DkUFhaic+fOCA0NRXJyMvLy8rBnzx4AwJNPPomlS5di+vTpWLx4MU6fPo233noLb7zx\nRqN17PnIND8/HwBgNBpt9lWDnvUdtbbe9Vmbv/PmaOkfRzPf9a+td31Hra13fUetrXd9rfLd5p7r\nvLw8REdHIzo6GlVVVXj99dcRHR2N119/HcDNk1hKSkos/Tt06IDs7GyUlpbCaDRi3rx5WLhwIebP\nn9/sF0JERMphvhMRKc/mnusRI0agtrb2jo9v3LixXtt9992Hffv2NW9mRESkKuY7EZHyFD/mmoiI\niIjIUXFxTURERESkEC6uiYiIiIgUwsU1EREREZFCuLgmIiIiIlKIXYvrtLQ0REREwNPTE0ajEbm5\nuY32z8zMxKBBg9ChQwd06dIF48aNs1xLlYiIWg7mOxGRsmwurjMyMpCYmIjFixejsLAQJpMJcXFx\nOH/+fIP9f/jhB4wbNw4jRoxAYWEh9uzZg6qqKjz66KOKT56IiO4e852ISHk2F9cpKSmIj4/HjBkz\n0LNnT6SmpiIoKAjp6ekN9i8sLERtbS1WrVqFyMhIREVF4eWXX8aPP/6IX3/9VfEXQEREd4f5TkSk\nvEYX19XV1SgoKEBsbKxVe2xsLA4ePNjgmCFDhqB9+/b48MMPUVNTg99++w2bNm3CgAED4Ovrq9zM\niYjorjHfiYjU0eji+uLFi6ipqUFAQIBVu7+/P8xmc4NjgoKCkJmZicWLF8PDwwMdO3bEyZMn8d//\n/le5WRMRUbMw34mI1GEQEbnTg6WlpejatSv279+PmJgYS/uyZcuwdetWFBcX1xtTUlKCQYMGIT4+\nHk8++SSuXLmC1157DQCQk5MDg8Fg6VtZWWn5nifEEFFb06NHD8v3Pj4+Os6kPuY7EdHdayzfXRob\n6OfnB2dnZ5SXl1u1l5eXIygoqMEx77//PkJDQ/HWW29Z2v75z38iNDQUhw4dgslkavILICIiZTHf\niYjU0eji2s3NDf369UNWVhbGjx9vac/OzsbEiRMbHCMicHKyPtqk7ufa2to71jIajTYnm5+fb3df\nNehZ31Fr612ftfk7b45b9962NMz3llFb7/qOWlvv+o5aW+/6WuW7zauFJCUlYdOmTdiwYQOKiorw\n4osvwmw2Y9asWQCA5ORkjBo1ytJ/7NixKCgowPLly3HmzBkUFBQgPj4ef/jDH9CvX79mvxgiIlIG\n852ISHmN7rkGgEmTJqGiogIrVqxAWVkZ+vTpg8zMTISGhgIAzGYzSkpKLP1jYmKQkZGBv/71r3j7\n7bfRrl07DB48GLt374anp6d6r4SIiJqE+U5EpDybi2sASEhIQEJCQoOPbdy4sV7bhAkTMGHChObN\njIiIVMd8JyJSll23PyciIiIiItu4uCYiIiIiUggX10RERERECuHimoiIiIhIIVxcExEREREphItr\nIiIiIiKF2LW4TktLQ0REBDw9PWE0GpGbm2tzzDvvvINevXrBw8MDwcHBSE5ObvZkiYhIWcx3IiJl\n2bzOdUZGBhITE5Geno6YmBisW7cOcXFxOHXqlOVGA7dLSkrCrl278Le//Q19+vRBZWUlysrKFJ88\nERHdPeY7EZHybC6uU1JSEB8fjxkzZgAAUlNTsXv3bqSnp2PlypX1+p8+fRpr167F8ePH0bNnT0t7\nVFSUgtMmIqLmYr4TESmv0cNCqqurUVBQgNjYWKv22NhYHDx4sMExn3/+OSIjI5GZmYnIyEhERERg\n+vTp+OWXX5SbNRERNQvznYhIHQYRkTs9WFpaiq5du2L//v2IiYmxtC9btgxbt25FcXFxvTGzZs3C\n5s2bcf/992P16tUAgIULFwIADh06BIPBYOlbWVlp+f7MmTPNfzVERC1Ijx49LN/7+PjoOJP6mO9E\nRHevsXy3eVhIU9XW1uL69evYsmULunfvDgDYsmULevbsifz8fPTv31/pkkREpAHmOxGRbY0urv38\n/ODs7Izy8nKr9vLycgQFBTU4JigoCC4uLpbgBYDu3bvD2dkZP/300x3D12g02pxsfn6+3X3VoGd9\nR62td33W5u+8OW7de9vSMN9bRm296ztqbb3rO2ptvetrle+NHnPt5uaGfv36ISsry6o9OzsbJpOp\nwTExMTG4ceMGSkpKLG0lJSWoqalBWFhYU+ZNREQqYb4TEanD5nWuk5KSsGnTJmzYsAFFRUV48cUX\nYTabMWvWLABAcnIyRo0aZek/atQoREdH45lnnkFhYSGOHDmCZ555BoMGDdLtryQiIqqP+U5EpDyb\nx1xPmjQJFRUVWLFiBcrKytCnTx9kZmZaroFqNput9mIYDAbs3LkTL7zwAoYNGwZPT0/ExsYiJSVF\nvVdBRERNxnwnIlKeXSc0JiQkICEhocHHNm7cWK8tMDAQ27Zta97MiIhIdcx3IiJl2XX7cyIiIiIi\nso2LayIiIiIihXBxTURERESkEC6uiYiIiIgUwsU1EREREZFC7Fpcp6WlISIiAp6enjAajcjNzbXr\nyc+cOQNvb294e3s3a5JERKQO5jsRkbJsLq4zMjKQmJiIxYsXo7CwECaTCXFxcTh//nyj46qrqzFl\nyhQMHz4cBoNBsQkTEZEymO9ERMqzubhOSUlBfHw8ZsyYgZ49eyI1NRVBQUFIT09vdNzLL7+M+++/\nHxMnToSIKDZhIiJSBvOdiEh5jS6uq6urUVBQgNjYWKv22NhYHDx48I7jdu3ahV27dmHNmjUMXiKi\nFoj5TkSkjkbv0Hjx4kXU1NQgICDAqt3f3x9ms7nBMaWlpZg5cyZ27NiBdu3aKTdTIiJSDPOdiEgd\ndt3+vCmefvppJCQkoH///k0al5+fr0pfNehZ31Fr612ftR2vvhK1e/ToocBMWo62nu/c3h2vtt71\nHbW23vXVzvdGDwvx8/ODs7MzysvLrdrLy8sRFBTU4Ji9e/di6dKlcHV1haurK5599llcu3YNrq6u\nWL9+/V1Mn4iIlMZ8JyJSR6N7rt3c3NCvXz9kZWVh/Pjxlvbs7GxMnDixwTEnTpyw+nnHjh148803\nkZeXh+Dg4DvWMhqNNidb95eGPX3VoGd9R62td33W5u+8OSorK5v9HGphvreM2nrXd9Taetd31Np6\n19cq320eFpKUlISnn34aAwYMgMlkwnvvvQez2YxZs2YBAJKTk5GXl4c9e/YAAHr37m01/ttvv4WT\nk1O9diIi0hfznYhIeTYX15MmTUJFRQVWrFiBsrIy9OnTB5mZmQgNDQUAmM1mlJSUNPocvA4qEVHL\nw3wnIlKeXSc0JiQkICEhocHHNm7c2OjY6dOnY/r06U2eGBERqY/5TkSkLLtuf05ERERERLZxcU1E\nREREpBAuromIiIiIFMLFNRERERGRQri4JiIiIiJSiN2L67S0NERERMDT0xNGoxG5ubl37PvVV1/h\n8ccfR3BwMLy8vBAVFWXzrHMiItIH852ISDl2La4zMjKQmJiIxYsXo7CwECaTCXFxcTh//nyD/Q8d\nOoSoqCh89tlnOHnyJBISEjBz5kx88sknik6eiIiah/lORKQsu65znZKSgvj4eMyYMQMAkJqait27\ndyM9PR0rV66s1z85Odnq51mzZmHv3r347LPPMHXqVAWmTURESmC+ExEpy+ae6+rqahQUFCA2Ntaq\nPTY2FgcPHrS7UGVlJXx9fZs+QyIiUgXznYhIeTb3XF+8eBE1NTUICAiwavf394fZbLaryM6dO5GT\nk9OksCYiInVple+55y7ZfJ7fPPzt7nurYC8XRPp5N2kMtU0lF39D6bUbdve/m22O2xvZw67DQprj\n66+/xlNPPYU1a9bAaDTesV9+fr7dz9mUvmrQs76j1ta7Pms7Xn0lavfo0UOBmbRc9ub7vP0Xm/Cs\n15s0h5UPuOPX/zvdpDF3wu29ddf+xcMfi440bfu5yf4xSm5vQNt431tjfbXz3ebi2s/PD87Ozigv\nL7dqLy8vR1BQUKNjc3NzMXr0aCxfvhzPP/+8ndOltk68/XDx/6l7FUg/11oYfmvKf+jUlnGbaxjz\nnYhIeTYX125ubujXrx+ysrIwfvx4S3t2djYmTpx4x3H79+/HmDFjsGzZMrzwwgs2J9LYXo86dX9p\n2NNXDXrWb0u1c89dwqJv1V2ErBnmh5ie4c1+nrb0vreW2mrU12ubq6ysVLVmc2mV72ry9vaG8b4/\nNOs52tr27qi1bx7ecTd7ru2nxPYGtK33vTXVV7J2Y/lu12EhSUlJePrppzFgwACYTCa89957MJvN\nmDVrFoCbZ4/n5eVhz549AG5eB3X06NGYO3cupk6dajl2z9nZGV26dGnu6yEiIoUw34mIlGXX4nrS\npEmoqKjAihUrUFZWhj59+iAzMxOhoaEAALPZjJKSEkv/zZs3o6qqCqtXr8bq1ast7eHh4Vb9iIhI\nX8x3IiJl2X1CY0JCAhISEhp87Pa7c23cuJF37CIiaiWY70REylH3DB8iIiIiIgfCxTURERERkUK4\nuCYiIiIiUojqN5GhhvFOUqS1pmxzvFseERHR3eHiWiel12408a5ldey/hueaYX6I9LuLEtQm3d02\n17RrxnKbI3Js/COetKTFjkqg6dtci1lc2/NC+Q+RmoufGBARqYd/xJOWtNhRCTR9m7NrcZ2WlobV\nq1fDbDbj3nvvxTvvvIOYmJg79j9+/Djmzp2LvLw8+Pr64vnnn8eSJUsardG0N4f/EOnu8BMDImta\n5LseuAeVtNRS96CSPmwurjMyMpCYmIj09HTExMRg3bp1iIuLw6lTpyw3GbjVlStX8PDDD2PEiBHI\nz89HUVER4uPj4eXlhaSkJFVeBDUd/+MhLfETg5apLee7nntQ9d7eme/a03sPqp6/c72395bI5uI6\nJSUF8fHxmDFjBgAgNTUVu3fvRnp6OlauXFmv/8cff4yqqips3rwZ7u7u6N27N4qLi5GSktLiwteR\nNwh+dKcPR/1Pj58YtExtOd/1pPf2znx3PHr+zvXe3luiRhfX1dXVKCgowEsvvWTVHhsbi4MHDzY4\n5tChQxg6dCjc3d2t+i9ZsgTnzp1DWFiYAtNWBjcI0hr/06OWoq3nOxGRXhq9zvXFixdRU1ODgIAA\nq3Z/f3+YzeYGx5jN5nr9636+0xgiItIW852ISB0GEZE7PVhaWoquXbti//79Vie4LFu2DFu3bkVx\ncXG9MY888ghCQ0Oxfv16S9tPP/2E8PBwHDp0CAMHDrS0V1ZWKvU6iIhaNB8fH72nYIX5TkSkjNvz\nvdE9135+fnB2dkZ5eblVe3l5OYKCghocExgYWG8PRt34wMDAJk+YiIiUx3wnIlJHo4trNzc39OvX\nD1lZWVbt2dnZMJlMDY4ZPHgwDhw4gOvXr1v1DwkJ4fF4REQtBPOdiEglYkNGRoa4ubnJ+vXr5dSp\nU/LCCy+It7e3/PTTTyIi8sorr8jIkSMt/SsrKyUwMFCmTJkiJ06ckM8++0w6dOggKSkptkoREZGG\nmO9ERMqzeSm+SZMmoaKiAitWrEBZWRn69OmDzMxMyzVQzWYzSkpKLP07dOiA7OxszJkzB0ajEb6+\nvli4cCHmz5+v3l8IRETUZMx3IiLlNXpCIxERERER2a/RY65bmrS0NERERMDT0xNGoxG5ubma1N2/\nfz/Gjh2Lrl27wsnJCZs3b9akLgCsWrUK/fv3h4+PD/z9/TF27FicPHlSk9rr1q1DVFQUfHx84OPj\nA5PJhMzMTE1q327VqlVwcnLCvHnzNKn3xhtvwMnJyeorODhYk9oAUFZWhr/85S/w9/eHp6cn7r33\nXuzfv1/1uuHh4fVet5OTE8aMGaN67Rs3bmDRokWIjIyEp6cnIiMjsWTJEtTU1Kheu85vv/2GxMRE\nhIeHo127dhgyZAjy8/M1q+/I9Mh3R812wHHzXe9sB5jveuS71tneahbXdbfpXbx4MQoLC2EymRAX\nF4fz58+rXvvatWvo27cv3n33XXh6esJgMKhes86+ffswd+5cHDp0CDk5OXBxccGoUaNw6VLT7tp3\nN0JDQ/H222/jyJEj+O677/DQQw9h3LhxOHr0qOq1b/XNN9/gww8/RN++fTV973v16gWz2Wz5On78\nuCZ1L1++jCFDhsBgMCAzMxPFxcVYu3Yt/P39Va/93XffWb3mgoICGAwGTJ48WfXaK1euxPvvv481\na9bg9OnTePfdd5GWloZVq1apXrvOs88+i+zsbHz00Uc4ceIEYmNjMWrUKJSWlmo2B0ekV747arYD\njp3vemU7wHzXK981z3a9D/q214ABA2TmzJlWbT169JDk5GRN59G+fXvZvHmzpjVvdfXqVXF2dpad\nO3fqUt/X11c++OADzepdvnxZunXrJl999ZWMGDFC5s2bp0nd119/Xe677z5Nat0uOTlZYmJidKl9\nuxUrVkinTp2kqqpK9VpjxoyR6dOnW7X9+c9/lscee0z12iIiv//+u7i4uMh//vMfq/Z+/frJ4sWL\nNZmDo2oJ+e7o2S7iGPmuZ7aLMN9vpVW+65HtrWLPdd1temNjY63aG7tNb1t15coV1NbWolOnTprW\nrampwaeffoqqqioMGzZMs7ozZ87ExIkTMXz4cIjGpweUlJQgJCQEkZGRmDp1Ks6ePatJ3R07dmDA\ngAGYPHkyAgIC8MADD2DdunWa1L6ViGDDhg2YNm2a1e2u1RIXF4ecnBycPn0aAHDq1Cns3bsXjz76\nqOq1gZsfW9bU1NR7rR4eHpodguaImO836ZXtgOPlu17ZDjDf9ch3XbJdlSW7wi5cuCAGg0EOHDhg\n1b506VLp2bOnpnPRe+/GxIkTJTo6WmprazWpd+zYMfHy8hIXFxfx9vbWdK/KBx98IEajUW7cEJvy\nbAAABMZJREFUuCEioume6//973/yr3/9S44fPy579uyRESNGSGBgoFRUVKhe293dXTw8PGTRokVS\nWFgoGzdulPbt28vatWtVr32rL774QgwGgxw7dkyzmsnJyWIwGMTV1VUMBoMsWbJEs9oiIiaTSYYO\nHSoXLlyQGzduyJYtW8TZ2Vl69eql6TwcSUvJd0fLdhHHzHc9s12E+a5Xvmud7VxcN5GeATx//nwJ\nCQmRs2fPalazurpafvzxRykoKJDk5GRp37695OXlqV63uLhYunTpIqdPn7a0DR8+XObOnat67YZc\nu3ZN/P39Nbmer6urqwwZMsSqbdGiRXLPPfeoXvtWEyZMkIEDB2pW791335XAwEDJyMiQEydOyJYt\nW8TX11c2bNig2Rx+/PFHGT58uBgMBnFxcZGBAwfKtGnTNH/vHUlLyXdHy3YR5ruIttkuwnzXK9+1\nzvZWsbi+fv26uLi4yPbt263aZ8+eLSNGjNB0LnoFcGJiogQHB1uFkR5GjRpV77gpNWzcuNHyj6Du\ny2AwiJOTk7i6ukp1dbXqc7jdgw8+KLNnz1a9TlhYmDz33HNWbR999JF4eXmpXrtOeXm55eYiWvH3\n95fU1FSrthUrVkj37t01m0Od33//Xcxms4iITJo0ScaMGaP5HBxFS8l3R892EcfNd62yXYT5fis9\n8l2rbG8Vx1zfzW1625IXX3wRGRkZyMnJwR//+Edd51JTU4Pa2lrV6/zpT3/CiRMncPToURw9ehSF\nhYUwGo2YOnUqCgsL4erqqvocblVVVYWioiIEBQWpXmvIkCEoLi62avv+++8RHh6ueu06mzZtgoeH\nB6ZOnapZTRGBk5N1JDk5OWl+rD0AeHp6IiAgAJcuXUJWVhYef/xxzefgKBw531tStgOOme9aZjvA\nfL+VHvmuWbarsmRXga3b9Krp6tWrcuTIETly5Ii0a9dOli1bJkeOHNGk9uzZs6VDhw6Sk5MjZWVl\nlq+rV6+qXvvll1+WAwcOyNmzZ+XYsWPyyiuviJOTk2RlZaleuyFafmy4YMEC2bdvn5SUlMg333wj\no0ePFh8fH01+53l5eeLq6ipvvvmmnDlzRrZt2yY+Pj6Slpamem0RkdraWunRo0e9qzeo7bnnnpOu\nXbvKrl275OzZs/Lvf/9bunTpIgsXLtRsDl988YVkZmZKSUmJZGVlSVR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uz9r8nTdHS780gvlu/drWrm+rta1d31ZrW7u+pfLd6JnrnJwcBAUFISgoCJWVlUhISEBQ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\n06dP47XXXoNGo8HMmTMBAHFxcRgzZoy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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1798,7 +1818,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.4.3" + "version": "3.4.1" } }, "nbformat": 4, diff --git a/04_One_Dimensional_Kalman_Filters.ipynb b/04_One_Dimensional_Kalman_Filters.ipynb index b1927ca..062591a 100644 --- a/04_One_Dimensional_Kalman_Filters.ipynb +++ b/04_One_Dimensional_Kalman_Filters.ipynb @@ -1601,7 +1601,7 @@ " \n", "**Predict**\n", "\n", - " 1. Based on the system behaves, predict its state at the next time step\n", + " 1. Based on the system behavior, predict state at the next time step\n", " 2. Adjust belief in that state to account for the uncertainty in prediction\n", " \n", "**Update**\n", @@ -2472,7 +2472,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.4.3" + "version": "3.4.1" } }, "nbformat": 4,