Merge pull request #408 from PebetoUofC/proof-read-ag-1

Proof read ag 1

05-Multivariate-Gaussians.ipynb

@@ -18,7 +18,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 2,
    "metadata": {
     "scrolled": true
    },
@@ -52,7 +52,7 @@
        "<IPython.core.display.HTML object>"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -123,19 +123,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<Figure size 648x288 with 1 Axes>"
+       "<Figure size 900x400 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -159,7 +157,7 @@
     "\n",
     "Where $\\mathbb E[X]$ is the *expected value* of X, defined as\n",
     "\n",
-    "$$\\mathbb E[X] =  \\begin{cases} \\sum_{i=1}^n p_ix_i & \\mbox{discrete}\\\\ \\int_{-\\infty}^\\infty f(x)\\, x & \\mbox{continuous}\\end{cases}$$\n",
+    "$$\\mathbb E[X] =  \\begin{cases} \\sum_{i=1}^n p_ix_i & \\mbox{discrete}\\\\ \\int_{-\\infty}^\\infty f(x)\\, x dx & \\mbox{continuous}\\end{cases}$$\n",
     "\n",
     "We assume each data point is equally likely, so the probability of each is $\\frac{1}{N}$, giving\n",
     "\n",
@@ -253,7 +251,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -263,7 +261,7 @@
        "       [  2.727, 327.235]])"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -289,7 +287,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -299,7 +297,7 @@
        "       [  2.182, 261.788]])"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -321,7 +319,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -331,7 +329,7 @@
        "       [6.956, 6.956]])"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -353,19 +351,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<Figure size 648x288 with 1 Axes>"
+       "<Figure size 900x400 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     },
     {
@@ -395,27 +391,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<Figure size 648x288 with 1 Axes>"
+       "<Figure size 900x400 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[10.433  2.934]\n",
-      " [ 2.934  2.317]]\n"
+      "[[10.456  3.183]\n",
+      " [ 3.183  2.454]]\n"
      ]
     }
    ],
@@ -438,27 +432,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<Figure size 648x288 with 1 Axes>"
+       "<Figure size 900x400 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[1.005 0.005]\n",
-      " [0.005 1.005]]\n"
+      "[[1.002 0.006]\n",
+      " [0.006 1.002]]\n"
      ]
     }
    ],
@@ -500,21 +492,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 10,
    "metadata": {
     "scrolled": true
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<Figure size 648x288 with 1 Axes>"
+       "<Figure size 900x400 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -548,7 +538,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -568,7 +558,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -584,7 +574,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -600,7 +590,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -617,7 +607,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -626,7 +616,7 @@
        "0.0315"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -645,7 +635,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -687,7 +677,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -727,7 +717,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 3 Axes>"
       ]
@@ -769,7 +759,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -805,7 +795,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -838,7 +828,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -881,7 +871,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -924,7 +914,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -980,7 +970,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1011,7 +1001,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1047,7 +1037,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "ae16868906cb4db9a9320aa237fda5da",
+       "model_id": "e4716140356f49ddb545348d43995247",
        "version_major": 2,
        "version_minor": 0
       },
@@ -1112,7 +1102,7 @@
     {
      "data": {
       "text/plain": [
-       "0.9539731096080194"
+       "0.9539731096080192"
       ]
      },
      "execution_count": 28,
@@ -1168,7 +1158,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1199,7 +1189,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1242,7 +1232,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1301,7 +1291,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1331,7 +1321,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1364,7 +1354,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1400,7 +1390,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1429,7 +1419,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1463,7 +1453,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 800x200 with 1 Axes>"
       ]
@@ -1494,7 +1484,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1525,7 +1515,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1558,7 +1548,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1598,7 +1588,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1625,7 +1615,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1659,7 +1649,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1686,7 +1676,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1715,7 +1705,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1746,7 +1736,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1831,7 +1821,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1898,7 +1888,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.8.3"
   },
   "widgets": {
    "application/vnd.jupyter.widget-state+json": {

06-Multivariate-Kalman-Filters.ipynb

@@ -155,7 +155,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6gAAAEpCAYAAACeMg98AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdeVhUZd8H8O9hX4ZdwFxxQSvF1FRMLMTcd0tTcV/e9Mmt1NTcwPRxe0tT9I3cQkNzyXwe1zRTTMldBJ/H1BREIEEEXNgclvv941xzZGQGBhgB8fu5rrkGzrnv+/zmzJT85t4kIYQAERERERERUQUzqegAiIiIiIiIiAAmqERERERERFRJMEElIiIiIiKiSoEJKhEREREREVUKTFCJiIiIiIioUmCCSkRERERERJUCE1QiIiIiIiKqFJigEhERERERUaXABJWIiIiIiIgqBSaoREREREREVCkwQSUiIiIiIqJKgQkqEREREVEJzJsHSBKwYoVx2uvWTW7v+HHjtEf0MpOEEKKigyAiIiIielFCQoA7d4AOHeRHWcTHA40aASoVEBMD2NqWPb6zZ4F33gFatAAuXgRM2IVErzB+/ImIiIioSgsJARYuBMLCyt7W3LlAVhYwc6ZxklMAaNsW6NoViIgAQkON0ybRy4oJKhERERGRARISgG3bAAsLYMwY47Y9YYL8bKxhw0QvKyaoREREREQG2LAByMsDevQAnJ2N27amzf/+FwgPN27bRC8TJqhERERkVB06yAu+BAbKf8yvWiXPrVOpADc3oF8/IDLyWfnMTGDxYqBpU3nIpIsLMGgQcPt20ddJTARmzwbeegtwcACsrID69YFx44Br13TXefQI2LEDGDoU8PKSEwIrK6BuXcDfX54LWJxdu4Du3QF3d8DcHHB0BDw9gT59gHXrgOxs7fIeHvL9CAnR3+aoUXKZUaO0jxe8lzk5wNdfA61aydeUJN1DVktzXyrze/Z8fELIiaK3N2BvD9jZyfM3dQ2NDQmR6508Kf++cKH8e8HHnTtFx6whBLBpk/yzv7/+chERha+h77FkybN6FhbAhx/KP69fb1hMRFWSICIiIjIiX18hACHmzBGiUyf5ZwsLIWxt5Z8BIVQqIS5cEOLBAyFatJCPWVkJYW39rIybmxCxsbqvsX+/3IamrLm5dvsWFkJs2VK4XkDAszKaOCwtn/0uSUKsXq3/tY0ZU7i+jY32sZgY7Tp168rHv/9ef7sjR8plRo7UfS9nzRKiXTv5ZzMzIZyc5J9PnDDOfanM71nB+ObNE6Jv32f3wd5e+94vWKBdb8cOIdzd5WsB8vXc3bUfd+/qf18Kiop6dp179/SX27Wr8DUKPuzsnrVz+LB23R9+eHYfiV5V7EElIiKiF+L//k/uTdq9G0hPB548Ac6fl3vM0tOBqVOB//kfIC0NOHIEyMiQjx87Bri6AvfvA3PmFG73/Hm5pyk9HRg/HvjzT3nRmvR0IDYW+OQTQK0Gxo6VV0QtqHp14LPP5J7StDQ5pqwsIDpajgcApk2T437e6dPA5s3yCqvLlwMpKXL9jAzgwQP5NYwcKfeEGdu6dUBUFPD998Djx0BqqnzNZs2Mc180KuN79vx9CAuTe0YfP5Z7xOPigN695fOLFwN//fWs/KBBcq9tu3by7zNmyL8XfNSubdh78Pvv8nPt2vLnSJ+BAwtfQ/M4d06+TwDQsyfg56dd19tbfr5/H7h+3bC4iKqcis6QiYiIqGrR9HYBQpw6Vfj8b789O29tLcRffxUus2nTs/Nqtfa51q3lc/Pn649hyhS5TN++JYt94kS53tixhc8tXy6f69KlZG0aowcVEGLfvqKvU5b7Utnfs4LxHT9e+Hx2thA1asjnFy/WXz8gQP/1izN8uNxGr16lq3/79rPPQr9+Qjx9qrucppd58+ZSh0r0UmMPKhEREb0Q7dvLj+f5+gKWlvLPAwYADRsWLtO1q/yclaXdIxYZCVy4IM/9nD5d/7VHjJCfjx2T51QaqmdP+fn06cLnHB3l5+TkkrVpDE2aPOsl1MVY96Wyv2c+PoV7HQE5Ns31o6L0X6Ms/v5bftb0gJbEzZvAe+/JvcUffST3UOvraXdx0b4e0avGrKIDICIioqqpTRvdx01NgWrV5C07WrfWXcbd/dnPaWnPftYkjvn5QOPG+q+tSXAyMuShuG5uz85FR8tDWU+ckBf1efJEbq+g+PjCbXbqJC/qExEBvPuuPBy1Y0egXj39cRiLj0/R541xX4DK+55paIbA6lKjhvycmqq/TFkkJ8vPJV2999o14P335SG+w4bJw5NNTfWXd3aWE1nN9YheNUxQiYiI6IWws9N/zsys6DJmBf5Cycl59rOmVykvD0hKMiyOzMxnP+/dCwwZAjx9+uyYvb2ceEqSPA8yLU1Okp5Xvz6wcaO8X+WZM/IDkHvU/PzklV379JHbMTZdyVpBZb0vGpXxPStpfAWvbUya1Zk1PcmGiIqSv9hITpb3Td2wQZ7DXBRra+3rEb1qOMSXiIiIXhqaXrbXXy+4dmvRDw8PuU5KiryNy9Oncs9nWJicCD16JCdOiYny0MuiDB0q924FB8sL8NSuLScfu3bJW7H4+sqL9xhbUT1uQNnuy4tWmWMrCc3Q24K9w0W5fFn+4iI5Wf5SY+PG4pNT4FkPsOZ6RK8aJqhERET00tCsnhodrbuXsyiHDsnJo5MTsH+/nExqeqs0EhOLb8fZWV6JdscO4O5d4NYteW9PSQJOnZL36ixI07NXVI/Yo0cleimFlOW+vGiVObaS0Mw9NWQI8blz8rDe1FR55eNvvzW8Z13TfmnmuhJVBUxQiYiI6KWhmYupVsvDdUsiLk5+btwYsLHRXebYsZLH1KABsHSpPMQXAH79Vfu8k5P29Z+Xn1/01iqGKMt9edEqQ2yankshSt/Gm2/Kz9HRRZc7fRro3Bl4+BD4/HPgm28Mv8aTJ/L2QQDwxhuli5PoZccElYiIiF4arVoBLVrIP8+dW/xCMgV7uxwc5OebN3X3Zl65Amzfrr+tgvNWddH0xj4/HPett+TnvXt1J0hbtuhelKkkynJfXrTKEJu9vfz88GHp23jvPfk5MlL/Z+HECaBbNznRnDcPWLGiZNe4eFH+wsLMrPiFsYiqKiaoRERE9NKQJHn+p6WlPLzW2xv46SftRXUSEoDQULkXa9asZ8e7dJF70lJT5bmkCQnycbVankPapUvRi/BMmiRvEbJnD3D//rPj6elyTFu3yr/36KFdb8gQ+fnPP4GPP5bnwgLycONVq+T5iSVdGfZ5ZbkvL1pliK1pU/n50KFn73tJ+fjIiaNaLX+Z8bxff5W3KcrIABYtkh8lde6c/NyyJaBSlS5OopcdE1QiIiJ6qbRpI88hdXEBYmKAgQPlHrJq1QBbW6BWLWD48MLDdT095SGXAPDzz3I5R0c5ERg0SH5es0b/dXNy5EWUBgyQt1Sxs5OH79rZAf/4h5y4tG8v9xIW9P77z/b43LhRjtPJSX5MmyYnrUXtcfqi70t5qOjYRo6UV2q+dQuoU0eeF+vhIT8M7b22t3+2T+6+fYXPz5sn7wErScDatfI19D1++033NTTtaoaLE72KmKASERHRS6dzZznZWLpUTgodHOThmyYm8lzBsWPlP/aDgrTrLVsm93S2aSMPyc3JARo2BObMkfc31eylqcv8+XIC27+/vCKtmZnce+rmJsezebO8MrCtbeG6mzcDq1cDzZvL183Pl3vkdu4sHGNF3JfyUJGxeXrKw2/79JEXH0pJkVdjjo0FcnMNb2f8ePl5+3bt4dp5ecDVq/LPQsirQhf1aNiwcNsxMfLWRdbWz77QIHoVSUKUZbo4EREREdGrIT8faNQIuH0bOHny2bxUY/jySyAgABg9Wv5Cg+hVxQSViIiIiMhAP/4oD8Ht3l2e02oMGRnycOMnT4AbN4C6dY3TLtHLiEN8iYiIiIgMNHiwPET88OFnixqV1dq18vYyU6YwOSUyq+gAiIiIiOjFS02VE6ETJ+SeOjs7wM9PXp24rKsIv0okCfjuO+Bf/3q2Z2lZ2doCgYHAp58apz2ilxmH+BIRERFVYfHx8lY2V64AiYnygj4aZmbyisTNm8tbwdSqVXFxEhEBTFCJiIiIqqyrV4FeveT9R4tTpw5w4ADg5fXi4yIi0ocJKhEREVEVFB8vb2VjSHKqUacOEB7OnlQiqjhcJImIiIioCpowoWTJKSCXnzDhxcRDRGQIJqhEREREVUxqqjzntDSuXAHS0owbDxGRoZigEhEREVUxa9fKCyKVRlISEBRk3HiIiAzFBJWIiIioijlxQnu13pLIzQXCwowaDhGRwZigEhEREVUxT55UbH0iotJigkpERERUxdjZVWx9IqLSYoJKREREVMX4+QGmpqWra2YGdOhg1HCIiAzGfVCJiIiIqpjUVKBZMyAhoeR1a9YErl4FnJyMHxcRUXHYg0pERERUxTg7A82bl65u8+ZMTomo4rAHlYiIiKgKio8H2rUD4uIMr1OnDhAeDtSq9eLiIiIqCntQiYiIiKqgWrWAgwflpNMQdeoABw4wOSWiisUeVCIiIqIqLD4emDABuHIFSEqS9znVMDMD3N3lYb3BwUxOiajiMUElIiIiegWkpgJr1wJhYfI+p3Z28mq9kybJc1aJiCoDs4oOgIiIiIhePGdnYPz4JNy7Fwi1Wo358+fDw8OjosMiItLCHlQiIiKiV8S7776L06dPAwA8PT1x48YNSJJUwVERET3DBJWIiIjoFfD06VNYW1uj4J9+d+/eRe3atSswKiIibVzFl4iIiOgVkJ+fj+f7JXILrphERFQJMEElIiIiIiKiSoEJKhEREREREVUKTFCJiIiIiIioUmCCSkRERERERJUCE1QiIiIiIiKqFJigEhERERERUaXABJWIiIiIiIgqBSaoREREREREVCkwQSULine truncated
       "text/plain": [
        "<Figure size 1100x300 with 1 Axes>"
       ]
@@ -836,7 +836,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1125,15 +1125,15 @@
     "\n",
     "The *measurement noise matrix* models the noise in our sensors as a covariance matrix. In practice this can be difficult. A complicated system may have many sensors, the correlation between them might not be clear, and usually their noise is not a pure Gaussian. For example, a sensor might be biased to read high if the temperature is high, and so the noise is not distributed equally on both sides of the mean. We will learn to deal with these problems later.\n",
     "\n",
-    "The Kalman filter equations uses a covariance matrix $\\mathbf R$ for the measurement noise. The matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is a covariance matrix to account for correlations between the sensors. We have only 1 sensor so R is:\n",
+    "The Kalman filter equations uses a covariance matrix $\\mathbf R$ for the measurement noise. The matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is a covariance matrix to account for correlations between the sensors. We have only 1 sensor so $\\mathbf R$ is:\n",
     "\n",
-    "$$R = \\begin{bmatrix}\\sigma^2_z\\end{bmatrix}$$\n",
+    "$$\\mathbf R = \\begin{bmatrix}\\sigma^2_z\\end{bmatrix}$$\n",
     "\n",
-    "If $\\sigma^2_z$ is 5 meters squared we'd have $R = \\begin{bmatrix}5\\end{bmatrix}$. \n",
+    "If $\\sigma^2_z$ is 5 meters squared we'd have $\\mathbf R = \\begin{bmatrix}5\\end{bmatrix}$. \n",
     "\n",
     "If we had two position sensors, the first with a variance of 5 m$^2$, the second with a variance of 3 m$^2$, we would write\n",
     "\n",
-    "$$R = \\begin{bmatrix}5&0\\\\0&3\\end{bmatrix}$$\n",
+    "$$\\mathbf R = \\begin{bmatrix}5&0\\\\0&3\\end{bmatrix}$$\n",
     "\n",
     "We put the variances on the diagonal because this is a *covariance* matrix, where the variances lie on the diagonal, and the covariances, if any, lie in the off-diagonal elements. Here we assume there is no correlation in the noise between the two sensors, so the covariances are 0.\n",
     "\n",
@@ -1165,8 +1165,6 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[1. 0.]] [[680.587 301.175]\n",
-      " [301.175 502.35 ]] [[5.]]\n",
       "x = [ 1.085 -0.64 ]\n"
      ]
     }
@@ -1328,7 +1326,7 @@
        "likelihood = 2.2250738585072014e-308\n",
        "mahalanobis = 0.0\n",
        "alpha = 1.0\n",
-       "inv = <function inv at 0x00000296F726A948>"
+       "inv = <function inv at 0x000002ABA27DE280>"
       ]
      },
      "execution_count": 29,
@@ -1390,7 +1388,7 @@
    "source": [
     "This is the complete code for the filter, and most of it is boilerplate. I've made it flexible enough to support several uses in this chapter, so it is a bit verbose. Let's work through it line by line. \n",
     "\n",
-    "The first lines checks to see if you provided it with measurement data in `data`. If not, it creates the data using the `compute_dog_data` function we wrote earlier.\n",
+    "The first lines checks to see if you provided it with measurement data in `zs`. If not, it creates the data using the `compute_dog_data` function we wrote earlier.\n",
     "\n",
     "The next lines uses our helper function to create a Kalman filter.\n",
     "\n",
@@ -1409,7 +1407,7 @@
     "        kf.update(z)\n",
     "```\n",
     "\n",
-    "Each call to `predict` and `update` modifies the state variables `x` and `P`. Therefore, after the call to `predict`, `kf.x` contains the prior. After the call to update, `kf.x` contains the posterior. `data` contains the actual position and measurement of the dog, so we use `[:, 1]` to get an array of measurements.\n",
+    "Each call to `predict` and `update` modifies the state variables `x` and `P`. Therefore, after the call to `predict`, `kf.x` contains the prior. After the call to update, `kf.x` contains the posterior. The states and covariances are saved in `xs` and `cov`.\n",
     "\n",
     "It really cannot get much simpler than that. As we tackle more complicated problems this code will remain largely the same; all of the work goes into setting up the `KalmanFilter` matrices; executing the filter is trivial.\n",
     "\n",
@@ -1425,7 +1423,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1435,7 +1433,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 2 Axes>"
       ]
@@ -1473,7 +1471,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x500 with 1 Axes>"
       ]
@@ -1634,7 +1632,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1771,7 +1769,7 @@
     "If you have some experience with linear algebra and statistics, this may help. The covariance due to the prediction can be modeled as the expected value of the error in the prediction step, given by this equation. \n",
     "\n",
     "$$\\begin{aligned}\n",
-    "\\bar{\\mathbf P} &= \\mathbb E[(\\mathbf{Fx - \\bar \\mu})(\\mathbf{Fx - \\bar\\mu})^\\mathsf T]\\\\\n",
+    "\\bar{\\mathbf P} &= \\mathbb E[(\\mathbf{Fx - F\\bar \\mu})(\\mathbf{Fx - F\\bar\\mu})^\\mathsf T]\\\\\n",
     " &= \\mathbf F\\, \\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]\\, \\mathbf F^\\mathsf T\n",
     "\\end{aligned}$$\n",
     "\n",
@@ -1789,7 +1787,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1834,7 +1832,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "a828518321f448be916ab551fe70519e",
+       "model_id": "8f04127ee78d437784e419afaf11eeb3",
        "version_major": 2,
        "version_minor": 0
       },
@@ -1948,7 +1946,7 @@
     "For the multivariate Kalman filter $\\mathbf K$ is a vector, not a scalar. Here is the equation again: $\\mathbf K = \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1}$. Is this a *ratio*? We can think of the inverse of a matrix as linear algebra's way of finding the reciprocal. Division is not defined for matrices, but it is useful to think of it in this way. So we can read the equation for $\\textbf{K}$ as meaning\n",
     "\n",
     "$$\\begin{aligned} \\mathbf K &\\approx \\frac{\\mathbf{\\bar P}\\mathbf H^\\mathsf T}{\\mathbf{S}} \\\\\n",
-    "\\mathbf K &\\approx \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{prediction} + \\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf H^\\mathsf T\n",
+    "\\mathbf K &\\approx \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf H^\\mathsf T\n",
     "\\end{aligned}$$\n",
     "\n",
     "The Kalman gain equation computes a ratio based on how much we trust the prediction vs the measurement. We did the same thing in every prior chapter. The equation is complicated because we are doing this in multiple dimensions via matrices, but the concept is simple. The $\\mathbf H^\\mathsf T$ term is less clear, I'll explain it soon. If you ignore that term the equation for the Kalman gain is the same as the univariate case: divide the uncertainty of the prior with the of the sum of the uncertainty of the prior and measurement.\n",
@@ -1974,7 +1972,7 @@
     "$$\\begin{aligned}\n",
     "\\mathbf x &= \\mathbf{\\bar x} + \\mathbf{Ky} \\\\\n",
     "&= \\mathbf{\\bar x} + \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1}\\mathbf y \\\\\n",
-    "&\\approx \\mathbf{\\bar x} + \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf H^\\mathsf T\\mathbf y\n",
+    "&\\approx \\mathbf{\\bar x} + \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf H^\\mathsf T \\mathbf y\n",
     "\\end{aligned}$$\n",
     "\n",
     "Perhaps a better way to *see* the ratio is to rewrite the estimate equation:\n",
@@ -2033,7 +2031,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2115,7 +2113,7 @@
     "\\\\\\end{aligned}\n",
     "$$\n",
     "\n",
-    "This notation uses the Bayesian $a\\mid b$ notation, which means $a$ given the evidence of $b$. The hat means estimate. Thus $\\hat{\\mathbf x}_{k\\mid k}$ means the estimate of the state $\\mathbf x$ at step $k$ (the first k) given the evidence from step $k$ (the second k). The posterior, in other words. $\\hat{\\mathbf x}_{k\\mid k-1}$ means the estimate for the state $\\mathbf x$ at step $k$ given the estimate from step $k - 1$. The prior, in other words. \n",
+    "This notation uses the Bayesian $a\\mid b$ notation, which means $a$ given the evidence of $b$. The hat means estimate. Thus $\\hat{\\mathbf x}_{k\\mid k}$ means the estimate of the state $\\mathbf x$ at step $k$ (the first $k$) given the evidence from step $k$ (the second $k$). The posterior, in other words. $\\hat{\\mathbf x}_{k\\mid k-1}$ means the estimate for the state $\\mathbf x$ at step $k$ given the estimate from step $k - 1$. The prior, in other words. \n",
     "\n",
     "This notation, copied from [Wikipedia](https://en.wikipedia.org/wiki/Kalman_filter#Details) [[1]](#[wiki_article]), allows a mathematician to express himself exactly. In formal publications presenting new results this precision is necessary. As a programmer I find it fairly unreadable. I am used to thinking about variables changing state as a program runs, and do not use a different variable name for each new computation. There is no agreed upon format in the literature, so each author makes different choices. I find it challenging to switch quickly between books and papers, and so have adopted my admittedly less precise notation. Mathematicians may write scathing emails to me, but I hope programmers and students will rejoice at my simplified notation.\n",
     "\n",
@@ -2162,7 +2160,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2252,7 +2250,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2269,7 +2267,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Here the performance of the two filters are similar, and perhaps the univariate filter is tracking more cloesly. But let's see what happens when the actual velocity `vel` is different from the control input `u`:"
+    "Here the performance of the two filters are similar, and perhaps the univariate filter is tracking more closely. But let's see what happens when the actual velocity `vel` is different from the control input `u`:"
    ]
   },
   {
@@ -2279,7 +2277,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2379,7 +2377,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2389,7 +2387,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2431,7 +2429,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2459,7 +2457,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2488,7 +2486,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2528,7 +2526,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2538,7 +2536,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
        "<Figure size 900x400 with 2 Axes>"
       ]
@@ -2581,7 +2579,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2591,7 +2589,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 2 Axes>"
       ]
@@ -2623,7 +2621,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2654,7 +2652,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2685,7 +2683,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 1000x600 with 2 Axes>"
       ]
@@ -2714,7 +2712,7 @@
     "plt.subplot(121)\n",
     "plot_covariances(R=5, Q=.02, count=20, title='$R = 5\\, m^2$')\n",
     "plt.subplot(122)\n",
-    "plot_covariances(R=.1, Q=.02, count=20, title='$R = 0.5\\, m^2$')"
+    "plot_covariances(R=.5, Q=.02, count=20, title='$R = 0.5\\, m^2$')"
    ]
   },
   {
@@ -2733,7 +2731,7 @@
     "\n",
     "Think about what this means physically. The x-axis of the ellipse denotes our uncertainty in position, and the y-axis our uncertainty in velocity. So, an ellipse that is taller than it is wide signifies that we are more uncertain about the velocity than the position. Conversely, a wide, narrow ellipse shows high uncertainty in position and low uncertainty in velocity. Finally, the amount of tilt shows the amount of correlation between the two variables. \n",
     "\n",
-    "The first plot, with $R=5 m^2$, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner.\n",
+    "The first plot, with `R=5` $m^2$, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner.\n",
     "\n",
     "In contrast, the second plot, with `R=0.5` $m^2$, has a final ellipse that is taller than wide. The ellipses in the second plot are all much smaller than the ellipses in the first plot. This stands to reason because a small $\\small\\mathbf R$ implies a small amount of noise in our measurements. Small noise means accurate predictions, and thus a strong belief in our position. "
    ]
@@ -2767,7 +2765,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2846,7 +2844,7 @@
     "\n",
     "$$\\mathbf P = \\begin{bmatrix}\\mathbf R_0 & 0 \\\\0 & vel_{max}^2\\end{bmatrix}$$\n",
     "\n",
-    "The diagonal of $\\mathbf P$ contains the variance of each state variable, so we populate it with reasonable values. $\\mathbf R$ is a reasonable variance for the position, and the maximum velocity squared is a reasonable variance for the velocity. It is squared because variance is squared: $\\sigma^2$.\n",
+    "The diagonal of $\\mathbf P$ contains the variance of each state variable, so we populate it with reasonable values. $\\mathbf R_0$ is a reasonable variance for the position, and the maximum velocity squared is a reasonable variance for the velocity. It is squared because variance is squared: $\\sigma^2$.\n",
     "\n",
     "You really need to understand the domain in which you are working and initialize your filter on the best available information. For example, suppose we were trying to track horses in a horse race. The initial measurements might be very bad, and provide you with a position far from the starting gate. We know that the horse must start at the starting gate; initializing the filter to the initial measurement would lead to suboptimal results. In this scenario we would want to always initialize the Kalman filter with the starting gate position of the horse."
    ]
@@ -2889,7 +2887,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2924,7 +2922,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -2965,7 +2963,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -3005,7 +3003,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -3060,7 +3058,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -3095,7 +3093,7 @@
     "\n",
     "Multivariate Gaussians allow us to simultaneously handle multiple dimensions, both spacial and others (velocity, etc). We made a key insight: hidden variables have the ability to significantly increase the accuracy of the filter. This is possible because the hidden variables are correlated with the observed variables. \n",
     "\n",
-    "I gave an intuitive definition of *observability*. Observability was invented by Dr. Kalman for linear systems, and there is a fair amount of theory behind it. It answers the question of whether a system state can be determined by observing the system's output. For our problems this has been easy to determine, but more complicated systems may require rigorous analysis. Wikipedia's [Observability](https://en.wikipedia.org/wiki/Observability) article has an overview; if you need to learn the topic [[Grewal2008]](#References) is a good source. \n",
+    "I gave an intuitive definition of *observability*. Observability was invented by Dr. Kalman for linear systems, and there is a fair amount of theory behind it. It answers the question of whether a system state can be determined by observing the system's output. For our problems this has been easy to determine, but more complicated systems may require rigorous analysis. Wikipedia's [Observability](https://en.wikipedia.org/wiki/Observability) article has an overview; if you need to learn the topic [[2]](#References) is a good source. \n",
     "\n",
     "There is one important caveat about hidden variables. It is easy to construct a filter that produces estimates for hidden variables. I could write a filter that estimates the color of a tracked car. But there is no way to compute car color from positions, so the estimate for the color will be nonsense. The designer must verify that these variables are being estimated correctly. If you do not have a velocity sensor and yet are estimating velocity, you will need to test that the velocity estimates are correct.; do not trust that they are. For example, suppose the velocity has a periodic component to it - it looks like a sine wave. If your sample time is less than 2 times the frequency you will not be able to accurately estimate the velocity (due to Nyquist's Theorem). Imagine that the sample period is equal to the frequency of the velocity. The filter will report that the velocity is constant because it samples the system at the same point on the sin wave. \n",
     "\n",
@@ -3128,7 +3126,7 @@
     "- <A name=\"[wiki_article]\">[1]</A> 'Kalman Filters'. Wikipedia\n",
     "https://en.wikipedia.org/wiki/Kalman_filter#Details\n",
     "\n",
-    "* **[Grewal2008]** Grewal, Mohinder S., Andrews, Angus P. *Kalman Filtering: Theory and Practice Using MATLAB*. Third Edition. John Wiley & Sons. 2008."
+    "- [2] Grewal, Mohinder S., Andrews, Angus P. *Kalman Filtering: Theory and Practice Using MATLAB*. Third Edition. John Wiley & Sons. 2008."
    ]
   }
  ],
@@ -3149,7 +3147,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.8.3"
   },
   "widgets": {
    "application/vnd.jupyter.widget-state+json": {

07-Kalman-Filter-Math.ipynb

@@ -148,7 +148,7 @@
     "$$\\mathbf x(t_k) = \\mathbf F(\\Delta t)\\mathbf x(t_{k-1}) + \\mathbf B(t_k)\\mathbf u (t_k)$$\n",
     "\n",
     "Convention allows us to write $\\mathbf x(t_k)$ as $\\mathbf x_k$, which means the \n",
-    "the value of $\\mathbf x$ at the k$^{th}$ value of $t$.\n",
+    "the value of $\\mathbf x$ at the $k^{th}$ value of $t$.\n",
     "\n",
     "$$\\mathbf x_k = \\mathbf{Fx}_{k-1} + \\mathbf B_k\\mathbf u_k$$\n",
     "\n",
@@ -157,10 +157,10 @@
     "Finding this matrix is often quite difficult. The equation $\\dot x = v$ is the simplest possible differential equation and we trivially integrate it as:\n",
     "\n",
     "$$ \\int\\limits_{x_{k-1}}^{x_k}  \\mathrm{d}x = \\int\\limits_{0}^{\\Delta t} v\\, \\mathrm{d}t $$\n",
-    "$$x_k-x_0 = v \\Delta t$$\n",
-    "$$x_k = v \\Delta t + x_0$$\n",
+    "$$x_k-x_{k-1} = v \\Delta t$$\n",
+    "$$x_k = v \\Delta t + x_{k-1}$$\n",
     "\n",
-    "This equation is *recursive*: we compute the value of $x$ at time $t$ based on its value at time $t-1$. This recursive form enables us to represent the system (process model) in the form required by the Kalman filter:\n",
+    "This equation is *recursive*: we compute the value of $x$ at time $k$ based on its value at time $k-1$. This recursive form enables us to represent the system (process model) in the form required by the Kalman filter:\n",
     "\n",
     "$$\\begin{aligned}\n",
     "\\mathbf x_k &= \\mathbf{Fx}_{k-1}  \\\\\n",
@@ -200,24 +200,24 @@
     "\n",
     "We define two new variables:\n",
     "\n",
-    "$$\\begin{aligned} x_1(u) &= x \\\\\n",
-    "x_2(u) &= \\dot x\n",
+    "$$\\begin{aligned} x_1(t) &= x \\\\\n",
+    "x_2(t) &= \\dot x\n",
     "\\end{aligned}$$\n",
     "\n",
-    "Now we will substitute these into the original equation and solve. The solution yields a set of first-order equations in terms of these new variables. It is conventional to drop the $(u)$ for notational convenience.\n",
+    "Now we will substitute these into the original equation and solve. The solution yields a set of first-order equations in terms of these new variables. It is conventional to drop the $(t)$ for notational convenience.\n",
     "\n",
     "We know that $\\dot x_1 = x_2$ and that $\\dot x_2 = \\ddot{x}$. Therefore\n",
     "\n",
     "$$\\begin{aligned}\n",
     "\\dot x_2 &= \\ddot{x} \\\\\n",
-    "         &= 6\\dot x - 9x + t\\\\\n",
-    "         &= 6x_2-9x_1 + t\n",
+    "         &= 6\\dot x - 9x + u\\\\\n",
+    "         &= 6x_2-9x_1 + u\n",
     "\\end{aligned}$$\n",
     "\n",
     "Therefore our first-order system of equations is\n",
     "\n",
     "$$\\begin{aligned}\\dot x_1 &= x_2 \\\\\n",
-    "\\dot x_2 &= 6x_2-9x_1 + t\\end{aligned}$$\n",
+    "\\dot x_2 &= 6x_2-9x_1 + u\\end{aligned}$$\n",
     "\n",
     "If you practice this a bit you will become adept at it. Isolate the highest term, define a new variable and its derivatives, and then substitute."
    ]
@@ -996,7 +996,7 @@
     "\n",
     "while not correct, is often a useful approximation. If you do this for an important application you will have to perform quite a few studies to guarantee that your filter works in a variety of situations. \n",
     "\n",
-    "If you do this, 'lower right term' means the most rapidly changing term for each variable. If the state is $x=\\begin{bmatrix}x & \\dot x & \\ddot{x} & y & \\dot{y} & \\ddot{y}\\end{bmatrix}^\\mathsf{T}$ Then Q will be 6x6; the elements for both $\\ddot{x}$ and $\\ddot{y}$ will have to be set to non-zero in $\\mathbf Q$."
+    "If you do this, 'lower right term' means the most rapidly changing term for each variable. If the state is $x=\\begin{bmatrix}x & \\dot x & \\ddot{x} & y & \\dot{y} & \\ddot{y}\\end{bmatrix}^\\mathsf{T}$ Then $\\mathbf Q$ will be 6x6; the elements for both $\\ddot{x}$ and $\\ddot{y}$ will have to be set to non-zero in $\\mathbf Q$."
    ]
   },
   {
@@ -1148,7 +1148,7 @@
     "\n",
     "$$\\mathbf P = \\mathbf{\\bar P} - \\mathbf{KH}\\mathbf{\\bar P} - \\mathbf{\\bar P}\\mathbf H^\\mathsf T \\mathbf K^\\mathsf T + \\mathbf K(\\mathbf H \\mathbf{\\bar P}\\mathbf H^\\mathsf T + \\mathbf R)\\mathbf K^\\mathsf T$$\n",
     "\n",
-    "Now we need to the the derivative of the trace of $\\mathbf P$ with respect to $\\mathbf T$: $\\frac{d\\, trace(\\mathbf P)}{d\\mathbf K}$.\n",
+    "Now we need to the the derivative of the trace of $\\mathbf P$ with respect to $\\mathbf K$: $\\frac{d\\, trace(\\mathbf P)}{d\\mathbf K}$.\n",
     "\n",
     "The derivative of the trace the first term with respect to $\\mathbf K$ is $0$, since it does not have $\\mathbf K$ in the expression.\n",
     "\n",
@@ -1208,14 +1208,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 13,
    "metadata": {
     "scrolled": true
    },
    "outputs": [
     {
      "data": {
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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1243,12 +1243,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1276,7 +1276,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1291,7 +1291,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -1319,12 +1319,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 2 Axes>"
       ]
@@ -1346,7 +1346,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -1427,7 +1427,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1463,7 +1463,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -1475,7 +1475,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1544,11 +1544,11 @@
     "\n",
     "In practice this is extremely reasonable, as many things have the *Markov property*. If you are driving in a parking lot, does your position in the next second depend on whether you pulled off the interstate or were creeping along on a dirt road one minute ago? No. Your position in the next second depends solely on your current position, speed, and control inputs, not on what happened a minute ago. Thus, cars have the Markov property, and we can make this simplification with no loss of precision or generality.\n",
     "\n",
-    "The next simplification we make is do define the *measurement model* as depending on the current state $\\mathbf x_k$ with the conditional probability of the measurement given the current state: $P(\\mathbf z_t \\mid \\mathbf x_x)$. We write:\n",
+    "The next simplification we make is do define the *measurement model* as depending on the current state $\\mathbf x_k$ with the conditional probability of the measurement given the current state: $P(\\mathbf z_k \\mid \\mathbf x_k)$. We write:\n",
     "\n",
-    "$$\\mathbf z_k \\sim P(\\mathbf z_t \\mid \\mathbf x_x)$$\n",
+    "$$\\mathbf z_k \\sim P(\\mathbf z_k \\mid \\mathbf x_k)$$\n",
     "\n",
-    "We have a recurrance now, so we need an initial condition to terminate it. Therefore we say that the initial distribution is the probablity of the state $\\mathbf x_0$:\n",
+    "We have a recurrence now, so we need an initial condition to terminate it. Therefore we say that the initial distribution is the probablity of the state $\\mathbf x_0$:\n",
     "\n",
     "$$\\mathbf x_0 \\sim P(\\mathbf x_0)$$\n",
     "\n",
@@ -1557,9 +1557,9 @@
     "\n",
     "The details of the mathematics for this computation varies based on the problem. The **Discrete Bayes** and **Univariate Kalman Filter** chapters gave two different formulations which you should have been able to reason through. The univariate Kalman filter assumes that for a scalar state both the noise and process are linear model are affected by zero-mean, uncorrelated Gaussian noise. \n",
     "\n",
-    "The Multivariate Kalman filter make the same assumption but for states and measurements that are vectors, not scalars. Dr. Kalman was able to prove that if these assumptions hold true then the Kalman filter is *optimal* in a least squares sense. Colloquially this means there is no way to derive more information from the noisy measurements. In the remainder of the book I will present filters that relax the constraints on linearity and Gaussian noise.\n",
+    "The Multivariate Kalman filter makes the same assumption but for states and measurements that are vectors, not scalars. Dr. Kalman was able to prove that if these assumptions hold true then the Kalman filter is *optimal* in a least squares sense. Colloquially this means there is no way to derive more information from the noisy measurements. In the remainder of the book I will present filters that relax the constraints on linearity and Gaussian noise.\n",
     "\n",
-    "Before I go on, a few more words about statistical inversion. As Calvetti and Somersalo write in *Introduction to Bayesian Scientific Computing*, \"we adopt the Bayesian point of view: *randomness simply means lack of information*.\"[3] Our state parameterizes physical phenomena that we could in principle measure or compute: velocity, air drag, and so on. We lack enough information to compute or measure their value, so we opt to consider them as random variables. Strictly speaking they are not random, thus this is a subjective position. \n",
+    "Before I go on, a few more words about statistical inversion. As Calvetti and Somersalo write in *Introduction to Bayesian Scientific Computing*, \"we adopt the Bayesian point of view: *randomness simply means lack of information*\"[3]. Our state parameterizes physical phenomena that we could in principle measure or compute: velocity, air drag, and so on. We lack enough information to compute or measure their value, so we opt to consider them as random variables. Strictly speaking they are not random, thus this is a subjective position. \n",
     "\n",
     "They devote a full chapter to this topic. I can spare a paragraph. Bayesian filters are possible because we ascribe statistical properties to unknown parameters. In the case of the Kalman filter we have closed-form solutions to find an optimal estimate. Other filters, such as the discrete Bayes filter or the particle filter which we cover in a later chapter, model the probability in a more ad-hoc, non-optimal manner. The power of our technique comes from treating lack of information as a random variable, describing that random variable as a probability distribution, and then using Bayes Theorem to solve the statistical inference problem."
    ]
@@ -1608,7 +1608,7 @@
     "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}  \\\\\n",
     " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}  \\\\\n",
     " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
-    " &= \\frac{\\sigma^2_{x'}}{b}\n",
+    " &= \\frac{\\sigma^2_{x}}{b}\n",
     " \\end{aligned}\n",
     "$$\n",
     "\n",
@@ -1617,7 +1617,7 @@
     "$$\n",
     "\\begin{aligned}\n",
     "\\mu_{x}&=x+ \\frac{a}{a+b}(y-x) \\\\\n",
-    "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
+    "&= x + \\frac{\\sigma^2_{x}}{b}(y-x) \\\\\n",
     "&= x + g_n(y-x)\n",
     "\\end{aligned}\n",
     "$$\n",
@@ -1674,7 +1674,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,

09-Nonlinear-Filtering.ipynb

@@ -141,7 +141,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -193,7 +193,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -225,7 +225,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 3 Axes>"
       ]
@@ -263,7 +263,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 3 Axes>"
       ]
@@ -302,7 +302,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
        "<Figure size 900x400 with 2 Axes>"
       ]
@@ -337,7 +337,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 3 Axes>"
       ]
@@ -367,8 +367,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "input  mean, variance: -0.0006, 1.0033\n",
-      "output mean, variance: -0.1243, 2.4105\n"
+      "input  mean, variance: 0.0027, 1.0005\n",
+      "output mean, variance: -0.1290, 2.4030\n"
      ]
     }
    ],
@@ -395,7 +395,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 3 Axes>"
       ]
@@ -407,7 +407,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "output mean, variance: 0.0009, 2.2575\n"
+      "output mean, variance: -0.0041, 2.2511\n"
      ]
     }
    ],
@@ -437,8 +437,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "linear    output mean, variance: 0.0511, 7506.6256\n",
-      "nonlinear output mean, variance: -9.0540, 30529.4381\n"
+      "linear    output mean, variance: -0.2363, 7485.6168\n",
+      "nonlinear output mean, variance: -9.6658, 30502.6258\n"
      ]
     }
    ],
@@ -473,7 +473,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 3 Axes>"
       ]
@@ -518,7 +518,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -547,7 +547,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -574,7 +574,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -603,7 +603,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -705,7 +705,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.8.3"
   }
  },
  "nbformat": 4,

10-Unscented-Kalman-Filter.ipynb

@@ -785,10 +785,10 @@
     "\n",
     "$$ \n",
     "\\boldsymbol{\\chi}_i = \\begin{cases}\n",
-    "\\mu + \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right ]_{i}& \\text{for i=1 .. n} \\\\\n",
-    "\\mu - \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} &\\text{for i=(n+1) .. 2n}\\end{cases}\n",
+    "\\mu + \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right ]_{i}& i=1..n \\\\\n",
+    "\\mu - \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} &i=(n+1)..2n\\end{cases}\n",
     "$$\n",
-    "The $i$ subscript chooses the i$^{th}$ roth vector of the matrix.\n",
+    "The $i$ subscript chooses the i$^{th}$ row vector of the matrix.\n",
     "\n",
     "In other words, we scale the covariance matrix by a constant, take the square root of it, and ensure symmetry by both adding and subtracting it from the mean. We will discuss how you take the square root of a matrix later.\n",
     "\n",
@@ -1191,7 +1191,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "A military grade radar achieves 1 meter RMS range accuracy, and 1 mrad RMS for elevation angle [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",
+    "A military grade radar achieves 1 meter RMS range accuracy, and 1 mrad RMS for elevation angle [3]. 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 is $\\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are 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 is altitude, which we assume is independent of $x$. That results in a block design for $\\mathbf Q$:\n",
     "\n",
@@ -1285,7 +1285,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Tracking Maneuevering Aircraft"
+    "### Tracking Maneuvering Aircraft"
    ]
   },
   {
@@ -2059,8 +2059,8 @@
     "$$\n",
     "\\begin{cases}\n",
     "\\mathcal{X}_0 = \\mu \\\\\n",
-    "\\mathcal{X}_i = \\mu +  \\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i, & \\texttt{for i=1..n} \\\\\n",
-    "\\mathcal{X}_i = \\mu - \\left[\\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} & \\texttt{for i=(n+1)..2n}\n",
+    "\\mathcal{X}_i = \\mu +  \\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i, & i=1..n \\\\\n",
+    "\\mathcal{X}_i = \\mu - \\left[\\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} & i=(n+1)..2n\n",
     "\\end{cases}\n",
     "$$\n",
     "\n",
@@ -2074,7 +2074,7 @@
     "\\Sigma = \\mathbf{SS}^\\mathsf T\n",
     "$$\n",
     "\n",
-    "This definition is favored because $\\mathbf S$ is computed using the [*Cholesky decomposition*](https://en.wikipedia.org/wiki/Cholesky_decomposition) [3]. It decomposes a Hermitian, positive-definite matrix into a triangular matrix and its conjugate transpose. The matrix can be either upper \n",
+    "This definition is favored because $\\mathbf S$ is computed using the [*Cholesky decomposition*](https://en.wikipedia.org/wiki/Cholesky_decomposition) [5]. It decomposes a Hermitian, positive-definite matrix into a triangular matrix and its conjugate transpose. The matrix can be either upper \n",
     "or lower triangular, like so:\n",
     "\n",
     "$$A=LL^{∗} \\\\ A=U^{∗}U$$\n",
@@ -3225,11 +3225,11 @@
     "\n",
     "- [2] Simon J. Julier. \"The Scaled Unscented Transformation\". Proceedings of the American Control Conference 6. IEEE. (2002)\n",
     "\n",
-    "- [1] http://www.esdradar.com/brochures/Compact%20Tracking%2037250X.pdf\n",
+    "- [3] http://www.esdradar.com/brochures/Compact%20Tracking%2037250X.pdf\n",
     "\n",
-    "- [2] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman  Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n",
+    "- [4] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman  Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n",
     "\n",
-    "- [3] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition"
+    "- [5] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition"
    ]
   }
  ],
@@ -3250,7 +3250,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.8.3"
   }
  },
  "nbformat": 4,

12-Particle-Filters.ipynb

@@ -81,7 +81,7 @@
     "\n",
     "* **multivariate**: we want to track several attributes, such as position, velocity, turn rates, etc.\n",
     "\n",
-    "* **unknown process model**: we may not know the process model of the system\n",
+    "* **unknown process model**: we may not know the process model of the system.\n",
     "\n",
     "None of the filters we have learned work well with all of these constraints. \n",
     "\n",
@@ -110,7 +110,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 2 Axes>"
       ]
@@ -180,7 +180,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 2 Axes>"
       ]
@@ -271,7 +271,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -323,7 +323,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvYAAAFfCAYAAAAlGoibAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/d3fzzAAAACXBIWXMAAA9hAAAPYQGoP6dpAABViklEQVR4nO3deVxU9eLG8c/MMIAgi8qqICLuK4r72ibtu0ubbVp5zUq5t25WVlq/bNc2rW6LbW5lZouldCu1tFQE3PcFFZBFZV8GZn5/oJQXNVHhwMzzfr14KYczp4fp6/Bw5nu+x+RwOByIiIiIiEi9ZjY6gIiIiIiInDsVexERERERJ6BiLyIiIiLiBFTsRUREREScgIq9iIiIiIgTULEXEREREXECKvYiIiIiIk7AzegA54vdbic1NRUfHx9MJpPRcUREREREzpnD4SAvL4+mTZtiNp/+nLzTFPvU1FTCw8ONjiEiIiIict7t37+fsLCw0+7jNMXex8cHqPimfX19DU7jfGw2G0uXLiU2Nhar1Wp0HDGIxoGAxoH8SWNBQOOgpuXm5hIeHl7ZdU/HaYr98ek3vr6+KvY1wGaz4eXlha+vr/7RujCNAwGNA/mTxoKAxkFtOZOp5rp4VkRERETECajYi4iIiIg4ARV7EREREREnoGIvIiIiIuIEVOxFRERERJyAir2IiIiIiBNQsRcRERERcQIq9iIiIiIiTkDFXkRERETECajYi4iIiIg4ATejA4iISN2TU2Rjb1YBe7IK2JddyJHCUnKKbBwtLKWotIzDh83Mz0jAzWKmkZeVJg09aNLQnVA/T1oF+hAV5I2Xu37EiIjUJr3qioi4uHK7g40Hc1i77wjrUo6QuO8IqTnFf/MoM9tzsk+7RzP/BkQ396d3ZGN6tmhM22AfzGbT+QsuIiInULEXEXFB+SVlLN+eyX+3ZPDLtgyyC0qr7BPk40GLAG9aNPEi0McD/wbu+HlZsZocJCYl0aVrNA5MHC20kVVQQnZ+KfsPF7IrM5+s/FIOHi3i4NEivlufBkATb3cuaR9MbMdg+rcKwNNqqe1vW0TEqanYi4i4CLvdwe97svli7QG+35hOka288ms+nm70atGY7hGN6Nbcn87N/PDxtJ70ODabDfOBRK7oGorVevJ9DheUsjU9l7V7j7Bm72ES9h0hu6CUeWv3M2/tfrzdLVzeOZSbeoYTE9EIk0ln8kVEzpWKvYiIk8sttjF3dQofr9rHgSNFldsjmngxpH0wF7UPomeLxlgt5289hcbe7vSLCqBfVAAAtnI7q/ccZummdJZuPkRaTjFfJBzgi4QDRAV6c0vvCEb0DKehh34siYicLb2Ciog4qdSjRbz/6x7mrdlPfkkZUHFm/uquTRkaE0a3cP9aO1NutZjp3yqA/q0CePqajiTsO8K8Nfv5dn0auzILeObbzbz243ZG9o3gzn6RBPp41EouERFnomIvIuJkMvKKmfHzLmb/kUJpuR2ANsENGT2gJddENzV8brvJZKJHi8b0aNGYJ6/uwKKkVD74dQ+7swp46+dd/GfFHm7vE8H9F7aikbe7oVlFROoTFXsRESeRV2xj5i+7+PC3vZXz5/u0bMyYwVEMbhNYJ+ex+3haua1PBDf3ak785kO8vWwXSfuP8t6xdxruG9ySuwdEaulMEZEzoFdKEZF6zm53sDDxIFO/30pWfgkA0eH+PHxpW/q3CjA43ZmxmE1c1imESzsGs3xHFi98v5XNabm8vHQ7n/y+j0lXdeDKzqF18pcTEZG6QsVeRKQe25yay6RFG0nYdwSAyABvHruiPZe0D6qXJdhkMjG4TSADWwXwzfpUXl66jf2Hixg3O5F5rfcz+ZqOtAxsaHRMEZE6ScVeRKQeKi2z8+ZPO5jxyy7K7A683C08cFFr7h7QAg+3+r8+vNls4troZlzaMYS3l+1ixi+7WLEji8umr+DBi1sxZnAUbudxFR8REWegYi8iUs9sOJDDw18kszU9D4DLO4Xw1NUdCfHzNDjZ+edptTD+kjZc360ZT329iV+2ZfLy0u3Ebz7EK8O70irIx+iIIiJ1hk53iIjUE+V2B2/+tIPrZvzG1vQ8mni789Yt3Zl5W4xTlvq/imjizYd39mTaiK74erqRfCCHK17/lfdW7MZudxgdT0SkTtAZexGReuBQbjHj5yaxanc2AFd2CWXKNR1p0tB11ns3mUxc3y2Mvi0DePTL9fyyLZNnv9vCbzuzeGV4NI21NKaIuDidsRcRqeN+3pbB5a+tYNXubLzcLbw8rCtv3tzNpUr9X4X4efLhnT35v+s74eFm5udtmVzx2gpW7zlsdDQREUOp2IuI1FF2u4M3/ruDu2et4XBBKR2b+vLNAwMYGhNWL1e8OZ9MJhO39o7gq/v70zLQm/TcYm56dxXvLt+Fw6GpOSLimlTsRUTqoPySMsZ+to5X4rfjcMBtfZrz5dh+RGmpxxO0D/Xlm3EDuKF7M+wOeG7xVuLmJ1N87AZdIiKuRHPsRUTqmL1ZBdzz8Vp2ZOTjbjEz5dqO3NSrudGx6ixvDzdeGdaVrmH+TPl2MwsTD7I7M593RvZw+ouKRUT+SmfsRUTqkNV7DnPtW7+xIyOfIB8P5t7XR6X+DJhMJu7o14JP7u6Fv5eV5AM5XP3mrySmHDE6mohIrVGxFxGpI75dn8pt7/1BTpGN6HB/vn1gAN2bNzI6Vr3Sr1UAX98/gLbBPmTmlXDzf37nx82HjI4lIlIrVOxFRAzmcDh4d/kuxs1OpLTcTmyHYObc04cgX00jORvNm3jx5dh+XNA2kGKbnXs/Wcuc1SlGxxIRqXEq9iIiBrLbHUz+ZjPPLd4KwJ39WjDzthgauFsMTla/eXu48Z/bezC8Rxh2B0z8cgOvxm/Xijki4tRU7EVEDFJWbidufhKzVu4F4Ikr2/PU1R2wmF17KcvzxWox88KNXXjwolYAvP7fHTy2cAPlulOtiDgprYojImKAkrJyHpidyNLNh3Azm3h1RDTXdG1qdCynYzKZiIttS7CfJ5O+2sic1fspKi3n5WFdcbPo3JaIOBe9qomI1LKi0nJGf7SWpZsP4e5m5u3bYlTqa9itvSN44+buuJlNfJWUygNzEiktsxsdS0TkvFKxFxGpRfklZdzxwWpW7MiigdXCh3f25JIOwUbHcglXdgll5m0xuFvMfL8xnTGfJuhGViLiVFTsRURqSUFJGXd+sJrVew/j4+HGJ6N60b9VgNGxXMqQDsH8544eeLiZ+WlrBqM/WqtyLyJOQ8VeRKQWFJaWcdesNazddwQfTzc+u6c3PVo0NjqWSxrcJpBZd/XCy93CrzuzuO+TBErKVO5FpP5TsRcRqWHH59Sv3nP8TH1vuoT5Gx3LpfWNasKHd/akgdXCsu2Z3P9ZIrZyzbkXkfpNxV5EpAYV28q595O1rNyVjbe7hVl39yI63N/oWAL0btmE945Ny/lxyyEemptImcq9iNRjKvYiIjWkrNzOuNmJrNiRhdexUh8T0cjoWPIX/VsF8M7IigtqF29I51+fJ2udexGpt1TsRURqgMPh4NEvN/DjlkN4uJl5/46e9NSc+jrpgrZBvHXrn0thTv5mk+5QKyL1koq9iEgNmPr9Vr5IOIDFbOLNW7rTN6qJ0ZHkNIZ0CGbaiGhMJvh41T7e/Gmn0ZFERKpNxV5E5Dx7e9ku3l2+G4Dnb+jMEK1TXy9c3bUpT1/dEYBX4rcz+48UgxOJiFSPir2IyHk0f81+nv9+KwATL2/HsB7hBieS6rijXwseuKgVAE98tYEfNqYZnEhE5MydVbGfMWMGkZGReHp6EhMTw4oVK06575dffsmQIUMIDAzE19eXvn37smTJkir7LViwgA4dOuDh4UGHDh1YuHDh2UQTETHMj5sP8eiX6wG4b1BL7hscZXAiORtxQ9pwc69w7A54cG4Sv+/ONjqSiMgZqXaxnzdvHuPHj+fxxx8nMTGRgQMHcvnll5OScvK3LJcvX86QIUNYvHgxCQkJXHjhhVx99dUkJiZW7rNq1SpGjBjByJEjSU5OZuTIkQwfPpw//vjj7L8zEZFatOFADg/MScTugGExYTx6eTujI8lZMplMPHNtJ2I7BFNaZueej9ayLT3P6FgiIn/L5Kjmpf+9e/eme/fuzJw5s3Jb+/btue6665g6deoZHaNjx46MGDGCJ598EoARI0aQm5vL999/X7nPZZddRqNGjZgzZ85Jj1FSUkJJSUnl57m5uYSHh5OVlYWvr291viU5Azabjfj4eIYMGYLVajU6jhhE4+DkUo8WMfSdP8jML2VAqya8e1s3rBbnnenoKuOgxFbOnR8lsHbfUZr5e/LFfb0JaOhhdKw6xVXGgpyexkHNys3NJSAggJycnL/tuG7VOXBpaSkJCQk8+uijJ2yPjY1l5cqVZ3QMu91OXl4ejRv/uezbqlWrmDBhwgn7XXrppUyfPv2Ux5k6dSqTJ0+usn3p0qV4eXmdURapvvj4eKMjSB2gcfCnojJ4baOFzCIToQ0cXNXoEPFLfjA6Vq1whXFwQyDsO2Th4NFibnrrF8Z1KMfdYnSquscVxoL8PY2DmlFYWHjG+1ar2GdlZVFeXk5w8IkrPAQHB5Oenn5Gx3jllVcoKChg+PDhldvS09OrfcyJEycSFxdX+fnxM/axsbE6Y18D9Nu4gMbB/7KV27nnk0TSirIJbOjO3Pt609S/gdGxapyrjYOeAwoY9s5q9uXb+DG/Ka+P6IrZbDI6Vp3gamNBTk7joGbl5uae8b7VKvbHmUwnvqA5HI4q205mzpw5PP300yxatIigoKBzOqaHhwceHlXfErVarRpUNUjPr4DGAVS8Rk36egO/7cqmgdXCB3f2IiLQtU4quMo4aB3izzsjY7jt/T9YsjmDaT/t1jUU/8NVxoKcnsZBzajOc1qtSaABAQFYLJYqZ9IzMjKqnHH/X/PmzWPUqFHMnz+fSy655ISvhYSLine truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -355,7 +355,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -548,7 +548,7 @@
     "\n",
     "$$\\displaystyle \\mu = \\frac{1}{N}\\sum_{i=1}^N w^ix^i$$\n",
     "\n",
-    "Here I adopt the notation $x^i$ to indicate the $\\mathtt{i}^{th}$ particle. A superscript is used because we often need to use subscripts to denote time steps the $\\mathtt{k}^{th}$ or $\\mathtt{k+1}^{th}$ particle, yielding the unwieldy $x^i_{k+1}$. \n",
+    "Here I adopt the notation $x^i$ to indicate the $\\mathtt{i}^{th}$ particle. A superscript is used because we often need to use subscripts to denote time steps, yielding the unwieldy $x^i_{k+1}$ for the $\\mathtt{k+1}^{th}$ time step for example. \n",
     "\n",
     "This function computes both the mean and variance of the particles:"
    ]
@@ -702,7 +702,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -831,7 +831,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -886,7 +886,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -936,7 +936,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -974,7 +974,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1029,7 +1029,7 @@
     "\n",
     "$q(x)$ is known to us, so we can compute $\\int f(x)q(x)$ using MC integration. That leaves us with  $\\pi(x)/q(x)$.  That is a ratio, and we define it as a *weight*. This gives us\n",
     "\n",
-    "$$\\mathbb{E}\\big[f(x)\\big] = \\sum\\limits_{i=1}^N f(x^i)w(x^i)$$\n",
+    "$$\\mathbb{E}\\big[f(x)\\big] = \\sum\\limits_{i=1}^N f(x^i)q(x^i)w(x^i)$$\n",
     "\n",
     "Maybe that seems a little abstract. If we want to compute the mean of the particles we would compute\n",
     "\n",
@@ -1104,7 +1104,7 @@
     },
     {
      "data": {
-      "image/png": "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\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1QAAABnCAYAAAAHZwPDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAIpElEQVR4nO3dT4iU9R/A8c/sTtuKsoJWiviH7Z8WhtYuiIVkBUZBIHXIFqrfoWghC9tLmkJblzoERWiFEEmR0SGSDh70lJbbYWVHPHio2NDC1eyw28RPp3R+B3F/yW5/nu8+szvOvl4guA/PfOezX55xfLvjTKFarVYDAACAzJqmegAAAIArlaACAABIJKgAAAASCSoAAIBEggoAACCRoAIAAEgkqAAAABIVa7Ho2bNno1Kp1GJpAACAJC0tLdHa2prrmrkH1dmzZ2PGnPaI/w7lvTQAAECy+fPnx+DgYK5RlXtQVSqVizHVdSKipS3v5aeN4f/MnuoRIGbvGp7qEa54w+GxDAD1YKQSsWj3UFQqlfoOqlEtbYJqAtpmTfUEEB7DObCDANDYvCkFAABAIkEFAACQSFABAAAkElQAAACJBBUAAEAiQQUAAJBIUAEAACQSVAAAAIkEFQAAQCJBBQAAkEhQAQAAJBJUAAAAiQQVAABAIkEFAACQSFABAAAkElQAAACJBBUAAEAiQQUAAJBIUAEAACQSVAAAAIkEFQAAQCJBBQAAkEhQAQAAJBJUAAAAiQQVAABAIkEFAACQSFABAAAkElQAAACJBBUAAEAiQQUAAJBIUAEAACQSVAAAAIkEFQAAQCJBBQAAkEhQAQAAJBJUAAAAiQQVAABAIkEFAACQSFABAAAkElQAAACJBBUAAEAiQQUAAJBIUAEAACQSVAAAAIkEFQAAQCJBBQAAkEhQAQAAJBJUAAAAiQQVAABAIkEFAACQSFABAAAkElQAAACJBBUAAEAiQQUAAJBIUAEAACQSVAAAAImKNVu5MlKzpaeDkfJUTwDhcZwDOwgA9WGkUpt1C9VqtZrngsPDw7Fw4cIolxUBAABQP2bNmhU//vhjzJ49O7c1c/8JVaFQiHK5HCdOnIi2tra8l58WRkZGYtGiRfaQKeU6nDh7CAD149LzcqFQyHXdmr3kr62tzV8gJsgeUg9chxNnDwGgcXlTCgAAgESCCgAAIFFzb29vb+6LNjfH2rVro1is3ZsINjp7SD1wHU6cPQSA+lGL5+Xc3+UPAABguvCSPwAAgESCCgAAIJGgAgAASCSoAAAAEgkqAACARElB9c4770R7e3u0trZGR0dHHDx48G/P//LLL6OjoyNaW1vj+uuvj/feey9p2EaSZQ9PnjwZXV1dsXTp0mhqaopNmzZN4qQ0sizX4VdffRV33XVXzJ07N2bMmBHLli2LN998cxKnrU9Z/zy85Ouvv45isRgrV66s8YQAMD0cOHAgHnrooViwYEEUCoXYs2fPP94mj07JHFSffvppbNq0KbZu3RoDAwOxZs2aeOCBB+L48ePjnj84OBgPPvhgrFmzJgYGBuKll16K559/Pj777LPMwzaKrHt47ty5uPbaa2Pr1q2xYsWKSZ6WRpX1Opw5c2Zs3LgxDhw4EMeOHYtt27bFtm3bYufOnZM8ef3IuoeXDA8PxxNPPBH33XffJE0KAI3vt99+ixUrVsT27dv/1fl5dUrmz6FatWpV3HHHHfHuu++OHrvlllti/fr18dprr405/8UXX4wvvvgijh07Nnqsu7s7jhw5En19fZmGbRRZ9/DP1q5dGytXroy33nqr1mPS4CZyHV7y8MMPx8yZM+Ojjz6q1Zh1LXUPN2zYEDfddFM0NzfHnj17olQqTca4ADBtFAqF+Pzzz2P9+vV/eU5enZLpJ1SVSiUOHz4c69atu+z4unXr4tChQ+Pepq+vb8z5999/f/T398fvv/+e5e4bQsoeQt7yuA4HBgbi0KFDcffdd9dixLqXuocffPBBfP/99/Hyyy/XekQA4G/k1SmZgurMmTNx/vz5mDdv3mXH582bF0NDQ+PeZmhoaNzz//jjjzhz5kyWu28IKXsIeZvIdbhw4cK4+uqro7OzM5599tl46qmnajlq3UrZw2+//TY2b94cH3/8cRSLxckYEwD4C3l1StIzeqFQuOzrarU65tg/nT/e8ekk6x5CLaRchwcPHoxyuRzffPNNbN68OW688cZ47LHHajlmXfu3e3j+/Pno6uqKV155JW6++ebJGg8A+Bt5dEqmoLrmmmuiubl5zL++nj59ekzdXTJ//vxxzy8WizF37twsd98QUvYQ8jaR67C9vT0iIm677bY4depU9Pb2TsugyrqHv/76a/T398fAwEBs3LgxIiIuXLgQ1Wo1isVi7Nu3L+69995JmR0AyK9TMr3kr6WlJTo6OmL//v2XHd+/f3/ceeed495m9erVY87ft29fdHZ2xlVXXZXl7htCyh5C3vK6DqvVapw7dy7v8a4IWfewra0tjh49GqVSafRXd3d3LF26NEqlUqxatWqyRgcAIr9OyfySv56ennj88cejs7MzVq9eHTt37ozjx49Hd3d3RERs2bIlfvrpp/jwww8j4uI7ZWzfvj16enri6aefjr6+vnj//ffjk08+yXrXDSPrHkbE6LuAlcvl+Pnnn6NUKkVLS0vceuutU/I9cOXLeh3u2LEjFi9eHMuWLYuIi59L9cYbb8Rzzz03Zd/DVMuyh01NTbF8+fLLbn/ddddFa2vrmOMAQHblcjm+++670a8HBwejVCrFnDlzYvHixTXrlMxB9eijj8Yvv/wSr776apw8eTKWL18ee/fujSVLlkTExQ+h/fNnsLS3t8fevXvjhRdeiB07dsSCBQvi7bffjkceeSTrXTeMrHsYEXH77beP/v7w4cOxe/fuWLJkSfzwww+TOToNJOt1eOHChdiyZUsMDg5GsViMG264IV5//fV45plnpupbmHIpj2UAoDb6+/vjnnvuGf26p6cnIiKefPLJ2LVrV806JfPnUAEAAHBRpv9DBQAAwP8JKgAAgESCCgAAIJGgAgAASCSoAAAAEgkqAACARIIKAAAgkaACAABIJKgAAAASCSoAAIBEggoAACDR/wD0sjs0OuVTTAAAAABJRU5ErkJggg==\n",
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1156,7 +1156,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1238,7 +1238,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1281,7 +1281,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1352,7 +1352,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1426,7 +1426,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1436,7 +1436,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1446,7 +1446,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1456,7 +1456,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -1537,7 +1537,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.8.3"
   }
  },
  "nbformat": 4,

13-Smoothing.ipynb

@@ -80,7 +80,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -105,7 +105,7 @@
    "source": [
     "After a period of near steady state, we have a very large change. Assume the change is past the limit of the aircraft's flight 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",
+    "* 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",
@@ -127,7 +127,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -157,7 +157,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -201,7 +201,7 @@
     "\n",
     "* Fixed-Interval Smoothing\n",
     "\n",
-    "This is a batch processing based filter. This filter waits for all of the data to be collected before making any estimates. For example, you may be a scientist collecting data for an experiment, and don't need to know the result until the experiment is complete. A fixed-interval smoother will collect all the data, then estimate the state at each measurement using all available previous and future measurements. 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",
+    "This is a batch processing based filter. This filter waits for all of the data to be collected before making any estimates. For example, you may be a scientist collecting data for an experiment, and don't need to know the result until the experiment is complete. A fixed-interval smoother will collect all the data, then estimate the state at each measurement using all available previous and future measurements. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters as it will provide much better results than the recursive forms of the filter from the previous chapters.\n",
     "\n",
     "\n",
     "* Fixed-Lag Smoothing\n",
@@ -286,7 +286,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -360,7 +360,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAFfCAYAAAAcfTnAAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/d3fzzAAAACXBIWXMAAA9hAAAPYQGoP6dpAACSTUlEQVR4nOzdd1hURxfA4d/SQZoNEAVRwYIa7AV7wW7s3YglNhRiNPbYEmPsBey9a6yxxN6NXey9IHZF6VIXdr8/9nPjCiZKEZHzPo9P9t6ZO3dmgngYzp2rUKvVaoQQQgghhBBfBL2M7oAQQgghhBDiHxKgCyGEEEII8QWRAF0IIYQQQogviAToQgghhBBCfEEkQBdCCCGEEOILIgG6EEIIIYQQXxAJ0IUQQgghhPiCGGR0B96nUql49uwZFhYWKBSKjO6OEEIIIYQQaUKtVhMZGYm9vT16eh9eJ//iAvRnz57h4OCQ0d0QQgghhBAiXTx+/Jh8+fJ9sPyLC9AtLCwATcctLS0/+/2VSiX79u2jXr16GBoafvb7Z2Yyd6kj85dyMncpJ3OXcjJ3qSPzl3IydymX0XMXERGBg4ODNt79kC8uQH+b1mJpaZlhAbqZmRmWlpbyRf+JZO5SR+Yv5WTuUk7mLuVk7lJH5i/lZO5S7kuZu/9K45aHRIUQQgghhPiCSIAuhBBCCCHEF0QCdCGEEEIIIb4gEqALIYQQQgjxBZEAXQghhBBCiC+IBOhCCCGEEEJ8QSRAF0IIIYQQ4gsiAboQQgghhBBfkFQF6L///jsKhYIBAwZoz6nVasaOHYu9vT2mpqbUrFmT69evp7afQgghhBBCZAkpDtDPnTvHwoUL+eabb3TOT548menTpzN79mzOnTuHnZ0dHh4eREZGprqzQgghhBBCpJRSqeTvv/8mLCwso7vyrwxSctGbN2/o1KkTixYtYvz48drzarWamTNnMnLkSFq2bAnAihUrsLW1Ze3atfTu3TtJW3FxccTFxWmPIyIiAM0EKpXKlHQvVd7eMyPundnJ3KWOzF/KydylnMxdysncpY7MX8pl1bmLiIjg0KFDhIaGkidPHmrVqoWxsfFHXfvq1SuWLFnC/PnzefbsGTlz5mTQoEHp3OOkPvb/mUKtVqs/tXFPT09y5MjBjBkzqFmzJqVKlWLmzJkEBARQqFAhLly4QOnSpbX1mzVrhrW1NStWrEjS1tixYxk3blyS82vXrsXMzOxTuyaEEEIIIb4i8fHxrF69mn379hEbG6s9b2VlRYsWLWjWrBkKhSLZawMCAvjrr784duyYTnBsa2vL3Llz0dfXT/f+vys6OpqOHTsSHh6OpaXlB+t98gr6+vXr8ff35/z580nKXrx4AWgG/S5bW1sePnyYbHvDhw9n4MCB2uOIiAgcHByoV6/ev3Y8vSiVSvbv34+HhweGhoaf/f6Zmcxd6sj8pZzMXcrJ3KWczF3qyPylXFaau/j4eJo3b86BAweSlIWHh7N8+XLMzMyYOXOm9nxCQgLbtm1jzpw5/P333zrXKBQKypcvz5gxY6hbt+4HA/v08jZT5L98UoD++PFjfvjhB/bt24eJickH670/WLVa/cEJMDY2TvbXE4aGhhn6RZfR98/MZO5SR+Yv5WTuUk7mLuVk7lJH5i/lssLczZs3TxucGxsb4+npiZubG0eOHGHjxo0AzJ07l1atWuHm5saiRYuYO3cujx8/1mnHysqK77//nl69enHz5s0M++HmY+/5SQG6v78/QUFBlC1bVnsuMTGRY8eOMXv2bG7fvg1oVtLz5MmjrRMUFJRkVV0IIYQQQogPUavVzJ49W3u8Z88eatasCYCXlxdz586lX79+AHTv3p2XL1/qpMAAFCtWDB8fHzp37oy5uTlKpZKbN29+tjGk1CcF6HXq1OHq1as657p160bRokUZOnQoBQsWxM7Ojv3792tz0OPj4zl69CiTJk1Ku14LIYQQQoiv2osXL7h79y4A7u7u2uAcNGksuXPnxsDAgISEBJ1UaoVCQZMmTfDx8aFOnTqfPY0lLXxSgG5hYUGJEiV0zmXLlo2cOXNqzw8YMIAJEybg4uKCi4sLEyZMwMzMjI4dO6Zdr4UQQgghxFctPj5e+zlnzpwAhISEsGTJEubMmZPk+UZLS0t69OhBv379KFSo0Gfta1pL0TaL/2bIkCHExMTg5eVFaGgoFStWZN++fVhYWKT1rYQQQgghxFcqT548WFhYEBkZyb59++jSpQubNm0iJiYmSV1HR0euX7+Oubl5BvQ07aU6QD9y5IjOsUKhYOzYsYwdOza1TQshhBBCiCxKX1+fatWqsWvXLuLi4li1apVOubGxsfZdOiNHjvxqgnNIxZtEhRBCCCGESGuhoaFMmzYNZ2dndu3apVuoZwD6HYAS2uDczc2NLl26fP6OpqM0T3ERQgghhBDiU924cQM/Pz9WrlxJdHS0Tpmeni0q1U/gag42j+FQTaA37u7ubNmy5V+3/86MJEAXQgghhBD/KTw8nM2bNxMYGEi2bNlo0KABbm5uqWozMTGRXbt24evrm+zLiMzzuvLGoAmqh78Delg9DcDKYRy1u4bg6XmYGjVqZMpdWv6LBOhCCCGEEOKDVCoV48ePZ/LkyURFRWnPDxs2jBo1arBixQry58//SW2Gh4ezbNky/Pz8CAgI0CkzNjZH374s0dVv8abADQiPpEnAr/zoY0StWgVRKFakybi+ZBKgCyGEEEKIDxo4cCCzZs1Ktuzo0aNUrVqVM2fOYG9v/59t3bp1i9mzZ7N8+XKdYB/A2rogUTnLEFf/JNgcBSCbKi+D6w5jeH0w0k/9WDILCdCFEEIIIUSy/P39tcG5np4e33//Pd9++y33799n2rRpPHr0iCdPnvDzzz+zdOnSZNtQqVTs2bMHX19f9u7dm6Tczq4eL/UrE9ZmCVhvAsBSYc+omiPo794DE4OvK7/8Y0iALoQQQgghkjV//nzt50mTJvHTTz9pj9u1a0fhwoWJiIhg3bp1TJ8+HWtra215REQEy5cvx8/Pj3v37um0q69vjKXld4SGDuTFi2KQ9wxYjyOHgT1j6gynV7nvs2Rg/pYE6EIIIYQQIlnnzp0DNKvnffv21SmztbWlTZs2LFmyhNjYWK5du0bVqlW5c+cOs2fPZtmyZbx58+a9Fq1A4UVicVtCLWNQnChEy5ZvGDmyIoEmW2jo0jBLB+ZvSYAuhBBCCCGSpVarAc2LKPX0kr4+x8Dgn1Dy9OnTTJgwgd27dyfTUhEw+RHKBkP5hWD9EJQGqC9Nw9/fHEfH85TO2SK9hpHpyIuKhBBCCCFEskqXLg1otkNctmyZTlloaCgbNmzQHg8ePFgnODc2NsU6ewcoMAs6uMCQfuAxEqwfYqVvTc6LVhD7msDAQKZNm/Z5BpRJSIAuhBBCCCGS1atXL+3nAQMGMGTIEE6cOMGUKVMoVKgQoaGhSa7JkSM/uXNPIS7uCWFFy4HnD1BkJ+glUsWhCku+XcLzoc84P+c8Bv9P5li8eDGJiYmfbVxfOklxEUIIIYQQyXJ3d6dbt24sW7YMpVLJlClTmDJlSrJ18zlWJ8isJCFxTeBBAywt4c2NSFSV9cn+xJKTc05SNFdRbX0nJydq1qzJgQMHePXqFUFBQeTJk+dzDe2LJgG6EEIIIYT4oOnTp/Pw4UMOHTqUpEyh0CeXUz1eORnxpPIBMDqG6fNbTCregK5dIU+eKUTNSMQ0jymFcxROcv27D5G+m8+e1UmKixBCCCFEFqJUKj8qnSQgIIBBgwbh5OSUJDg3Ns2OWXEP1N0L8MpzN9TYBkZR5DUuzNjO9enfX42FBVSuXBnU8OzZM/744w+dNk6cOMHp06cBcHFxIVeuXGk3yExOflQRQgghhPjKRUREMH/+fBYtWsS9e/fQ09OjatWq9OvXj9atW2t3aFGr1Rw6dAhfX1927Nih3cXlLSenGoSF+RDWdBYU2g+AgcqMJgXaMah2d6o4VEGhUGjre3l5ceDAAQC6dOnCkSNHqFGjBhcuXGDevHk69d69LquTAF0IIYQQ4iv25MkT6taty+3bt7XnVCoVx44d49ixY7Rv35758+ezfv16fH19uXHjhs71RkbG5HVqxuNHgwgMrACA9aNILJ2V/FizBz0qtsXC2CLZezdv3pz27duzfv16EhISWLhwIQsXLtSpU7169SR7rGd1EqALIYQQQnyl1Go1LVq00AnOy5QpQ2hoKA8ePABg/fr1/Pnnn8TGxupcmzNnPsytu/EwbygPqi+CQ+Uor6zAgAHQqlUXjI09//P+CoWCVatW4eTkhJ+fH1FRUdoyIyMjunTpwsyZMzE2Nk6bAX8lJEAXQgghhPhKHTp0iPPnzwOaXVN27tyJq6srhw8fZtiwYdo3hb4bnBcsWJU30V4EOTwnuNYEMAsGoFqnExztOxhNJsrHp6MYGBjw+++/M3z4cHbu3MnLly/Jnj07jRo1wsbGJs3G+jWRAF0IIYQQ4iv17oOZv/zyC6dOnaJDhw5cvXo1Sd18+VoSHDKCANN70GQE5AgAwNm6GDMaTqaxS2NSkyZuaWlJx44dU95AFiIBuhBCCCHEVyooKEj72cfHh7CwMJ3ybNlyEBXVEJjKkyd24DEEqmj2ObfNZsevtX6hW+luGOhJyPg5yTaLQgghhBBfGbVazbFjx7h8+bL23LvBubOzO46O64mKegGsAuwoXfoFi/p1x8rYinE1x3HP5y49y/aU4DwDyIwLIYQQQnwG4eHhrFq1imPHjhEXF4erqyvdu3fHxcXlk9pRq9VJtj98KyYmhnXr1uHr66sTnGsoKFKkLS9f/sS9e+XA/AU06QPqO5gdjubo0SNYWNjRoeFTshllS+EoRVqQAF0IIYQQIp1t3LiRHj16EBkZqT23fft2Jk6cSL9+/Zg5c+a/vklTqVSycuVKFixYwIULF1Cr1ZQuXZo+ffrg6enJixcvmDdvHgsLine truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -387,7 +387,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAFfCAYAAAAh71imAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/d3fzzAAAACXBIWXMAAA9hAAAPYQGoP6dpAADFd0lEQVR4nOzdd1QUVxvH8e/SixQ7oogNe++9i4oF22I39q4xatSYmGA0tjdRoyb2HhuIvfdu7L33ggUbqNSFnfePDRMI2JBlUZ/PORx3Z+7OPDui/Lh7516NoigKQgghhBBCiE+SmakLEEIIIYQQQiSdBHohhBBCCCE+YRLohRBCCCGE+IRJoBdCCCGEEOITJoFeCCGEEEKIT5gEeiGEEEIIIT5hEuiFEEIIIYT4hFmYuoCPpdfrefDgAQ4ODmg0GlOXI4QQQgghRLJQFIVXr17h6uqKmdmb++E/+UD/4MED3NzcTF2GEEIIIYQQRnHv3j2yZcv2xv2ffKB3cHAADG/U0dExxc+v0+nYtm0bnp6eWFpapvj5P2Vy7ZJOrt3HkeuXdHLtkk6uXdLJtfs4cv2SztTX7uXLl7i5ual5900++UAfO8zG0dHRZIHezs4OR0dH+UfygeTaJZ1cu48j1y/p5NolnVy7pJNr93Hk+iVdarl27xpWLjfFCiGEEEII8QmTQC+EEEIIIcQnTAK9EEIIIYQQnzAJ9EIIIYQQQnzCJNALIYQQQgjxCfvkZ7kRQgghhBCpj06n49SpU7x69Qo3Nzfy5s1r6pI+W9JDL4QQQgghko1Op+OXX34he/bslCtXjtq1a5MvXz7KlSvH5s2bTV3eZ0kCvRBCCCGESBY6nY5mzZrxww8/8OjRo3j7jh49ipeXF3PmzDFRdZ8vCfRCCCGEECJZ/P7772zYsAEwLIbk7e3NkCFDKFKkiNqmZ8+eXLt2zVQlfpYk0AshhBBCiI8WExPD1KlT1efbtm1jzZo1jB8/njNnztCrVy+13fTp001V5mdJAr0QQgghhPhoV69e5e7duwDUqVOH2rVrq/s0Gg2jRo3C3NwcgK1btxq1liNHjtCpUycKFixIgQIFaNOmDXv37kVRFKOe11RklhshhBBCCPHRQkND1cc5c+ZMsD9dunQ4Ojry4sWLeG2Tk16v5+uvv2batGnxtl++fJlly5bRpk0bFixYgKWlpVHObyoS6IUQQgghUqkHDx5w8+ZNbG1tKVy4MNbW1qYu6Y2yZ8+ORqNBURQ2b95MVFQUVlZW6v4DBw7w4sULIPHAnxx+/vnneGHe0tISMzMzIiMjAVi6dClp06ZNEPg/dTLkRgghhBAilTl+/DheXl5ky5aNKlWqULp0adzc3Pjhhx8IDw83dXmJypQpE15eXgDcu3ePVq1acevWLRRFYfv27XTo0EFt27Fjx2Q/f0hICL/++isAZmZmTJo0ieDgYF6+fMmcOXPUX4ZmzJhBYGBgsp/flCTQCyGEEEKkIlu3bqVy5cps3rw53pjvJ0+e8Msvv1CnTh3CwsJMWOGb/fjjj2qv/OrVq8mVKxdWVlZ4enpy+/ZtAAoXLkzLli2T/dwBAQHqUJ6uXbsyYMAA7OzssLKyokuXLgwaNAgw3JS7ZMmSZD+/KUmgF0IIIYRIJYKDg2nVqpU6RCR79uz07duXZs2aqTeUHjx4kBEjRpiyzDcqW7YsAQEB2Nvbq9uio6PVx8WKFWPLli3Y2Ngk+7ljb8gFaNiwYYL9cbfduXMn2c9vSjKGXgghhBAilVi4cCHBwcEANGjQgFWrVqk93idOnKBixYpERUUxZ84cRo4cSZo0aUxYbeIaNmzIzZs3mTNnDps2beLly5dkz56dDh060LRpU6PdkBr3Wly/fj3B/rhz36fG6/YxUqyHfuzYsWg0GgYMGKBuUxQFX19fXF1dsbW1pXr16ly4cCGlShJCCCGESFW2bNmiPh47dmy8m0pLlSpF69atAXj58iWHDh1K8freV6ZMmRg+fDgHDhzg7NmzbNiwAR8fH6POLlOvXj318W+//RZvnPyzZ88YO3as+jx2rP/nIkUC/bFjx5g1axZFixaNt33ChAlMnDiRadOmcezYMVxcXKhTpw6vXr1KibKEEEIIIVKV169fq4/z5MmTYH/cbXHbCsPY/Ni57wMDA8mXLx8dOnSgS5cu5MmTh8uXLwNQvHhxqlataspSk53RA/3r169p27Yts2fPJm3atOp2RVGYPHky33//Pc2aNaNw4cIsXLiQsLAwli5dauyyhBBCCCFSHXd3d/Xx+vXr4+1TFIWNGzcm2lYYzJ8/nxw5cgCGefEX/3WaefP06jCmTJkysXz5cjQazTuP9fDhQ/78808mTJiQ6hekMvoY+j59+tCgQQNq167N6NGj1e23bt3i0aNHeHp6qtusra2pVq0ahw4dokePHokeLzIyUr1RBAwfOQHodDp0Op2R3sWbxZ7TFOf+1Mm1Szq5dh9Hrl/SybVLOrl2SfclXbu2bduqM7D069cPKysr6tevz/Pnz/nll1/4+++/AShUqBBFihR5r2vyJV2/zJkzs3//fn4YMY7FF56gL34DFvyGJSdo2bIYvr6+ZM+e/Y3X4tGjR6xevZqVK1dy4MABNcgfOnSISpUqpeRbAd7/78yogX758uWcOHGC48ePJ9j36NEjwHDh48qcOfNb7zweO3YsI0eOTLB927Zt2NnZfWTFSbd9+3aTnftTJ9cu6eTafRy5fkkn1y7p5Nol3Zdw7fR6PYUKFeLChQsEBQXRtGlTrK2tiYqKitdL3KhRIzZv3vxBx/4Srh/AwaNOLA8PRt/AD4AsDX9leE1f3NzMOX/+POfPn4/X/sWLFxw+fJiDBw9y8eLFRHvjZ8+eTUhISEqUH8/7Tk9qtEB/7949vv76a7Zt2/bWqYn++5GHoihv/Rjku+++Y+DAgerzly9f4ubmhqenJ46Ojh9f+AfS6XRs376dOnXqfHbLCBubXLukk2v3ceT6JZ1cu6STa5d0X9q1q1ixIk2bNuXw4cMA8UYmmJubM2nSJHr27Pnex/tSrt/9+9Bt6C12ptdCgbOgN+OrbL8w67uBCbLl48ePWbNmDStXrmTfvn2JhngPDw+aNWtGlixZ6Nq1a7wblFNK7EiUdzFaoD9x4gRBQUGUKlVK3RYTE8O+ffuYNm0aV65cAQw99VmyZFHbBAUFJei1j8va2jrRZY8tLS1N+k1q6vN/yuTaJZ1cu48j1y/p5NolnVy7pPtSrl3mzJnZt28f69evZ968eVy7dg1bW1tq1apFz549E71Z9n18rtcvOhqmTYPvFqwlon4HsHmJnZIJ/1bL8SpQQ20XFBTEqlWr8PPzY+/evej1+gTH8vDwwMfHBx8fH4oUKUJ0dDSbNm3CysrKJNfufc9ptEBfq1Ytzp07F29bp06dyJ8/P0OHDiVXrly4uLiwfft2SpQoAUBUVBR79+5l/PjxxipLCCGEECLVs7CwoGnTpjRt2tTUpaRqx49Djx5w8iTguQ9sXlI8XUU2fOVHVsesaoj39/dnz549iYb4PHnyqCG+aNGi73XDbGpjtEDv4OBA4cKF422zt7cnffr06vYBAwYwZswYPDw88PDwYMyYMdjZ2dGmTRtjlSWEEEIIIT5xL1/CDz/AH3+AXg/OzjCm2TiiirmjzdGC9cvW4+/vz+7du98Y4rVaLT4+PhQrVuyTDPFxmXSl2CFDhhAeHk7v3r158eIF5cqVY9u2bTg4OJiyLCGEEEIIkQzWXl7LnFNzqJe7Hi0LtySDXYaPOp6iQEAAfP01PDA/BM0n09pqCd9/F8zBg6vZMGI9g3YPJCYmJsFrc+fOjY+PD1qtluLFi3/yIT6uFA30e/bsifdco9Hg6+uLr69vSpYhhBBCCCGM7ELQBVoHtCY8OpwNVzcwYOsAvDy8aFekHU3yN8HS/MPGpN++DX37wsaNCpSbClUGwpUYjt46SbFitxMN8bly5VJDfIkSJT6rEB+XSXvohRBCCCHE5ydMF4bPSh/Co8Mp7VqaGH0Mpx6dYt2Vdey/s5/G+Rq/97F0Opg0CUaOhDDdHSjVAp4ch98ABW5wI177nDlzqiG+ZMmSn22Ij0sCvRBCCCGESFZmGjOquVfjefhzNrbZSCb7TFwIusCSc0uwMrfC2sIwY6GiKNRaVIvy2crTvmh7CmQsEO84hw9Dly7PuHRpDVjOh+iDcCLh+XLkyKGG+FKlSn0RIT4uCfRCCCGEECJZ2VjY8GeDPxlVYxTp7dIDUChTIcbUGhOv3eH7h9l9eze7b+9m7IGxlMxSkvZF21MhTV2G9TvMnj1+wE4gGv6zaKq7u7s6O82XGOLjkkAvhBBCCCGSxZPQJ6SzTYe5mTmAGubfpGSWkvi18OOvc3+x8exGTm46ycn/nYSbQMLJabBOb02Xdl3o2LYjpUuX/qJDfFwS6IUQQgghxEeLjI6k/pL6OFg7sLTZUrI4ZHnna8JfhRN6LBSdnw62ayA6YZvs2bMbbmqtVQIfT58Pvpn2SyCBXgghhBBCfLRhO4Zx4uEJ0tmmI0ZJOONMrBcvXrB27Vr8/f3Zvn07Op0uQZs0TlkoVjcP//tmPOXLlZee+HeQQC+EEEIIIT7K+ivrmXxkMgALvBeQzTFbvP3BwcFqiN+2bVuiIR6y4eam5ddffWjRoixmZmbGL/wzIYFeCCGEEEIk2b2Qe3Rc2xGAAeUG0ChfIwBCQkLUEL9169Y3hnhogZOTD7//Xo4OHcyQzvgPJ4FeCCGEEEIkcOvWLVavXs3Tp0/JmDEjzZs3J3v27PHaROujabOqDc/Dn1MqSym+K/MdixcvVkN8VFRUguOmS5eViAgtYWFaoDydO5sxYQKkf/v9s+ItJNALIYQQQgjVy5cv6d69O35+fiiKom4fPHgwbdu2Zfr06djb2wMwet9oDlw9gM0NG5z+dsKtn1uiId7V1RVPTy0XL2o5erQCYEb+/DBjBlSrllLLine truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -425,7 +425,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -463,7 +463,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 800x200 with 1 Axes>"
       ]
@@ -510,7 +510,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 900x400 with 1 Axes>"
       ]
@@ -585,11 +585,9 @@
    "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",
+    "- [1] H. Rauch, F. Tung, and C. Striebel. \"Maximum likelihood estimates of linear dynamic systems,\" *AIAA Journal*, **3**(8), pp. 1445-1450 (August 1965). http://arc.aiaa.org/doi/abs/10.2514/3.3166\n",
     "\n",
-    "[2] Dan Simon. \"Optimal State Estimation,\" John Wiley & Sons, 2006.\n",
-    "\n",
-    "http://arc.aiaa.org/doi/abs/10.2514/3.3166"
+    "- [2] Dan Simon. \"Optimal State Estimation,\" John Wiley & Sons, 2006."
    ]
   }
  ],
@@ -610,7 +608,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,