Explained IMM requires all x to have same shape.

IMM will not work if the x attribute in the filters have
different shapes.

14-Adaptive-Filtering.ipynb

@@ -16,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -255,7 +255,7 @@
        "<IPython.core.display.HTML object>"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -302,7 +302,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -370,7 +370,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -397,14 +397,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAicAAADvCAYAAAApdHQtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzs3XlYlNfZ+PHvAMO+74ssiiyCuLKomGoMMcZds2jiFpu+Jt3St2/TJmmTxqZ2Td/UvElrkppEE2uMW1yqRoNrIgqyyCYKgqAIsq/DDDAzz+8PfkxCxGhaHRDuz3VxXcyznLnPGeC6Oec856gURVEQQgghhOgnLPo6ACGEEEKIr5LkRAghhBD9iiQnQgghhOhXJDkRQgghRL8iyYkQQggh+hVJToQQQgjRr0hyIsRd7K233sLR0bGvwxBCiNtKkhMh/gMqleobv0JCQvo6RLN4/vnnUalUJCYmXnfu9OnTpvaora3tg+gGpuTkZFQqFdeuXevrUIS47SQ5EeI/UFlZafravXs3AGlpaaZjZ86c6fW+jo4Oc4ZpFr6+vqSnp5Ofn9/j+DvvvENwcHAfRfXtDcTPRoi7jSQnQvwHfH19TV/u7u4AeHl5mY55eXmZrvvNb37DqlWrcHd357777gPgL3/5C6NGjcLBwQF/f3+WLl1KdXV1j/e4cOECCxYswM3NDXt7e8aMGcOhQ4d6jaetrY3Zs2czZswYKisrrztfV1eHjY0NO3fu7HG8tLQUCwsLjh07BsD27dsZPXo09vb2uLm5MXHiRPLy8r6xLTw8PJg3bx7r1683HWtubmbr1q08+eST111//vx55s2bh4uLC+7u7syYMYNz586ZztfU1PDYY48RGBiInZ0dkZGRvPHGGz3KyM7OJikpCVdXVxwcHIiKiuLjjz8GQKfToVKp2L59e497Jk+ezNNPP216faPPprm5mR/+8If4+fnh4OBAbGwse/fu7RG/SqVi69at3HfffdjZ2REVFUVKSgplZWVMnz4dBwcHYmJiOH369Leqe/dw3bFjx0yfQ0JCAtnZ2ab777//fgD8/PxQqVTMmDHjpm0ixN1CkhMhzOR///d/CQ4OJjU1lXfeeQcACwsL1q5dS15eHtu2baOwsJBly5aZ7ikvLycxMRGdTsf+/fvJzc3l17/+da/l19bWMm3aNNra2jhx4gR+fn7XXePh4cHMmTPZuHFjj+ObNm0iKCiIKVOmcPnyZRYvXsx3v/td8vPzOXnyJD/4wQ+wtLS8aR1XrVrFBx98QHt7u6nc4cOHExcX1+O6q1evMnnyZEJCQjh58iQpKSkEBwdz77330tDQAIBWq2X8+PHs2bOHc+fO8fzzz/OLX/yCjz76yFTOI488wpAhQzh16hS5ubm8+uqrODs73zTOr/v6Z2M0GnnwwQe5cOECO3bsICcnh5UrV7Jw4UK++OKLHve++OKL/PSnPyU7O5uQkBAee+wxVq5cyY9//GOysrIICQlhyZIlGAyGW647QHt7O6tXr2bdunWkp6djb2/P4sWLMRqNhIWFsXXrVgBycnKorKw0tcvtahMh+pQihLgtPv/8cwVQLl26dN05Hx8fZebMmTctIyUlRQGU2tpaRVEU5dlnn1WGDBmiaLXaXq9ft26d4uDgoJSUlCjh4eHKo48+qrS3t3/je3zyySeKWq1WampqTMfCw8OVF1980RSDSqVSKioqbhpvt+eee06Jjo5WjEajEhoaqmzevFlRFEUZM2aM8re//U05cOCAApje87nnnlOmTJnSowyDwaAEBAQo69atu+H7rFq1Spk9e7aiKIpiNBoVGxsb5aOPPur1Wq1WqwDKtm3behxPTExUnnrqKdPr3j6bAwcOKPb29kpra2uP44899piyaNEiRVEUpaCgQAF6xHvixAkFUN58803Tse7PtKio6Jbrvm7dOgVQ8vPzTdccPXpUAZTS0lJFURTls88+UwClsrLSdM3N2kSIu4X0nAhhJvHx8dcdS05O5v777ycwMBAnJyeSkpIAKCsrAyAjI4N77rkHW1vbG5bb0dHBpEmTSEhIYMuWLVhbW39jHLNmzcLZ2dn0n3ZqaiqFhYUsX74cgLi4OKZMmUJERAQPPfQQb7zxBlevXr2lOqpUKr73ve/xj3/8g7S0NAoLC1myZMl11505c4aTJ0/i6Oho+nJ2dqayspKioiIA9Ho9a9asYdSoUXh4eODo6Mj7779vahuVSsWzzz7LsmXLmDZtGq+88opp2OPb+vpnc+bMGbRaLT4+Pj1i3L59uym+bqNHjzZ97+vrC8CoUaOuO9Y9XHcrdQewsbFhxIgRptcBAQEAVFVV3bAet7NNhOhLkpwIYSYODg49Xl+8eJHZs2cTERHBxx9/THp6Otu2bQN6TspUqVTfWK5arWbGjBkkJydz/vz5m8ahVqt57LHH+OCDDwD44IMPmDhxImFhYQBYWVlx5MgRDh06xNixY9myZQthYWF89tlnt1TPlStXcvLkSZ5//nkeffRRXFxcrrvGaDQyc+ZMzp492+PrwoULvPDCCwD84Q9/4LXXXuNnP/sZycnJnD17luXLl/domzVr1lBQUMDChQvJysoiLi6O3/72t0DXkBmA8rWN1zs7O6+L5+ufjdFoxNvb+7r4zp07x65du65rz27dn1Vvx4xG4y3XHbo+h69+9l8v50a+qU2EuFtIciJEH0lNTaWzs5O1a9cyadIkIiIirnssdPz48Zw4cQKdTnfDclQqFe+99x6zZ89m6tSpN524CrB8+XLS09PJycnh448/ZsWKFdeVOWHCBF588UVOnjxJfHw8GzZsuKV6+fj4MHfuXI4ePcp//dd/9XpNbGwseXl5BAUFMXz48B5fnp6eAJw4cYI5c+awYsUKxo4dy/Dhw6/rtQAYPnw4P/rRj/jkk0/45S9/yVtvvQWAtbU1Li4uVFRUmK5ta2vjwoULN61DbGws1dXVKIpyXXyBgYG31A7fVPbN6n4runvIuueyfNWN2kSIu4UkJ0L0kfDwcIxGI3/961+5dOkSO3bs4A9/+EOPa5555hk0Gg0LFizg1KlTlJSUsGfPnut6MVQqFW+//TaPPPII995770278uPi4oiKimLFihW0trayaNEi07ljx47x+9//nrS0NC5fvsyhQ4c4d+4cUVFRt1y3Dz74gJqaGiZNmtTr+f/+7/+mtbWVhQsXcvLkSUpLS/n88895/vnnSU9PByAiIoLk5GQ+//xzLly4wC9+8QvOnj1rKqO+vp5nnnmGo0ePUlpaSkZGBp999lmPOJOSknjzzTdJTU0lNzeX5cuX37TnAeDBBx9k8uTJzJ07lz179nDp0iXS09NZu3btLSdpN3Irdb8V3Wvo7Nu3j+rqapqbm2+pTYS4G0hyIkQfiYuL47XXXuP1118nKiqKN954g7/+9a89rgkMDOSLL75ArVbzwAMPEBMTw8svv9xreSqVijfffNM03yAjI+Mb33/58uWcPXuWOXPm4Orqajru5uZm6rUICwtj1apVPPnkkzz33HO3XDc7O7tv7AUICAjg1KlTODo6Mm/ePCIiIli2bBkVFRX4+PgA8Jvf/IaEhARmzpxJYmIiHR0dPR4Btra2prq6mpUrVxIREcHMmTMJCQkxDVcBrF27luHDh5OUlMTs2bN58MEHe8wHuRELCwsOHDjArFmz+PGPf0xERASzZ8/m0KFDDBs27Jbb4d+t+60ICgrit7/9LatXr8bX15dHH330ltpEiLuBSvn6gKwQQgghRB+SnhMhhBBC9CuSnAghhBCiX5HkRAghhBD9ilVfB3Crmpqa+joEIYQQQtxmva2FJD0nQgghhOhXJDkRQgghRL9y1wzrfFVvXUCDQfcCTbGxsX0cSf8hbdI7aZfeSbv0Ttqld9Iu17tdbXKzqRrScyKEEEKIfuWu7DkRQoi7VUNDAxkZGdTU1ODi4sK4ceNMOxcLIbpIciKEEGZSVFTExx9/jF6vNx1LS0tj5syZxMfH92FkQvQvMqwjhBBm0NnZyc6dO9Hr9YwYMYJHHnmEuLg4AA4cOEBDQ0MfRyhE/yE9J0IIYQZFRUVotVr8/Px49NFHUalUREdHo9PpyM3NJScnhylTpvR1mEL0C9JzIoQQZtDW1gaAt7c3KpXKdLx7J+Lu80IISU6EEMIs/Pz8ALhw4YLpMUqdTkd2djYA/v7+fRabEP2NDOsIIYQZ+Pv7M3ToUC5dusQbb7xBYGAg165dQ6vV4ubmRlRUVF+HKES/IT0nQghhBiqVikcffZTIyEj0ej2XLl1Cq9UyZMgQli9fjlqt7usQheg3pOdECDHo6XQ6UlJSOHfuHAaDgaFDh5KYmIiHh8dtfR87OzsWL15MQ0MDtbW1ODs7m+acCCG+JMmJEGJQ0+l0vPvuu9TU1JiONTQ0kJ+fz8qVK+/IAmlubm64ubnd9nKFGCgkORFCDGqnTp2ipqYGT09PZs2ahZ2dHUeOHKGwsJCDBw+yYsUK07WdnZ3k5ORw6dIlLC0tiYyMJCIiAgsLGSEX4naS5EQIMagVFBQAMHPmTIYOHQrAwoULefXVV7l06RI6nQ5bW1s0Gg0bN26kurradG92djbh4eEsWrQIS0vLPolfiIFI0n0hxKDWvZS8ra2t6ZharTYlGwaDAYDPPvuM6upqPDw8mD17NtOnT8fOzo7CwkLS0tLMH7gQA5gkJ0KIQa27t+TIkSNotVoMBgPHjh2jo6MDb29v7O3t0ev15OXlAbBkyRJiY2OZNGkSc+fOBTCtVfJ1e/dCfb156iHEQCLDOkKIQS0xMZH8/HwuXrzIX/7yFywtLeno6ABg2rRpqFQqOjo60Ov1WFtb95jI2v2kjUaj6VGmosDvfgcvvQQ//Sm89pr56iPEQCA9J0KIQc3d3Z2VK1cSGhqKwWAw9ZgsXryYyMhIoOsRYBcXFzo6OsjJyQFAURTOnDkDfLn6K4BLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f27d3e7b8>"
+       "<matplotlib.figure.Figure at 0x28b96ef38d0>"
       ]
      },
      "metadata": {},
@@ -461,7 +461,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -498,16 +498,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 9,
    "metadata": {
     "scrolled": true
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f27d22198>"
+       "<matplotlib.figure.Figure at 0x28b96f04940>"
       ]
      },
      "metadata": {},
@@ -544,16 +544,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 10,
    "metadata": {
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f27d22e10>"
+       "<matplotlib.figure.Figure at 0x28b972314a8>"
       ]
      },
      "metadata": {},
@@ -587,14 +587,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28ba0978>"
+       "<matplotlib.figure.Figure at 0x28b96f2b588>"
       ]
      },
      "metadata": {},
@@ -625,14 +625,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28b28908>"
+       "<matplotlib.figure.Figure at 0x28b97d782b0>"
       ]
      },
      "metadata": {},
@@ -665,7 +665,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -688,14 +688,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28c04ba8>"
+       "<matplotlib.figure.Figure at 0x28b97d4e828>"
       ]
      },
      "metadata": {},
@@ -755,16 +755,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 15,
    "metadata": {
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28c1f470>"
+       "<matplotlib.figure.Figure at 0x28b98ddcba8>"
       ]
      },
      "metadata": {},
@@ -854,16 +854,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 16,
    "metadata": {
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f27d223c8>"
+       "<matplotlib.figure.Figure at 0x28b96f046d8>"
       ]
      },
      "metadata": {},
@@ -904,16 +904,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 17,
    "metadata": {
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28018ac8>"
+       "<matplotlib.figure.Figure at 0x28b9903da90>"
       ]
      },
      "metadata": {},
@@ -985,16 +985,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 18,
    "metadata": {
     "scrolled": true
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f27d34f60>"
+       "<matplotlib.figure.Figure at 0x28b99084080>"
       ]
      },
      "metadata": {},
@@ -1082,14 +1082,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28c2a2b0>"
+       "<matplotlib.figure.Figure at 0x28b99069a58>"
       ]
      },
      "metadata": {},
@@ -1109,14 +1109,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29e2df60>"
+       "<matplotlib.figure.Figure at 0x28b99053748>"
       ]
      },
      "metadata": {},
@@ -1136,14 +1136,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f2a072080>"
+       "<matplotlib.figure.Figure at 0x28b990f8908>"
       ]
      },
      "metadata": {},
@@ -1151,9 +1151,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29fba6d8>"
+       "<matplotlib.figure.Figure at 0x28b9913b860>"
       ]
      },
      "metadata": {},
@@ -1176,16 +1176,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 22,
    "metadata": {
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29d62be0>"
+       "<matplotlib.figure.Figure at 0x28b98e519b0>"
       ]
      },
      "metadata": {},
@@ -1193,9 +1193,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29d0b978>"
+       "<matplotlib.figure.Figure at 0x28b98e71860>"
       ]
      },
      "metadata": {},
@@ -1203,9 +1203,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28082a58>"
+       "<matplotlib.figure.Figure at 0x28b98e71c50>"
       ]
      },
      "metadata": {},
@@ -1213,9 +1213,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29d629b0>"
+       "<matplotlib.figure.Figure at 0x28b98df0dd8>"
       ]
      },
      "metadata": {},
@@ -1223,9 +1223,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29f30be0>"
+       "<matplotlib.figure.Figure at 0x28b99224d30>"
       ]
      },
      "metadata": {},
@@ -1289,14 +1289,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29f04048>"
+       "<matplotlib.figure.Figure at 0x28b993302e8>"
       ]
      },
      "metadata": {},
@@ -1415,16 +1415,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 24,
    "metadata": {
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29eaa0f0>"
+       "<matplotlib.figure.Figure at 0x28b992f20f0>"
       ]
      },
      "metadata": {},
@@ -1446,16 +1446,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 25,
    "metadata": {
     "scrolled": true
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29f39550>"
+       "<matplotlib.figure.Figure at 0x28b99410f28>"
       ]
      },
      "metadata": {},
@@ -1501,16 +1501,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 26,
    "metadata": {
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f2a0a1630>"
+       "<matplotlib.figure.Figure at 0x28b99233f28>"
       ]
      },
      "metadata": {},
@@ -1553,14 +1553,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28ba3e80>"
+       "<matplotlib.figure.Figure at 0x28b98df0278>"
       ]
      },
      "metadata": {},
@@ -1629,14 +1629,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f29d68588>"
+       "<matplotlib.figure.Figure at 0x28b98f12198>"
       ]
      },
      "metadata": {},
@@ -1699,7 +1699,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [
     {
@@ -1708,7 +1708,7 @@
        "array([0.7, 0.3])"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1738,7 +1738,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 30,
    "metadata": {
     "scrolled": true
    },
@@ -1747,7 +1747,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f2a0d4710>"
+       "<matplotlib.figure.Figure at 0x28b97d61128>"
       ]
      },
      "metadata": {},
@@ -1776,7 +1776,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [
     {
@@ -1786,7 +1786,7 @@
        "       [0.05, 0.95]])"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1819,7 +1819,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
@@ -1828,7 +1828,7 @@
        "array([0.694, 0.306])"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1865,7 +1865,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 33,
    "metadata": {},
    "outputs": [
     {
@@ -1874,7 +1874,7 @@
        "array([0.802, 0.198])"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1942,7 +1942,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
@@ -1952,7 +1952,7 @@
        "       [0.013, 0.886]])"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2005,14 +2005,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28ba33c8>"
+       "<matplotlib.figure.Figure at 0x28b98fd5748>"
       ]
      },
      "metadata": {},
@@ -2098,16 +2098,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 36,
    "metadata": {
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x19f28b22208>"
+       "<matplotlib.figure.Figure at 0x28b98fd50f0>"
       ]
      },
      "metadata": {},
@@ -2122,6 +2122,76 @@
     "plt.axis('equal');"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Limitations of the IMM\n",
+    "\n",
+    "I haven't extensively worked with the IMM, so I am unable to address this as well as I would like. However, the IMM was invented to track maneuvering aircraft for air traffic control, and by all reports it performs superbly in that role. \n",
+    "\n",
+    "That use case assumes a few things. Foremost among them is the requirement that all of the filters in the bank have the same dimensional design. A review of the math should show why. To create the mixed estimate the IMM performs this computation:\n",
+    "\n",
+    "$$\\mathbf x = \\sum_{j=1}^N \\mu_j{\\bar{\\mathbf x}}_j$$\n",
+    "\n",
+    "This is computable if and only if the state $x$ in each filter is of the same dimension. Furthermore, the interpretation of $x[i]$ must be the same for each filter. \n",
+    "\n",
+    "For example, suppose we tried to filter that uses a constant velocity model and another with a constant acceleration model. This doesn't work because the dimension of $x$ are different. `FilterPy` will raise a `ValueError` if you try to use filters with different dimensions."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "tags": [
+     "raises-exception"
+    ]
+   },
+   "outputs": [
+    {
+     "ename": "ValueError",
+     "evalue": "All filters must have the same state dimension",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[1;32m<ipython-input-38-e96cb02ea05b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      5\u001b[0m                   [0.03, 0.97]])\n\u001b[0;32m      6\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mimm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mIMMEstimator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mca\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcv\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrans\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[1;32mC:\\Users\\rlabbe\\Dropbox\\filterpy\\filterpy\\kalman\\IMM.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, filters, mu, M)\u001b[0m\n\u001b[0;32m     90\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mf\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mfilters\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     91\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mx_shape\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 92\u001b[1;33m                 \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'All filters must have the same state dimension'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     93\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     94\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_shape\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;31mValueError\u001b[0m: All filters must have the same state dimension"
+     ]
+    }
+   ],
+   "source": [
+    "ca = KalmanFilter(3, 1)\n",
+    "cv = KalmanFilter(2, 1)\n",
+    "\n",
+    "trans = np.array([[0.97, 0.03],\n",
+    "                  [0.03, 0.97]])\n",
+    "\n",
+    "imm = IMMEstimator([ca, cv], (0.5, 0.5), trans)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "I occasionally get emails or bug reports about this. In the past I have recommended designing the filter with constant velocity to be of dimension 3, and then implement `F` to ignore acceleration\n",
+    "\n",
+    "```python\n",
+    "F = np.array([[1, dt, 0],\n",
+    "              [0, 1,  0],\n",
+    "              [0, 0,  0]])\n",
+    "```\n",
+    "\n",
+    "In retrospect I am not sure if this is a sound recommendation. It allows the IMM to work, but clearly the estimate for acceleration will be incorrect, since one filter will have an accurate estimate of acceleration, and the other filter will have an estimate of 0. This inaccurate acceleration will then be used to perform the next predict cycle. \n",
+    "\n",
+    "Consider a more extreme case. Suppose one of your filters interprets `x[2]` to be acceleration, and another filter interprets it as angular rotation rate. Clearly `x[2]` of the mixed estimate will be meaningless since you cannot sum (linear) acceleration with a rotation rate.\n",
+    "\n",
+    "As I said I am not particularly well versed in the IMM. Perhaps the literature explains how to handle these situations. All I can say is that the IMM implemented by FilterPy will not work for these use cases.\n",
+    "\n",
+    "The IMM as designed for air traffic control uses filters with different process assumptions. An aircraft can be flying level, it can be descending/ascending, it can be performing a coordinated turn, or an uncoordinated turn. You can design a filter for each case with a different `F` and `Q` matrix, but the state estimate `x` will be the same for all. "
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -2166,6 +2236,7 @@
  ],
  "metadata": {
   "anaconda-cloud": {},
+  "celltoolbar": "Tags",
   "kernelspec": {
    "display_name": "Python 3",
    "language": "python",