Changed to use 1D x state array.

09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:3fb14452fc76dc0ecb66a465a2f6e18412940cc33adec8dac76e80111450e30e"
+  "signature": "sha256:4db242846680cf526af37ab95e44669118d013f7246b8266ac5f982419b68658"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -261,7 +261,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f99f50405c0>"
+        "<IPython.core.display.HTML at 0x7fb60cedb5c0>"
        ]
       }
      ],
@@ -354,9 +354,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7fb197f4ae10>"
+        "<matplotlib.figure.Figure at 0x7fb5f0343e48>"
        ]
       }
      ],
@@ -386,9 +386,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7fb197b4d860>"
+        "<matplotlib.figure.Figure at 0x7fb5efc73978>"
        ]
       }
      ],
@@ -420,9 +420,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7fb197af0ba8>"
+        "<matplotlib.figure.Figure at 0x7fb5eeb7e0b8>"
        ]
       }
      ],
@@ -456,9 +456,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fb197b4aac8>"
+        "<matplotlib.figure.Figure at 0x7fb60cecea58>"
        ]
       }
      ],
@@ -485,8 +485,8 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "input  mean, variance: 0.0006, 1.0019\n",
-        "output mean, variance: -0.0286, 2.2455\n"
+        "input  mean, variance: -0.0021, 1.0008\n",
+        "output mean, variance: -0.0242, 2.2456\n"
        ]
       }
      ],
@@ -515,16 +515,16 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fb196a26710>"
+        "<matplotlib.figure.Figure at 0x7fb5efa83f98>"
        ]
       },
       {
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "output mean, variance: -0.0009, 2.2544\n"
+        "output mean, variance: 0.0032, 2.2518\n"
        ]
       }
      ],
@@ -559,8 +559,8 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "linear    output mean, variance: -0.0532, 7496.3696\n",
-        "nonlinear output mean, variance: -1.9719, 26248.5350\n"
+        "linear    output mean, variance: 0.1856, 7487.7480\n",
+        "nonlinear output mean, variance: -1.4677, 26256.5001\n"
        ]
       }
      ],
@@ -607,9 +607,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fb196ba5128>"
+        "<matplotlib.figure.Figure at 0x7fb5efbd2c18>"
        ]
       }
      ],
@@ -642,9 +642,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fb196bb44a8>"
+        "<matplotlib.figure.Figure at 0x7fb5eeb53710>"
        ]
       }
      ],
@@ -683,9 +683,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fb196b77f98>"
+        "<matplotlib.figure.Figure at 0x7fb5eeb21160>"
        ]
       }
      ],
@@ -754,17 +754,17 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fb196b48048>"
+        "<matplotlib.figure.Figure at 0x7fb5eeb20860>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fb196b89ef0>"
+        "<matplotlib.figure.Figure at 0x7fb5efbe2128>"
        ]
       }
      ],
@@ -953,15 +953,15 @@
       "def HJacobian_at(x):\n",
       "    \"\"\" compute Jacobian of H matrix for state x \"\"\"\n",
       "\n",
-      "    horiz_dist = x[0,0]\n",
-      "    altitude   = x[2,0]\n",
+      "    horiz_dist = x[0]\n",
+      "    altitude   = x[2]\n",
       "    denom = sqrt(horiz_dist**2 + altitude**2)\n",
       "    return array ([[horiz_dist/denom, 0., altitude/denom]])"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 15
+     "prompt_number": 13
     },
     {
      "cell_type": "markdown",
@@ -979,12 +979,12 @@
       "    to state x.\n",
       "    \"\"\"\n",
       "    \n",
-      "    return (x[0,0]**2 + x[2,0]**2) ** 0.5"
+      "    return (x[0]**2 + x[2]**2) ** 0.5"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 5
+     "prompt_number": 14
     },
     {
      "cell_type": "markdown",
@@ -1030,7 +1030,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 11
+     "prompt_number": 15
     },
     {
      "cell_type": "markdown",
@@ -1049,7 +1049,7 @@
       "    \n",
       "We will initialize the filter near the airplane's actual position\n",
       "\n",
-      "    rk.x = array([[radar.pos, radar.vel-10, radar.alt+100]]).T\n",
+      "    rk.x = array([radar.pos, radar.vel-10, radar.alt+100])\n",
       "    \n",
       "We assign the system matrix using the first term of the Taylor series expansion we computed above.\n",
       "\n",
@@ -1075,12 +1075,13 @@
       "from filterpy.kalman import ExtendedKalmanFilter\n",
       "from numpy import eye, array, asarray\n",
       "\n",
+      "dt = 0.05\n",
       "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
       "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
       "\n",
-      "rk.x = array([[radar.pos, radar.vel+100, radar.alt+1000]]).T\n",
+      "rk.x = array([radar.pos, radar.vel+100, radar.alt+1000])\n",
+      "\n",
       "\n",
-      "dt = 0.05\n",
       "rk.F = eye(3) + array ([[0, 1, 0],\n",
       "                        [0, 0, 0],\n",
       "                        [0, 0, 0]])*dt\n",
@@ -1097,8 +1098,8 @@
       "for i in range(int(20/dt)):\n",
       "    z = radar.get_range()\n",
       "    \n",
-      "    rk.update(array([[z]]), HJacobian_at, hx)\n",
-      "    xs.append(rk.x.T[0])\n",
+      "    rk.update(array([z]), HJacobian_at, hx)\n",
+      "    xs.append(rk.x)\n",
       "    rk.predict()\n",
       "\n",
       "\n",
@@ -1123,29 +1124,29 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAF2CAYAAAA83m0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAF2CAYAAAA83m0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f11361aa1d0>"
+        "<matplotlib.figure.Figure at 0x7fb5eebfcf28>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f113630e780>"
+        "<matplotlib.figure.Figure at 0x7fb5eea7c898>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f11362ed048>"
+        "<matplotlib.figure.Figure at 0x7fb5eea48b38>"
        ]
       }
      ],
-     "prompt_number": 40
+     "prompt_number": 16
     },
     {
      "cell_type": "markdown",
@@ -1181,7 +1182,7 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 4,
+       "prompt_number": 17,
        "text": [
         "\u23a1       x_pos                    x_alt        \u23a4\n",
         "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  0  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
@@ -1191,7 +1192,7 @@
        ]
       }
      ],
-     "prompt_number": 4
+     "prompt_number": 17
     },
     {
      "cell_type": "markdown",
@@ -1255,7 +1256,7 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 5,
+       "prompt_number": 18,
        "text": [
         "\u23a1           3      2                2      2             2            \u23a4\n",
         "\u23a2  \\Delta{t} \u22c5w_vel        \\Delta{t} \u22c5w_vel     \\Delta{t} \u22c5w_alt\u22c5w_vel\u23a5\n",
@@ -1274,7 +1275,7 @@
        ]
       }
      ],
-     "prompt_number": 5
+     "prompt_number": 18
     },
     {
      "cell_type": "heading",
@@ -1304,13 +1305,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fb1b0f91668>"
+        "<matplotlib.figure.Figure at 0x7fb60cecea20>"
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 19
     },
     {
      "cell_type": "markdown",
@@ -1339,7 +1340,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 17
+     "prompt_number": 19
     }
    ],
    "metadata": {}