Adjusted to use upper case x for filter state.

01_gh_filter/g-h_filter.ipynb

@@ -1,7 +1,7 @@
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@@ -43,6 +43,8 @@
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+        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
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@@ -129,9 +131,9 @@
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@@ -257,13 +259,13 @@
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+        "<IPython.core.display.HTML at 0x7f72b8c41518>"
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05_Kalman_Filters/Kalman_Filters.ipynb

@@ -275,7 +275,7 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style."
+      "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step."
      ]
     },
     {
@@ -2331,25 +2331,6 @@
       "\n",
       "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work."
      ]
-    },
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-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 33
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "**author notes**:\n",
-      "    clean up the code - same stuff duplicated over and over - write a 'clean implementation' at the end.\n",
-      "    \n",
-      "    "
-     ]
     }
    ],
    "metadata": {}

05_Kalman_Filters/Kalman_Filters_Animations.ipynb

@@ -1,7 +1,7 @@
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@@ -21,236 +21,22 @@
       "# use same formatting as rest of book so that the plots are\n",
       "# consistant with that look and feel.\n",
       "import book_format\n",
-      "book_format.load_style()"
+      "book_format.load_style()\n",
+      "\n",
+      "\n",
+      "\n",
+      "def update(mu1, var1, mu2, var2):\n",
+      "    mean = (var1*mu2 + var2*mu1) / (var1+var2)\n",
+      "    variance = 1 / (1/var1 + 1/var2)\n",
+      "    return (mean, variance)\n",
+      "\n",
+      "def predict(pos, variance, movement, movement_variance):\n",
+      "    return (pos + movement, variance + movement_variance)"
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
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-        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
-        "                \"HTML-CSS\": {\n",
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-       "text": [
-        "<IPython.core.display.HTML at 0x7f829807fa58>"
-       ]
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+     "outputs": [],
+     "prompt_number": 4
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      "cell_type": "markdown",
@@ -316,8 +102,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 1
+     "outputs": []
     },
     {
      "cell_type": "code",
@@ -330,13 +115,6 @@
       "import stats\n",
       "from gif_animate import animate\n",
       "\n",
-      "def update(mu1, var1, mu2, var2):\n",
-      "    mean = (var1*mu2 + var2*mu1) / (var1+var2)\n",
-      "    variance = 1 / (1/var1 + 1/var2)\n",
-      "    return (mean, variance)\n",
-      "\n",
-      "def predict(pos, variance, movement, movement_variance):\n",
-      "    return (pos + movement, variance + movement_variance)\n",
       "\n",
       "\n",
       "sensor_error = 1.2**2\n",
@@ -389,17 +167,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f82796e75c0>"
-       ]
-      }
-     ],
-     "prompt_number": 2
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -412,6 +180,13 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
+      "from __future__ import print_function, division\n",
+      "import matplotlib.pyplot as plt\n",
+      "import numpy.random as random\n",
+      "import math\n",
+      "import stats\n",
+      "from gif_animate import animate\n",
+      "\n",
       "# assume dog is always moving 1m to the right\n",
       "movement = 1\n",
       "movement_error = .05\n",
@@ -450,7 +225,7 @@
       "    plt.subplot(212)\n",
       "    plt.cla()\n",
       "    stats.plot_gaussian(pos[0], pos[1], xlim=[0,N*1.2])\n",
-      "    plt.ylim([0,1])\n",
+      "    plt.ylim(0, 1)\n",
       "    plt.tight_layout()\n",
       "\n",
       "\n",
@@ -458,7 +233,17 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAc8AAAHNCAYAAAB4sPAgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f3d805b4d68>"
+       ]
+      }
+     ],
+     "prompt_number": 9
     },
     {
      "cell_type": "markdown",

06_Multivariate_Kalman_filter/Multivariate_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:39dc7ee4f5366bda0cc718285beedfd331aa0ea52f68e6a39d4073247dd51726"
+  "signature": "sha256:a4dbdbf1a3ffcafdf9db53065cd9b449ac720ba488ba785046ba9d0f074b2a92"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -43,6 +43,8 @@
        "html": [
         "<style>\n",
         "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
         "\n",
         "    div.cell{\n",
         "        width: 850px;\n",
@@ -129,9 +131,9 @@
         "        white-space: nowrap;\n",
         "    }\n",
         "    div.text_cell_render{\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
         "        line-height: 135%;\n",
-        "        font-size: 110%;\n",
+        "        font-size: 125%;\n",
         "        width:750px;\n",
         "        margin-left:auto;\n",
         "        margin-right:auto;\n",
@@ -257,13 +259,13 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 1,
+       "prompt_number": 2,
        "text": [
-        "<IPython.core.display.HTML at 0x7ff134c2acc0>"
+        "<IPython.core.display.HTML at 0x7f279583df28>"
        ]
       }
      ],
-     "prompt_number": 1
+     "prompt_number": 2
     },
     {
      "cell_type": "heading",
@@ -389,13 +391,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff131bb32e8>"
+        "<matplotlib.figure.Figure at 0x7f27ae3f37b8>"
        ]
       }
      ],
-     "prompt_number": 2
+     "prompt_number": 3
     },
     {
      "cell_type": "markdown",
@@ -443,7 +445,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 3
+     "prompt_number": 4
     },
     {
      "cell_type": "markdown",
@@ -465,7 +467,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 4
+     "prompt_number": 5
     },
     {
      "cell_type": "markdown",
@@ -483,7 +485,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 5
+     "prompt_number": 6
     },
     {
      "cell_type": "markdown",
@@ -502,7 +504,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 6
+     "prompt_number": 7
     },
     {
      "cell_type": "markdown",
@@ -528,7 +530,7 @@
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 8
     },
     {
      "cell_type": "markdown",
@@ -557,13 +559,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1107cb710>"
+        "<matplotlib.figure.Figure at 0x7f279639df98>"
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 9
     },
     {
      "cell_type": "markdown",
@@ -611,13 +613,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1108b5a90>"
+        "<matplotlib.figure.Figure at 0x7f27897c2c88>"
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 10
     },
     {
      "cell_type": "markdown",
@@ -709,13 +711,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff110a479b0>"
+        "<matplotlib.figure.Figure at 0x7f27897dff98>"
        ]
       }
      ],
-     "prompt_number": 10
+     "prompt_number": 11
     },
     {
      "cell_type": "markdown",
@@ -736,13 +738,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1107f6d68>"
+        "<matplotlib.figure.Figure at 0x7f278858dbe0>"
        ]
       }
      ],
-     "prompt_number": 11
+     "prompt_number": 12
     },
     {
      "cell_type": "markdown",
@@ -763,13 +765,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1107a5c50>"
+        "<matplotlib.figure.Figure at 0x7f278858b7b8>"
        ]
       }
      ],
-     "prompt_number": 12
+     "prompt_number": 13
     },
     {
      "cell_type": "markdown",
@@ -794,13 +796,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1108c8b38>"
+        "<matplotlib.figure.Figure at 0x7f27895e5208>"
        ]
       }
      ],
-     "prompt_number": 13
+     "prompt_number": 14
     },
     {
      "cell_type": "markdown",
@@ -859,13 +861,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff11084a358>"
+        "<matplotlib.figure.Figure at 0x7f2796381978>"
        ]
       }
      ],
-     "prompt_number": 14
+     "prompt_number": 15
     },
     {
      "cell_type": "heading",
@@ -991,7 +993,7 @@
        ]
       }
      ],
-     "prompt_number": 15
+     "prompt_number": 16
     },
     {
      "cell_type": "markdown",
@@ -1020,7 +1022,7 @@
        ]
       }
      ],
-     "prompt_number": 16
+     "prompt_number": 17
     },
     {
      "cell_type": "markdown",
@@ -1049,7 +1051,7 @@
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 18
     },
     {
      "cell_type": "markdown",
@@ -1093,7 +1095,7 @@
        ]
       }
      ],
-     "prompt_number": 18
+     "prompt_number": 19
     },
     {
      "cell_type": "markdown",
@@ -1126,7 +1128,7 @@
        ]
       }
      ],
-     "prompt_number": 19
+     "prompt_number": 20
     },
     {
      "cell_type": "markdown",
@@ -1161,7 +1163,7 @@
        ]
       }
      ],
-     "prompt_number": 20
+     "prompt_number": 21
     },
     {
      "cell_type": "markdown",
@@ -1244,7 +1246,7 @@
       "            Default value of 0 indicates it is not used.\n",
       "        \"\"\"\n",
       "\n",
-      "        self.x = np.zeros((dim_x,1)) # state\n",
+      "        self.X = np.zeros((dim_x,1)) # state\n",
       "        self.P = np.eye(dim_x)       # uncertainty covariance\n",
       "        self.Q = np.eye(dim_x)       # process uncertainty\n",
       "        self.u = np.zeros((dim_x,1)) # motion vector\n",
@@ -1293,7 +1295,7 @@
       "        K = dot(P, H.T).dot(linalg.inv(S))\n",
       "\n",
       "        # predict new x with residual scaled by the kalman gain\n",
-      "        self.x = self.x + dot(K, y)\n",
+      "        self.X += + dot(K, y)\n",
       "\n",
       "        I_KH = self._I - dot (K, H)\n",
       "        self.P = dot(I_KH).dot(P).dot(I_KH.T) + dot(K, R).dot(K.T)\n",
@@ -1308,13 +1310,13 @@
       "            to create the control input into the system.\n",
       "        \"\"\"\n",
       "  \n",
-      "        self.x = dot(self.F, self.x) + dot(self.B, u)\n",
+      "        self.X = dot(self.F, self.X) + dot(self.B, u)\n",
       "        self.P = self.F.dot(self.P).dot(self.F.T) + self.Q"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 21
+     "prompt_number": 22
     },
     {
      "cell_type": "markdown",
@@ -1338,7 +1340,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 22
+     "prompt_number": 23
     },
     {
      "cell_type": "heading",
@@ -1372,7 +1374,7 @@
       "##### **Step 1:** Choose the State Variables and Set Initial Conditions\n",
       "\n",
       "\n",
-      "In the previous chapter we tracked a dog in one dimension by using a Gaussian. The mean ($\\mu$) represented the most likely position, and the variance ($\\sigma^2$) represented the probability distribution of the position. In that problem the position is the *state* of the system, and we call $\\mu$ the *state variable*.\n",
+      "In the previous chapter we tracked a dog in one dimension by using a Gaussian. The mean $(\\mu)$ represented the most likely position, and the variance ($\\sigma^2$) represented the probability distribution of the position. In that problem the position is the *state* of the system, and we call $\\mu$ the *state variable*.\n",
       "\n",
       "In this chapter we will be tracking both the position and velocity of the dog, so we have two state variables. State variables can either be *observed variables* - directly measured by a sensor, or *unobserved variables* - inferred from the observed variables. For our dog tracking problem, our observed state variable is position, and th unobserved variable is velocity. \n",
       "\n",
@@ -1545,7 +1547,7 @@
       "\n",
       "The Kalman filter equation that performs this step is:\n",
       "\n",
-      "$$\\textbf{y} := \\mathbf{z} - \\mathbf{H x^-} \\;\\;\\;(3)$$\n",
+      "$$\\textbf{y} = \\mathbf{z} - \\mathbf{H x^-} \\;\\;\\;(3)$$\n",
       "\n",
       "where $\\textbf{y}$ is the residual, $\\mathbf{x^-}$ is the predicted value for $\\mathbf{x}$, $\\textbf{z}$ is the measurement, and $\\textbf{H}$ is the measurement function. It is just a matrix that we multiply the state into to convert it into a measurement.\n",
       "\n",
@@ -1680,7 +1682,7 @@
        ]
       }
      ],
-     "prompt_number": 23
+     "prompt_number": 24
     },
     {
      "cell_type": "heading",
@@ -1745,7 +1747,7 @@
         "    You will have to assign reasonable values to all of these before\n",
         "    running the filter. All must have dtype of float\n",
         "    \n",
-        "    x : ndarray (dim_x, 1), default = [0,0,0...0]\n",
+        "    X : ndarray (dim_x, 1), default = [0,0,0...0]\n",
         "        state of the filter\n",
         "    \n",
         "    P : ndarray (dim_x, dim_x), default identity matrix\n",
@@ -1769,7 +1771,7 @@
        ]
       }
      ],
-     "prompt_number": 24
+     "prompt_number": 25
     },
     {
      "cell_type": "markdown",
@@ -1784,7 +1786,7 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "dog_filter.x = np.array([[0], [0]])     # initial state (location and velocity)\n",
+      "dog_filter.X = np.array([[0], [0]])     # initial state (location and velocity)\n",
       "dog_filter.F = np.array([[1,1], [0,1]]) # state transition matrix\n",
       "dog_filter.H = np.array([[1,0]])        # Measurement function\n",
       "dog_filter.R *= 5                       # measurement noise\n",
@@ -1794,7 +1796,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 25
+     "prompt_number": 26
     },
     {
      "cell_type": "markdown",
@@ -1814,7 +1816,7 @@
       "\n",
       "    pos = (0,500)\n",
       "    \n",
-      "Multidimensional Kalman filters stores the state variables in $\\mathbf{x}$ and their *covariance* in $\\mathbf{P}$. These are $\\verb,f.x,$ and $\\verb,f.P,$ in the code above. Notionally, this is similar as the one dimension case, but instead of having a mean and variance we have a mean and covariance. For the multidimensional case, we have\n",
+      "Multidimensional Kalman filters stores the state variables in $\\mathbf{x}$ and their *covariance* in $\\mathbf{P}$. These are $\\verb,f.X,$ and $\\verb,f.P,$ in the code above. Notionally, this is similar as the one dimension case, but instead of having a mean and variance we have a mean and covariance. For the multidimensional case, we have\n",
       "\n",
       "$$\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(\\mathbf{x},\\mathbf{P})$$\n",
       "\n",
@@ -1840,7 +1842,7 @@
       "\n",
       "def dog_tracking_filter(R,Q=0,cov=1.):\n",
       "    dog_filter = KalmanFilter (dim_x=2, dim_z=1)\n",
-      "    dog_filter.x = np.array([[0], \n",
+      "    dog_filter.X = np.array([[0], \n",
       "                             [0]])   # initial state (location and velocity)\n",
       "    dog_filter.F = np.array([[1,1],\n",
       "                             [0,1]])  # state transition matrix\n",
@@ -1870,14 +1872,14 @@
       "\n",
       "    dog_filter = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
       "    if initial_x is not None:\n",
-      "        dog_filter.x = initial_x\n",
+      "        dog_filter.X = initial_x\n",
       "\n",
       "    pos = [None] * count\n",
       "    cov = [None] * count\n",
       "    \n",
       "    for t in range(count):\n",
       "        z = zs[t]\n",
-      "        pos[t] = dog_filter.x[0,0]\n",
+      "        pos[t] = dog_filter.X[0,0]\n",
       "        cov[t] = dog_filter.P\n",
       "    \n",
       "        # perform the kalman filter steps\n",
@@ -1889,7 +1891,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 26
+     "prompt_number": 27
     },
     {
      "cell_type": "markdown",
@@ -1962,7 +1964,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 27
+     "prompt_number": 28
     },
     {
      "cell_type": "markdown",
@@ -1983,21 +1985,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff110673cf8>"
+        "<matplotlib.figure.Figure at 0x7f27896dd4e0>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff131bb32e8>"
+        "<matplotlib.figure.Figure at 0x7f27963ac198>"
        ]
       }
      ],
-     "prompt_number": 28
+     "prompt_number": 29
     },
     {
      "cell_type": "markdown",
@@ -2073,7 +2075,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 29
+     "prompt_number": 30
     },
     {
      "cell_type": "markdown",
@@ -2102,7 +2104,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 30
+     "prompt_number": 31
     },
     {
      "cell_type": "markdown",
@@ -2125,7 +2127,7 @@
       "\n",
       "    # initialize the filters\n",
       "    f = mkf_filter(R, Q)\n",
-      "    f.x[0,0] = 0.\n",
+      "    f.X[0,0] = 0.\n",
       "    f.P[0,0] = p0\n",
       "    pos = (x0, p0)\n",
       "    for i in range(50):\n",
@@ -2134,7 +2136,7 @@
       "        f.update(z)\n",
       "\n",
       "        x1.append(pos[0])\n",
-      "        x2.append(f.x[0,0])\n",
+      "        x2.append(f.X[0,0])\n",
       "\n",
       "        p1.append(pos[1])\n",
       "        p2.append(f.P[0,0])\n",
@@ -2160,21 +2162,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff11065dac8>"
+        "<matplotlib.figure.Figure at 0x7f27898b01d0>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff110945b38>"
+        "<matplotlib.figure.Figure at 0x7f2789734128>"
        ]
       }
      ],
-     "prompt_number": 31
+     "prompt_number": 32
     },
     {
      "cell_type": "markdown",
@@ -2336,7 +2338,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 32
+     "prompt_number": 33
     },
     {
      "cell_type": "markdown",
@@ -2368,12 +2370,12 @@
       "\n",
       "    # initialize the filters\n",
       "    f1 = mkf_filter(R, Q)\n",
-      "    f1.x[0,0] = 0.\n",
+      "    f1.X[0,0] = 0.\n",
       "    f1.P[0,0] = p0\n",
       "    \n",
       "    f2 = pos_vel_filter(R, Q)\n",
-      "    f2.x[0,0] = 0.\n",
-      "    f2.x[1,0] = 1.\n",
+      "    f2.X[0,0] = 0.\n",
+      "    f2.X[1,0] = 1.\n",
       "    f2.P *= p0\n",
       "    \n",
       "    for i in range(50):\n",
@@ -2385,8 +2387,8 @@
       "        f1.update(z)\n",
       "        f2.update(z)\n",
       "        \n",
-      "        x1.append(f1.x[0,0])\n",
-      "        x2.append(f2.x[0,0])\n",
+      "        x1.append(f1.X[0,0])\n",
+      "        x2.append(f2.X[0,0])\n",
       "\n",
       "    plt.plot(x1, label='1D Filter')\n",
       "    plt.scatter(range(len(x2)), x2, c='r', label='2D Filter')\n",
@@ -2402,13 +2404,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1108ba6a0>"
+        "<matplotlib.figure.Figure at 0x7f278856bcc0>"
        ]
       }
      ],
-     "prompt_number": 33
+     "prompt_number": 34
     },
     {
      "cell_type": "markdown",
@@ -2462,21 +2464,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
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+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff11082ce80>"
+        "<matplotlib.figure.Figure at 0x7f279633f7f0>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff110a321d0>"
+        "<matplotlib.figure.Figure at 0x7f278855ff28>"
        ]
       }
      ],
-     "prompt_number": 34
+     "prompt_number": 35
     },
     {
      "cell_type": "markdown",
@@ -2585,13 +2587,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1107f8748>"
+        "<matplotlib.figure.Figure at 0x7f278855f630>"
        ]
       }
      ],
-     "prompt_number": 35
+     "prompt_number": 36
     },
     {
      "cell_type": "markdown",
@@ -2655,13 +2657,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1107d3c18>"
+        "<matplotlib.figure.Figure at 0x7f27898734a8>"
        ]
       }
      ],
-     "prompt_number": 36
+     "prompt_number": 37
     },
     {
      "cell_type": "markdown",
@@ -2684,13 +2686,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1108560b8>"
+        "<matplotlib.figure.Figure at 0x7f27965cfe80>"
        ]
       }
      ],
-     "prompt_number": 37
+     "prompt_number": 38
     },
     {
      "cell_type": "markdown",
@@ -2754,13 +2756,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1108b9f98>"
+        "<matplotlib.figure.Figure at 0x7f2788546e10>"
        ]
       }
      ],
-     "prompt_number": 38
+     "prompt_number": 39
     },
     {
      "cell_type": "markdown",
@@ -2783,13 +2785,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff1107c7b00>"
+        "<matplotlib.figure.Figure at 0x7f279633f400>"
        ]
       }
      ],
-     "prompt_number": 39
+     "prompt_number": 40
     },
     {
      "cell_type": "markdown",
@@ -2817,13 +2819,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff11072f1d0>"
+        "<matplotlib.figure.Figure at 0x7f2789744f60>"
        ]
       }
      ],
-     "prompt_number": 40
+     "prompt_number": 41
     },
     {
      "cell_type": "markdown",
@@ -2848,13 +2850,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAENCAYAAAD0eSVZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff110a75dd8>"
+        "<matplotlib.figure.Figure at 0x7f27897ec198>"
        ]
       }
      ],
-     "prompt_number": 41
+     "prompt_number": 42
     },
     {
      "cell_type": "markdown",
@@ -2886,7 +2888,7 @@
       "    for t in range (count):\n",
       "        z = dog.sense()\n",
       "        f.update (z)\n",
-      "        ps.append (f.x[0,0])\n",
+      "        ps.append (f.X[0,0])\n",
       "        cov.append(f.P)\n",
       "        zs.append(z)\n",
       "        f.predict()\n",
@@ -2920,21 +2922,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff11092be80>"
+        "<matplotlib.figure.Figure at 0x7f2789798d68>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff110886208>"
+        "<matplotlib.figure.Figure at 0x7f2789730c18>"
        ]
       }
      ],
-     "prompt_number": 42
+     "prompt_number": 43
     },
     {
      "cell_type": "markdown",
@@ -3003,13 +3005,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff10ee2b3c8>"
+        "<matplotlib.figure.Figure at 0x7f27885178d0>"
        ]
       }
      ],
-     "prompt_number": 43
+     "prompt_number": 44
     },
     {
      "cell_type": "markdown",
@@ -3069,7 +3071,7 @@
       "        self.dim_x = dim_x\n",
       "        self.dim_z = dim_z\n",
       "\n",
-      "        self.x = np.zeros((dim_x,1)) # state\n",
+      "        self.X = np.zeros((dim_x,1)) # state\n",
       "        self.P = np.eye(dim_x)       # uncertainty covariance\n",
       "        self.Q = np.eye(dim_x)       # process uncertainty\n",
       "        self.u = 0                   # control input vector\n",
@@ -3083,7 +3085,7 @@
       "\n",
       "More than anything this method exists to document for you what the variable names are in the filter. To do anything useful with this filter you will have to modify most of these values. Some are set to useful values. For example, `R` is set to an identity matrix; if you want the diagonals of `R` to be 10. you may write (as we did earlier in this chapter) `my_filter.R += 10.`.\n",
       "\n",
-      "The names used for each variable matches the math symbology used in this chapter. Thus, `self.P` is the covariance matrix, `self.x` is the state, and so on.\n",
+      "The names used for each variable matches the math symbology used in this chapter. Thus, `self.P` is the covariance matrix, `self.X` is the state, and so on.\n",
       "\n",
       "The predict function implements the predict step of the Kalman equations, which are \n",
       "\n",
@@ -3097,12 +3099,12 @@
       "The corresponding code is\n",
       "\n",
       "    def predict(self):        \n",
-      "        self.x = self.F.dot(self.x) + self.B.dot(self.u)\n",
+      "        self.X = self.F.dot(self.X) + self.B.dot(self.u)\n",
       "        self.P = self.F.dot(self.P).dot(self.F.T) + self.Q\n",
       "\n",
       "I haven't discussed the use of numpy much until now, but this method illustrates the power of that package. We use numpy's `array` class to store our data and perform the linear algebra for our filters. `array` implements matrix multiplication using the `.dot()` method; if you use `*` you will get element-wise multiplication. As a heavy user of linear algebra this design is somewhat distressing as I use matrix multiplication far more often than element-wise multiplication. However, this design is due to historical developments in the library and we must live with it. The Python community has recognized this problem, and in Python 3.5 we will have the `@` operator to implement matrix multiplication. \n",
       "\n",
-      "With that in mind, the Python code `self.F.dot(self.x)` implements the math expression $\\mathbf{F x}$.\n",
+      "With that in mind, the Python code `self.F.dot(self.X)` implements the math expression $\\mathbf{F x}$.\n",
       "\n",
       "Numpy's `array` implements matrix transposition by using the `.T` property. Therefore, `F.T` is the python implementation of $\\mathbf{F}^\\mathsf{T}$.\n",
       "\n",
@@ -3142,7 +3144,7 @@
       "            R = np.eye(self.dim_z) * R\n",
       "\n",
       "        # error (residual) between measurement and prediction\n",
-      "        self.residual = Z - self.H.dot(self.x)\n",
+      "        self.residual = Z - self.H.dot(self.X)\n",
       "\n",
       "        # project system uncertainty into measurement space\n",
       "        self.S = self.H.dot(self.P).dot(self.H.T) + R\n",
@@ -3151,7 +3153,7 @@
       "        self.K = self.P.dot(self.H.T).dot(linalg.inv(self.S))\n",
       "\n",
       "        # predict new x with residual scaled by the kalman gain\n",
-      "        self.x = self.x + self.K.dot(self.residual)\n",
+      "        self.X += self.K.dot(self.residual)\n",
       "\n",
       "        KH = self.K.dot(self.H)\n",
       "        I_KH = self._I - KH\n",

06_Multivariate_Kalman_filter/animations.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:fb878db70d2e2bac86ef693ff529bb1bc61ee98d134d493d94e761e628da7f9e"
+  "signature": "sha256:ccfeea4057cfb93e8b563fb0ec892cef60906a7bd909fb3ea390ab1cc98ff004"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -29,6 +29,8 @@
        "html": [
         "<style>\n",
         "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
         "\n",
         "    div.cell{\n",
         "        width: 850px;\n",
@@ -115,9 +117,9 @@
         "        white-space: nowrap;\n",
         "    }\n",
         "    div.text_cell_render{\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
         "        line-height: 135%;\n",
-        "        font-size: 110%;\n",
+        "        font-size: 125%;\n",
         "        width:750px;\n",
         "        margin-left:auto;\n",
         "        margin-right:auto;\n",
@@ -243,13 +245,13 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 1,
+       "prompt_number": 2,
        "text": [
-        "<IPython.core.display.HTML at 0x7f3e158449e8>"
+        "<IPython.core.display.HTML at 0x7f3431146c50>"
        ]
       }
      ],
-     "prompt_number": 1
+     "prompt_number": 2
     },
     {
      "cell_type": "markdown",
@@ -332,7 +334,8 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [],
+     "prompt_number": 3
     },
     {
      "cell_type": "code",
@@ -364,7 +367,24 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f34310bbd68>"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f34310bbe48>"
+       ]
+      }
+     ],
+     "prompt_number": 4
     },
     {
      "cell_type": "markdown",
@@ -391,7 +411,7 @@
       "\n",
       "def dog_tracking_filter(R,Q=0,cov=1.):\n",
       "    dog_filter = KalmanFilter (dim_x=2, dim_z=1)\n",
-      "    dog_filter.x = np.array([[0], \n",
+      "    dog_filter.X = np.array([[0], \n",
       "                             [0]])   # initial state (location and velocity)\n",
       "    dog_filter.F = np.array([[1,1],\n",
       "                             [0,1]])  # state transition matrix\n",
@@ -419,16 +439,16 @@
       "    \n",
       "    plt.gca().set_xlim(-100,100)\n",
       "    if frame == 0:\n",
-      "        stats.plot_covariance_ellipse ((0, f.x[0,0]), cov=f.P, axis_equal=True, \n",
+      "        stats.plot_covariance_ellipse ((0, f.X[0,0]), cov=f.P, axis_equal=True, \n",
       "                                       facecolor='g', edgecolor=None, alpha=0.2)\n",
-      "        xs.append (f.x[0,0])\n",
+      "        xs.append (f.X[0,0])\n",
       "        \n",
       "    z = dog.sense()\n",
       "    zs.append(z)\n",
       "    f.update(z)\n",
-      "    xs.append (f.x[0,0])\n",
+      "    xs.append (f.X[0,0])\n",
       "    \n",
-      "    stats.plot_covariance_ellipse ((frame+1, f.x[0,0]), cov=f.P, axis_equal=True, \n",
+      "    stats.plot_covariance_ellipse ((frame+1, f.X[0,0]), cov=f.P, axis_equal=True, \n",
       "                                       facecolor='g', edgecolor=None, alpha=0.5,\n",
       "                                       xlim=(-5,30), ylim=(-5,30))\n",
       "    \n",
@@ -446,11 +466,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3df4261d30>"
+        "<matplotlib.figure.Figure at 0x7f342966a048>"
        ]
       }
      ],
-     "prompt_number": 18
+     "prompt_number": 7
     },
     {
      "cell_type": "markdown",

07_Kalman_Filter_Math/Kalman_Filter_Math.ipynb

@@ -363,7 +363,7 @@
       "\n",
       "$$\\mathbf{v}=\\dot{\\mathbf{x}}$$\n",
       "\n",
-      "where $\\dot{\\mathbf{x}}$ is the notation for the derivative of $\\mathbf{x}$, or $\\frac{d \\mathbf{x}}{d t}$.\n",
+      "where $\\dot{\\mathbf{x}}$ is the notation for the derivative of $\\mathbf{x}$ with respect to t, or $\\frac{d \\mathbf{x}}{d t}$.\n",
       "\n",
       "In general terms we can then say that a dynamic system consists of equations of the form\n",
       "\n",
@@ -441,7 +441,7 @@
       "\n",
       "$$ \\Phi(t) = e^{\\mathbf{F}t} = \\mathbf{I} + \\mathbf{F}t  + \\frac{(\\mathbf{F}t)^2}{2!} + \\frac{(\\mathbf{F}t)^3}{3!} + ... $$\n",
       "\n",
-      "This is much easier to compute, and is the typical approach used in Kalman filter design when the filter is reasonably small. If you are wondering where $e$ came from, I again point to wikipedia - this time the matrix exponential article [2]. Here the important point is to recognize the very simple and regular form this equation takes.\n",
+      "This is much easier to compute, and is the typical approach used in Kalman filter design when the filter is reasonably small. If you are wondering where $e$ came from, I again point to wikipedia - this time the matrix exponential article [2]. Here the important point is to recognize the very simple and regular form this equation takes. We will put this form into use in the next chapter, so I will not belabor its use here. \n",
       "\n",
       "Finally, there are numerical techniques to find $\\Phi$. As filters get larger finding analytical solutions becomes very tedious (though packages like Sympy make it easier). C. F. van Loan [3] has developed a technique that finds both $\\Phi$ and $Q$ numerically.\n",
       "\n",
@@ -489,7 +489,7 @@
       "I will start with the update step, as that is what we started with in the one dimensional Kalman filter case. Our first equation is\n",
       "\n",
       "$$\n",
-      "\\mathbf{\\gamma} = \\mathbf{z} - \\mathbf{H x}\\tag{3}\n",
+      "\\mathbf{y} = \\mathbf{z} - \\mathbf{H x}\\tag{3}\n",
       "$$\n",
       "\n",
       "On the right we have $\\mathbf{Hx}$. That should be recognizable as the measurement function. Multiplying $\\mathbf{H}$ with $\\mathbf{x}$ puts $\\mathbf{x}$ into *measurement space*; in other words, the same basis and units as the sensor's measurements. The variable $\\mathbf{z}$ is just the measurement; it is typical, but not universal to use $\\mathbf{z}$ to denote measurements in the literature ($\\mathbf{y}$ is also sometimes used). Do you remember this chart?"
@@ -520,7 +520,7 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "The blue point labeled \"prediction\" is the output of $\\mathbf{Hx}$, and the dot labeled \"measurement\" is $\\mathbf{z}$. Therefore, $\\gamma = \\mathbf{z} - \\mathbf{Hx}$ is how we compute the residual, drawn in red, where $\\gamma$ is the residual.\n",
+      "The blue point labeled \"prediction\" is the output of $\\mathbf{Hx}$, and the dot labeled \"measurement\" is $\\mathbf{z}$. Therefore, $\\mathbf{y} = \\mathbf{z} - \\mathbf{Hx}$ is how we compute the residual, drawn in red, where $\\mathbf{z}$ is the residual.\n",
       "\n",
       "The next two lines are the formidable:\n",
       "\n",
@@ -587,7 +587,7 @@
      "metadata": {},
      "source": [
       "Our next line is:\n",
-      " $$\\mathbf{x}=\\mathbf{x}' +\\mathbf{K\\gamma}\\tag{5}$$\n",
+      " $$\\mathbf{x}=\\mathbf{x}' +\\mathbf{Ky}\\tag{5}$$\n",
       "\n",
       "This just multiplies the residual by the Kalman gain, and adds it to the state variable. In other words, this is the computation of our new estimate.\n",
       "\n",

08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
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         "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
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+        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
         "\n",
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@@ -141,12 +143,12 @@
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         "        overflow-x: auto;\n",
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@@ -259,7 +261,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f411c73f358>"
+        "<matplotlib.figure.Figure at 0x7fe9e05cd358>"
        ]
       }
      ],
@@ -612,9 +614,9 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "f1.x = np.array([[0,0,0,0]]).T\n",
+      "f1.X = np.array([[0,0,0,0]]).T\n",
       "f1.P = np.eye(4) * 500.\n",
-      "print(f1.x)\n",
+      "print(f1.X)\n",
       "print()\n",
       "print (f1.P)"
      ],
@@ -672,7 +674,7 @@
       "f1.R = np.eye(2) * 5\n",
       "f1.Q = np.eye(4) * .1\n",
       "\n",
-      "f1.x = np.array([[0,0,0,0]]).T\n",
+      "f1.X = np.array([[0,0,0,0]]).T\n",
       "f1.P = np.eye(4) * 500.\n",
       "\n",
       "# initialize storage and other variables for the run\n",
@@ -689,8 +691,8 @@
       "    f1.predict ()\n",
       "    f1.update (z)\n",
       "\n",
-      "    xs.append (f1.x[0,0])\n",
-      "    ys.append (f1.x[2,0])\n",
+      "    xs.append (f1.X[0,0])\n",
+      "    ys.append (f1.X[2,0])\n",
       "    pxs.append (pos[0]*.3048)\n",
       "    pys.append(pos[1]*.3048)\n",
       "\n",
@@ -702,12 +704,20 @@
      "language": "python",
      "metadata": {},
      "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stderr",
+       "text": [
+        "/home/rlabbe/anaconda/lib/python3.4/site-packages/matplotlib/cbook.py:133: MatplotlibDeprecationWarning: The \"loc\" positional argument to legend is deprecated. Please use the \"loc\" keyword instead.\n",
+        "  warnings.warn(message, mplDeprecation, stacklevel=1)\n"
+       ]
+      },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f411c73f2e8>"
+        "<matplotlib.figure.Figure at 0x7fe9e05cd3c8>"
        ]
       }
      ],
@@ -742,7 +752,7 @@
       "f1.R = np.eye(2) * 5\n",
       "f1.Q = np.eye(4) * .1\n",
       "\n",
-      "f1.x = np.array([[0,0,0,0]]).T\n",
+      "f1.X = np.array([[0,0,0,0]]).T\n",
       "f1.P = np.eye(4) * 500.\n",
       "\n",
       "# initialize storage and other variables for the run\n",
@@ -759,8 +769,8 @@
       "    f1.predict ()\n",
       "    f1.update (z)\n",
       "\n",
-      "    xs.append (f1.x[0,0])\n",
-      "    ys.append (f1.x[2,0])\n",
+      "    xs.append (f1.X[0,0])\n",
+      "    ys.append (f1.X[2,0])\n",
       "    pxs.append (pos[0]*.3048)\n",
       "    pys.append(pos[1]*.3048)\n",
       "\n",
@@ -768,9 +778,9 @@
       "    cov = np.array([[f1.P[0,0], f1.P[2,0]], \n",
       "                    [f1.P[0,2], f1.P[2,2]]])\n",
       " \n",
-      "    #e = stats.sigma_ellipse (cov=cov, x=f1.x[0,0], y=f1.x[2,0])\n",
+      "    #e = stats.sigma_ellipse (cov=cov, x=f1.X[0,0], y=f1.X[2,0])\n",
       "    #stats.plot_sigma_ellipse(ellipse=e)\n",
-      "    stats.plot_covariance_ellipse((f1.x[0,0], f1.x[2,0]), cov=cov,\n",
+      "    stats.plot_covariance_ellipse((f1.X[0,0], f1.X[2,0]), cov=cov,\n",
       "                                  facecolor='g', alpha=0.2)\n",
       "\n",
       "        \n",
@@ -787,9 +797,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f411c73ac18>"
+        "<matplotlib.figure.Figure at 0x7fe9e01f4a90>"
        ]
       },
       {
@@ -804,7 +814,7 @@
        ]
       }
      ],
-     "prompt_number": 27
+     "prompt_number": 11
     },
     {
      "cell_type": "markdown",
@@ -865,20 +875,20 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "[[ 0.08204134  0.02434904]\n",
-        " [ 0.02434904  0.00955614]]\n"
+        "[[ 0.30660483  0.12566239]\n",
+        " [ 0.12566239  0.24399092]]\n"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4114e6edd8>"
+        "<matplotlib.figure.Figure at 0x7fe9e02b0cf8>"
        ]
       }
      ],
-     "prompt_number": 26
+     "prompt_number": 13
     },
     {
      "cell_type": "markdown",
@@ -1022,17 +1032,17 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f411c497dd8>"
+        "<matplotlib.figure.Figure at 0x7fe9d49847b8>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4114e64a90>"
+        "<matplotlib.figure.Figure at 0x7fe9d4a5ecf8>"
        ]
       }
      ],
@@ -1167,7 +1177,7 @@
       "    \n",
       "    f1.Q *= 0.\n",
       "\n",
-      "    f1.x = np.array([[x, vx, y, vy, -g]]).T\n",
+      "    f1.X = np.array([[x, vx, y, vy, -g]]).T\n",
       "    \n",
       "    return f1"
      ],
@@ -1196,11 +1206,11 @@
       "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[0,0])\n",
       "f1 = ball_kf(x,y,theta,v0,dt)\n",
       "t = 0\n",
-      "while f1.x[2,0] > 0:\n",
+      "while f1.X[2,0] > 0:\n",
       "    t += dt\n",
       "    f1.predict() \n",
       "    x,y = ball.step(dt)\n",
-      "    p1 = plt.scatter(f1.x[0,0], f1.x[2,0], color='black', marker='+', s=75)\n",
+      "    p1 = plt.scatter(f1.X[0,0], f1.X[2,0], color='black', marker='+', s=75)\n",
       "    p2 = plt.scatter(x, y,                 color='green', marker='o', s=75, alpha=0.5)\n",
       "\n",
       "plt.legend([p1,p2], ['Kalman filter', 'idealized'])\n",
@@ -1212,9 +1222,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f411451b358>"
+        "<matplotlib.figure.Figure at 0x7fe9d4763e48>"
        ]
       }
      ],
@@ -1318,7 +1328,7 @@
       "    vx = cos(omega) * v0\n",
       "    vy = sin(omega) * v0\n",
       "\n",
-      "    f1.x = np.mat([x, vx, y, vy, -g]).T\n",
+      "    f1.X = np.array([[x, vx, y, vy, -g]]).T\n",
       "    \n",
       "    \n",
       "With all the steps done we are ready to implement our filter and test it. First, the implementation:"
@@ -1336,15 +1346,14 @@
       "    f1 = KalmanFilter(dim_x=5, dim_z=2)\n",
       "\n",
       "    ay = .5*dt**2\n",
-      "    f1.F = np.mat ([[1, dt,  0,  0,  0],   # x   = x0+dx*dt\n",
-      "                    [0,  1,  0,  0,  0],   # dx  = dx\n",
-      "                    [0,  0,  1, dt, ay],   # y   = y0 +dy*dt+1/2*g*dt^2\n",
-      "                    [0,  0,  0,  1, dt],   # dy  = dy0 + ddy*dt \n",
-      "                    [0,  0,  0,  0, 1]])   # ddy = -g.\n",
+      "    f1.F = np.array ([[1, dt,  0,  0,  0],   # x   = x0+dx*dt\n",
+      "                      [0,  1,  0,  0,  0],   # dx  = dx\n",
+      "                      [0,  0,  1, dt, ay],   # y   = y0 +dy*dt+1/2*g*dt^2\n",
+      "                      [0,  0,  0,  1, dt],   # dy  = dy0 + ddy*dt \n",
+      "                      [0,  0,  0,  0, 1]])   # ddy = -g.\n",
       "\n",
-      "    f1.H = np.mat([\n",
-      "                [1, 0, 0, 0, 0],\n",
-      "                [0, 0, 1, 0, 0]])\n",
+      "    f1.H = np.array([[1, 0, 0, 0, 0],\n",
+      "                     [0, 0, 1, 0, 0]])\n",
       "    \n",
       "    f1.R *= r\n",
       "    f1.Q *= q\n",
@@ -1353,7 +1362,7 @@
       "    vx = cos(omega) * v0\n",
       "    vy = sin(omega) * v0\n",
       "\n",
-      "    f1.x = np.mat([x,vx,y,vy,-9.8]).T\n",
+      "    f1.X = np.array([[x, vx, y, vy, -9.8]]).T\n",
       "    \n",
       "    return f1"
      ],
@@ -1385,14 +1394,14 @@
       "t = 0\n",
       "xs = []\n",
       "ys = []\n",
-      "while f1.x[2,0] > 0:\n",
+      "while f1.X[2,0] > 0:\n",
       "    t += dt\n",
       "    x,y = ball.step(dt)\n",
-      "    z = np.mat([[x,y]]).T\n",
+      "    z = np.array([[x,y]]).T\n",
       "\n",
       "    f1.update(z)\n",
-      "    xs.append(f1.x[0,0])\n",
-      "    ys.append(f1.x[2,0])\n",
+      "    xs.append(f1.X[0,0])\n",
+      "    ys.append(f1.X[2,0])\n",
       "    \n",
       "    f1.predict() \n",
       "    \n",
@@ -1408,9 +1417,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4114f44780>"
+        "<matplotlib.figure.Figure at 0x7fe9d4579400>"
        ]
       }
      ],
@@ -1549,9 +1558,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f411460ed68>"
+        "<matplotlib.figure.Figure at 0x7fe9d49e2358>"
        ]
       }
      ],
@@ -1653,17 +1662,17 @@
       "xs2 = []\n",
       "ys2 = []\n",
       "\n",
-      "while f1.x[2,0] > 0:\n",
+      "while f1.X[2,0] > 0:\n",
       "    t += dt\n",
       "    x,y = ball.update(dt)\n",
-      "    z = np.mat([[x,y]]).T\n",
+      "    z = np.array([[x, y]]).T\n",
       "\n",
       "    f1.update(z)\n",
       "    f2.update(z)\n",
-      "    xs.append(f1.x[0,0])\n",
-      "    ys.append(f1.x[2,0])\n",
-      "    xs2.append(f2.x[0,0])\n",
-      "    ys2.append(f2.x[2,0])    \n",
+      "    xs.append(f1.X[0,0])\n",
+      "    ys.append(f1.X[2,0])\n",
+      "    xs2.append(f2.X[0,0])\n",
+      "    ys2.append(f2.X[2,0])    \n",
       "    f1.predict() \n",
       "    f2.predict()\n",
       "    \n",
@@ -1682,9 +1691,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f411c6ac898>"
+        "<matplotlib.figure.Figure at 0x7fe9d457ee10>"
        ]
       }
      ],
@@ -1724,14 +1733,14 @@
       "    xs = []\n",
       "    ys = []\n",
       "\n",
-      "    while f1.x[2,0] > 0:\n",
+      "    while f1.X[2,0] > 0:\n",
       "        t += dt\n",
       "        x,y = ball.update(dt)\n",
-      "        z = np.mat([[x,y]]).T\n",
+      "        z = np.array([[x,y]]).T\n",
       "\n",
       "        f1.update(z)\n",
-      "        xs.append(f1.x[0,0])\n",
-      "        ys.append(f1.x[2,0]) \n",
+      "        xs.append(f1.X[0,0])\n",
+      "        ys.append(f1.X[2,0]) \n",
       "        f1.predict() \n",
       "\n",
       "\n",
@@ -1750,17 +1759,17 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f411456b320>"
+        "<matplotlib.figure.Figure at 0x7fe9d49e26d8>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4114f3dac8>"
+        "<matplotlib.figure.Figure at 0x7fe9e02a3fd0>"
        ]
       }
      ],
@@ -1788,17 +1797,17 @@
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4115281da0>"
+        "<matplotlib.figure.Figure at 0x7fe9d4763198>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4114eb2208>"
+        "<matplotlib.figure.Figure at 0x7fe9d45cbe48>"
        ]
       }
      ],

09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:19938ddfba204e20c435b33acc3d723467354126675c5aa78dc8200036994fad"
+  "signature": "sha256:f9b7acba67bef2276a493d93976a5cf0997cb86a8644ecb6817597f4a3759b01"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -43,6 +43,8 @@
        "html": [
         "<style>\n",
         "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
         "\n",
         "    div.cell{\n",
         "        width: 850px;\n",
@@ -129,9 +131,9 @@
         "        white-space: nowrap;\n",
         "    }\n",
         "    div.text_cell_render{\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
         "        line-height: 135%;\n",
-        "        font-size: 110%;\n",
+        "        font-size: 125%;\n",
         "        width:750px;\n",
         "        margin-left:auto;\n",
         "        margin-right:auto;\n",
@@ -141,12 +143,12 @@
         "    div.output_subarea.output_text.output_pyout {\n",
         "        overflow-x: auto;\n",
         "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
+        "        max-height: 50000px;\n",
         "    }\n",
         "    div.output_subarea.output_stream.output_stdout.output_text {\n",
         "        overflow-x: auto;\n",
         "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
+        "        max-height: 50000px;\n",
         "    }\n",
         "    code{\n",
         "      font-size: 70%;\n",
@@ -259,7 +261,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7fb1b0f91a20>"
+        "<IPython.core.display.HTML at 0x7fa5b3193048>"
        ]
       }
      ],

11_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:3185a085ad316dcb4614b3dba3381282f39a7cc587dcf3de18fd06f2b0ba2fed"
+  "signature": "sha256:2fac195271ec54000f2c80a5066167e42e5fea10f2ec75c3e505927d8bf9b6d1"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -43,6 +43,8 @@
        "html": [
         "<style>\n",
         "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
         "\n",
         "    div.cell{\n",
         "        width: 850px;\n",
@@ -129,9 +131,9 @@
         "        white-space: nowrap;\n",
         "    }\n",
         "    div.text_cell_render{\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
         "        line-height: 135%;\n",
-        "        font-size: 110%;\n",
+        "        font-size: 125%;\n",
         "        width:750px;\n",
         "        margin-left:auto;\n",
         "        margin-right:auto;\n",
@@ -141,12 +143,12 @@
         "    div.output_subarea.output_text.output_pyout {\n",
         "        overflow-x: auto;\n",
         "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
+        "        max-height: 50000px;\n",
         "    }\n",
         "    div.output_subarea.output_stream.output_stdout.output_text {\n",
         "        overflow-x: auto;\n",
         "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
+        "        max-height: 50000px;\n",
         "    }\n",
         "    code{\n",
         "      font-size: 70%;\n",
@@ -259,7 +261,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f227ab379e8>"
+        "<IPython.core.display.HTML at 0x7ff94701a128>"
        ]
       }
      ],
@@ -402,9 +404,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f2265b10908>"
+        "<matplotlib.figure.Figure at 0x7ff92e4599e8>"
        ]
       }
      ],
@@ -772,7 +774,7 @@
       "f1.R *= 1.\n",
       "f1.Q *= .1\n",
       "\n",
-      "f1.x = np.array([[1,0,1,0]], dtype=float).T\n",
+      "f1.X = np.array([[1,0,1,0]], dtype=float).T\n",
       "f1.P = np.eye(4) * 5.\n",
       "\n",
       "# initialize storage and other variables for the run\n",
@@ -794,15 +796,15 @@
       "    # compute the difference in range between the nominal track and measured \n",
       "    # ranges\n",
       "    ra,rb = d.range_of(pos)\n",
-      "    rx,ry = d.range_of((pos[0]+f1.x[0,0], pos[1]+f1.x[2,0]))\n",
+      "    rx,ry = d.range_of((pos[0]+f1.X[0,0], pos[1]+f1.X[2,0]))\n",
       "    z = np.array([[ra-rx],[rb-ry]])\n",
       "\n",
       "    # compute linearized H for this time step\n",
       "    f1.H = H_of (pos, pos_a, pos_b)\n",
       "\n",
       "    # store stuff so we can plot it later\n",
-      "    xs.append (f1.x[0,0]+i)\n",
-      "    ys.append (f1.x[2,0]+i)\n",
+      "    xs.append (f1.X[0,0]+i)\n",
+      "    ys.append (f1.X[2,0]+i)\n",
       "    pxs.append (pos[0])\n",
       "    pys.append(pos[1])\n",
       "    \n",
@@ -813,7 +815,7 @@
       "\n",
       "p1, = plt.plot (xs, ys, 'r--')\n",
       "p2, = plt.plot (pxs, pys)\n",
-      "plt.legend([p1,p2], ['filter', 'ideal'], 2)\n",
+      "plt.legend([p1,p2], ['filter', 'ideal'], loc=2)\n",
       "plt.show()"
      ],
      "language": "python",
@@ -822,13 +824,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f2264ac0b00>"
+        "<matplotlib.figure.Figure at 0x7ff92d1d2f98>"
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 10
     },
     {
      "cell_type": "heading",

12_HInfinity_Filters/HInfinity_Filters.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:8c68f422d155e6e256b984c1601ed17d878240844f686e8559510bac3b24b183"
+  "signature": "sha256:14e099a145d5cd78a060a4c1c38c37a41238078ce93f0a43c52e3fcd938220e9"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -42,6 +42,8 @@
        "html": [
         "<style>\n",
         "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
+        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
         "\n",
         "    div.cell{\n",
         "        width: 850px;\n",
@@ -128,9 +130,9 @@
         "        white-space: nowrap;\n",
         "    }\n",
         "    div.text_cell_render{\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
         "        line-height: 135%;\n",
-        "        font-size: 110%;\n",
+        "        font-size: 125%;\n",
         "        width:750px;\n",
         "        margin-left:auto;\n",
         "        margin-right:auto;\n",
@@ -140,12 +142,12 @@
         "    div.output_subarea.output_text.output_pyout {\n",
         "        overflow-x: auto;\n",
         "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
+        "        max-height: 50000px;\n",
         "    }\n",
         "    div.output_subarea.output_stream.output_stdout.output_text {\n",
         "        overflow-x: auto;\n",
         "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
+        "        max-height: 50000px;\n",
         "    }\n",
         "    code{\n",
         "      font-size: 70%;\n",
@@ -256,13 +258,13 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 2,
+       "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f5f82564358>"
+        "<IPython.core.display.HTML at 0x7f4aa3b661d0>"
        ]
       }
      ],
-     "prompt_number": 2
+     "prompt_number": 1
     },
     {
      "cell_type": "markdown",
@@ -297,7 +299,7 @@
       "             [0., 1.]])\n",
       "\n",
       "f.H = array([[0., 1.]])\n",
-      "f.x = array([[0., 0.]]).T\n",
+      "#f.X = array([[0., 0.]]).T\n",
       "f.G = array([[dt**2 / 2, dt]]).T\n",
       "\n",
       "f.P = 0.01\n",
@@ -314,8 +316,8 @@
       "for i in range(1,40):\n",
       "    f.update (5)\n",
       "    #print(f.x.T)\n",
-      "    xs.append(f.x[0,0])\n",
-      "    vs.append(f.x[1,0])\n",
+      "    xs.append(f.X[0,0])\n",
+      "    vs.append(f.X[1,0])\n",
       "    f.predict(u=u)\n",
       "\n",
       "plt.subplot(211)\n",
@@ -334,11 +336,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f5f616b2ac8>"
+        "<matplotlib.figure.Figure at 0x7f4a86c94f98>"
        ]
       }
      ],
-     "prompt_number": 14
+     "prompt_number": 2
     }
    ],
    "metadata": {}