UKF chapter updated for Merwe parametization.

Chapter is not complete; checking in because I am beginning to alter
the formulation of unscented_transform in filterpy.

10_Extended_Kalman_Filters.ipynb

@@ -312,7 +312,7 @@
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truncated
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+       "<matplotlib.figure.Figure at 0x751ac88>"
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x57e9a58>"
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@@ -436,7 +436,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x510d2b0>"
+       "<matplotlib.figure.Figure at 0x445e0b8>"
       ]
      },
      "metadata": {},
@@ -772,9 +772,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwYAAAEtCAYAAACyMncIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x808c710>"
+       "<matplotlib.figure.Figure at 0x87649b0>"
       ]
      },
      "metadata": {},
@@ -782,9 +782,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x593d5f8>"
+       "<matplotlib.figure.Figure at 0x87eb828>"
       ]
      },
      "metadata": {},
@@ -792,9 +792,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwMAAAEtCAYAAABUG7xMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x58c5668>"
+       "<matplotlib.figure.Figure at 0x86e8e80>"
       ]
      },
      "metadata": {},
@@ -897,7 +897,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nUqOHbKQnT/0tv+59MpOT+AmTXbj1s0kQCQAAAABJRU5ErkJggg==\n",
       "text/latex": [
        "$$\\left[\\begin{matrix}\\frac{x_{pos}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}}\\end{matrix}\\right]$$"
       ],
@@ -1046,7 +1046,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8067a90>"
+       "<matplotlib.figure.Figure at 0x87c4a90>"
       ]
      },
      "metadata": {},
@@ -1402,12 +1402,12 @@
    "source": [
     "from math import sqrt\n",
     "\n",
-    "def H_of(x, p):\n",
+    "def H_of(x, landmark_pos):\n",
     "    \"\"\" compute Jacobian of H matrix where h(x) computes the range and\n",
     "    bearing to a landmark for state x \"\"\"\n",
     "\n",
-    "    px = p[0]\n",
-    "    py = p[1]\n",
+    "    px = landmark_pos[0]\n",
+    "    py = landmark_pos[1]\n",
     "    hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2\n",
     "    dist = sqrt(hyp)\n",
     "\n",
@@ -1435,12 +1435,12 @@
    "outputs": [],
    "source": [
     "from math import atan2\n",
-    "def Hx(x, p):\n",
+    "def Hx(x, landmark_pos):\n",
     "    \"\"\" takes a state variable and returns the measurement that would\n",
     "    correspond to that state.\n",
     "    \"\"\"\n",
-    "    px = p[0]\n",
-    "    py = p[1]\n",
+    "    px = landmark_pos[0]\n",
+    "    py = landmark_pos[1]\n",
     "    dist = sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2)\n",
     "\n",
     "    Hx = array([[dist],\n",
@@ -1479,7 +1479,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 17,
    "metadata": {
     "collapsed": true
    },
@@ -1582,7 +1582,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 113,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1632,7 +1632,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 110,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1640,9 +1640,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa0b1550>"
+       "<matplotlib.figure.Figure at 0xa5e3f28>"
       ]
      },
      "metadata": {},
@@ -1652,7 +1652,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.01969482  0.02094075  0.00154535]\n"
+      "[ 0.0199192   0.02067011  0.00153754]\n"
      ]
     }
    ],
@@ -1677,7 +1677,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 109,
+   "execution_count": 21,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1685,9 +1685,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAEWCAYAAABL+3CVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x806fd30>"
+       "<matplotlib.figure.Figure at 0x86db438>"
       ]
      },
      "metadata": {},
@@ -1697,7 +1697,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.02126405  0.04551132  0.00022729]\n"
+      "[ 0.01938022  0.04634068  0.00022408]\n"
      ]
     }
    ],
@@ -1716,7 +1716,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 114,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -1724,9 +1724,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xafeb7b8>"
+       "<matplotlib.figure.Figure at 0x86dbf60>"
       ]
      },
      "metadata": {},
@@ -1736,7 +1736,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.26908765  0.8039095   0.00355399]\n"
+      "[ 0.29442198  0.82419287  0.00369511]\n"
      ]
     }
    ],
@@ -1755,16 +1755,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 119,
+   "execution_count": 23,
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "scrolled": true
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x5834ac8>"
+       "<matplotlib.figure.Figure at 0xa642940>"
       ]
      },
      "metadata": {},
@@ -1774,7 +1775,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.00883285  0.00866094  0.00077284]\n"
+      "[ 0.00881439  0.0086407   0.00077058]\n"
      ]
     }
    ],
@@ -1786,6 +1787,19 @@
     "                      sigma_range=0.3, sigma_bearing=0.1)\n",
     "print(ekf.P.diagonal())"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Discussion\n",
+    "\n",
+    "I said that this was a 'real' problem, and in some ways it is. I've seen alternative presentations that used robot motion models that led to much easier Jacobians. On the other hand, my model of a automobile's movement is itself simplistic in several ways. First, it uses the *bicycle model* to compute how it moves. A real car has two sets of tires, and each travels on a different radius. The wheels do not grip the surface perfectly. I also assumed that the robot was able to instaneously respond to my control input changes. In fact, I didn't even bother changing the control input during the run. Sebastian Thrun writes in *Probabalistic Robots* that simplied models are justified because the filters perform well when used to track real vehicles. The lesson here is that while you have to have a reasonably accurate nonlinear model, it does not need to be perfect to operate well. As a designer you will need to balance the fidelity of your model with the difficulty of the math and the computation required to implement the equations. \n",
+    "\n",
+    "Another way in which this problem was simplistic is that we assumed that we knew the correspondance between the landmarks and measurements. But suppose we are using radar - how would we know that a specific signal return corresponded to a specific building in the local scene? This question hints at SLAM algorithms - simultaneous localization and mapping. SLAM is not the point of this book, so I will not elaborate on this topic. \n",
+    "\n",
+    "However, this example should underscore how difficult EKFs can be. EKF have a well deserved reputation for difficulty. Especially when the problem is highly nonlinear you must design "
+   ]
   }
  ],
  "metadata": {
@@ -1804,7 +1818,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3"
+   "version": "3.4.1"
   }
  },
  "nbformat": 4,

code/ukf_internal.py

@@ -4,12 +4,13 @@ Created on Tue May 27 21:21:19 2014
 
 @author: rlabbe
 """
+from filterpy.kalman import UnscentedKalmanFilter as UKF
+from filterpy.kalman import MerweScaledSigmaPoints
 import matplotlib.pyplot as plt
 from matplotlib.patches import Ellipse,Arrow
-import stats
-import numpy as np
 import math
-from filterpy.kalman import UnscentedKalmanFilter as UKF
+import numpy as np
+import stats
 from stats import plot_covariance_ellipse
 
 def _sigma_points(mean, sigma, kappa):
@@ -59,8 +60,6 @@ def show_three_gps():
     plt.show()
 
 
-
-
 def show_four_gps():
     circle1=plt.Circle((-4,2),5,color='#004080',fill=False,linewidth=20, alpha=.7)
     circle2=plt.Circle((5.5,1),5,color='#E24A33', fill=False, linewidth=8, alpha=.7)
@@ -77,21 +76,24 @@ def show_four_gps():
 
     plt.axis('equal')
     plt.show()
-def show_sigma_transform():
+
+
+def show_sigma_transform(with_text=False):
     fig = plt.figure()
     ax=fig.gca()
 
     x = np.array([0, 5])
     P = np.array([[4, -2.2], [-2.2, 3]])
 
-    plot_covariance_ellipse(x, P, facecolor='b', variance=9, alpha=0.5)
-    S = UKF.sigma_points(x=x, P=P, alpha=.5, kappa=0)
+    plot_covariance_ellipse(x, P, facecolor='b', alpha=0.6, variance=9)
+    sigmas = MerweScaledSigmaPoints(2, alpha=.5, beta=2., kappa=0.)
+
+    S = sigmas.sigma_points(x=x, P=P)
     plt.scatter(S[:,0], S[:,1], c='k', s=80)
 
     x = np.array([15, 5])
     P = np.array([[3, 1.2],[1.2, 6]])
-    plot_covariance_ellipse(x, P, facecolor='g', variance=9, alpha=0.5)
-
+    plot_covariance_ellipse(x, P, facecolor='g', variance=9, alpha=0.3)
 
     ax.add_artist(arrow(S[0,0], S[0,1], 11, 4.1, 0.6))
     ax.add_artist(arrow(S[1,0], S[1,1], 13, 7.7, 0.6))
@@ -102,21 +104,30 @@ def show_sigma_transform():
     ax.axes.get_xaxis().set_visible(False)
     ax.axes.get_yaxis().set_visible(False)
 
+    if with_text:
+        plt.text(2.5, 1.5, r"$\chi$", fontsize=32)
+        plt.text(13, -1, r"$\mathcal{Y}$", fontsize=32)
+
     #plt.axis('equal')
     plt.show()
 
 
+
 def show_2d_transform():
 
+    plt.cla()
     ax=plt.gca()
 
     ax.add_artist(Ellipse(xy=(2,5), width=2, height=3,angle=70,linewidth=1,ec='k'))
-    ax.add_artist(Ellipse(xy=(7,5), width=2.2, alpha=0.3, height=3.8,angle=150,linewidth=1,ec='k'))
+    ax.add_artist(Ellipse(xy=(7,5), width=2.2, alpha=0.3, height=3.8,angle=150,fc='g',linewidth=1,ec='k'))
 
     ax.add_artist(arrow(2, 5, 6, 4.8))
-
     ax.add_artist(arrow(1.5, 5.5, 7, 3.8))
     ax.add_artist(arrow(2.3, 4.1, 8, 6))
+    ax.add_artist(arrow(3.3, 5.1, 6.5, 4.3))
+    ax.add_artist(arrow(1.3, 4.8, 7.2, 6.3))
+    ax.add_artist(arrow(1.1, 5.2, 8.2, 5.3))
+    ax.add_artist(arrow(2, 4.4, 7.3, 4.5))
 
     ax.axes.get_xaxis().set_visible(False)
     ax.axes.get_yaxis().set_visible(False)
@@ -139,27 +150,34 @@ def show_3_sigma_points():
 
 def show_sigma_selections():
     ax=plt.gca()
-    ax.add_artist(Ellipse(xy=(2,5), alpha=0.5, width=2, height=3,angle=0,linewidth=1,ec='k'))
-    ax.add_artist(Ellipse(xy=(5,5), alpha=0.5, width=2, height=3,angle=0,linewidth=1,ec='k'))
-    ax.add_artist(Ellipse(xy=(8,5), alpha=0.5, width=2, height=3,angle=0,linewidth=1,ec='k'))
     ax.axes.get_xaxis().set_visible(False)
     ax.axes.get_yaxis().set_visible(False)
 
-    plt.scatter([1.5,2,2.5],[5,5,5],c='k', s=50)
-    plt.scatter([2,2],[4.5, 5.5],c='k', s=50)
+    x = np.array([2, 5])
+    P = np.array([[3, 1.1], [1.1, 4]])
 
-    plt.scatter([4.8,5,5.2],[5,5,5],c='k', s=50)
-    plt.scatter([5,5],[4.8, 5.2],c='k', s=50)
+    points = MerweScaledSigmaPoints(2, .05, 2., 1.)
+    sigmas = points.sigma_points(x, P)
+    plot_covariance_ellipse(x, P, facecolor='b', alpha=0.6, variance=[.5])
+    plt.scatter(sigmas[:,0], sigmas[:, 1], c='k', s=50)
 
-    plt.scatter([7.2,8,8.8],[5,5,5],c='k', s=50)
-    plt.scatter([8,8],[4,6],c='k' ,s=50)
+    x = np.array([5, 5])
+    points = MerweScaledSigmaPoints(2, .15, 2., 1.)
+    sigmas = points.sigma_points(x, P)
+    plot_covariance_ellipse(x, P, facecolor='b', alpha=0.6, variance=[.5])
+    plt.scatter(sigmas[:,0], sigmas[:, 1], c='k', s=50)
+
+    x = np.array([8, 5])
+    points = MerweScaledSigmaPoints(2, .4, 2., 1.)
+    sigmas = points.sigma_points(x, P)
+    plot_covariance_ellipse(x, P, facecolor='b', alpha=0.6, variance=[.5])
+    plt.scatter(sigmas[:,0], sigmas[:, 1], c='k', s=50)
 
     plt.axis('equal')
     plt.xlim(0,10); plt.ylim(0,10)
     plt.show()
 
 
-
 def show_sigmas_for_2_kappas():
     # generate the Gaussian data
 
@@ -190,9 +208,41 @@ def show_sigmas_for_2_kappas():
     plt.show()
 
 
+def plot_sigma_points():
+    x = np.array([0, 0])
+    P = np.array([[4, 2], [2, 4]])
+
+    sigmas = MerweScaledSigmaPoints(n=2, alpha=.3, beta=2., kappa=1.)
+    S0 = sigmas.sigma_points(x, P)
+    Wm0, Wc0 = sigmas.weights()
+
+    sigmas = MerweScaledSigmaPoints(n=2, alpha=1., beta=2., kappa=1.)
+    S1 = sigmas.sigma_points(x, P)
+    Wm1, Wc1 = sigmas.weights()
+
+    def plot_sigmas(s, w, **kwargs):
+        min_w = min(abs(w))
+        scale_factor = 100 / min_w
+        return plt.scatter(s[:, 0], s[:, 1], s=abs(w)*scale_factor, alpha=.5, **kwargs)
+
+    plt.subplot(121)
+    plot_sigmas(S0, Wc0, c='b')
+    plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, variance=[1, 4])
+    plt.title('alpha=0.3')
+    plt.subplot(122)
+    plot_sigmas(S1, Wc1,  c='b', label='Kappa=2')
+    plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, variance=[1, 4])
+    plt.title('alpha=1')
+    plt.show()
+    print(sum(Wc0))
 
 if __name__ == '__main__':
-    show_four_gps()
+
+    #show_2d_transform()
+    #show_sigma_selections()
+
+    show_sigma_transform(True)
+    #show_four_gps()
     #show_sigma_transform()
     #show_sigma_selections()
 

experiments/ukfloc.py

@@ -16,33 +16,23 @@ from numpy.random import randn
 
 
 
-def normalize_angle(x, index):
-    def normalize(x):
-        if x > np.pi:
-            x -= 2*np.pi
-        if x < -np.pi:
-            x = 2*np.pi
-        return x
+def normalize_angle(x):
+    if x > np.pi:
+        x -= 2*np.pi
+    if x < -np.pi:
+        x = 2*np.pi
+    return x
 
-    if x.ndim > 1:
-        for i in range(len(x)):
-            x[i, index] = normalize(x[i, index])
-
-    else:
-        x[index] = normalize(x[index])
-
-
-def residual(a,b , index=1):
+def residual_h(a, b):
     y = a - b
-    normalize_angle(y, index)
+    y[1] = normalize_angle(y[1])
     return y
 
 
-def residual_h(a, b):
-    return residual(a, b, 1)
-
 def residual_x(a, b):
-    return residual(a, b, 2)
+    y = a - b
+    y[2] = normalize_angle(y[2])
+    return y
 
 
 def move(x, u, dt, wheelbase):