Expanded coverage.

Probably mostly just the Fading memory, but also played with
length of data, noise settings, etc.

15_Adaptive_Filtering/Adaptive_Filtering.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:c029584dd374b0f2f2bec0b527d961fdac43c5e14ab9d708333e9400e6d719f1"
+  "signature": "sha256:0adb3177d0f465a38bed1a6cd92dbad50949762c108800f0867d362caa213ab5"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -260,13 +260,13 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 2,
+       "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f3c6cf44630>"
+        "<IPython.core.display.HTML at 0x7f14d0924240>"
        ]
       }
      ],
-     "prompt_number": 2
+     "prompt_number": 1
     },
     {
      "cell_type": "heading",
@@ -363,7 +363,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 3
+     "prompt_number": 2
     },
     {
      "cell_type": "markdown",
@@ -389,7 +389,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 4
+     "prompt_number": 3
     },
     {
      "cell_type": "markdown",
@@ -442,11 +442,11 @@
        "output_type": "display_data",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAxIAAAGNCAYAAACFa0d0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6cf5de80>"
+        "<matplotlib.figure.Figure at 0x7f14b44c8860>"
        ]
       }
      ],
-     "prompt_number": 5
+     "prompt_number": 4
     },
     {
      "cell_type": "markdown",
@@ -471,13 +471,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAx0AAAGNCAYAAAB0YBz5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6ceebb70>"
+        "<matplotlib.figure.Figure at 0x7f14b41e37b8>"
        ]
       }
      ],
-     "prompt_number": 6
+     "prompt_number": 5
     },
     {
      "cell_type": "markdown",
@@ -509,7 +509,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 7
+     "prompt_number": 6
     },
     {
      "cell_type": "markdown",
@@ -556,13 +556,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAxcAAAGkCAYAAABD4djOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6ccc7a90>"
+        "<matplotlib.figure.Figure at 0x7f14b41ee668>"
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 7
     },
     {
      "cell_type": "markdown",
@@ -578,7 +578,7 @@
       "# reinitialize filter\n",
       "cvfilter.x = array([0., 0.])\n",
       "\n",
-      "pos2, zs2 = generate_data(250, noise_factor)\n",
+      "pos2, zs2 = generate_data(120, noise_factor)\n",
       "xs2 = pos2[:,0]\n",
       "z_xs2 = zs2[:,0]\n",
       "t = np.arange(0, len(xs2) * dt, dt)\n",
@@ -596,13 +596,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6ccd5b38>"
+        "<matplotlib.figure.Figure at 0x7f14ac3eb5f8>"
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 39
     },
     {
      "cell_type": "markdown",
@@ -633,13 +633,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6ce4b208>"
+        "<matplotlib.figure.Figure at 0x7f14b44c8f98>"
        ]
       }
      ],
-     "prompt_number": 10
+     "prompt_number": 40
     },
     {
      "cell_type": "markdown",
@@ -670,13 +670,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAxkAAAGdCAYAAAB+Xb4YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6ce1ceb8>"
+        "<matplotlib.figure.Figure at 0x7f14ac4cb9b0>"
        ]
       }
      ],
-     "prompt_number": 11
+     "prompt_number": 41
     },
     {
      "cell_type": "markdown",
@@ -703,7 +703,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 12
+     "prompt_number": 42
     },
     {
      "cell_type": "code",
@@ -722,13 +722,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAxkAAAGdCAYAAAB+Xb4YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6ce4b7f0>"
+        "<matplotlib.figure.Figure at 0x7f14b41eeda0>"
        ]
       }
      ],
-     "prompt_number": 13
+     "prompt_number": 43
     },
     {
      "cell_type": "markdown",
@@ -775,11 +775,11 @@
        "output_type": "display_data",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAxYAAAGaCAYAAACSU9UtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6cc8e438>"
+        "<matplotlib.figure.Figure at 0x7f14afea5b38>"
        ]
       }
      ],
-     "prompt_number": 14
+     "prompt_number": 13
     },
     {
      "cell_type": "markdown",
@@ -792,7 +792,7 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "pos2, zs2 = generate_data(250, noise_factor=0.2)\n",
+      "pos2, zs2 = generate_data(120, noise_factor=0.2)\n",
       "xs2 = pos2[:,0]\n",
       "z_xs2 = zs2[:,0]\n",
       "\n",
@@ -808,7 +808,7 @@
       "    res.append(cvfilter.y[0])\n",
       "xs = np.asarray(xs)\n",
       "plt.subplot(121)\n",
-      "plt.plot(t, z_xs2, label='measurment')\n",
+      "plt.plot(t, z_xs2, label='measurement')\n",
       "plt.plot(t, xs, label='filter')\n",
       "plt.legend(loc=4)\n",
       "plt.subplot(122)\n",
@@ -824,13 +824,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6ce71d30>"
+        "<matplotlib.figure.Figure at 0x7f14b41b5f98>"
        ]
       }
      ],
-     "prompt_number": 15
+     "prompt_number": 45
     },
     {
      "cell_type": "markdown",
@@ -916,13 +916,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6cde05f8>"
+        "<matplotlib.figure.Figure at 0x7f14ac40c0f0>"
        ]
       }
      ],
-     "prompt_number": 16
+     "prompt_number": 46
     },
     {
      "cell_type": "markdown",
@@ -968,8 +968,8 @@
       "        cvfilter.Q /= Q_scale_factor\n",
       "        count -= 1\n",
       "        \n",
-      "plt.plot(t[0:100], z_xs2[0:100], label='measurement')\n",
-      "plt.plot(t[0:100], xs[0:100], label='filter')\n",
+      "plt.plot(t, z_xs2, label='measurement')\n",
+      "plt.plot(t, xs, label='filter')\n",
       "plt.ylabel('$\\epsilon$')\n",
       "plt.xlabel('time (sec)')\n",
       "plt.legend(loc=4)\n",
@@ -981,13 +981,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3c6cbeac18>"
+        "<matplotlib.figure.Figure at 0x7f14b4175550>"
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 48
     },
     {
      "cell_type": "markdown",
@@ -995,6 +995,171 @@
      "source": [
       "The performance of this filter is markedly better than the constant velocity filter. The constant velocity filter took roughly 10 seconds to reacquire the signal after the start of the manuever. The adaptive filter takes under a second to do the same. "
      ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Fading Memory Filter"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Fading memory filters are not normally classified as an adaptive filter since they do not adapt to the the input, but they do provide good performance with manuevering targets. They also have the benefit of having a very simple computational form for first, second, and third order kinematic filters (e.g. the filters we are using in this chapter). This simple form does not require the Ricatti equations to compute the gain of the Kalman filter, which drastically reduces the amount of computation. However, there is also a form that works with the standard Kalman filter. I will focus on the latter in this chapter since our focus is more on adaptive filters. Both forms of the fading memory filter are implemented in `FilterPy`.\n",
+      "\n",
+      "The Kalman filter is recursive, but it incorporates all of the previous measurements into the current computation of the filter gain. If the target behavior is consistant with the process model than this allows the Kalman filter to find the optimal estimate for every measurement. Consider a ball in flight - we can clearly estimate the position of the ball at time t better if we take into account all the previous measurement. If we only used some of the measurements we would be less certain about the current position, and thus more influenced by the noise in the measurement. If this is still not clear, consider the worst case. Suppose we forget all but the last measurement and estimates. We would then have no confidence in the position and trajectory of the ball, and would little choice but to weight the current measurement heavily. If the measurement is noisy, the estimate is noisy. We see this effect every time a Kalman filter is initialized. The early estimates are noisy, but then they settle down as more measurements are acquired.\n",
+      "\n",
+      "However, if the target is manuevering it is not always behaving like the process model predicts. In this case remembering all of the past measurements and estimates is a liability. We can see this in all of the charts above. The target initiates a turn, and the Kalman filter continues to project movement in a straight line. This is because the filter has built a history of the target's movement, and incorrectly 'feels' confident that the target is moving in a straight line at a given heading and velocity. \n",
+      "\n",
+      "The fading memory filter accounts for this problem by giving less weight to older measurements, and greater weight to the more recent measurements. \n",
+      "\n",
+      "There are many formulations for the fading memory Filter; I use the one provided by Dan simon in *Optimal State Estimation* [1]. I will not go through his derivation, but only provide the results.\n",
+      "\n",
+      "The Kalman filter equation for the covariances of the estimation error is\n",
+      "\n",
+      "$$ \\mathbf{P} = \\mathbf{FPF}^\\mathtt{T} + \\mathbf{Q}$$\n",
+      "\n",
+      "We can force the filter to forget past measurements by multiplying a term $\\alpha$\n",
+      "\n",
+      "$$ \\tilde{\\mathbf{P}} = \\alpha^2\\mathbf{FPF}^\\mathtt{T} + \\mathbf{Q}$$\n",
+      "\n",
+      "where $\\alpha > 1.0$. If $\\alpha == 1$ then we get the normal Kalman filter performance. $\\alpha$ is an attribute of `FilterPy`s Kalman filter class; its value defaults to 1 so the filter acts like a Kalman filter unless $\\alpha$ is assigned a value other than 1. There is no hard and fast rule for choosing $\\alpha$, but it is typically very close to 1, such as 1.01. You will need to make many runs with either simulated or real data to determine a value that responds to manuevers without causing the estimate to become too noisy due to overly weighting the noisy measurement.\n",
+      "\n",
+      "Why does this work? If we increase the estimate error covariance the filter becomes more uncertain about it's estimate, hence it gives more weight to the measurement. \n",
+      "\n",
+      "One caveat - if we use $\\alpha$ than we are computing $\\tilde{\\mathbf{P}}$, not $\\mathbf{P}$. In other words, `KalmanFilter.P` *is not* equal to the covariance of the estimation error, so do not treat it as if it is.\n",
+      "\n",
+      "Let's filter our data using the fading memory filter and see the result. I will inject a lot of error into the system so that we can compare various approaches."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# reinitialize filter\n",
+      "\n",
+      "pos2, zs2 = generate_data(70, noise_factor=1.2)\n",
+      "xs2 = pos2[:,0]\n",
+      "z_xs2 = zs2[:,0]\n",
+      "\n",
+      "\n",
+      "cvfilter.x = array([0., 0.])\n",
+      "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
+      "cvfilter.alpha = 1.00\n",
+      "\n",
+      "xs = []\n",
+      "res = []\n",
+      "for z in z_xs2:\n",
+      "    cvfilter.predict()\n",
+      "    cvfilter.update([z])\n",
+      "    xs.append(cvfilter.x[0])\n",
+      "    res.append(cvfilter.y[0])\n",
+      "xs = np.asarray(xs)\n",
+      "plt.subplot(221)\n",
+      "plt.plot(t[0:100], z_xs2, label='measurement', alpha=0.5)\n",
+      "plt.plot(t[0:100], xs, label='filter')\n",
+      "plt.legend(loc=2)\n",
+      "plt.title('Standard Kalman Filter')\n",
+      "\n",
+      "cvfilter.x = array([0., 0.])\n",
+      "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=20.)\n",
+      "cvfilter.alpha = 1.00\n",
+      "\n",
+      "xs = []\n",
+      "res = []\n",
+      "for z in z_xs2:\n",
+      "    cvfilter.predict()\n",
+      "    cvfilter.update([z])\n",
+      "    xs.append(cvfilter.x[0])\n",
+      "    res.append(cvfilter.y[0])\n",
+      "    \n",
+      "xs = np.asarray(xs)\n",
+      "\n",
+      "plt.subplot(222)\n",
+      "plt.plot(t[0:100], z_xs2, label='measurement', alpha=0.5)\n",
+      "plt.plot(t[0:100], xs, label='filter')\n",
+      "plt.legend(loc=2)\n",
+      "plt.title('$\\\\mathbf{Q}=20$')\n",
+      "\n",
+      "\n",
+      "cvfilter.x = array([0., 0.])\n",
+      "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
+      "cvfilter.alpha = 1.02\n",
+      "\n",
+      "xs = []\n",
+      "res = []\n",
+      "for z in z_xs2:\n",
+      "    cvfilter.predict()\n",
+      "    cvfilter.update([z])\n",
+      "    xs.append(cvfilter.x[0])\n",
+      "    res.append(cvfilter.y[0])\n",
+      "xs = np.asarray(xs)\n",
+      "plt.subplot(223)\n",
+      "plt.plot(t[0:100], z_xs2, label='measurement', alpha=0.5)\n",
+      "plt.plot(t[0:100], xs, label='filter')\n",
+      "plt.legend(loc=2)\n",
+      "plt.title('Fading Memory ($\\\\alpha$ = 1.02)')\n",
+      "\n",
+      "cvfilter.x = array([0., 0.])\n",
+      "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
+      "cvfilter.alpha = 1.05\n",
+      "\n",
+      "xs = []\n",
+      "res = []\n",
+      "for z in z_xs2:\n",
+      "    cvfilter.predict()\n",
+      "    cvfilter.update([z])\n",
+      "    xs.append(cvfilter.x[0])\n",
+      "    res.append(cvfilter.y[0])\n",
+      "xs = np.asarray(xs)\n",
+      "plt.subplot(224)\n",
+      "plt.plot(t[0:100], z_xs2, label='measurement', alpha=0.5)\n",
+      "plt.plot(t[0:100], xs, label='filter')\n",
+      "plt.legend(loc=2)\n",
+      "plt.title('Fading Memory ($\\\\alpha$ = 1.05)')\n",
+      "\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f14aa800d30>"
+       ]
+      }
+     ],
+     "prompt_number": 79
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The first plot shows the performance of the Kalman filter. The filter diverges when the manuever starts and does not reacquire the signal until about 10 seconds. I then made the filter track the manuever very quickly by making the process noise large, but this has the cost of making the filter estimate very noisy due to unduly weighting the noisy measurements. I then implemented a fading memory filter with $\\alpha=1.02$. The filtered estimate is very smooth, but it does take a few seconds to converge when the target regains steady state behavior. However, the time to do so is considerably smaller than for the Kalman filter, and the amount of lag is much smaller - the estimate for the fading memory is much closer to the actual track than the Kalman filter's track is. Finally, I bumped up $\\alpha$ to 1.05. Here we can see that the filter responds almost instantly to the manuever, but that the estimate is not as straight during the steady state operation because the filter is forgetting the past measurements. \n",
+      "\n",
+      "This is quite good performance for such a small change in code! Note that there is no 'correct' choice here. You will need to design your filter based on your needs and the characteristics of the measurement noise, process noise, and manuevering behavior of the target."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "References"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "* [1] Dan Simon. \"Optimal State Estimation.\" John Wiley & Sons. p. 208-212. (2006)"
+     ]
     }
    ],
    "metadata": {}