diff --git a/Extended_Kalman_Filters.ipynb b/Extended_Kalman_Filters.ipynb index 273c14b..ccaa892 100644 --- a/Extended_Kalman_Filters.ipynb +++ b/Extended_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:a543c963e2375474d406b99de024c80765b4fd311e4b9ef7f8df686b92a8e0ac" + "signature": "sha256:accc4aa29e12d5a5ed17db77c8d414aad014c9ab74372dff107bdcaaa8e97d40" }, "nbformat": 3, "nbformat_minor": 0, @@ -22,6 +22,8 @@ "input": [ "#format the book\n", "%matplotlib inline\n", + "from __future__ import division, print_function\n", + "import matplotlib.pyplot as plt\n", "import book_format\n", "book_format.load_style()" ], @@ -239,7 +241,7 @@ "output_type": "pyout", "prompt_number": 1, "text": [ - "" + "" ] } ], @@ -278,12 +280,11 @@ "cell_type": "code", "collapsed": false, "input": [ - "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from numpy.random import normal\n", "\n", - "normals = normal(loc=0.0, scale=1, size=500000)\n", - "ys = 2*normals + 1\n", + "data = normal(loc=0.0, scale=1, size=500000)\n", + "ys = 2*data + 1\n", "\n", "plt.hist(ys,1000)\n", "plt.show()" @@ -294,13 +295,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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E2MDmGs/QLAPoDM0ykIDcHfphrTOgZJZhKmonbJHYLL/99tvavXu3Dh48GN1zXVeHDx/W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\n3Nsy6q74NLPkB9qadmmwe6i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"text": [ - "" + "" ] } ], - "prompt_number": 2 + "prompt_number": 13 }, { "cell_type": "markdown", @@ -318,7 +319,7 @@ "def g(x):\n", " return 2*x+1\n", "\n", - "plot_transfer_func (normals, g, lims=(-10,10), num_bins=100)" + "plot_transfer_func (data, g, lims=(-10,10), num_bins=300)" ], "language": "python", "metadata": {}, @@ -326,9 +327,9 @@ { "metadata": {}, "output_type": "display_data", - "png": 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4UHu3Go+GtKuhUysvLnA6HFegd8gc8mUO+QKs5aZjamtFsx58q1Y/XjhGM/KH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\notGZicpOcaatwu05i2YUxQAARJnefkM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OnKhXX33V7NMDCBPdnl69U9agNZsO61CTS+kJ0XriqvHMSWoBxm0ES4urR/e9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\nCvof9ODZiwfRi0Xx4MmD4B8QehC8CFLrodAeShW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"text": [ - "" + "" ] } ], @@ -350,9 +351,9 @@ "from nonlinear_plots import plot_transfer_func\n", "\n", "def g(x):\n", - " return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-0.9*x\n", + " return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x\n", "\n", - "plot_transfer_func (normals, g, lims=(-4,4), num_bins=300)" + "plot_transfer_func (data, g, lims=(-4,4), num_bins=300)" ], "language": "python", "metadata": {}, @@ -360,9 +361,48 @@ { "metadata": {}, "output_type": "display_data", - "png": 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dFn74xkGUVVbjkRtmQamQhJ3TRfoZGmlblDmG4xUY4+XOnD2q9gaTyYSrr74a69evx+LF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\njJ3pPX78+NQXnUm+bK60bfN/7YPUlc/+TG+ujlm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nMpnQfFlB+82pUpTWNsFNoTDfFuStxoyhIXLEsytn7OntDuds6kpzqwmbdEX4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\nqFj0EhEROSCTyYTqhhYsmRwHdzf+ObeF/MoGfHO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"text": [ - "" + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This result may be somewhat suprising to you. The transfer function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a Gaussian. Recall the equations for multiplying two univariate Gaussians:\n", + "$$\\begin{align*}\n", + "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n", + "\\sigma = \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n", + "\\end{align*}$$\n", + "\n", + "These equations do not hold for non-Gaussians, and certainly do not hold for the probability distribution shown in the 'output' chart above. \n", + "\n", + "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the transfer function again, simulating the next step time step of the Kalman filter.\n", + "\n", + "**process function? what is the correct name**\n", + "\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "y=g(data)\n", + "plot_transfer_func (y, g, lims=(-4,4), num_bins=300)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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GRJSat9olIpIJH3c3zB8TjUmJAXhz53lsySrHw+NiEGHhOuVEIupWTW9nWB/m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\nq/vuu8/pOIrH49qxY4csy5Ik3X///brjjjscTiUNDg7qhRd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+ "text": [ + "" ] } ], @@ -372,7 +412,114 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This result may be somewhat suprising to you. The transfer function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a " + "As you can see the probability function is futher distorted from the original Gaussian. However, the graph is still somewhat symmetric around $0$, let's see what the mean is." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print ('input mean, variance: %.4f, %.4f'% (np.average(data), np.std(data)**2))\n", + "print ('output mean, variance: %.4f, %.4f'% (np.average(y), np.std(y)**2))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "input mean, variance: 0.0005, 0.9988\n", + "output mean, variance: -0.0285, 2.2400" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's compare that to the linear function that passes through (-2,3) and (2,-3), which is very close to the nonlinear function we have plotted. Using the equation of a line we have\n", + "$$m=\\frac{-3-3}{2-(-2)}=-1.5$$" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def h(x): return -1.5*x\n", + "plot_transfer_func (data, h, lims=(-4,4), num_bins=300)\n", + "out = h(data)\n", + "print ('output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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232YUtfnRpdFkwpgYP8QGuNsxofNgTS91FyXV9XhnTw6yS2qx+IZo9Am2/Yu7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\n", + "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "output mean, variance: 0.0003, 2.2552\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Although the shapes are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "out = h(data)\n", + "out2 = g(data)\n", + "\n", + "for i in range(10):\n", + " out = h(out)\n", + " out2 = g(out2)\n", + "print ('linear output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))\n", + "print ('nonlinear output mean, variance: %.4f, %.4f'% (np.average(out2), np.std(out2)**2))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "linear output mean, variance: -0.0168, 7495.4511\n", + "nonlinear output mean, variance: -1.9141, 26283.7039\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Unfortunately we can see that the nonlinear version is not stable. We have drifted significantly from the mean of 0, and the variance is half an order of magnitude larger. " ] } ], diff --git a/nonlinear_plots.py b/nonlinear_plots.py index 68b1f2d..b277cf6 100644 --- a/nonlinear_plots.py +++ b/nonlinear_plots.py @@ -11,7 +11,6 @@ import matplotlib.pyplot as plt from numpy.random import normal - def plot_transfer_func(data, f, lims,num_bins=1000): ys = f(data) @@ -31,6 +30,7 @@ def plot_transfer_func(data, f, lims,num_bins=1000): plt.plot([0,0,lims[0]],[lims[0],isct,isct],c='r') plt.xlim(lims) plt.ylim(lims) + plt.title('transfer function') # plot input plt.subplot(2,2,4) @@ -40,64 +40,3 @@ def plot_transfer_func(data, f, lims,num_bins=1000): plt.title('input') plt.show() - -''' -normals = normal(loc=0.0, scale=1, size=5000000) - -#rint h(normals).sort() - - -def f(x): - return 2*x + 1 - -def g(x): - return (cos(4*(x/2+0.7)))*sin(0.3*x)-0.9*x - return (cos(4*(x/3+0.7)))*sin(0.3*x)-0.9*x - #return -x+1.2*np.sin(0.7*x)+3 - return sin(5-.2*x) - -def h(x): return cos(.4*x)*x - -plot_transfer_func (normals, g, lims=(-4,4),num_bins=500) -del(normals) - -#plt.plot(g(np.arange(-10,10,0.1))) - -''' - -''' -ys = f(normals) - - -r = np.linspace (min(normals), max(normals), num_bins) - -h= np.histogram(ys, num_bins,density=True) -print h -print len(h[0]), len(h[1][0:-1]) - -#plot output -plt.subplot(2,2,1) -h = np.histogram(ys, num_bins,normed=True) - -p, = plt.plot(h[0],h[1][1:]) -plt.ylim((-10,10)) -plt.xlim((max(h[0]),0)) - - -# plot transfer function -plt.subplot(2,2,2) -x = np.arange(-10,10) -y = 1.2*x + 1 -plt.plot (x,y) -plt.plot([0,0],[-10,f(0)],c='r') -plt.ylim((-10,10)) - -# plot input -plt.subplot(2,2,4) -h = np.histogram(normals, num_bins,density=True) -plt.plot(h[1][1:],h[0]) -plt.xlim((-10,10)) - - -plt.show() -'''