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      "The Extended Kalman Filter"
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     "source": [
      "The Kalman filter that we have developed to this point is extremely good, but it is also limited. Its derivation is in the linear space, and hence it only works for linear problems. Let's be a bit more rigorous here. You can, and we have in this book, apply the Kalman filter to nonlinear problems. For example, in the g-h filter chapter we explored using a g-h filter in a problem with constant acceleration. It 'worked', in that it remained numerically stable and the filtered output did track the input, but there was always a lag. It is easy to prove that there will always be a lag when $\\mathbf{\\ddot{x}}>0$. The filter no longer produces an optimal result. If we make our time step arbitrarily small we can still handle many problems, but typically we are using Kalman filters with physical sensors and solving real-time problems. Either fast enough sensors do not exist, are prohibitively expensive, or the computation time required is excessive. It is not a workable solution.\n",
      "\n",
      "The early adopters of Kalman filters were the radar people, and this fact was not lost on them. Radar is inherently nonlinear. Radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n",
      "$$x=\\sqrt{slant^2 - altitude^2}$$\n",
      "\n",
      "So shortly after the Kalman filter was enthusiastically taken up by the radar industry people began working on how to extend the Kalman filter into nonlinear problems. It is still an area of ongoing research, and in the Unscented Kalman filter chapter we will implement a powerful, recent result of that research. But in this chapter we will cover the most common form, the Extended Kalman filter, or EKF. Today, most real world \"Kalman filters\" are actually EKFs. The Kalman filter in your car's and phone's GPS is an EKF, for example. "
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     "source": [
      "The Problem with Nonlinearity"
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     "source": [
      "You may not realize it, but the only math you really know how to do is linear math. Equations of the form \n",
      "$$ A\\mathbf{x}=\\mathbf{b}$$.\n",
      "\n",
      "That may strike you as hyperbole. After all, in this book we have integrated a polynomial to get distance from velocity and time:\n",
      " We know how to integrate a polynomial, for example, and so we are able to find the closed form equation for distance given velocity and time:\n",
      "$$\\int{(vt+v_0)}\\,dt = \\frac{a}{2}t^2+v_0t+d_0$$\n",
      "\n",
      "That's nonlinear. But it is also a very special form. You spent a lot of time, probably at least a year, learning how to integrate various terms, and you still can not integrate some arbitrary equation - no one can. We don't know how. If you took freshman Physics you perhaps remember homework involving sliding frictionless blocks on a plane and other toy problems. At the end of the course you were almost entirely unequipped to solve real world problems because the real world is nonlinear, and you were taught linear, closed forms of equations. It made the math tractable, but mostly useless. \n",
      "\n",
      "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output."
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     "source": [
      "The Effect of Nonlinear Transfer Functions on Gaussians"
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     "source": [
      "Unfortunately Gaussians are not closed under an arbitrary nonlinear function. Recall the equations of the Kalman filter - at each step of its evolution we do things like pass the covariances through our process function to get the new covariance at time $k$. Our process function was always linear, so the output was always another Gaussian.  Let's look at that on a graph. I will take an arbitrary Gaussian and pass it through the function $f(x) = 2x + 1$ and plot the result. We know how to do this analytically, but lets do this with sampling. I will generate 500,000 points on the Gaussian curve, pass it through the function, and then plot the results. I will do it this way because the next example will be nonlinear, and we will have no way to compute this analytically."
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      "import numpy as np\n",
      "from numpy.random import normal\n",
      "\n",
      "data = normal(loc=0.0, scale=1, size=500000)\n",
      "ys = 2*data + 1\n",
      "\n",
      "plt.hist(ys,1000)\n",
      "plt.show()"
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yMEGCJpmVP5g2k3UeRTAefUOWtuewEgDYCN4yYTXyZmYlpUkms2yfiud3rSoX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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x222e950>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is an unsuprising result. The result of passing the Gaussian through $f(x)=2x+1$ is another Gaussian centered around 1. Let's look at the input, transfer function, and output at once."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from nonlinear_plots import plot_transfer_func\n",
      "\n",
      "def g(x):\n",
      "    return 2*x+1\n",
      "\n",
      "plot_transfer_func (data, g, lims=(-10,10), num_bins=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Pzk/Hg9OGsSAWGY/b5C2tZhsee78EAoBNd2TKHYeoF1F7ii0WC7Kzs3HkyBGY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\neVMX/n97dxPSyB2HcfxJ4iS+ZPOym3ZxK12qIii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       "text": [
        "<matplotlib.figure.Figure at 0x22bf3d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The plot labelled 'input' is the histogram of the original data. This is passed through the transfer function $f(x)=2x+1$ which is displayed in the chart to the upper right. The red lines shows how one value, $x=0$ is passed through the function. Each value from input is passed through in the same way to the output function on the left. The output looks like a Gaussian, and is in fact a Gaussian. We can see that it is altered -the variance in the output is larger than the variance in the input, and the mean has been shifted from 0 to 1, which is what we would expect given the transfer function $f(x)=2x+1$ The $2x$ affects the variance, and the $+1$ shifts the mean.\n",
      "\n",
      "Now let's look at a nonlinear function and see how it affects the probability distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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)-1.6*x\n",
      "\n",
      "plot_transfer_func (data, g, lims=(-4,4), num_bins=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wu6b3zTffRH5+PhoaGpCbm6v4zvPqj9JEpqSsgLLyKikr4Ni8DU1mnCmtbfG1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\nrDB3mTnkAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3f6bfd0>"
       ]
      }
     ],
     "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",
      "$$\\begin{aligned}\n",
      "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n",
      "\\sigma = \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
      "\\end{aligned}$$\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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REiciIiJ78XRxwuLxEZgy0A+v7buC3ZlleOT6SIRyuUeSsV7V9HaH9WFiMhgM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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3f6d910>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "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: 0.0013, 0.9985\n",
        "output mean, variance: -0.0293, 2.2394\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "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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hMx29PEySt+eV22lpaULlaS1fWVkZAECv1yMpKQndjYh99mUiHCNXbsv9b8ap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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x22d0210>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "output mean, variance: -0.0019, 2.2466\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "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: -0.1088, 7470.5861\n",
        "nonlinear output mean, variance: -2.0348, 26163.5214\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "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. "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}