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      "Multidimensional Kalman Filters"
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      "#format the book\n",
      "%matplotlib inline\n",
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    {
     "cell_type": "heading",
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     "metadata": {},
     "source": [
      "Introduction"
     ]
    },
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The techniques in the last chapter are very powerful, but they only work in one dimension. The gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field. You may retort that you could use two Kalman filters for that case, one tracks the x coordinate and the other tracks the y coordinate. That does work in some cases, but put that thought aside, because soon you will see some enormous benefits to implementing the multidimensional case.\n",
      "\n",
      "In this chapter I am purposefully glossing over many aspects of the mathematics behind Kalman filters. If you are familiar with the topic you will read statements that you disagree with because they contain simplifications that do not necessarily hold in more general cases. If you are not familiar with the topic, expect some paragraphs to be somewhat 'magical' - it will not be clear how I derived a certaina result. I prefer that you develop an intuition for how these filters work through several worked examples. If I started by presenting a rigorous mathematical formulation you would be left scratching your head about what all these terms mean and how you might apply them to your problem. In later chapters I will provide a more rigorous mathematical foundation, and at that time I will have to either correct approximations that I made in this chapter or provide additional information that I did not cover here. "
     ]
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    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Multivariate Normal Distributions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What might a *multivariate normal distribution* look like? In this context, multivariate just means multiple variables. Our goal is to be able to represent a normal distribution across multiple dimensions. Consider the 2 dimensional case. Let's say we believe that $x = 2$ and $y = 7$. Therefore we can see that for $N$ dimensions, we need $N$ means, like so:\n",
      "\n",
      "$$\n",
      "\\mu = \\begin{bmatrix}{\\mu}_1\\\\{\\mu}_2\\\\ \\vdots \\\\{\\mu}_n\\end{bmatrix}\n",
      "$$\n",
      "\n",
      "Therefore for this example we would have\n",
      "\n",
      "$$\n",
      "\\mu = \\begin{bmatrix}2\\\\7\\end{bmatrix} \n",
      "$$\n",
      "\n",
      "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 8, like so. \n",
      "\n",
      "$$\\sigma^2 = \\begin{bmatrix}10\\\\8\\end{bmatrix}$$ \n",
      "\n",
      "While this is possible, it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are *correlated*. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. It turns out that we use the following matrix to denote *covariances* with multivariate normal distributions. You might guess, correctly, that *covariance* is short for *correlated variances*."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$\n",
      "\\Sigma = \\begin{pmatrix}\n",
      "  \\sigma_1^2 & p\\sigma_1\\sigma_2 & \\cdots & p\\sigma_1\\sigma_n \\\\\n",
      "  p\\sigma_2\\sigma_1 &\\sigma_2^2 & \\cdots & p\\sigma_2\\sigma_n \\\\\n",
      "  \\vdots  & \\vdots  & \\ddots & \\vdots  \\\\\n",
      "  p\\sigma_n\\sigma_1 & p\\sigma_n\\sigma_2 & \\cdots & \\sigma_n^2\n",
      " \\end{pmatrix}\n",
      "$$\n",
      "\n",
      "If you haven't seen this before it is probably a bit confusing at the moment. Rather than explain the math right now, we will take our usual tactic of building our intuition first with various physical models. At this point, note that the diagonal contains the variance for each state variable, and that all off-diagonal elements are a product of the $\\sigma$ corresponding to the $i$th (row) and $j$th (column) state variable multiplied by a constant $p$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, without explanation, here is the full equation for the multivarate normal distribution in $n$ dimensions.\n",
      "\n",
      "$$\\mathcal{N}(\\mu,\\,\\Sigma) = (2\\pi)^{-\\frac{n}{2}}|\\Sigma|^{-\\frac{1}{2}}\\, e^{ -\\frac{1}{2}(\\mathbf{x}-\\mu)'\\Sigma^{-1}(\\mathbf{x}-\\mu) }$$\n",
      "\n",
      "I urge you to not try to remember this function. We will program it in a Python function and then call it when we need to compute a specific value. However, if you look at it briefly you will note that it looks quite similar to the *univarate normal distribution*  except it uses matrices instead of scalar values, and the root of $\\pi$ is scaled by $n$. Here is the *univariate* equation for reference:\n",
      "\n",
      "$$ \n",
      "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 }\n",
      "$$\n",
      "\n",
      "If you are reasonably well-versed in linear algebra this equation should look quite managable; if not, don't worry! If you want to learn the math we will cover it in detail in the next optional chapter. If you choose to skip that chapter the rest of this book should still be managable for you\n",
      "\n",
      "I have programmed it and saved it in the file `stats.py` with the function name `multivariate_gaussian`. I am not showing the code here because I have taken advantage of the linear algebra solving apparatus of numpy to efficiently compute a solution - the code does not correspond to the equation in a one to one manner. If you wish to view the code, I urge you to either load it in an editor, or load it into this worksheet by putting `%load -s multivariate_gaussian stats.py` in the next cell and executing it with ctrl-enter. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      ">As of version 0.14 scipy.stats has implemented the multivariate normal equation with the function `multivariate_normal()`. It is superior to my function in several ways. First, it is implemented in Fortran, and is therefore faster than mine. Second, it implements a 'frozen' form where you set the mean and covariance once, and then calculate the probability for any number of values for x over any arbitrary number of calls. This is much more efficient then recomputing everything in each call. So, if you have version 0.14 or later you may want to substitute my function for the built in version. Use `scipy.version.version` to get the version number. I deliberately named my function `multivariate_gaussian()` to ensure it is never confused with the built in version.\n",
      "\n",
      "> If you intend to use Python for Kalman filters, you will want to read the <a href=\"http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\">tutorial</a>[1] for the `scipy.stats` module, which explains 'freezing' distributions and other very useful features. As of this date, it includes an example of using the multivariate_normal function, which does work a bit differently from my function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from stats import gaussian, multivariate_gaussian"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n",
      "\n",
      "First, let's find the probability for our dog being at (2.5, 7.3) if we believe he is at (2,7) with a variance of 8 for $x$ and a variance of 10 for $y$. This function requires us to pass everything in as numpy arrays (we will soon provide a more robust version that works with numpy matrices, numpy arrays, and/or scalars in any combinations. That code contains a lot of boilerplate which obscures the algorithm).\n",
      "\n",
      "Start by setting $x$ to (2.5,7.3):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "x = np.array([2.5, 7.3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we set the mean of our belief:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = np.array([2,7])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we have to define our covariance matrix. In the problem statement we did not mention any correlation between $x$ and $y$, and we will assume there is none. This makes sense; a dog can choose to independently wander in either the $x$ direction or $y$ direction without affecting the other. If there is no correlation between the values you just fill in the diagonal of the covariance matrix with the variances. I will use the seemingly arbitrary name $\\textbf{P}$ for the covariance matrix. The Kalman filters use the name $\\textbf{P}$ for this matrix, so I will introduce the terminology now to avoid explaining why I change the name later. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = np.array([[8.,0],[0,10.]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now just call the function"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(multivariate_gaussian(x,mu,P))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.0174395374407\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's check the probability for the dog being at exactly (2,7)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import print_function\n",
      "\n",
      "x = np.array([2,7])\n",
      "print(\"Probability dog is at (2,7) is %.2f%%\" % (multivariate_gaussian(x,mu,P) * 100.))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Probability dog is at (2,7) is 1.78%\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These numbers are not easy to interpret. Let's plot this in 3D, with the $z$ (up) coordinate being the probability."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pylab as pylab\n",
      "from matplotlib import cm\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "import numpy as np\n",
      "\n",
      "pylab.rcParams['axes.color_cycle'] = '348ABD, 7A68A6, A60628, 467821, CF4457, 188487, E24A33'\n",
      "\n",
      "P = np.array([[8.,0],[0,4.]])\n",
      "mu = np.array([2,7])\n",
      "\n",
      "xs, ys = np.arange(-8, 13, .5), np.arange(-8, 20, .5)\n",
      "xv, yv = np.meshgrid (xs, ys)\n",
      "\n",
      "zs = np.array([100.* multivariate_gaussian(np.array([x,y]),mu,P) \\\n",
      "               for x,y in zip(np.ravel(xv), np.ravel(yv))])\n",
      "zv = zs.reshape(xv.shape)\n",
      "\n",
      "ax = plt.figure().add_subplot(111, projection='3d')\n",
      "ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n",
      "\n",
      "ax.set_xlabel('X')\n",
      "ax.set_ylabel('Y')\n",
      "\n",
      "ax.contour(xv, yv, zv, zdir='x', offset=-9, cmap=cm.autumn)\n",
      "ax.contour(xv, yv, zv, zdir='y', offset=20, cmap=cm.BuGn)\n",
      "plt.xlim((-10,15))\n",
      "plt.ylim((-10,20))"
     ],
     "language": "python",
     "metadata": {},
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       "output_type": "pyout",
       "prompt_number": 8,
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        "(-10, 20)"
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ZvabmLeoS47hs1pl4ysUiAeVYZWvZV5amuZM49QEFV5UGiVWP8IMwsymlLenT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       "text": [
        "<matplotlib.figure.Figure at 0x2c9d250>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The result is clearly a 3D bell shaped curve. We can see that the gaussian is centered around (2,7), and that the probability quickly drops away in all directions. On the sides of the plot I have drawn the Gaussians for $x$ in greens and for $y$ in orange.\n",
      "\n",
      "As beautiful as this is, it is perhaps a bit hard to get useful information. For example, it is not easy to tell if $x$ and $y$ both have the same variance or not. So for most of the rest of this book we will display multidimensional Gaussian using contour plots. I will use some helper functions in `gaussian.py` to plot them. If you are interested in linear algebra go ahead and look at the code used to produce these contours, otherwise feel free to ignore it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import stats\n",
      "\n",
      "P = np.array([[2,0],[0,2]])\n",
      "plt.subplot(131)\n",
      "stats.plot_covariance_ellipse((2,7), cov=P, title='|2 0|\\n|0 2|')\n",
      "\n",
      "plt.subplot(132)\n",
      "P = np.array([[2,0],[0,9]])\n",
      "stats.plot_covariance_ellipse((2,7), P, title='|2 0|\\n|0 9|')\n",
      "\n",
      "plt.subplot(133)\n",
      "P = np.array([[2,1.2],[1.2,2]])\n",
      "stats.plot_covariance_ellipse((2,7), P, title='|2 1.2|\\n|1.2 2|')\n",
      "\n",
      "plt.tight_layout()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ssQj06eNEp04u0V1RDa6ZIqJg8ifn8M4UEanKyJEjcebMGVgsFkydOlV0d1Rr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\nNjJDQiL7JUMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2eb4350>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From a mathematical perspective these display the values that the multivariate gaussian takes for a specific sigma (in this case $\\sigma^2=1$. Think of it as taking a horizontal slice through the 3D surface plot we did above. However, thinking about the physical interpretation of these plots clarifies their meaning.\n",
      "\n",
      "The first plot uses the mean and covariance matrices of\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{\\mu} &= \\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n",
      "\\mathbf{\\sigma}^2 &= \\begin{bmatrix}2&0\\\\0&2\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$ \n",
      "\n",
      "Let this be our current belief about the position of our dog in a field. In other words, we believe that he is positioned at (2,7) with a variance of $\\sigma^2=2$ for both x and y. The contour plot shows where we believe the dog is located with the '+' in the center of the ellipse. The ellipse shows the boundary for the $1\\sigma^2$ probability - points where the dog is quite likely to be based on our current knowledge. Of course, the dog might be very far from this point, as Gaussians allow the mean to be any value. For example, the dog could be at (3234.76,189989.62), but that has vanishing low probability of being true. Generally speaking displaying  the $1\\sigma^2$ to $2\\sigma^2$ contour captures the most likely values for the distribution. An equivelent way of thinking about this is the circle/ellipse shows us the amount of error in our belief. A tiny circle would indicate that we have a very small error, and a very large circle indicates a lot of error in our belief. We will use this throughout the rest of the book to display and evaluate the accuracy of our filters at any point in time. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second plot uses the mean and covariance matrices of\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n",
      "\\sigma^2 &= \\begin{bmatrix}2&0\\\\0&9\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This time we use a different variance for $x$ (2) vs $y$ (9). The result is an ellipse. When we look at it we can immediately tell that we have a lot more uncertainty in the $y$ value vs the $x$ value. Our belief that the value is (2,7) is the same in both cases, but errors are different. This sort of thing happens naturally as we track objects in the world - one sensor has a better view of the object, or is closer, than another sensor, and so we end up with different error rates in the different axis."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The third plot uses the mean and covariance matrices of:\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n",
      "\\sigma^2 &= \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This is the first contour that has values in the off-diagonal elements of $cov$, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling use the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow **correlated**. We denote that in the covariance matrix with values off the diagonal. What does this mean in physical terms? Think of trying to park your car in a parking spot. You can not pull up beside the spot and then move sideways into the space because most cars cannot go purely sideways. $x$ and $y$ are not independent. This is a consequence of the steering system in a car. When your tires are turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, he cannot vary $x$ and $y$ independently, which means he cannot walk straight forward to to the side. If $x$ changes, $y$ must also change in a defined way. \n",
      "\n",
      "So when we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". The size of the ellipse shows how much error we have in each axis, and the slant shows how strongly correlated the values are.\n",
      "\n",
      "A word about **correlation** and **independence**. If variables are **independent** they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also **uncorrelated**. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Unobserved Variables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's say we are tracking an aircraft and we get the following data for the $x$ coordinate at time $t$=1,2, and 3 seconds. What does your intuition tell you the value of $x$ will be at time $t$=4 seconds?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import mkf_internal\n",
      "mkf_internal.show_position_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x2f27b90>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It appears that the aircraft is flying in a straight line because we can draw a line between the three points, and we know that aircraft cannot turn on a dime. The most reasonable guess is that $x$=4 at $t$=4. I will depict that with a green arrow."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mkf_internal.show_position_prediction_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x2eb39d0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If this is data from a Kalman filter, then each point has both a mean and variance. Let's try to show that by showing the approximate error for each point. Don't worry about why I am using a covariance matrix to depict the variance at this point, it will become clear in a few paragraphs. The intent at this point is to show that while we have $x$=1,2,3 that there is a lot of error associated with each measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mkf_internal.show_x_error_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gl2/Yib3iYuC008LYsMHaxlu97+MJUZnGUjby8ssvY9myZbj55puhqvqXnHDC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\nas+ZM2c0OTmpeDyuH374QVu2bLH+dwFApaEkAwA8snPnTg0PD+u1115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       "text": [
        "<matplotlib.figure.Figure at 0x2edb050>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that there is a lot of error associated with each value of $x$. We could write a 1D Kalman filter as we did in the last chapter, but suppose this is the output of that filter, and not just raw sensor measurements. Are we out of luck?\n",
      "\n",
      "Let us think about how we predicted that $x$=4 at $t$=4. In one sense we just drew a straight line between the points and saw where it lay at $t$=4. My constant refrain: what is the physical interpretation of that? What is the difference in $x$ over time? In other words, what is $\\frac{\\partial x}{\\partial t}$? The derivative, or difference in distance over time is *velocity*. \n",
      "\n",
      "This is the **key point** in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). It does not have any kind of sensor that provides velocity to us. But based on the position estimates we can compute velocity. In Kalman filters we would call the velocity an *unobserved variable*. Unobserved means what it sounds like - there is no sensor that is measuring velocity directly. Since the velocity is based on the position, and the position has error, the velocity will have error as well. What happens if we draw the velocity errors over the positions errors?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mkf_internal.show_x_with_unobserved()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3wj1Fabzs3h35Hrf+RJ8oE2aKvbHOfrDYQFbGqCQKYnbQ1+vDA1jFo/Ejbuai668HxM0c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042/+i5bUTfE8+AYXyXuE/XJ9qVh/l0zmlgYKErW4QMPTW5rxTmrs5h3NAZ6E8YhNlAr9Ef/mMt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\nmDATERERESXwPwjLG3uuIvteAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2e387d0>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Think about what this plot means. We have a lot of error in our position estimates. We therefore have a lot of error in our velocity estimates. But look at the intersections between the velocity and the positions. Take the intersection at $t$=2. The intersection between the velocity and the position is where our aircraft is most likely to be, which I have roughly depicted with a red ellipse ('roughly' because I set the size via eyeball, not via math). The size of the error is much smaller than the error of the positions, despite the fact that velocity was derived from position. \n",
      "\n",
      "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of the this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the position measurement is not in the direction of the assumed velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way.  "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Kalman Filter Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So in general terms we can show how a multidimensional Kalman filter works. In the example above, we compute velocity from the previous position measurements using something called the *measurement function*. Then we predict the next position by using the current estimate and something called the *state transition function*. In our example above,\n",
      "\n",
      "$$new\\_position = old\\_position + velocity*time$$ \n",
      "\n",
      "Next, we take the measurement from the sensor, and compare it to the prediction we just made. In a world with perfect sensors and perfect airplanes the prediction will always match the measured value. In the real world they will always be at least slightly different. We call the difference between the two the *residual*. Finally, we use something called the *Kalman gain* to update our estimate to be somewhere between the measured position and the predicted position. I will not describe how the gain is set, but suppose we had perfect confidence in our measurement - no error is possible. Then, clearly, we would set the gain so that 100% of the position came from the measurement, and 0% from the prediction. At the other extreme, if he have no confidence at all in the sensor (maybe it reported a hardware fault), we would set the gain so that 100% of the position came from the prediction, and 0% from the measurement. In normal cases, we will take a ratio of the two: maybe 53% of the measurement, and 47% of the prediction. The gain is updated on every cycle based on the variance of the variables (in a way yet to be explained). It should be clear that if the variance of the measurement is low, and the variance of the prediction is high we will favor the measurement, and vice versa. \n",
      "\n",
      "The chart shows a prior estimate of $x=1$ and $\\dot{x}=1$ ($\\dot{x}$ is the shorthand for the derivative of x, which is velocity). Therefore we predict $\\hat{x}=2$. However, the new measurement $x^{'}=1.3$, giving a residual $r=0.7$. Finally, Kalman filter gain $k$ gives us a new estimate of $\\hat{x^{'}}=1.8$.\n",
      "\n",
      "** CHECK SYMBOLOGY!!!!**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mkf_internal import *\n",
      "show_residual_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DD376/PPP1bBhngYN6iGbrfT2kJAwxcR01zfflL48t2hRpJCQkot+vMzM+rLb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\nLrmEygMAAIC34ZPgXEhJSXEsq6N6yNI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       "text": [
        "<matplotlib.figure.Figure at 0x32590d0>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Equations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The brilliance of the Kalman filter is taking the insights of the chapter up to this point and finding an optimal mathematical solution. The Kalman filter finds what is called a *least squared fit* to the set of measurements to produce an optimal output. We will not trouble ourselves with the derivation of these equations. It runs to several pages, and offers a lot less insight than the words above, in my opinion. Furthermore, to create a Kalman filter for your application you will not be manipulating these equations, but only specifing a number of parameters that are used by them. It would be going too far to say that you will never need to understand these equations; but to start we can pass them by and I will present the code that implements them. So, first, let's see the equations. \n",
      "> Kalman Filter Predict Step:\n",
      "\n",
      "> $$\n",
      "\\begin{aligned}\n",
      "\\hat{\\mathbf{x}}_{t|t-1} &= \\mathbf{\\Phi_t}\\hat{\\mathbf{x}}_{t-1} + \\mathbf{B u}_t\\;\\;\\;&(1) \\\\\n",
      "\\mathbf{P}_{t|t-1} &= \\mathbf{\\Phi_tP}_{t-1}\\mathbf{\\Phi}^T_t + \\mathbf{Q}_t\\;\\;\\;&(2)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "> Kalman Filter Update Step:\n",
      "\n",
      ">$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{\\gamma} &= \\mathbf{z}_t - \\mathbf{H}_t\\hat{\\mathbf{x}}_t\\;\\;\\;&(3) \\\\\n",
      "\\mathbf{K}_t &= \\mathbf{P}_t \\mathbf{H}^T_t (\\mathbf{H}_t \\mathbf{P}_t \\mathbf{H}^T_t + \\mathbf{R}_t)^{-1}\\;\\;\\;(4) \\\\\n",
      "\\\\\n",
      "\\hat{\\mathbf{x}}_t &= \\hat{\\mathbf{x}}_{t|t-1} + \\mathbf{K}_t \\gamma \\;\\;\\;&(5) \\\\\n",
      "\\mathbf{P}_{t|t} &= (\\mathbf{I} - \\mathbf{K}_t \\mathbf{H}_t)\\mathbf{P}_{t|t-1} \\;\\;\\;&(6)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Dash off, wipe the blood out of your eyes, and we'll disuss what this means. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These are nothing more than linear algebra equations that implement the algorithm we used in the last chapter, but using multidimensional Gaussians instead of univariate Gaussians, and optimized for a least squares fit. Each capital letter denotes a matrix or vector. The subscripts indicate which time step the data comes from; $t$ is now, $t-1$ is the previous step. $A^T$ is the transpose of A, and $A^{-1}$ is the inverse. Finally, the hat denotes an estimate, so $\\hat{x}_t$ is the estimate of $x$ at time $t$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Kalman Equations Expressed as an Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Different texts use different notation and variable names for the Kalman filter. Later we will expose you to these different forms to prepare you for reading the original literature. However, I find much of the notation very dense, and unnecessary for writing code. The subscripts indicate the time step, but we know the left hand side is for this time step, and the right hand side is for the previous step. For most of this book I'm going to use the following simplified equations, which express an algorithm.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\text{Predict Step}\\\\\n",
      "\\mathbf{x}' &= \\mathbf{F x} + \\mathbf{B u}\\;\\;\\;&(1) \\\\\n",
      "\\mathbf{P} &= \\mathbf{FP{F}}^T + \\mathbf{Q}\\;\\;\\;&(2) \\\\\n",
      "\\\\\n",
      "\\text{Update Step}\\\\\n",
      "\\mathbf{\\gamma} &= \\mathbf{z} - \\mathbf{H x} \\;\\;\\;&(3)\\\\\n",
      "\\mathbf{K}&= \\mathbf{PH}^T (\\mathbf{HPH}^T + \\mathbf{R})^{-1}\\;\\;\\;&(4) \\\\\n",
      "\\mathbf{x}&=\\mathbf{x}' +\\mathbf{K\\gamma} \\;\\;\\;&(5)\\\\\n",
      "\\mathbf{P}&= (\\mathbf{I}-\\mathbf{KH})\\mathbf{P}\\;\\;\\;&(6)\n",
      "\\end{aligned}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is an algorithm, so $=$ denotes assignment, not equality. For example, equation (6) has P on both sides of the $=$. This equation updates the value of P by the computation on the right hand side. \n",
      "\n",
      "Here, a $'$ means estimate, so $\\mathbf{x}'$ is the estimate of the state $\\mathbf{x}$. Many texts use $\\hat{\\mathbf{x}}$ or $\\mathbf{x}^*$ to express this. I find these choices unfortunate because we will often want to express these in matrix form. The notation of a hat over a matrix is clumsy at best, and an asterisk followin a matrix normally means the *complex congugate* of the matrix, which is *not* what is intended. So I use $'$. \n",
      "\n",
      "What do all of the variables mean? What is $\\mathbf{P}$, for example? Don't worry right now. Instead, I am just going to design a Kalman filter, and introduce the names as we go. Then we will just pass them into Python function that implement the equations above, and we will have our solution. Later sections will then delve into more detail about each step and equation. I think learning by example and practice is far easier than trying to memorize a dozen abstract facts at once.  \n",
      "\n",
      "Look at the code below for the predict step (which we will present a bit later). \n",
      "\n",
      "    def predict():\n",
      "        x = F*x + B*u      # equation (1)\n",
      "        P = F*P*F.T + Q    # equation (2)\n",
      "        \n",
      "Notice how simple it really is. It really isn't much different from the predict step in the previous chapter, and it is a nearly exact transliteration of the equations above. As you become familiar with this notation you will find yourself able to read textbooks and paper and implement the equations without much difficulty. \n",
      "        \n",
      "> Later, if you become interested in the details of numerical computation you may change the implementation to be faster or more numerically stable than this written form, but for most of this book our code will follow the Kalman filter equations almost exactly. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking a Dog"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's go back to our tried and true problem of tracking our dog. This time we will include the fundamental insight of this chapter - that of using *unobserved variables* to improve our estimates. In simple terms, our algorithm is:\n",
      "\n",
      "    1. predict the next value for x with \"x + vel*time\"\n",
      "    2. get measurement for x\n",
      "    3. compute residual as: \"x - x_prediction\"\n",
      "    4. compute kalman gain based on noise levels\n",
      "    5. compute new position as \"residual * kalman gain\"\n",
      "    \n",
      "That is the entire Kalman filter algorithm. It is both what we described above in words, and it is what the rather obscure Kalman Filter equations do. The Kalman filter equations just express this algorithm by using linear algebra. \n",
      "\n",
      "As I mentioned above, there is actually very little programming involved in creating a Kalman filter. We will just be defining several matrices and parameters that get passed into  the Kalman filter algorithm code. Rather than try to explain each of the steps ahead of time, which can be a bit abstract and hard to follow, let's just do it for our by now well known dog tracking problem. Naturally this one example will not cover every use case of the Kalman filter, but we will learn by starting with a simple problem and then slowly start addressing more complicated situations.\n",
      "\n",
      "\n",
      "##### **Step 1:** Choose the State Variables\n",
      "\n",
      "*State variables* are the variables that the Kalman filter estimates. They include the *observed variables* - the data that is directly measured by a sensor, and the *unobserved variables*, which we can infer from the observed variables.\n",
      "\n",
      "For our dog tracking problem, our observed state variable is position, and the unobserved variable is velocity. \n",
      "\n",
      "The Kalman filter is implemented using linear algebra. We use an $n\\times 1$ matrix to store  $n$ state variables. For the dog tracking problem, we use $x$ to denote position, and the first derivative of $x$, $\\dot{x}$, for velocity. The Kalman filter equations use $\\mathbf{x}$ for the state, so we define $\\mathbf{x}$ as:\n",
      "\n",
      "$$\\mathbf{x} =\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 2:** Design State Transition Function\n",
      "\n",
      "\n",
      "The next step in designing a Kalman filter is designing what is called the *State Transition Function.* This is a set of equations that mathematically describe the behavior of the system we are filtering. So, for the dog tracking problem we are tracking a moving object, so we just need the Newtonian equations for motion. In other words, these are the equations that we use to predict the next state from the current state. \n",
      "\n",
      "We know from elementary physics how to compute a new position given a previous position, velocity, and time, like so:\n",
      "\n",
      "$$ x' = {velocity}*{time} + x_{previous}$$\n",
      "\n",
      "In more formal mathematics we would write:\n",
      "\n",
      "$$x' = \\dot{x}(\\Delta t) + x$$\n",
      "\n",
      "where $\\dot{x}$ is velocity, and $\\Delta t$ is the amount of time between $t-1$ and $t$. In our problems we will be running the Kalman filter at fixed time intervals, so $\\Delta t$ is a constant for us. We will just set it to $1$ and worry about the units later.\n",
      "\n",
      "As in step one we must express this in the form of matrices so that our linear algebra software and solve the equations for us. The Kalman filter equations require that we write it in the form:\n",
      "\n",
      "$$ \\mathbf{x}' = \\mathbf{Fx}$$\n",
      "\n",
      "where as in step 1 $\\mathbf{x}$ is the matrix containing the state variables, and $\\mathbf{F}$ is the matrix that when multiplied by $\\mathbf{x}$ yields our equations. Note that this is just part of the Kalman filter equation (1) above. We will deal with the second half of equation (1) in the next step.\n",
      "\n",
      "Since $\\mathbf{x}$ is a $2{\\times}1$ matrix $\\mathbf{F}$ must be a $2{\\times}2$ matrix to yield another $2{\\times}1$ matrix as a result. The first row of the F is easy to derive:\n",
      "\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}' &=\\begin{bmatrix}1&\\Delta t \\\\ ?&?\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "When we multiply the first row of $\\mathbf{F}$ that out we get:\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "x' &= 1 \\times x + \\Delta t * \\dot{x} \\mbox{, or} \\\\\n",
      "x' &= \\dot{x}(\\Delta t) + x\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Now we have to account for the second row. I've let it somewhat unstated up to now, but we are assuming constant velocity for this problem. Naturally this assumption is not true; if our dog moves it must accelerate and deaccelerate. If you cast your mind back to the *g-h Filter* chapter we explored the effect of assuming constant velocity. So long as the acceleration is small compared to $\\Delta t$ the filter will still perform well. \n",
      "\n",
      "Therefore we will assume that\n",
      "\n",
      "$$\\dot{x}' = \\dot{x}$$\n",
      "\n",
      "which gives us the second row of $\\mathbf{F}$ as follows, once we set $\\Delta t = 1$:\n",
      "\n",
      "\n",
      "$$\n",
      "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}' =\\begin{bmatrix}1&1 \\\\ 0&1\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n",
      "$$\n",
      "\n",
      "Which, when multiplied out, yields our desired equations:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "x' &= x + \\dot{x} \\\\\n",
      "\\dot{x}' &= \\dot{x}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "In the vocabulary of Kalman filters we call this *transforming the state matrix*. We take our state matrix, which for us is $(\\begin{smallmatrix}x \\\\ \\dot{x}\\end{smallmatrix})$,and multipy it by a matrix we will call $F$ to compute the new state. In this case, $F=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$. \n",
      "\n",
      "\n",
      "You will do this for every Kalman filter you ever design. Your state matrix will change depending on how many state random variables you have, and then you will create $F$ so that it updates your state based on whatever the physics of your problem dictates. $F$ is always a matrix of constants. If this is not fully clear, don't worry, we will do this many times in this book.\n",
      "\n",
      "Refer back to the first Kalman filter equation $\\hat{\\mathbf{x}}_{t|t-1} = \\mathbf{F_t}\\hat{\\mathbf{x}}_{t-1} + \\mathbf{B u}_t$. There is an unexplained $\\mathbf{B u}_t$ term in there, but shorn of all the diacritics it should be clear that we just designed $F$ for this equation!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 3**: Design the Motion Function\n",
      "\n",
      "The Kalman filter does not just filter data, it allows us to incorporate control inputs for systems like robots and airplanes. Consider the state transition function we wrote for the dog:\n",
      "\n",
      "$$x_t = \\dot{x}(\\Delta t) + x_{t-1}$$\n",
      "\n",
      "Suppose that instead of passively tracking our dog we were actively controlling a robot. At each time step we would send control signals to the robot based on our current position vs desired position. Kalman filter equations incorporate that knowledge into the filter equations, creating a predicted position based both on current velocity *and* control inputs to the drive motors. \n",
      "\n",
      "We will cover this use case later, but for now passive tracking applications we set those terms to 0. In step 2 there was the unexplained term $\\mathbf{Bu}$ in equation (1):\n",
      "\n",
      "$$\\mathbf{x}' = \\mathbf{Fx} + \\mathbf{Bu}$$.\n",
      "\n",
      "Here $\\mathbf{u}$ is the control input, and $\\mathbf{B}$ is its transfer function. For example, $\\mathbf{u}$ might be a voltage controlling how fast the wheel's motor turns, and multiplying by $\\mathbf{B}$ yields $\\begin{smallmatrix}x\\\\\\dot{x}\\end{smallmatrix}$. Since we do not need these terms we will set them both to zero and not concern ourselves with them for now.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 4**: Design the Measurement Function\n",
      "\n",
      "Now we need a way to compute the state variables to our measurements. In our problem we have one sensor for the position, and it outputs position directly. We do not have a sensor for velocity. If we put this in linear algebra terms we get:\n",
      "\n",
      "$$\n",
      "z = \\begin{bmatrix}1&0\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n",
      "$$\n",
      "\n",
      "In other words, the measurement sensor provides one times the sensor's measurement of $x$, and zero times the nonexistent velocity measurement. This is simple, because the problem is simple! A slightly more complicated problem might use a temperature sensor might, for example, output a voltage, and we would need to provide an equation to convert from voltage to temperature. \n",
      "\n",
      "In the nomenclature of Kalman filters the $[1\\space\\space0]$ matrix is called $H$. If you scroll up to the Kalman filter equations you will see an $H$ term in the update step.\n",
      "\n",
      "$$\\mathbf{\\gamma} = \\mathbf{z} - \\mathbf{H x}\\tag{3}$$\n",
      "\n",
      "Believe it or not, we have designed the majority of our Kalman filter!! All that is left is to model the noise in our sensors."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 5**: Design the Measurement Noise Matrix\n",
      "\n",
      "The *measurement noise* is a matrix that models the noise in our sensors as a covariance matrix. This can be admittedly a very difficult thing to do in practice. A complicated system may have many sensors, the correlation between them might not be clear, and usually their noise is not a pure Gaussian. For example, a sensor might be biased to already read high if the temperature is high, and so the noise is not distributed equally on both sides of the mean. Later we will address this topic in detail. For now I just want you to get used to the idea of the measurement noise matrix so we will keep it deliberately simple.\n",
      "\n",
      "In the last chapter we used a variance of 5 for our position sensor. Let's use the same value here.  The Kalman filter equations uses the symbol $R$ for this matrix.\n",
      "\n",
      "$$R = 5$$\n",
      "\n",
      "In general the matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is $m{\\times}m$ because it is a covariance matrix, as there may be correlations between the sensors. We have only 1 sensor here so we write:\n",
      "\n",
      "$$R = \\begin{bmatrix}5\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 6**: Design the Process Noise Matrix\n",
      "\n",
      "What is *process noise*? Consider the motion of a thrown ball. In a vacuum and with constant gravitational force it moves in a parabola. However, if you throw the ball on the surface of the earth you will also need to model factors like rotation and air drag. However, even when you have done all of that there is usually things you cannot account for. For example, consider wind. On a windy day the ball's trajectory will differ from the computed trajectory, perhaps by a significant amount. Without wind sensors, we may have no way to model the wind. Wind can come from any direction, so it is likely to have a near Gaussian distribution. The Kalman filter models this as *process noise*, and calls it $\\small\\mathbf{Q}$.\n",
      "\n",
      "Astute readers will realize that we can inspect the ball's path and extract wind as an unobserved state variable, but the point to grasp here is there will always be some unmodelled noise in our process, and the Kalman filter gives us a way to model it.\n",
      "\n",
      "Designing the process noise matrix can be quite demanding. For our first example, we will set it to 0, like so: $\\small\\mathbf{Q}=0$. It is unlikely that you would do that for a real filter.\n",
      "\n",
      "> Some books and papers use $\\small\\mathbf{R}$ for measurement noise and $\\small\\mathbf{Q}$ for the process noise. Others do the opposite, using $\\small\\mathbf{Q}$ for measurement noise and $\\small\\mathbf{R}$ for the process noise! Read carefully, and make sure you don't get confused. I use the following mnemonic. Radars are used to measure positions, and they have measurement error. So, for me, $\\small\\mathbf{R}$ is the **R**adar's measurement noise. I've read a lot of Kalman filter literature in the context of radar tracking, so it makes sense to me. I don't have a good one for $\\small\\mathbf{Q}$, other than to note that it alphabetically follows the p in **P**rocess."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### **Step 7**: Design Initial Conditions\n",
      "\n",
      "Finally, we need to specify the initial conditions for the state variables and their associated covariance matrix. If you have a rough idea of the values you can use that as your initial settings, or, you could always read the sensors for the first time, and calculate a initial value. The Kalman filter will converge and find the solution even if your initial conditions are far off, but the more accurate they are the faster and better the output will be. \n",
      "\n",
      "The covariance matrix ($\\small{\\mathbf{P}}$) is a $n{\\times}n$ matrix that specifies the variances and covariances of each state variable. This is a complicated topic, and I'd rather demostrate the matrix rather than talk about it abstractly here. For now, recognize that the Kalman filter will be calculating the covariance matrix at each step, just like the 1-D filter computed the variance of the mean at each step. So as with those examples we can make an initial guess and trust that $\\small{\\mathbf{P}}$ will converge to a smaller value as the filter progresses. I find this description somewhat unsatisfactory for several reasons, but until you've seen some examples it is hard to talk about in an understandable way."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementing the Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As promised, the Kalman filter equations are already programmed for you. In many circumstances you will never have to write your own Kalman filter equations. We will look at the code later, but for now we will just import the code and use it. It lives in `filterpy.kalman` so let's start by importing it and creating a filter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import filterpy.kalman as kf\n",
      "dog_filter = kf.KalmanFilter (dim_x=2, dim_z=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That's it. We import the filter, and create a filter that uses 2 state variables. We specify the number of state variables with the 'dim=2' expression (dim means dimensions).\n",
      "\n",
      "The Kalman filter class contains a number of variables that you need to set. x is the state, F is the state transition function, and so on. Rather than talk about it, let's just do it!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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",
      "dog_filter.Q *= 0                       # process noise\n",
      "dog_filter.P *= 500.                    # covariance matrix "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's look at this line by line. \n",
      "\n",
      "**1**: We just assign the initial value for our state. Here we just initialize both the position and velocity to zero. \n",
      "\n",
      "**2**: We set $\\textbf{F}=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$, as in design step 2 above. \n",
      "\n",
      "**3**: We set $\\textbf{H}=(\\begin{smallmatrix}1&0\\end{smallmatrix})$, as in design step 3 above.\n",
      "\n",
      "**4**: We set $\\textbf{R} = 5$ and $\\mathbf{Q}=0$ as in steps 5 and 6.\n",
      "\n",
      "**5**: Recall in the last chapter we set our initial belief to $\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(0,500)$ to signify our lack of knowledge about the initial conditions. We implemented this in Python with a list that contained both $\\mu$ and $\\sigma^2$ in the variable $pos$:\n",
      "\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",
      "\n",
      "$$\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(\\mathbf{x},\\mathbf{P})$$\n",
      "\n",
      "$\\mathbf{P}$ is initialized to the identity matrix of size $n{\\times}n$, so multiplying by 500 assigns a variance of 500 to $x$ and $\\dot{x}$. So $\\verb,f.P,$ contains\n",
      "\n",
      "$$\\begin{bmatrix} 500&0\\\\0&500\\end{bmatrix}$$\n",
      "\n",
      "This will become much clearer once we look at the covariance matrix in detail in later sessions. For now recognize that each diagonal element $e_{ii}$ is the variance for the $ith$ state variable, and that the *500* is just a statement that we are very uncertain about our initial value by some *amount*. \n",
      "\n",
      "> Summary: For our dog tracking problem, in the 1-D case $\\mu$ was the position, and $\\sigma^2$ was the variance. In the 2-D case $\\mathbf{x}$ is our position and velocity, and $\\mathbf{P}$ is the *covariance* of the position and velocity. It is the same thing, just in higher dimensions!\n",
      "\n",
      "\n",
      "All that is left is to run the code! The `DogSensor` class from the previous chapter has been placed in `DogSensor.py`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from DogSensor import DogSensor\n",
      "import filterpy.kalman as kf\n",
      "\n",
      "def dog_tracking_filter(R,Q=0,cov=1.):\n",
      "    dog_filter = kf.KalmanFilter (dim_x=2, dim_z=1)\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",
      "    dog_filter.H = np.array([[1,0]])  # Measurement function\n",
      "    dog_filter.R *= R                 # measurement uncertainty\n",
      "    dog_filter.P *= cov               # covariance matrix \n",
      "    if np.isscalar(Q):\n",
      "        dog_filter.Q = np.array([[0,0],\n",
      "                                 [0,Q]])\n",
      "    else:\n",
      "        dog_filter.Q = Q\n",
      "    return dog_filter\n",
      "\n",
      "\n",
      "def filter_dog(noise=0, count=0, R=0, Q=0, P=500., data=None, initial_x=None):\n",
      "    \"\"\" Kalman filter 'count' readings from the DogSensor.\n",
      "    'noise' is the noise scaling factor for the DogSensor.\n",
      "    'data' provides the measurements. If set, noise will\n",
      "    be ignored and data will not be generated for you.\n",
      "    \n",
      "    returns a tuple of (positions, measurements, covariance)\n",
      "    \"\"\"\n",
      "    if data is None:    \n",
      "        dog = DogSensor(velocity=1, noise=noise)\n",
      "        zs = [dog.sense() for t in range(count)]\n",
      "    else:\n",
      "        zs = data\n",
      "\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",
      "\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",
      "        cov[t] = dog_filter.P\n",
      "    \n",
      "        # perform the kalman filter steps\n",
      "        dog_filter.update (z)\n",
      "        dog_filter.predict()\n",
      "        \n",
      "    return (pos, zs, cov)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is the complete code for the filter, and most of it is just boilerplate. The first function `dog_tracking_filter()` is a helper function that creates a `KalmanFilter` object with specified $\\mathbf{R}$, $\\mathbf{Q}$ and $\\mathbf{P}$ matrices. We've shown this code already, so I will not discuss it more here. \n",
      "\n",
      "The function `filter_dog()` implements the filter itself.  Lets work through it line by line. The first line creates the simulation of the DogSensor, as we have seen in the previous chapter.\n",
      "\n",
      "    dog = DogSensor(velocity=1, noise=noise)\n",
      "\n",
      "The next line uses our helper function to create a Kalman filter.\n",
      "\n",
      "    dog_filter = dog_tracking_filter(R=R, Q=Q, cov=500.)\n",
      "    \n",
      "We will want to plot the filtered position, the measurements, and the covariance, so we will need to store them in lists. The next three lines initialize empty lists of length *count* in a pythonic way.\n",
      "\n",
      "    pos = [None] * count\n",
      "    zs  = [None] * count\n",
      "    cov = [None] * count\n",
      "    \n",
      "Finally we get to the filter. All we need to do is perform the update and predict steps of the Kalman filter for each measurement. The `KalmanFilter` class provides the two functions `update()` and `predict()` for this purpose. `update()` performs the measurement update step of the Kalman filter, and so it takes a variable containing the sensor measurement. \n",
      "\n",
      "Absent the bookkeeping work of storing the filter's data, the for loop reads:\n",
      "\n",
      "    for t in range (count):\n",
      "        z = dog.sense()\n",
      "        dog_filter.update (z)\n",
      "        dog_filter.predict()\n",
      "    \n",
      "It really cannot get much simpler than that. As we tackle more complicated problems this code will remain largely the same; all of the work goes into setting up the `KalmanFilter` variables; executing the filter is trivial.\n",
      "\n",
      "Now let's look at the result. Here is some code that calls `filter_track()` and then plots the result. It is fairly uninteresting code, so I will not walk through it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_track(noise=None, count=0, R=0, Q=0, P=500., initial_x=None,\n",
      "               data=None, plot_P=True, title='Kalman Filter'):\n",
      "    \n",
      "    ps, zs, cov = filter_dog(noise=noise, data=data, count=count,\n",
      "                             R=R, Q=Q, P=P, initial_x=initial_x)\n",
      "    \n",
      "    p0, = plt.plot([0,count],[0,count],'g')\n",
      "    p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n",
      "    p2, = plt.plot(range(1,count+1),ps, c='b')\n",
      "    plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n",
      "    plt.ylim((0-10,count+10))\n",
      "    plt.title(title)\n",
      "    plt.show()\n",
      "    \n",
      "    if plot_P:\n",
      "        plt.subplot(121)\n",
      "        plot_covariance(cov, (0,0))\n",
      "        plt.subplot(122)\n",
      "        plot_covariance(cov, (1,1))\n",
      "        plt.show()\n",
      "    \n",
      "def plot_covariance(P, index=(0,0)):\n",
      "    ps = []\n",
      "    for p in P:\n",
      "        ps.append(p[index[0],index[1]])\n",
      "    plt.plot(ps)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, call it. We will start by filtering 100 measurements with a noise factor of 30, $\\mathbf{R}=5$ and $\\mathbf{Q}=0$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track (noise=30, R=5, Q=0, count=100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ra8prO3fiGhpKzJo1/52MjcVl3jwebNiQBZ8GHmzalCXtpiXPJMiFCxdySjt3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       "text": [
        "<matplotlib.figure.Figure at 0x324abd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x3392850>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is still a lot to learn, but we have implemented our first, full Kalman filter using the same theory and equations as published by Nobert Kalman! Code very much like this runs inside of your GPS and phone, inside every airliner, inside of robots, and so on. \n",
      "\n",
      "The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely.\n",
      "\n",
      "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now I will leave it at that.\n",
      "\n",
      "In the previous chapter we filtered very noisy signals with much simpler code than the code above. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. In contrast, we can implement very complicated, multidimensional filter with this code merely by altering are assignments to the filter's variables. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and accelerations in 3D (which requires 9 state variables). We can do that with the code in this chapter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Walking Through the KalmanFilter Code (Optional)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# -*- coding: utf-8 -*-\n",
      "\"\"\"\n",
      "Created on Fri Oct 18 18:02:07 2013\n",
      "\n",
      "@author: rlabbe\n",
      "\"\"\"\n",
      "\n",
      "import numpy as np\n",
      "import scipy.linalg as linalg\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy.random as random\n",
      "\n",
      "class KalmanFilter:\n",
      "\n",
      "    def __init__(self, dim_x, dim_z, use_short_form=False):\n",
      "        \"\"\" Create a Kalman filter with 'dim_x' state variables, and\n",
      "        'dim_z' measurements. You are responsible for setting the various\n",
      "        state variables to reasonable values; the defaults below will\n",
      "        not give you a functional filter.\n",
      "        \"\"\"\n",
      "\n",
      "        self.x = 0 # 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",
      "        self.B = 0\n",
      "        self.F = 0 # state transition matrix\n",
      "        self.H = 0 # Measurement function (maps state to measurements)\n",
      "        self.R = np.eye(dim_z) # state uncertainty\n",
      "        \n",
      "        # identity matrix. Do not alter this. \n",
      "        self._I = np.eye(dim_x)\n",
      "        \n",
      "        if use_short_form:\n",
      "            self.update = self.update_short_form\n",
      "\n",
      "\n",
      "    def update(self, Z, R=None):\n",
      "        \"\"\"\n",
      "        Add a new measurement (Z) to the kalman filter. \n",
      "        \n",
      "        Optionally provide R to override the measurement noise for this \n",
      "        one call, otherwise  self.R will be used.\n",
      "        \n",
      "        self.residual, self.S, and self.K are stored in case you want to\n",
      "        inspect these variables. Strictly speaking they are not part of the\n",
      "        output of the Kalman filter, however, it is often useful to know\n",
      "        what these values are in various scenarios.\n",
      "        \"\"\"\n",
      "        \n",
      "        if R is None:\n",
      "            R = self.R\n",
      "        elif np.isscalar(R):\n",
      "            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",
      "        \n",
      "        # project system uncertainty into measurement space \n",
      "        self.S = self.H.dot(self.P).dot(self.H.T) + R   \n",
      "\n",
      "        # map system uncertainty into kalman gain\n",
      "        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",
      "\n",
      "        KH = self.K.dot(self.H)\n",
      "        I_KH = self._I - KH\n",
      "        self.P = (I_KH.dot(self.P.dot(I_KH.T)) + \n",
      "                 self.K.dot(self.R.dot(self.K.T)))\n",
      "\n",
      "\n",
      "    def predict(self):\n",
      "        \"\"\" predict next position \"\"\"\n",
      "    \n",
      "        self.x = self.F.dot(self.x)\n",
      "        if self.B != 0:\n",
      "           self.x += self.B.dot(self.u)\n",
      "        self.P = self.F.dot(self.P).dot(self.F.T) + self.Q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Adjusting the Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Your results will vary slightly depending on what numbers your random generator creates for the noise componenet of the noise, but the filter in the last section should track the actual position quite well. Typically as the filter starts up the first several predictions are quite bad, and varies a lot. But as the filter builds its state the estimates become much better. \n",
      "\n",
      "Let's start varying our parameters to see the effect of various changes. This is a *very normal* thing to be doing with Kalman filters. It is difficult, and often impossible to exactly model our sensors. An imperfect model means imperfect output from our filter. Engineers spend a lot of time tuning Kalman filters so that they perform well with real world sensors. We will spend time now to learn the effect of these changes. As you learn the effect of each change you will develop an intuition for how to design a Kalman filter. As I wrote earlier, designing a Kalman filter is as much art as science. The science is, roughly, designing the ${\\mathbf{H}}$ and ${\\mathbf{F}}$ matrices - they develop in an obvious manner based on the physics of the system we are modelling. The art comes in modelling the sensors and selecting appropriate values for the rest of our variables.\n",
      "\n",
      "Let's look at the effects of the noise parameters ${\\mathbf{R}}$ and ${\\mathbf{Q}}$. I will only run the filter for twenty steps to ensure we can see see the difference between the measurements and filter output. I will start by holding ${\\mathbf{R}}$ to 5 and vary ${\\mathbf{Q}}$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dog = DogSensor(velocity=1, noise=30)\n",
      "zs = [dog.sense() for t in range(30)]\n",
      "\n",
      "plot_track (data=zs, R=5, Q=10,count=30, plot_P=False, title='R = 5, Q = 10')\n",
      "plot_track (data=zs, R=5, Q=.02,count=30, plot_P=False, title='R = 5, Q = 0.02')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LKs6cUdOyZelvvqylFLJiLISoAFInp2wSP+VSSuz0erXNq8XX69OnkPXrs/j0Ux2PPx5A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\n6f8BneZaHdAYpkwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3384590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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w28l47TWsnTp5elZCRXTHjuG7ahUZb7xxz/MOHdLRt28Qc+em06OH5Z7nKgq8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\nBAD4f3RuYl2ItiCIAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3384810>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The filter in the first plot should follow the noisy measurement almost exactly. In the second plot the filter should vary from the measurement quite a bit, and be much closer to a straight line than in the first graph. \n",
      "\n",
      "In the Kalman filter ${\\mathbf{R}}$ is the *measurement noise* and ${\\mathbf{Q}}$ is the *process uncertainty*. ${\\mathbf{R}}$ is the same in both plots, so ignore it for the moment. Why does ${\\mathbf{Q}}$ affect the plots this way?\n",
      "\n",
      "Let's remind ourselves of what the term *process uncertainty* means. Consider the problem of tracking a ball. We can accurately model its behavior in statid air with math, but if there is any wind our model will diverge from reality. \n",
      "\n",
      "In the first case we set ${\\mathbf{Q}}=10$, which is quite large. In physical terms this is telling the filter \"I don't trust my motion prediction step\". Strictly speaking, we are telling the filter there is a lot of external noise that we are not modeling with $\\small{\\mathbf{F}}$, but the upshot of that is to not trust the motion prediction step. So the filter will be computing velocity ($\\dot{x}$), but then mostly ignoring it because we are telling the filter that the computation is extremely suspect. Therefore the filter has nothing to use but the measurements, and thus it follows the measurements closely. \n",
      "\n",
      "In the second case we set ${\\mathbf{Q}}=0.02$, which is quite small. In physical terms we are telling the filter \"trust the motion computation, it is really good!\". Again, more strictly this actually says there is very small amounts of process noise, so the motion computation will be accurate. So the filter ends up ignoring some of the measurement as it jumps up and down, because the variation in the measurement does not match our trustworthy velocity prediction.\n",
      "\n",
      "**AUTHOR'S NOTE: move covariance matrix coverage here, then do R, then Q. Order as below is confusing.**"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Designing $\\textbf{Q}$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But what does \"quite large\" and \"quite small\" mean, and what should $\\textbf{Q}$ contain? The numbers in the $\\textbf{Q}$ matrix are not arbitrary, but the variances of the process noise. This means that they have the same units as the rest of the system. So, suppose the noise of our sensor has a standard deviation of $0.5m$, and the rest of our system is specified in meters as well. Variance is the standard deviation squared, so if $\\sigma=0.5$, then $\\sigma^2 = 0.25$.\n",
      "\n",
      "If we have $m$ state variables then $\\textbf{Q}$ will be an $m{\\times}m$ matrix. $\\textbf{Q}$ is a covariance matrix for the state variables, so it will contain the variances and covariances for the process noise for each state variable. \n",
      "\n",
      "Let's make this concrete. Assume our state variables are $x=\\begin{bmatrix}x&\\dot{x}\\end{bmatrix}^T$. (**note**: it is customary to use this transpose form of writing an matrix in text. It is how we denote that $x$ is a column matrix without taking up a lot of line space). Then $\\textbf{Q}$ will contain:\n",
      "\n",
      "$$Q = \\begin{bmatrix}\n",
      "\\sigma_x^2 & p\\sigma_x\\sigma_{\\dot{x}} \\\\\n",
      "p\\sigma_x\\sigma_{\\dot{x}}& \\sigma_{\\dot{x}}^2\n",
      "\\end{bmatrix}\n",
      "$$\n",
      "\n",
      "But again, what does this *mean*? This is a one dimensional problem, where our variables are $x$ and $\\dot{x}$. Assume we are tracking a person walking in 1D, so $x$ is their position, and  $\\dot{x}$ is their velocity. We have no state variable for $\\ddot{x}$, so we are assuming aceleration is zero, and thus their velocity is constant. No one walks with constant velocity, even if they are trying to do so. The *process noise* specifies how much variance there is in each state variable due to the changes in velocity that inevitably happen.\n",
      "\n",
      "You will very typically see Q expressed in this form (indeed, this is what the code immediately above does):\n",
      "\n",
      "$$\\begin{bmatrix}\n",
      "0&0 \\\\\n",
      "0&0.1\n",
      "\\end{bmatrix}\n",
      "$$\n",
      "\n",
      "Why all zeros but in the last row and column. This is a useful approximation that we can use for $\\textbf{Q}$ under certain circumstances. Think about the person. As they accelerate, that will also alter their velocity, and eventually their position. But if the acceleration is small compared to our time sample rate, then the changes to distance will small. This follows from the Newtonian equations:\n",
      "$$\n",
      "\\begin{aligned}\n",
      "v&=a\\Delta t \\\\\n",
      "d&=\\frac{a}{2}{\\Delta t}^2\n",
      "\\end{aligned}\n",
      "$$\n",
      "If t is small and a is small than the contribution of $\\frac{a}{2}{\\Delta t}^2$ will be extremely small. In this case it is safe to set all of the terms in $\\mathbf{Q}$ to 0 except the variance for the last term. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On the other hand, let's suppose this is not the case. How should Q be designed? Our design of the system is:\n",
      "\n",
      "$$ X_{n+1} = \\Phi X_n + U_n$$\n",
      "\n",
      "where $\\Phi X_n$ is our state transition, which computes $\\mathbf{x}$ at time $n+1$ using Newtonan equations, and $U_n$ is the white noise associated with the process. For a walking human, based on the equations above we get\n",
      "\n",
      "$$U_n = \\begin{bmatrix}\\frac{a{\\Delta t}^2}{2} \\\\ \\Delta t\\end{bmatrix}$$\n",
      "\n",
      "So white noise has the variance $U_n$ and a mean of 0, which we notate as $w \\sim \\mathcal{N}(0,Q)$. \n",
      "\n",
      "Finding an analytic value for $\\textbf{Q}$ in a simple problem like this is not difficult, but it quickly becomes difficult to impossible as the number of state variables increase. So in this chapter we will use the simplification that only the variance of the last term is important. In the Kalman filter math chapter we will discuss finding an analytic solution ofr $\\textbf{Q}$, and then present C. F. van Loan's extremely useful numerical technique for finding $\\textbf{Q}$, which is what you will typically use in practice. \n",
      "\n",
      "**author's note: text needs to move to kalman math chapter. leaving here for now **"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Designing R"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's leave ${\\mathbf{Q}}=0.1$, but bump ${\\mathbf{R}}$ up to $1000$. This is telling the filter that the measurement noise is very large. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track (data=zs, R=1000, Q=0.1,count=30, plot_P=False, title='R = 1000, Q = 0.1')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PZ+rUqYwYMYLAwEDuvvtuUlNTAdi6dSsdOnSgfv36PP7448THx+ed07t3bxo3bsyMGTNo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\nMRERERERACbGREREREQAgP8H8k/U19HsAP0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2db6b50>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The filter output should be much closer to the green line, especially after 10-20 cycles. If you are running this in Ipython Notebook, I strongly urge you to run this many times in a row (click inside the code box, and press CTRL-Enter). Most times the filter tracks almost exactly with the actual position, randomly going slightly above and below the green line, but sometimes it stays well over or under the green line for a long time. What is happening in the latter case?\n",
      "\n",
      "The filter is strongly preferring the motion update to the measurement, so if the prediction is off it takes a lot of measurements to correct it. It will eventually correct because the velocity is a hidden variable - it is computed from the measurements, but it will take awhile.\n",
      "\n",
      "To some extent you can get similar looking output by varying either ${\\mathbf{R}}$ or ${\\mathbf{Q}}$, but I urge you to not 'magically' alter these until you get output that you like. Always think about the physical implications of these assignments, and vary ${\\mathbf{R}}$ and/or ${\\mathbf{Q}}$ based on your knowledge of the system you are filtering."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "A Detailed Examination of the Covariance Matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far I have not given a lot of coverage of the covariance matrix. $\\mathbf{P}$, the covariance matrix is nothing more than the variance of our state - such as the position of our dog. It has many elements in it, but don't be daunted; we will learn how to interpret a very large $9{\\times}9$ covariance matrix, or even larger.\n",
      "\n",
      "Recall the beginning of the chapter, where we provided the equation for the covariance matrix. It read:\n",
      "\n",
      "$$\n",
      "\\mathbf{P} = \\begin{pmatrix}\n",
      "  {{\\sigma}_{1}}^2 & p{\\sigma}_{1}{\\sigma}_{2} & \\cdots & p{\\sigma}_{1}{\\sigma}_{n} \\\\\n",
      "  p{\\sigma}_{2}{\\sigma}_{1} &{{\\sigma}_{2}}^2 & \\cdots & p{\\sigma}_{2}{\\sigma}_{n} \\\\\n",
      "  \\vdots  & \\vdots  & \\ddots & \\vdots  \\\\\n",
      "  p{\\sigma}_{n}{\\sigma}_{1} & p{\\sigma}_{n}{\\sigma}_{2} & \\cdots & {{\\sigma}_{n}}^2\n",
      " \\end{pmatrix}\n",
      "$$\n",
      "\n",
      "(I have subtituted $\\mathbf{P}$ for $\\Sigma$ because of the nomenclature used by the Kalman filter literature).\n",
      "\n",
      "The diagonal contains the variance of each of our state variables. So, if our state variables are\n",
      "\n",
      "$$\\begin{pmatrix}x\\\\\\dot{x}\\end{pmatrix}$$\n",
      "\n",
      "and the covariance matrix happens to be\n",
      "$$\\begin{pmatrix}2&0\\\\0&6\\end{pmatrix}$$\n",
      "\n",
      "we know that the variance of $x$ is 2, and the variance of $\\dot{x}$ is 6. The off diagonal elements are all 0, so we also know that $x$ and $\\dot{x}$ are not correlated. Recall the ellipses that we drew of the covariance matrices. Let's look at the ellipse for the matrix."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = np.array([[2,0],[0,6]])\n",
      "stats.plot_covariance_ellipse ((0,0), P, title='|2 0|\\n|0 6|')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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S0axZ+3XZZdn65z+ZkgNghqScrT788EN1795daWns5egUzDaZi+zqrVrl0cSJmZozp0oF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3392450>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Of course it is unlikely that the position and velocity of an object remain uncorrelated for long. Let's look at a more typical covariance matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = np.array([[2,2.4],[2.4,6]])\n",
      "stats.plot_covariance_ellipse ((0,0), P, title ='|2.0  2.4|\\n|2.4  6.0|')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Vr15AX35ZoL59rWt4D2vbtloTJpRq2LAklZZaW8uJcO+Zjfycj5VeAIhy69a59fvfJykQ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\nRn7Ox5ZlAKLSvn0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XQTHbZC47Z8eL2E7MDvmtXRujefO8+sMfyq0uxSh2yA6hIz/no+kF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\njQL6619LNHRokv75zyKde651873bt7s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       "text": [
        "<matplotlib.figure.Figure at 0x2da7290>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here the ellipse is slanted, signifying that $x$ and $\\dot{x}$ are correlated (and, of course, dependent - all correlated variables are dependent). You may or may not have noticed that the off diagonal elements were set to the same value, 2.4. This was not an accident. Let's look at the equation for the covariance for the case where the number of dimensions is two.\n",
      "\n",
      "$$\n",
      "\\mathbf{P} = \\begin{pmatrix}\n",
      "  \\sigma_1^2 & p\\sigma_1\\sigma_2 \\\\\n",
      "  p\\sigma_2\\sigma_1 &\\sigma_2^2 \n",
      " \\end{pmatrix}\n",
      "$$\n",
      "\n",
      "Look at the computation for the off diagonal elements. \n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mathbf{P}_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n",
      "\\mathbf{P}_{1,0}&=p\\sigma_2\\sigma_1.\n",
      "\\end{aligned}$$\n",
      "\n",
      "If we re-arrange terms we get\n",
      "$$\\begin{aligned}\n",
      "\\mathbf{P}_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n",
      "\\mathbf{P}_{1,0}&=p\\sigma_1\\sigma_1 \\mbox{, yielding}  \\\\\n",
      "\\mathbf{P}_{0,1}&=P_{1,0}\n",
      "\\end{aligned}$$\n",
      "\n",
      "In general, we can state that $\\small\\mathbf{P}_{i,j}=\\small\\mathbf{P}_{j,i}$.\n",
      "\n",
      "So for my example I multiplied the diagonals, 2 and 6, to get 12, and then scaled that with the arbitrarily chosen $p=.2$ to get 2.4."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's get back to concrete terms. Let's start by revisting plotting a track. I will hard code the data and noise to avoid being at the mercy of the random number generator, which might generate data that does not illustrate what I want to talk about. I will start by using the same parameters as a chart above: `R=5`, `Q=.02`, and `P=500`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# guarantee the noise is the same each time so I can be sure of\n",
      "# what the graphs look like.\n",
      "zs = [-6.947, 12.467, 6.899, 2.643, 6.980, 5.820, 5.788, 10.614, 5.210, \n",
      "      14.338, 11.401, 19.138, 14.169, 19.572, 25.471, 13.099, 27.090,\n",
      "      12.209, 14.274, 21.302, 14.678, 28.655, 15.914, 28.506, 23.181, \n",
      "      18.981, 28.197, 39.412, 27.640, 31.465, 34.903, 28.420, 33.889, \n",
      "      46.123, 31.355, 30.473, 49.861, 41.310, 42.526, 38.183, 41.383, \n",
      "      41.919, 52.372, 42.048, 48.522, 44.681, 32.989, 37.288, 49.141, \n",
      "      54.235, 62.974, 61.742, 54.863, 52.831, 61.122, 61.187, 58.441, \n",
      "      47.769, 56.855, 53.693, 61.534, 70.665, 60.355, 65.095, 63.386]\n",
      "\n",
      "plot_track (data=zs, R=5, Q=.02, P=500., count=len(zs), plot_P=False, title='P=500')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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587lz5w6NGzfmySef5LPPPksz61yU4lqcyBpLdUn81SXxV09Gsdfv25ecGNvJ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RwdHY3L5Wo+vvA3WLGO3gNrud1usrOzmTJlCnFxcbhcLuVvQHx8PLGxscTGxip/CxQX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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2dc88d0>"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Looking at the output we see a very large spike in the filter output at the beginning. If you look at the data (dotted red line) you will see a corresponding, smaller spike in the beginning of the data. We set `P=500`, which corresponds to $\\text{P}=[\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix}]$. We now have enough information to understand what this means, and how the Kalman filter treats it. The 500 in the upper left hand corner corresponds to $\\sigma^2_x$; therefore we are saying the standard deviation of `x` is $\\sqrt{500}$, or roughly 22.36 meters, assuming our measurements are in meters. If we recall how standard deviations work, roughly 99% of the samples occur withing $3\\sigma$, therefore `P=500` is telling the Kalman filter that the initial estimate could be up to 67 meters off. That is a pretty large error, so when the measurement spikes the Kalman filter distrusts its own estimate and jumps wildly to try to incorporate the measurement. Then, as the filter evolves $\\mathbf{P}$ quickly converges to a more realistic value.\n",
      "\n",
      "Now let us see the effect of a smaller initial value for `P`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track (data=zs, R=5, Q=.02, P=1., count=len(zs), plot_P=False, title='P=1')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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n7K9jrHekkzJlyjB27Fj69u2LxWIhLCyM2rVrM2LECHr27AnA2LFjHWlaCCGE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LrOGHd3K+PMGSWnTzdTFAAAAMadcTFj7PzXv5Szbp3tMgAAADCBpGVjzM09Rg+zTvaQvV3kbxf5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\nGeMuqhd7AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x324acd0>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This plot does not have the spike that the former plot did; the filter starts tracking the measurements and doesn't take any time to 'settle' to the signal.\n",
      "\n",
      "Do not conclude from this that the 'magic' is to just use a small $\\text{P}$. Yes, this will avoid having the Kalman filter take time to accurately track the signal, but if we are truly uncertain about the initial measurements this can cause the filter to generate very bad results. If we are tracking a living object we are probably very uncertain about where it is before we start tracking it. On the other hand, if we are filtering the output of a thermometer, we are just as certain about the first measurement as the 1000th. For your Kalman filter to perform well you must set $\\text{P}$ to a value that truly reflects your knowledge about the data. \n",
      "\n",
      "\n",
      "Let's see the result of a bad initial estimate coupled with a very small $\\text{P}$ We will set our initial estimate at 100m (whereas the dog starts at 0m), but set $\\text{P=1}$.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([[100,0]]).T\n",
      "plot_track(data=zs, R=5, Q=.02, P=1., initial_x=x,count=len(zs),\n",
      "           plot_P=False, title='P=1')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MMfHVVyZ+/DEZf/+S33zjWgsXGvn2WxO//JJ0wy5zUXFRhB4IJfx4OF3qdWFY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\nIiIiAsDGmIiIiIgIAPBf8sizpKTBk6MAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2ea89d0>"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the initial estimates are terrible, up to around step 15 to 20. This is because we told the Kalman filter that we strongly believe in our initial estimate of 100m.\n",
      "\n",
      "Now, let's provide a more reasonable value for P and see the difference."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([[100,0]]).T\n",
      "plot_track(data=zs, R=5, Q=.02, P=500., initial_x=x,count=len(zs),\n",
      "           plot_P=False, title='P=500')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xMTEAdO/enfbt2wP3Vkmyu19L586dCQgI4Ntvv2XGjBkEBATw6quvZjjmnXfe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\nR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       "text": [
        "<matplotlib.figure.Figure at 0x15a11d0>"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this case the Kalman filter is very uncertain about the initial state, so it converges onto the signal much faster. It is producing good output after only 5 to 6 evolutions. With the theory we have developed so far this is about as good as we can do. However, this scenario is a bit artificial; if we do not know where the object is when we start tracking we do not initialize the filter to some arbitrary value, such as 0 or 100. Instead, we would normally take the first measurement, use that to initialize the Kalman filter, and proceed from there. But this is an engineering decision. You really need to understand the domain in which you are working and initialize your filter on the best available information. For example, suppose we were trying to track horses in a horse race. The initial measurements might be very bad, and provide you with a position far from the starting gate. We know that the horse must of started at the starting gate; initializing the filter to the initial measurement would lead to suboptimal results. In this scenario we would want to always initialize the Kalman filter with the starting gate position. \n",
      "\n",
      "If we have the luxury of not needing to perform the filtering in real time, as the data comes in, we can take advantage of other techniques. We can 'eyeball' the data and see that  the initial measurements are giving us reasonable values for the dog's position because we can see all of the data at once. A `fixed lag smoother` will look N steps ahead before computing the state, and other filters will do things like first run forwards, than backwards over the data. This will be the subject of later chapters. It is worthwhile to keep in mind that whenever possible we should prefer this sort of batch processing because it takes advantage of all available information. It does incur cost of additional processing time and increased storage due to the requirement to store some or all of the measurements. And, of course, batch processing does not work if we need real time results, such as when using GPS in our car."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Lets do another Kalman filter for our dog, and this time plot the covariance ellipses on the same plot as the position."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_track_ellipses(noise, count, R, Q=0, P=20., plot_P=True, title='Kalman Filter'):\n",
      "    dog = DogSensor(velocity=1, noise=noise)\n",
      "    f = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
      "\n",
      "    ps = []\n",
      "    zs = []\n",
      "    cov = []\n",
      "    for t in range (count):\n",
      "        z = dog.sense()\n",
      "        f.update (z)\n",
      "        ps.append (f.x[0,0])\n",
      "        cov.append(f.P)\n",
      "        zs.append(z)\n",
      "        f.predict()\n",
      "\n",
      "    p0, = plt.plot([0,count],[0,count],'g')\n",
      "    p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n",
      "    p2, = plt.plot(range(1,count+1),ps, c='b')\n",
      "    plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n",
      "    plt.title(title)\n",
      "\n",
      "    for i,p in enumerate(cov):\n",
      "        stats.plot_covariance_ellipse ((i+1, ps[i]), cov=p)\n",
      "\n",
      "        if i == len(cov)-1:\n",
      "            s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n",
      "            plt.text (30,1,s,fontsize=18)\n",
      "            s = ('$\\sigma^2_{vel} = %.2f$' % p[1,1])\n",
      "            plt.text (30,-4,s,fontsize=18)\n",
      "    plt.xlim((0,40))\n",
      "    plt.ylim((0,40))\n",
      "    plt.axis('equal')\n",
      "    \n",
      "    plt.show()\n",
      "\n",
      "\n",
      "plot_track_ellipses (noise=5, R=5, Q=5, count=20, title='R = 5')\n",
      "plot_track_ellipses (noise=5, R=.5, Q=5, count=20, title='R = 0.5')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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82Z5bbLNB48YWVq82EBgYmeX5P/kklmee8eDllxOSV1DTHj5MfMmy9BpQikaN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\nIYQQJcr/AzdyC5bjFKaTAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2edb310>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hxPP2anc9WzKLm8Odrz1R/iQACyGEcElsrI6YGMc7nhXXuLGJw4dvTgB2tGXx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UP4bvPzp8eu/bhJdzkfekz168mPm/4978/dRBctWgRnMDqdzumtn/R6PaZNm9Z8E9xDDz2E3bt3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\n4XA4vPrd6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       "text": [
        "<matplotlib.figure.Figure at 0x32c1990>"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The output on these is a bit messy, but you should be able to see what is happening. In both plots we are drawing the covariance matrix for each point. We start with the covariance $\\mathbf{P}=(\\begin{smallmatrix}50&0\\\\0&50\\end{smallmatrix})$, which signifies a lot of uncertainty about our initial belief. After we receive the first measurement the Kalman filter updates this belief, and so the variance is no longer as large. In the top plot the first ellipse (the one on the far left) should be a slighly squashed ellipse. As the filter continues processing the measurements the covariance ellipse quickly shifts shape until it settles down to being a long, narrow ellipse tilted in the direction of movement.\n",
      "\n",
      "Think about what this means physically. The x-axis of the ellipse denotes our uncertainty in position, and the y-axis our uncertainty in velocity. So, an ellipse that is taller than it is wide signifies that we are more uncertain about the velocity than the position. Conversely, a wide, narrow ellipse shows high uncertainty in position and low uncertainty in velocity. Finally, the amount of tilt shows the amount of correlation between the two variables. \n",
      "\n",
      "The first plot, with $\\mathbf{R}=5$, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner. The variance for position is 3.85, and the variance for velocity is 3.0. \n",
      "\n",
      "In contrast, the second plot, with $\\mathbf{R}=0.5$, has a final ellipse that is taller than wide. The ellipses in the second plot are all much smaller than the ellipses in the first plot. This stands to reason because a small $\\small\\mathbf{R}$ implies a small amount of noise in our measurements. Small noise means accurate predictions, and thus a strong belief in our position. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Question: Explain Ellipse Differences"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Why are the ellipses for $\\mathbf{R}=5$ shorter, and more tilted than the ellipses for $\\mathbf{R}=0.5$. Hint: think about this in the context of what these ellipses mean physically, not in terms of the math. If you aren't sure about the answer,change $\\mathbf{R}$ to truly large and small numbers such as 100 and 0.1, observe the changes, and think about what this means. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The $x$ axis is for position, and $y$ is velocity. An ellipse that is vertical, or nearly so, says there is no correlation between position and velocity, and an ellipse that is diagnal says that there is a lot of correlation. Phrased that way, it sounds unlikely - either they are correlated or not. But this is a measure of the *output of the filter*, not a description of the actual, physical world. When $\\mathbf{R}$ is very large we are telling the filter that there is a lot of noise in the measurements. In that case the Kalman gain $\\mathbf{K}$ is set to favor the prediction over the measurement, and the prediction comes from the velocity state variable. So, there is a large correlation between $x$ and $\\dot{x}$. Conversely, if $\\mathbf{R}$ is small, we are telling the filter that the measurement is very trustworthy, and $\\mathbf{K}$ is set to favor the measurement over the prediction. Why would the filter want to use the prediction if the measurement is nearly perfect? If the filter is not using much from the prediction there will be very little correlation reported. \n",
      "\n",
      "**This is a critical point to understand!**. The Kalman filter is just a mathematical model for a real world system. A report of little correlation *does not mean* there is no correlation in the physical system, just that there was no correlation in the mathematical model. It's just a report of how much measurement vs prediction was incorporated into the model.  \n",
      "\n",
      "Let's bring that point home with a truly large measurement error. We will set $\\mathbf{R}=500$. Think about what the plot will look like before scrolling down. To emphasize the issue, I will set the amount of noise injected into the measurements to 0, so the measurement will exactly equal the actual position. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track_ellipses (noise=0, R=500, Q=5, count=7, title='R = 500')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ysrKYO3cu7du391axhSjxsrNh40Yzq1ZZWLnSzNGjKnfd5SQhwcWwYdnUrCmT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\nWj76yEmLFk5Kl8653oJWK0RFiWzcKLJ1q8grr3ho1MhJ5TI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6f15Lv35+SJKGiAgzb76Z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BwwYYKO+fP9Et1V19dQasjSFmX+FRQUfBVF8HmImzcFGjXKQIMGdgYNssYtFOrXd7B+vdxeftq0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\nAQAAAIBP/QNmscCUEv0F8gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x331bcd0>"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I hope the result was what you were expecting. The ellipse quickly became very wide and not very tall. It did this because the Kalman filter mostly used the prediction vs the measurement to produce the filtered result. We can also see how the filter output is slow to acquire the track. The Kalman filter assumes that the measurements are extremely noisy, and so it is very slow to update its estimate for $\\dot{x}$. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Keep looking at these plots until you grasp how to interpret the covariance matrix $\\mathbf{P}$. When you start dealing with a, say, $9{\\times}9$ matrix it may seem overwhelming - there are 81 numbers to interpret. Just break it down - the diagonal contains the variance for each state variable, and all off diagonal elements are the product of two variances and a scaling factor $p$. You will not be able to plot a $9{\\times}9$ matrix on the screen because it would require living in 10-D space, so you have to develop your intution and understanding in this simple, 2-D case. \n",
      "\n",
      "> **sidebar**: when plotting covariance ellipses, make sure to always use *plt.axis('equal')* in your code. If the axis use different scales the ellipses will be drawn distorted. For example, the ellipse may be drawn as being taller than it is wide, but it may actually be wider than tall."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[1] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.htmly"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}