Kalman-and-Bayesian-Filters-in-Python-master/11-Extended-Kalman-Filters.ipynb

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    "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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   "source": [
    "# The Extended Kalman Filter"
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   "source": [
    "#format the book\n",
    "%matplotlib inline\n",
    "from __future__ import division, print_function\n",
    "from book_format import load_style\n",
    "load_style()"
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   "source": [
    "We have developed the theory for the linear Kalman filter. Then, in the last two chapters we broached the topic of using Kalman filters for nonlinear problems. In this chapter we will learn the Extended Kalman filter (EKF). The EKF handles nonlinearity by linearizing the system at the point of the current estimate, and then the linear Kalman filter is used to filter this linearized system. It was one of the very first techniques used for nonlinear problems, and it remains the most common technique. \n",
    "\n",
    "The EKF provides significant mathematical challenges to the designer of the filter; this is the most challenging chapter of the book. I do everything I can to avoid the EKF in favor of other techniques that have been developed to filter nonlinear problems. However, the topic is unavoidable; all classic papers and a majority of current papers in the field use the EKF. Even if you do not use the EKF in your own work you will need to be familiar with the topic to be able to read the literature. "
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    "## Linearizing the Kalman Filter\n",
    "\n",
    "The Kalman filter uses linear equations, so it does not work with nonlinear problems. Problems can be nonlinear in two ways. First, the process model might be nonlinear. An object falling through the atmosphere encounters drag which reduces its acceleration. The drag coefficient varies based on the velocity the object. The resulting behavior is nonlinear - it cannot be modeled with linear equations. Second, the measurements could be nonlinear. For example, a radar gives a range and bearing to a target. We use trigonometry, which is nonlinear, to compute the position of the target.\n",
    "\n",
    "For the linear filter we have these equations for the process and measurement models:\n",
    "\n",
    "$$\\begin{aligned}\\dot{\\mathbf x} &= \\mathbf{Ax} + w_x\\\\\n",
    "\\mathbf z &= \\mathbf{Hx} + w_z\n",
    "\\end{aligned}$$\n",
    "\n",
    "Where $\\mathbf A$ is the systems dynamic matrix. Using the state space methods covered in the **Kalman Filter Math** chapter these equations can be tranformed into \n",
    "$$\\begin{aligned}\\bar{\\mathbf x} &= \\mathbf{Fx} \\\\\n",
    "\\mathbf z &= \\mathbf{Hx}\n",
    "\\end{aligned}$$\n",
    "\n",
    "where $\\mathbf F$ is the *fundamental matrix*. The noise $w_x$ and $w_z$ terms are incorporated into the matrices $\\mathbf R$ and $\\mathbf Q$. This form of the equations allow us to compute the state at step $k$ given a measurement at step $k$ and the state estimate at step $k-1$. In earlier chapters I built your intuition and minimized the math by using problems describable with Newton's equations. We know how to design $\\mathbf F$ based on high school physics.\n",
    "\n",
    "\n",
    "For the nonlinear model the linear expression $\\mathbf{Fx} + \\mathbf{Bu}$ is replaced by a nonlinear function $f(\\mathbf x, \\mathbf u)$, and the linear expression $\\mathbf{Hx}$ is replaced by a nonlinear function $h(\\mathbf x)$:\n",
    "\n",
    "$$\\begin{aligned}\\dot{\\mathbf x} &= f(\\mathbf x, \\mathbf u) + w_x\\\\\n",
    "\\mathbf z &= h(\\mathbf x) + w_z\n",
    "\\end{aligned}$$\n",
    "\n",
    "You might imagine that we could proceed by finding a new set of Kalman filter equations that optimally solve these equations. But if you remember the charts in the **Nonlinear Filtering** chapter you'll recall that passing a Gaussian through a nonlinear function results in a probability distribution that is no longer Gaussian. So this will not work.\n",
    "\n",
    "The EKF does not alter the Kalman filter's linear equations. Instead, it *linearizes* the nonlinear equations at the point of the current estimate, and uses this linearization in the linear Kalman filter. \n",
    "\n",
    "*Linearize* means what it sounds like. We find a line that most closely matches the curve at a defined point. The graph below linearizes the parabola $f(x)=x^2−2x$ at $x=1.5$."
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dU4o5HSttX57BHaZiZmIOJI1ts2jLFK7fvaDnZEIIIUTe9OBJIAs2fsXTqCcA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\nt56eZPRDLHMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e3791908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import code.ekf_internal as ekf_internal\n",
    "ekf_internal.show_linearization()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the curve above is the process model, then the dotted lines shows the linearization of that curve for the estimate $x=1.5$.\n",
    "\n",
    "We linearize systems by taking the derivative, which finds the slope of a curve:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "f(x) &= x^2 -2x \\\\\n",
    "\\frac{df}{dx} &= 2x - 2\n",
    "\\end{aligned}$$\n",
    "\n",
    "and then evaluating it at $x$:\n",
    "\n",
    "$$\\begin{aligned}m &= f'(x=1.5) \\\\&= 2(1.5) - 2 \\\\&= 1\\end{aligned}$$ \n",
    "\n",
    "Linearizing systems of differential equations is similar. We linearize $f(\\mathbf x, \\mathbf u)$, and $h(\\mathbf x)$ by taking the partial derivatives of each to evaluate $\\mathbf A$ and $\\mathbf H$ at the point $\\mathbf x_t$ and $\\mathbf u_t$. We call the partial derivative of a matrix the [*Jacobian*](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant). This gives us the the system dynamics matrix and measurement model matrix:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf A \n",
    "&= {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}} \\\\\n",
    "\\mathbf H &= \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t} \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Finally, we find the discrete state transition matrix $\\mathbf F$ by using the Taylor series expansion of $e^{\\mathbf A \\Delta t}$:\n",
    "\n",
    "$$\\mathbf F = e^{\\mathbf A\\Delta t} = \\mathbf{I} + \\mathbf A\\Delta t  + \\frac{(\\mathbf A\\Delta t)^2}{2!} + \\frac{(\\mathbf A\\Delta t)^3}{3!} + ... $$\n",
    "\n",
    "Alternatively, you can use one of the other techniques we learned in the **Kalman Math** chapter. \n",
    "\n",
    "This leads to the following equations for the EKF. I put boxes around the differences from the linear filter:\n",
    "\n",
    "$$\\begin{array}{l|l}\n",
    "\\text{linear Kalman filter} & \\text{EKF} \\\\\n",
    "\\hline \n",
    "& \\boxed{\\mathbf A = {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}}} \\\\\n",
    "& \\boxed{\\mathbf F = e^{\\mathbf A \\Delta t}} \\\\\n",
    "\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu} & \\boxed{\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)}  \\\\\n",
    "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q  & \\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q \\\\\n",
    "\\hline\n",
    "& \\boxed{\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}} \\\\\n",
    "\\textbf{y} = \\mathbf z - \\mathbf{H \\bar{x}} & \\textbf{y} = \\mathbf z - \\boxed{h(\\bar{x})}\\\\\n",
    "\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} & \\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} \\\\\n",
    "\\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} & \\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} \\\\\n",
    "\\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}} & \\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}}\n",
    "\\end{array}$$\n",
    "\n",
    "We don't normally use $\\mathbf{Fx}$ to propagate the state for the EKF as the linearization causes inaccuracies. It is typical to compute $\\bar{\\mathbf x}$ using a suitable numerical integration technique such as Euler or Runge Kutta. Thus I wrote $\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)$. For the same reasons we don't use $\\mathbf{H\\bar{x}}$ in the computation for the residual, opting for the more accurate $h(\\bar{\\mathbf x})$.\n",
    "\n",
    "I think the easiest way to understand the EKF is to start off with an example. Later you may want to come back and reread this section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Tracking a Airplane\n",
    "\n",
    "This example tracks an airplane using ground based radar. We implemented a UKF for this problem in the last chapter. Now we will implement an EKF for the same problem so we can compare both the filter performance and the level of effort required to implement the filter.\n",
    "\n",
    "Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
    "\n",
    "The relationship between the radar's slant range distance $r$ and elevation angle $\\epsilon$ with the horizontal position $x$ and altitude $y$ of the aircraft is illustrated in the figure below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Xduj6k9yhrjERd/T772aSw59/NrNLd+0KoaGurkrkrvTo0cPh55kzZ+Lv78/2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\niIjH+v8zBQ7kMei6aAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e679ac88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.show_radar_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives us the equalities:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\theta &= \\tan^{-1} \\frac y x\\\\\n",
    "r^2 &= x^2 + y^2\n",
    "\\end{aligned}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "We want to track the position of an aircraft assuming a constant velocity and altitude, and measurements of the slant distance to the aircraft. That means we need 3 state variables - horizontal distance, horizonal velocity, and altitude:\n",
    "\n",
    "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude}\\end{bmatrix}=    \\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Process Model\n",
    "\n",
    "We assume a Newtonian, kinematic system for the aircraft. We've used this model in previous chapters, so by inspection you may recognize that we want\n",
    "\n",
    "$$\\mathbf F = \\left[\\begin{array}{cc|c} 1 & \\Delta t & 0\\\\\n",
    "0 & 1 & 0 \\\\ \\hline\n",
    "0 & 0 & 1\\end{array}\\right]$$\n",
    "\n",
    "I've partioned the matrix into blocks to show the upper left block is a constant velocity model for $x$, and the lower right block is a constant position model for $y$.\n",
    "\n",
    "However, let's practice finding these matrix for a nonlinear system. We model nonlinear systems with a set of differential equations. We need an equation in the form \n",
    "\n",
    "$$\\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{w}$$\n",
    "where $\\mathbf{w}$ is the system noise. \n",
    "\n",
    "The variables $x$ and $y$ are independent so we can compute them separately. The differential equations for motion in one dimension are:\n",
    "\n",
    "$$\\begin{aligned}v &= \\dot x \\\\\n",
    "a &= \\ddot{x} = 0\\end{aligned}$$\n",
    "\n",
    "Now we put the differential equations into state-space form. If this was a second or greater order differential system we would have to first reduce them to an equivalent set of first degree equations. The equations are first order, so we put them in state space matrix form as\n",
    "\n",
    "$$\\begin{aligned}\\begin{bmatrix}\\dot x \\\\ \\ddot{x}\\end{bmatrix} &= \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \n",
    "\\dot x\\end{bmatrix} \\\\ \\dot{\\mathbf x} &= \\mathbf{Ax}\\end{aligned}$$\n",
    "where $\\mathbf A=\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}$. \n",
    "\n",
    "Recall that $\\mathbf A$ is the *system dynamics matrix*. It describes a set of linear differential equations. From it we must compute the state transition matrix $\\mathbf F$. $\\mathbf F$ describes a discrete set of linear equations which compute $\\mathbf x$ for a discrete time step $\\Delta t$.\n",
    "\n",
    "A common way to compute $\\mathbf F$ is to use the power series expansion of the matrix exponential:\n",
    "\n",
    "$$\\mathbf F(\\Delta t) = e^{\\mathbf A\\Delta t} = \\mathbf{I} + \\mathbf A\\Delta t  + \\frac{(\\mathbf A\\Delta t)^2}{2!} + \\frac{(\\mathbf A \\Delta t)^3}{3!} + ... $$\n",
    "\n",
    "\n",
    "$\\mathbf A^2 = \\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}$, so all higher powers of $\\mathbf A$ are also $\\mathbf{0}$. Thus the power series expansion is:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf F &=\\mathbf{I} + \\mathbf At + \\mathbf{0} \\\\\n",
    "&= \\begin{bmatrix}1&0\\\\0&1\\end{bmatrix} + \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}\\Delta t\\\\\n",
    "\\mathbf F &= \\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\n",
    "\\end{aligned}$$\n",
    "\n",
    "This is the same result used by the kinematic equations! This exercise was unnecessary other than to illustrate finding the state transition matrix from linear differential equations. We will conclude the chapter with an example that will require the use of this technique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "The measurement function takes the state estimate of the prior $\\bar{\\mathbf x}$ and turn it into a measurement of the slant range distance. We use the Pythagorean theorem to derive:\n",
    "\n",
    "$$h(\\bar{\\mathbf x}) = \\sqrt{x^2 + y^2}$$\n",
    "\n",
    "The relationship between the slant distance and the position on the ground is nonlinear due to the square root. We linearize it by evaluating its partial derivative at $\\mathbf x_t$:\n",
    "\n",
    "$$\n",
    "\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x})}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}\n",
    "$$\n",
    "\n",
    "The partial derivative of a matrix is called a Jacobian, and takes the form \n",
    "\n",
    "$$\\frac{\\partial \\mathbf H}{\\partial \\bar{\\mathbf x}} = \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial h_1}{\\partial x_1} & \\frac{\\partial h_1}{\\partial x_2} &\\dots \\\\\n",
    "\\frac{\\partial h_2}{\\partial x_1} & \\frac{\\partial h_2}{\\partial x_2} &\\dots \\\\\n",
    "\\vdots & \\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "In other words, each element in the matrix is the partial derivative of the function $h$ with respect to the $x$ variables. For our problem we have\n",
    "\n",
    "$$\\mathbf H = \\begin{bmatrix}{\\partial h}/{\\partial x} & {\\partial h}/{\\partial \\dot{x}} & {\\partial h}/{\\partial y}\\end{bmatrix}$$\n",
    "\n",
    "Solving each in turn:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial x} &= \\frac{\\partial}{\\partial x} \\sqrt{x^2 + y^2} \\\\\n",
    "&= \\frac{x}{\\sqrt{x^2 + y^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial \\dot{x}} &=\n",
    "\\frac{\\partial}{\\partial \\dot{x}} \\sqrt{x^2 + y^2} \\\\ \n",
    "&= 0\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial y} &= \\frac{\\partial}{\\partial y} \\sqrt{x^2 + y^2} \\\\ \n",
    "&= \\frac{y}{\\sqrt{x^2 + y^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "giving us \n",
    "\n",
    "$$\\mathbf H = \n",
    "\\begin{bmatrix}\n",
    "\\frac{x}{\\sqrt{x^2 + y^2}} & \n",
    "0 &\n",
    "&\n",
    "\\frac{y}{\\sqrt{x^2 + y^2}}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "This may seem daunting, so step back and recognize that all of this math is doing something very simple. We have an equation for the slant range to the airplane which is nonlinear. The Kalman filter only works with linear equations, so we need to find a linear equation that approximates $\\mathbf H$. As we discussed above, finding the slope of a nonlinear equation at a given point is a good approximation. For the Kalman filter, the 'given point' is the state variable $\\mathbf x$ so we need to take the derivative of the slant range with respect to $\\mathbf x$. For the linear Kalman filter $\\mathbf H$ was a constant that we computed prior to running the filter. For the EKF $\\mathbf H$ is updated at each step as the evaluation point $\\bar{\\mathbf x}$ changes at each epoch.\n",
    "\n",
    "To make this more concrete, let's now write a Python function that computes the Jacobian of $h$ for this problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def HJacobian_at(x):\n",
    "    \"\"\" compute Jacobian of H matrix at x \"\"\"\n",
    "\n",
    "    horiz_dist = x[0]\n",
    "    altitude   = x[2]\n",
    "    denom = sqrt(horiz_dist**2 + altitude**2)\n",
    "    return array ([[horiz_dist/denom, 0., altitude/denom]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's provide the code for $h(\\bar{\\mathbf x})$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def hx(x):\n",
    "    \"\"\" compute measurement for slant range that\n",
    "    would correspond to state x.\n",
    "    \"\"\"\n",
    "    \n",
    "    return (x[0]**2 + x[2]**2) ** 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's write a simulation for our radar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "import math\n",
    "\n",
    "class RadarSim(object):\n",
    "    \"\"\" Simulates the radar signal returns from an object\n",
    "    flying at a constant altityude and velocity in 1D. \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, dt, pos, vel, alt):\n",
    "        self.pos = pos\n",
    "        self.vel = vel\n",
    "        self.alt = alt\n",
    "        self.dt = dt\n",
    "        \n",
    "    def get_range(self):\n",
    "        \"\"\" Returns slant range to the object. Call once \n",
    "        for each new measurement at dt time from last call.\n",
    "        \"\"\"\n",
    "        \n",
    "        # add some process noise to the system\n",
    "        self.vel = self.vel  + .1*randn()\n",
    "        self.alt = self.alt + .1*randn()\n",
    "        self.pos = self.pos + self.vel*self.dt\n",
    "    \n",
    "        # add measurement noise\n",
    "        err = self.pos * 0.05*randn()\n",
    "        slant_dist = math.sqrt(self.pos**2 + self.alt**2)\n",
    "        \n",
    "        return slant_dist + err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design Process and Measurement Noise\n",
    "\n",
    "The radar measures the range to a target. We will use $\\sigma_{range}= 5$ meters for the noise. This gives us\n",
    "\n",
    "$$\\mathbf R = \\begin{bmatrix}\\sigma_{range}^2\\end{bmatrix} = \\begin{bmatrix}25\\end{bmatrix}$$\n",
    "\n",
    "\n",
    "The design of $\\mathbf Q$ requires some discussion. The state $\\mathbf x= \\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are position (down range distance) and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of $\\mathbf Q$. The third element of  $\\mathbf x$ is altitude, which we are assuming is independent of the down range distance. That leads us to a block design of $\\mathbf Q$ of:\n",
    "\n",
    "$$\\mathbf Q = \\begin{bmatrix}\\mathbf Q_\\mathtt{x} & 0 \\\\ 0 & \\mathbf Q_\\mathtt{y}\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "`FilterPy` provides the class `ExtendedKalmanFilter`. It works similarly to the `KalmanFilter` class we have been using, except that it allows you to provide a function that computes the Jacobian of $\\mathbf H$ and the function $h(\\mathbf x)$. \n",
    "\n",
    "We start by importing the filter and creating it. The dimension of `x` is 3 and `z` has dimension 1.\n",
    "\n",
    "```python\n",
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "```\n",
    "We create the radar simulator:\n",
    "```python\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "```\n",
    "We will initialize the filter near the airplane's actual position:\n",
    "\n",
    "```python\n",
    "rk.x = array([radar.pos, radar.vel-10, radar.alt+100])\n",
    "```\n",
    "\n",
    "We assign the system matrix using the first term of the Taylor series expansion we computed above:\n",
    "\n",
    "```python\n",
    "dt = 0.05\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]])*dt\n",
    "```\n",
    "\n",
    "After assigning reasonable values to $\\mathbf R$, $\\mathbf Q$, and $\\mathbf P$ we can run the filter with a simple loop. We pass the functions for computing the Jacobian of $\\mathbf  H$ and $h(x)$ into the `update` method.\n",
    "\n",
    "```python\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    rk.predict()\n",
    "```\n",
    "\n",
    "Adding some boilerplate code to save and plot the results we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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INVtM5OQGgimQTTsd27q5QLsm4OVu+3PTOtA8HBrX0uVmkbJOgVFERIrt3j6D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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e688bdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZjgKuXbs2ffr0wTRNPvzwQ5o2bUqFChXs9jEMg4IFCxIcHEzbtm2ztFi5NaF1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\nRM1QAUgIIYQQomb+H3Qs5aN6+G0WAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e78d1748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jR7ZqA4mIiIio/ekdEisrK1FZWYnExEQkJibqLBdFEYIg8OxmIiIiovuA3iFx1qxZ2LZt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\nkYiIiIi0sEgkIiIiIi0sEomIiIhIy/8Ai1iF5guWg54AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e7920ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.common import Q_discrete_white_noise\n",
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "from numpy import eye, array, asarray\n",
    "import numpy as np\n",
    "\n",
    "dt = 0.05\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "\n",
    "# make an imperfect starting guess\n",
    "rk.x = array([radar.pos-100, radar.vel+100, radar.alt+1000])\n",
    "\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]]) * dt\n",
    "\n",
    "range_std = 5. # meters\n",
    "rk.R = np.diag([range_std**2])\n",
    "rk.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n",
    "rk.Q[2,2] = 0.1\n",
    "rk.P *= 50\n",
    "\n",
    "xs, track = [], []\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    track.append((radar.pos, radar.vel, radar.alt))\n",
    "    \n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    xs.append(rk.x)\n",
    "    rk.predict()\n",
    "\n",
    "xs = asarray(xs)\n",
    "track = asarray(track)\n",
    "time = np.arange(0, len(xs)*dt, dt)\n",
    "ekf_internal.plot_radar(xs, track, time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using SymPy to compute Jacobians\n",
    "\n",
    "Depending on your experience with derivatives you may have found the computation of the Jacobian difficult. Even if you found it easy, a slightly more difficult problem easily leads to very difficult computations.\n",
    "\n",
    "As explained in Appendix A, we can use the SymPy package to compute the Jacobian for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMsAAAAmBAMAAACYD3JcAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nbvXGjjdK38CrVvEPoeYc6sIOZHkAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{x}{\\sqrt{x^{2} + y^{2}}} & 0 & \\frac{y}{\\sqrt{x^{2} + y^{2}}}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡     x                y      ⎤\n",
       "⎢────────────  0  ────────────⎥\n",
       "⎢   _________        _________⎥\n",
       "⎢  ╱  2    2        ╱  2    2 ⎥\n",
       "⎣╲╱  x  + y       ╲╱  x  + y  ⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "sympy.init_printing(use_latex=True)\n",
    "\n",
    "x, x_vel, y = sympy.symbols('x, x_vel y')\n",
    "\n",
    "H = sympy.Matrix([sympy.sqrt(x**2 + y**2)])\n",
    "\n",
    "state = sympy.Matrix([x, x_vel, y])\n",
    "H.jacobian(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result is the same as the result we computed above, and with much less effort on our part!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robot Localization\n",
    "\n",
    "It's time to try a real problem. I warn you that this section is difficult. However, most books choose simple, textbook problems with simple answers, and you are left wondering how to solve a real world problem. \n",
    "\n",
    "We will consider the problem of robot localization. We already implemented this in the **Unscented Kalman Filter** chapter, and I recommend you read it now if you haven't already.  In this scenario we have a robot that is moving through a landscape using a sensor to detect landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. It might be one of those small robots that vacuum your house, or a robot in a warehouse.\n",
    "\n",
    "The robot has 4 wheels in the same configuration used by automobiles. It maneuvers by pivoting the front wheels. This causes the robot to pivot around the rear axle while moving forward. This is nonlinear behavior which we will have to model. \n",
    "\n",
    "The robot has a sensor that measures the range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n",
    "\n",
    "Both the process model and measurement models are nonlinear. The EKF accommodates both, so we provisionally conclude that the EKF is a viable choice for this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Robot Motion Model\n",
    "\n",
    "At a first approximation an automobile steers by pivoting the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modeling steering requires a complicated set of differential equations. \n",
    "\n",
    "For lower speed robotic applications a simpler *bicycle model* has been found to perform well. This is a depiction of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3Ol8bhqHgYGvCDEoWAQNAmVTamyvLkmrVKuvUqYIf7X47qwJG48buz0Hp2LGj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\njoABAAAsR8AAAACW+780ZYQOic7fMwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e674a198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.plot_bicycle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the **Unscented Kalman Filter** chapter we derived these equations:\n",
    "\n",
    "$$\\begin{aligned} \n",
    "\\beta &= \\frac d w \\tan(\\alpha) \\\\\n",
    "x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\theta &= \\theta + \\beta\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $\\theta$ is the robot's heading.\n",
    "\n",
    "You do not need to understand this model in detail if you are not interested in steering models. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "For our filter we will maintain the position $x,y$ and orientation $\\theta$ of the robot:\n",
    "\n",
    "$$\\mathbf x = \\begin{bmatrix}x \\\\ y \\\\ \\theta\\end{bmatrix}$$\n",
    "\n",
    "Our control input $\\mathbf u$ is the velocity $v$ and steering angle $\\alpha$:\n",
    "\n",
    "$$\\mathbf u = \\begin{bmatrix}v \\\\ \\alpha\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the System Model\n",
    "\n",
    "We model our system as a nonlinear motion model plus noise.\n",
    "\n",
    "$$\\bar x = x + f(x, u) + \\mathcal{N}(0, Q)$$\n",
    "\n",
    "\n",
    "\n",
    "Using the motion model for a robot that we created above, we can expand this to\n",
    "\n",
    "$$\\bar{\\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix}} = \\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix} + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}$$\n",
    "\n",
    "We find The $\\mathbf F$ by taking the Jacobian of $f(x,u)$.\n",
    "\n",
    "$$\\mathbf F = \\frac{\\partial f(x, u)}{\\partial x} =\\begin{bmatrix}\n",
    "\\frac{\\partial \\dot x}{\\partial x} & \n",
    "\\frac{\\partial \\dot x}{\\partial y} &\n",
    "\\frac{\\partial \\dot x}{\\partial \\theta}\\\\\n",
    "\\frac{\\partial \\dot y}{\\partial x} & \n",
    "\\frac{\\partial \\dot y}{\\partial y} &\n",
    "\\frac{\\partial \\dot y}{\\partial \\theta} \\\\\n",
    "\\frac{\\partial \\dot{\\theta}}{\\partial x} & \n",
    "\\frac{\\partial \\dot{\\theta}}{\\partial y} &\n",
    "\\frac{\\partial \\dot{\\theta}}{\\partial \\theta}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "When we calculate these we get\n",
    "\n",
    "$$\\mathbf F = \\begin{bmatrix}\n",
    "1 & 0 & -R\\cos(\\theta) + R\\cos(\\theta+\\beta) \\\\\n",
    "0 & 1 & -R\\sin(\\theta) + R\\sin(\\theta+\\beta) \\\\\n",
    "0 & 0 & 1\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "We can double check our work with SymPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & - \\frac{w \\cos{\\left (\\theta \\right )}}{\\tan{\\left (\\alpha \\right )}} + \\frac{w}{\\tan{\\left (\\alpha \\right )}} \\cos{\\left (\\frac{t v}{w} \\tan{\\left (\\alpha \\right )} + \\theta \\right )}\\\\0 & 1 & - \\frac{w \\sin{\\left (\\theta \\right )}}{\\tan{\\left (\\alpha \\right )}} + \\frac{w}{\\tan{\\left (\\alpha \\right )}} \\sin{\\left (\\frac{t v}{w} \\tan{\\left (\\alpha \\right )} + \\theta \\right )}\\\\0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                        ⎛t⋅v⋅tan(α)    ⎞⎤\n",
       "⎢                   w⋅cos⎜────────── + θ⎟⎥\n",
       "⎢        w⋅cos(θ)        ⎝    w         ⎠⎥\n",
       "⎢1  0  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(α)            tan(α)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎢                        ⎛t⋅v⋅tan(α)    ⎞⎥\n",
       "⎢                   w⋅sin⎜────────── + θ⎟⎥\n",
       "⎢        w⋅sin(θ)        ⎝    w         ⎠⎥\n",
       "⎢0  1  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(α)            tan(α)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎣0  0                  1                 ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "from sympy.abc import alpha, x, y, v, w, R, theta\n",
    "from sympy import symbols, Matrix\n",
    "sympy.init_printing(use_latex=\"mathjax\", fontsize='16pt')\n",
    "time = symbols('t')\n",
    "d = v*time\n",
    "beta = (d/w)*sympy.tan(alpha)\n",
    "r = w/sympy.tan(alpha)\n",
    "\n",
    "fxu = Matrix([[x-r*sympy.sin(theta) + r*sympy.sin(theta+beta)],\n",
    "              [y+r*sympy.cos(theta)- r*sympy.cos(theta+beta)],\n",
    "              [theta+beta]])\n",
    "F = fxu.jacobian(Matrix([x, y, theta]))\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks a bit complicated. We can use SymPy to substitute terms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & - R \\cos{\\left (\\theta \\right )} + R \\cos{\\left (\\beta + \\theta \\right )}\\\\0 & 1 & - R \\sin{\\left (\\theta \\right )} + R \\sin{\\left (\\beta + \\theta \\right )}\\\\0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0  -R⋅cos(θ) + R⋅cos(β + θ)⎤\n",
       "⎢                              ⎥\n",
       "⎢0  1  -R⋅sin(θ) + R⋅sin(β + θ)⎥\n",
       "⎢                              ⎥\n",
       "⎣0  0             1            ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reduce common expressions\n",
    "B, R = symbols('beta, R')\n",
    "F = F.subs((d/w)*sympy.tan(alpha), B)\n",
    "F.subs(w/sympy.tan(alpha), R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This form  verifies that the computation of the Jacobian is correct.\n",
    "\n",
    "Now we can turn our attention to the noise. Here, the noise is in our control input, so it is in *control space*. In other words, we command a specific velocity and steering angle, but we need to convert that into errors in $x, y, \\theta$. In a real system this might vary depending on velocity, so it will need to be recomputed for every prediction. I will choose this as the noise model; for a real robot you will need to choose a model that accurately depicts the error in your system. \n",
    "\n",
    "$$\\mathbf{M} = \\begin{bmatrix}\\sigma_{vel}^2 & 0 \\\\ 0 & \\sigma_\\alpha^2\\end{bmatrix}$$\n",
    "\n",
    "If this was a linear problem we would convert from control space to state space using the by now familiar $\\mathbf{FMF}^\\mathsf T$ form. Since our motion model is nonlinear we do not try to find a closed form solution to this, but instead linearize it with a Jacobian which we will name $\\mathbf{V}$. \n",
    "\n",
    "$$\\mathbf{V} = \\frac{\\partial f(x, u)}{\\partial u} \\begin{bmatrix}\n",
    "\\frac{\\partial \\dot x}{\\partial v} & \\frac{\\partial \\dot x}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial \\dot y}{\\partial v} & \\frac{\\partial \\dot y}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial \\dot{\\theta}}{\\partial v} & \\frac{\\partial \\dot{\\theta}}{\\partial \\alpha}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "These partial derivatives become very difficult to work with. Let's compute them with SymPy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}t \\cos{\\left (\\beta + \\theta \\right )} & \\frac{d \\cos{\\left (\\beta + \\theta \\right )}}{\\tan{\\left (\\alpha \\right )}} \\left(\\tan^{2}{\\left (\\alpha \\right )} + 1\\right) - \\frac{w \\sin{\\left (\\theta \\right )}}{\\tan^{2}{\\left (\\alpha \\right )}} \\left(- \\tan^{2}{\\left (\\alpha \\right )} - 1\\right) + \\frac{w \\sin{\\left (\\beta + \\theta \\right )}}{\\tan^{2}{\\left (\\alpha \\right )}} \\left(- \\tan^{2}{\\left (\\alpha \\right )} - 1\\right)\\\\t \\sin{\\left (\\beta + \\theta \\right )} & \\frac{d \\sin{\\left (\\beta + \\theta \\right )}}{\\tan{\\left (\\alpha \\right )}} \\left(\\tan^{2}{\\left (\\alpha \\right )} + 1\\right) + \\frac{w \\cos{\\left (\\theta \\right )}}{\\tan^{2}{\\left (\\alpha \\right )}} \\left(- \\tan^{2}{\\left (\\alpha \\right )} - 1\\right) - \\frac{w \\cos{\\left (\\beta + \\theta \\right )}}{\\tan^{2}{\\left (\\alpha \\right )}} \\left(- \\tan^{2}{\\left (\\alpha \\right )} - 1\\right)\\\\\\frac{t}{R} & \\frac{d}{w} \\left(\\tan^{2}{\\left (\\alpha \\right )} + 1\\right)\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                ⎛   2       ⎞                ⎛     2       ⎞            ⎛    \n",
       "⎢              d⋅⎝tan (α) + 1⎠⋅cos(β + θ)   w⋅⎝- tan (α) - 1⎠⋅sin(θ)   w⋅⎝- ta\n",
       "⎢t⋅cos(β + θ)  ────────────────────────── - ──────────────────────── + ───────\n",
       "⎢                        tan(α)                        2                      \n",
       "⎢                                                   tan (α)                   \n",
       "⎢                                                                             \n",
       "⎢                ⎛   2       ⎞                ⎛     2       ⎞            ⎛    \n",
       "⎢              d⋅⎝tan (α) + 1⎠⋅sin(β + θ)   w⋅⎝- tan (α) - 1⎠⋅cos(θ)   w⋅⎝- ta\n",
       "⎢t⋅sin(β + θ)  ────────────────────────── + ──────────────────────── - ───────\n",
       "⎢                        tan(α)                        2                      \n",
       "⎢                                                   tan (α)                   \n",
       "⎢                                                                             \n",
       "⎢                                                  ⎛   2       ⎞              \n",
       "⎢     t                                          d⋅⎝tan (α) + 1⎠              \n",
       "⎢     ─                                          ───────────────              \n",
       "⎣     R                                                 w                     \n",
       "\n",
       " 2       ⎞           ⎤\n",
       "n (α) - 1⎠⋅sin(β + θ)⎥\n",
       "─────────────────────⎥\n",
       "      2              ⎥\n",
       "   tan (α)           ⎥\n",
       "                     ⎥\n",
       " 2       ⎞           ⎥\n",
       "n (α) - 1⎠⋅cos(β + θ)⎥\n",
       "─────────────────────⎥\n",
       "      2              ⎥\n",
       "   tan (α)           ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V = fxu.jacobian(Matrix([v, alpha]))\n",
    "V = V.subs(sympy.tan(alpha)/w, 1/R) \n",
    "V = V.subs(time*v/R, B)\n",
    "V = V.subs(time*v, 'd')\n",
    "V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This should give you an appreciation of how quickly the EKF become mathematically intractable. \n",
    "\n",
    "This gives us the final form of our prediction equations:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{\\bar x} &= \\mathbf x + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}\\\\\n",
    "\\mathbf{\\bar P} &=\\mathbf{FPF}^{\\mathsf T} + \\mathbf{VMV}^{\\mathsf T}\n",
    "\\end{aligned}$$\n",
    "\n",
    "This form of linearization is not the only way to predict $\\mathbf x$. For example, we could use a numerical integration technique such as *Runge Kutta* to compute the movement\n",
    "of the robot. This will be required if the time step is relatively large. Things are not as cut and dried with the EKF as for the Kalman filter. For a real problem you have to carefully model your system with differential equations and then determine the most appropriate way to solve that system. The correct approach depends on the accuracy you require, how nonlinear the equations are, your processor budget, and numerical stability concerns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "The robot's sensor provides a noisy bearing and range measurement to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf T$ into a range and bearing to the landmark. If $\\mathbf p$ \n",
    "is the position of a landmark, the range $r$ is\n",
    "\n",
    "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n",
    "\n",
    "The sensor provides bearing relative to the orientation of the robot, so we must subtract the robot's orientation from the bearing to get the sensor reading, like so:\n",
    "\n",
    "$$\\phi = \\arctan(\\frac{p_y - y}{p_x - x}) - \\theta$$\n",
    "\n",
    "\n",
    "Thus our measurement model $h$ is\n",
    "\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf z& = h(\\bar{\\mathbf x}, \\mathbf p) &+ \\mathcal{N}(0, R)\\\\\n",
    "&= \\begin{bmatrix}\n",
    "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n",
    "\\arctan(\\frac{p_y - y}{p_x - x}) - \\theta \n",
    "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n",
    "\\end{aligned}$$\n",
    "\n",
    "This is clearly nonlinear, so we need linearize $h$  at $\\mathbf x$ by taking its Jacobian. We compute that with SymPy below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{- p_{x} + x}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & \\frac{- p_{y} + y}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & 0\\\\- \\frac{- p_{y} + y}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & - \\frac{p_{x} - x}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & -1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡          -pₓ + x                      -p_y + y             ⎤\n",
       "⎢───────────────────────────  ───────────────────────────  0 ⎥\n",
       "⎢   ________________________     ________________________    ⎥\n",
       "⎢  ╱         2            2     ╱         2            2     ⎥\n",
       "⎢╲╱  (pₓ - x)  + (p_y - y)    ╲╱  (pₓ - x)  + (p_y - y)      ⎥\n",
       "⎢                                                            ⎥\n",
       "⎢       -(-p_y + y)                   -(pₓ - x)              ⎥\n",
       "⎢  ──────────────────────       ──────────────────────     -1⎥\n",
       "⎢          2            2               2            2       ⎥\n",
       "⎣  (pₓ - x)  + (p_y - y)        (pₓ - x)  + (p_y - y)        ⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "px, py = symbols('p_x, p_y')\n",
    "z = Matrix([[sympy.sqrt((px-x)**2 + (py-y)**2)],\n",
    "            [sympy.atan2(py-y, px-x) - theta]])\n",
    "z.jacobian(Matrix([x, y, theta]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Now we need to write that as a Python function. For example we might write:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "\n",
    "def H_of(x, landmark_pos):\n",
    "    \"\"\" compute Jacobian of H matrix where h(x) computes \n",
    "    the range and bearing to a landmark for state x \"\"\"\n",
    "\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2\n",
    "    dist = sqrt(hyp)\n",
    "\n",
    "    H = array(\n",
    "        [[-(px - x[0, 0]) / dist, -(py - x[1, 0]) / dist, 0],\n",
    "         [ (py - x[1, 0]) / hyp,  -(px - x[0, 0]) / hyp, -1]])\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We also need to define a function that converts the system state into a measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import atan2\n",
    "\n",
    "def Hx(x, landmark_pos):\n",
    "    \"\"\" takes a state variable and returns the measurement\n",
    "    that would correspond to that state.\n",
    "    \"\"\"\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    dist = sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2)\n",
    "\n",
    "    Hx = array([[dist],\n",
    "                [atan2(py - x[1, 0], px - x[0, 0]) - x[2, 0]]])\n",
    "    return Hx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design Measurement Noise\n",
    "\n",
    "It is reasonable to assume that the noise of the range and bearing measurements are independent, hence\n",
    "\n",
    "$$\\mathbf R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Implementation\n",
    "\n",
    "We will use `FilterPy`'s `ExtendedKalmanFilter` class to implement the filter. Its `predict()` method uses the standard linear equations for the process model. Ours is nonlinear, so we will have to override `predict()` with our own implementation.  I'll want to also use this class to simulate the robot, so I'll add a method `move()` that computes the position of the robot which both `predict()` and my simulation can call.\n",
    "\n",
    "The matrices for the prediction step are quite large. While writing this code I made several errors before I finally got it working. I only found my errors by using SymPy's `evalf` function. `evalf` evaluates a SymPy `Matrix` with specific values for the variables. I decided to demonstrate this technique to you, and used `evalf` in the Kalman filter code. You'll need to understand a couple of points.\n",
    "\n",
    "First, `evalf` uses a dictionary to specify the values. For example, if your matrix contains an `x` and `y`, you can write\n",
    "\n",
    "```python\n",
    "    M.evalf(subs={x:3, y:17})\n",
    "```\n",
    "    \n",
    "to evaluate the matrix for `x=3` and `y=17`. \n",
    "\n",
    "Second, `evalf` returns a `sympy.Matrix` object. Use `numpy.array(M).astype(float)` to convert it to a NumPy array. `numpy.array(M)` creates an array of  type `object`, which is not what you want.\n",
    "\n",
    "Here is the code for the EKF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from filterpy.kalman import ExtendedKalmanFilter as EKF\n",
    "from numpy import dot, array, sqrt\n",
    "class RobotEKF(EKF):\n",
    "    def __init__(self, dt, wheelbase, std_vel, std_steer):\n",
    "        EKF.__init__(self, 3, 2, 2)\n",
    "        self.dt = dt\n",
    "        self.wheelbase = wheelbase\n",
    "        self.std_vel = std_vel\n",
    "        self.std_steer = std_steer\n",
    "\n",
    "        a, x, y, v, w, theta, time = symbols(\n",
    "            'a, x, y, v, w, theta, t')\n",
    "        d = v*time\n",
    "        beta = (d/w)*sympy.tan(a)\n",
    "        r = w/sympy.tan(a)\n",
    "    \n",
    "        self.fxu = Matrix(\n",
    "            [[x-r*sympy.sin(theta)+r*sympy.sin(theta+beta)],\n",
    "             [y+r*sympy.cos(theta)-r*sympy.cos(theta+beta)],\n",
    "             [theta+beta]])\n",
    "\n",
    "        self.F_j = self.fxu.jacobian(Matrix([x, y, theta]))\n",
    "        self.V_j = self.fxu.jacobian(Matrix([v, a]))\n",
    "\n",
    "        # save dictionary and it's variables for later use\n",
    "        self.subs = {x: 0, y: 0, v:0, a:0, \n",
    "                     time:dt, w:wheelbase, theta:0}\n",
    "        self.x_x, self.x_y, = x, y \n",
    "        self.v, self.a, self.theta = v, a, theta\n",
    "\n",
    "    def predict(self, u=0):\n",
    "        self.x = self.move(self.x, u, self.dt)\n",
    "\n",
    "        self.subs[self.theta] = self.x[2, 0]\n",
    "        self.subs[self.v] = u[0]\n",
    "        self.subs[self.a] = u[1]\n",
    "\n",
    "        F = array(self.F_j.evalf(subs=self.subs)).astype(float)\n",
    "        V = array(self.V_j.evalf(subs=self.subs)).astype(float)\n",
    "\n",
    "        # covariance of motion noise in control space\n",
    "        M = array([[self.std_vel*u[0]**2, 0], \n",
    "                   [0, self.std_steer**2]])\n",
    "\n",
    "        self.P = dot(F, self.P).dot(F.T) + dot(V, M).dot(V.T)\n",
    "\n",
    "    def move(self, x, u, dt):\n",
    "        hdg = x[2, 0]\n",
    "        vel = u[0]\n",
    "        steering_angle = u[1]\n",
    "        dist = vel * dt\n",
    "\n",
    "        if abs(steering_angle) > 0.001: # is robot turning?\n",
    "            beta = (dist / self.wheelbase) * tan(steering_angle)\n",
    "            r = self.wheelbase / tan(steering_angle) # radius\n",
    "\n",
    "            dx = np.array([[-r*sin(hdg) + r*sin(hdg + beta)], \n",
    "                           [r*cos(hdg) - r*cos(hdg + beta)], \n",
    "                           [beta]])\n",
    "        else: # moving in straight line\n",
    "            dx = np.array([[dist*cos(hdg)], \n",
    "                           [dist*sin(hdg)], \n",
    "                           [0]])\n",
    "        return x + dx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a angular difference of $-358^\\circ$, whereas the correct value is $2^\\circ$. We have to write code to correctly compute the bearing residual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def residual(a, b):\n",
    "    \"\"\" compute residual (a-b) between measurements containing \n",
    "    [range, bearing]. Bearing is normalized to [-pi, pi)\"\"\"\n",
    "    y = a - b\n",
    "    y[1] = y[1] % (2 * np.pi)    # force in range [0, 2 pi)\n",
    "    if y[1] > np.pi:             # move to [-pi, pi)\n",
    "        y[1] -= 2 * np.pi\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest of the code runs the simulation and plots the results, and shouldn't need too much comment by now. I create a variable `landmarks` that contains the landmark coordinates. I update the simulated robot position 10 times a second, but run the EKF only once per second. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from filterpy.stats import plot_covariance_ellipse\n",
    "from math import sqrt, tan, cos, sin, atan2\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dt = 1.0\n",
    "\n",
    "def z_landmark(lmark, sim_pos, std_rng, std_brg):\n",
    "    x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "    d = np.sqrt((lmark[0] - x)**2 + (lmark[1] - y)**2)  \n",
    "    a = atan2(lmark[1] - y, lmark[0] - x) - sim_pos[2, 0]\n",
    "    z = np.array([[d + randn()*std_rng],\n",
    "                  [a + randn()*std_brg]])\n",
    "    return z\n",
    "\n",
    "def ekf_update(ekf, z, landmark):\n",
    "    ekf.update(z, HJacobian=H_of, Hx=Hx, \n",
    "               residual=residual,\n",
    "               args=(landmark), hx_args=(landmark))\n",
    "    \n",
    "                \n",
    "def run_localization(landmarks, std_vel, std_steer, \n",
    "                     std_range, std_bearing,\n",
    "                     step=10, ellipse_step=20, ylim=None):\n",
    "    ekf = RobotEKF(dt, wheelbase=0.5, std_vel=std_vel, \n",
    "                   std_steer=std_steer)\n",
    "    ekf.x = array([[2, 6, .3]]).T # x, y, steer angle\n",
    "    ekf.P = np.diag([.1, .1, .1])\n",
    "    ekf.R = np.diag([std_range**2, std_bearing**2])\n",
    "\n",
    "    sim_pos = ekf.x.copy() # simulated position\n",
    "    # steering command (vel, steering angle radians)\n",
    "    u = array([1.1, .01]) \n",
    "\n",
    "    plt.figure()\n",
    "    plt.scatter(landmarks[:, 0], landmarks[:, 1],\n",
    "                marker='s', s=60)\n",
    "    \n",
    "    track = []\n",
    "    for i in range(200):\n",
    "        sim_pos = ekf.move(sim_pos, u, dt/10.) # simulate robot\n",
    "        track.append(sim_pos)\n",
    "\n",
    "        if i % step == 0:\n",
    "            ekf.predict(u=u)\n",
    "\n",
    "            if i % ellipse_step == 0:\n",
    "                plot_covariance_ellipse(\n",
    "                    (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], \n",
    "                     std=6, facecolor='k', alpha=0.3)\n",
    "\n",
    "            x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "            for lmark in landmarks:\n",
    "                z = z_landmark(lmark, sim_pos,\n",
    "                               std_range, std_bearing)\n",
    "                ekf_update(ekf, z, lmark)\n",
    "\n",
    "            if i % ellipse_step == 0:\n",
    "                plot_covariance_ellipse(\n",
    "                    (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2],\n",
    "                    std=6, facecolor='g', alpha=0.8)\n",
    "    track = np.array(track)\n",
    "    plt.plot(track[:, 0], track[:,1], color='k', lw=2)\n",
    "    plt.axis('equal')\n",
    "    plt.title(\"EKF Robot localization\")\n",
    "    if ylim is not None: plt.ylim(*ylim)\n",
    "    plt.show()\n",
    "    return ekf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PFzMKPLR1B2nuDNLd20dPdw/xmAIddHSsVm2Evf36j1ktGoYRx2XXcTlsOG1W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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e86c16a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.0244  0.042  0.00223]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have plotted the landmarks as solid squares. The path of the robot is drawn with a black line. The covariance ellipses for the predict step are light gray, and the covariances of the update are shown in green. To make them visible at this scale I have set the ellipse boundary at 6$\\sigma$.\n",
    "\n",
    "We can see that there is a lot of uncertainty added by our motion model, and that most of the error in in the direction of motion. We determine that from the shape of the blue ellipses. After a few steps we can see that the filter incorporates the landmark measurements and the errors improve.\n",
    "\n",
    "I used the same initial conditions and landmark locations in the UKF chapter. The UKF achieves much better accuracy in terms of the error ellipse. Both perform roughly as well as far as their estimate for $\\mathbf x$ is concerned. \n",
    "\n",
    "Now let's add another landmark."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tNpRSKEZyNLwzRooPlOPSPEwv9JLlto0EVt1RdFcmddNruXBWKfYJphLFuUeC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\nfDp9j5WtFq+t9qj1BQE+kTIc9B0RIRAQgRIo6K6O0TYw10xG0wqjlk8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Z/v37L32dz+ev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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e679a748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.0201  0.0204  0.00153]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15], [20, 5]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "plt.show()\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The uncertainly in the estimates near the end of the track are smaller.  We can see the effect that multiple landmarks have on our uncertainty by only using the first two landmarks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+85959NFHsdlszJ49m++++w4/P78GxdXK35PVz4yjU3Ak+vJwso5G4/jNU41G\nn0KsjkrScotxOGTdlahJkishhBBNZsbIvni5+lGc3q7ORMXNtwD3sOPklmfy7OptmEssJCYmct11\n17F27Vrc3d355JNPWLp0KXq9c97q1raVL6vmjqVTcFsMpW3IO349dpsBAFV1oBgqqLRbyS4odUp/\nonmR5EoIIUSTmRjTlTaBgaiVvpTkBtdZzyfiNA5TFkm5Gcz4fy8THR1NfHw8nTp1Yu/evUyaNMnp\nsXWLDOKjv0+ga+t2uJRFkPvrzRRnhQAKqr4Cu8PKuRyz0/sV1z5JroQQQjQZvV7HPTf3wsvFl+LU\n9nVu4KmqCn7t4sn79Vu+emcRZrOZO+64g/3791/2+qr66Bjuz0fzJtA3PAJfwik6NYC0A0Owl3vh\nqjfSKazmk45C1Cu52rFjB2PHjiUsLAxVVVmzZk2ddR944IGqdzcJIYQQf2TGyD6EeAeglQVQVlD7\neil7qZ38z07gOLUfUOgcM5nPPvsMLy+vRo+vbStfXpnWj/tv7k6HgA7404UQt3BGRLfH28PY6P2L\na0+9JqdLSkro2bMn06dPZ9q0aXXW+/zzz9m/fz+hobUvTBRCCCF+z81oYGJMN5Z9lUVRajvc/aq/\nGNlyzkL6mgwcZjuquw5d35GUBvfh4y1HuWdErysSo06nMm5gBHOm38qhxEwcDo2YPpFXpG9x7anX\nyNWoUaNYsmQJ48ePr3rZ5e8lJyfzxBNP8PHHHzttQaEQQoiW4X/GRBPoGYC9qBUluQFVx817zaT+\nIxWH2Y5rhCsRfw3HJ7qEfEsOb63fS0l55RWN08vDSEyfSIZFtUVVa/8+FMIpa67sdjt333038+fP\np3Pnzs5oUgghRAvi52Vi5qg++LoGUJjUBVu5g6zPssj5IgfsQE9XmOBFid6KV6s0NFMOyblZvL1+\nX1OHLkQNTkmuFixYQFBQEH/5y1+c0ZwQQogW6OFxA2gXHIKSq3JueRbF+4tR9ApBk4IwjvQmvJU3\nPh4mFAV8Ik9grsxn3dajlFmsTR26ENU0eP5u69atrF69mri4uEs+NzY2tqHdX/VawjU6g9yn+pN7\nVX9yr+rvarlXbSqPsWvbh2j2SnT+BgIm+2EINuBabsVisVTVU93S0FxzSMn2YvG7XzPx+sgrEt/V\ncp+uBc39XnXs2LHOsgaPXG3bto3MzExCQkIwGAwYDAaSk5OZM2cOERERDW1eCCFEC2CxWHj++ef5\n6L3X0Oy6XdneAAAgAElEQVSV6EO74TJ8OIbg8xt3epoM1eorCri3OkWpvYgfDqVjszmaImwhatXg\nkauHH36YiRMnVjs2YsQI7r77bu6///6LnhsdHd3Q7q9aFzL25nyNziD3qf7kXtWf3Kv6q+tenTyX\nx9rN8VTabER3as3tgzvjYtDV1kSDnTx5klmzZhEXF4erqysLnnuRNfF6ks1nsJXk4xGQW+t5rqH5\nlKUXkVdWxpkSE3ff3LNR4gP5TF2KlnKvzOa6N5CtV3JVWlpKYmIimqbhcDhISUkhLi4OPz8/wsPD\nCQgIqFbfYDAQEhJy0SEzIYQQV6eConIeeG0DR1KSsWs2Ptjkwfs/HObxiYO4KaqdU/v69NNPmTVr\nFiUlJXTs2JHPPvuM3r174/LpLt74ooS8xJ4YPf+D3rXmuipF0fAIPYM5yZ/3fzzM5Bu7o6qyN7Zo\nevX6FMbGxtK3b1/69euHxWJh4cKFREVFsXDhwlrr17VdgxBCiKvfd3tPcSI1g2IyIDCeXGsy2xLi\n+Z/Xv2HVxkNodW2jfgksFgsPPvggkydPpqSkhEmTJhEbG0vv3r0BeHzCQPp1iMRNCybnRO863zvo\nGZxKpVrI8XOZ/HzwbIPjEsIZ6jVyFRMTg8NR//nsM2fOXHZAQgghmta5bDOVDgumwHT8OyTgE3mS\ngjOdScup5Nk1P1NqsfLIHQMuu/3ExETuuusuDh06hIuLC2+++Sb/8z//U+0f5nq9jrcfv5Uxfyvk\nVK6FwnN5+LWpmTzp9BruwakUZwXy9a4T3Bzd/rLjEsJZZPxUCCFENSXllThwoOpsAOgMVvw7HcEt\n/BiZZam8tm4H//r2wGW1/cknn9CvXz8OHTpEu3bt2L17Nw8++GCtMx4RQd48f99NBJpCKD3XlbJC\nn1rbdA/MoNxWys74c1it9suKSwhnkuRKCCFENa4GPQoKDvt/vyIUBXzbJOIenkBmWRovfbSdjXtP\n1bvNkpISZs6cyZQpUygqKmLChAkcPHiQqKioi55323WduPumPvi5BpN3og+2ypoTLq4exSjGIrKL\nCtn2a3L9L1SIRiLJlRBCiGq6tw3CRWfEWupdo8wn4jSmVifJKk1n/spfSM8t+sP2Dh48SL9+/Vi1\nahVGo5F33nmHzz77DG/vmu3XZvGMofRtF4mbI5jshCgctuqjXIoCRp8cyq2l7JDkSlwFJLkSQghR\nTXTnVhj1JqwlPmiOmomMX9uTaB6ZnM1J5fG3f8Rur31NrsPh4I033mDQoEGcPHmSHj16EBsbywMP\nPHBJDz4Z9DpWPD6KdoER6ErCyT7eF8fvZv+MvrlU2MvZdzz9kq9XCGeT5EoIIUQ1bYJ9iAjyQacZ\nsZhrrnNSVI3AzocpJYedx07z+rrdNepkZ2czevRonnzySaxWKw8//DD79u2je/fulxVTZIgv/54z\nlkj/NmCOJPt4Hxz2/yZoru7F2DQb+UXll9W+EM4kyZUQQoga+ncOxahzozQ/qNZyg8mCb4d48ixZ\nvPvd/mrTcZs2baJXr15s3LgRPz8/vvrqK95++21MJlODYurdPph3nxxNG98IKGxH1rEo7NbzG5uq\nOg0NjUqrrc5tG4S4UiS5EkIIUcMdf+qCp4s3ZdlhNdY4XeARmIUp5DTZJZksWPULJSVlzJkzhxEj\nRpCVlUVMTAxxcXGMHTvWaXFd1z2cVXPH0SGwLfri9qQfiKEoIxSbxRUFcGjgcMI+XEI0hCRXQggh\nahjcI5xOYcEYHF4U54TUWc+v7XGshlyOnoinW59+vPrqq+h0Op577jm2bNlCWFiY02Pr3yWUD/82\nnsGduxGgb0fJ6Wgy467HTe9J344h6HXy1SaaVoPfLSiEEKL5URSFycO6cyQ5BXNGJN6tMmqvp3Pg\nUryVnM0pYLcSFh7Bp598zODBgxs1vu5tg/j2hSms+SmOld8fJiO/mLYhvsy+67pG7VeI+pDkSggh\nRK0m39iD5V/upSDXn/IiL0xe1bddKM63ULKhgNKjpQC4hHbn9kcXN3pidYGqqswY2Zfpt/ShzGLF\n1UUvo1biqiCfQiGEELVyN7kwckAHPPReFKW1qVZWmlBK9lvplB4tRTWq+I2LgKgb2RSXyvHk3Csa\np6IouJtcJLESVw35JAohhKjT/aP74WP0pSIvDEuJO45KB+mfZZKxKgOt1IE+woWAh1vhN9gFY2Aq\neWW5vLpuV1OHLUSTkuRKCCFEnTqE+nH7dV3wMviRFxvAuTfPUba/5Py3x/UmPO7xR+9zfoWJT5tT\nlNrNbI87S2rOH+/cLkRzJcmVEEKIi3py4kA4vZ/yjT9jzbXiEuxC+GPheN7gTYCPO26uBgBcTBZc\nfDMxWwpZtfFQE0ctRNOR5EoIIUSdEhMTuWvcreQe/h40DV2nbrR+JAzX1q54urnWqO/VKpkSq5lv\ndp2k0mqvpUUhmj9JroQQQtSgaRrvvfceffr0Yc+ePYSGhtF97GyMXW+lOOf84vYLI1a/ZfLNR3Mt\nJD0/j6/+k3ClwxbiqiDJlRBCXEPSc4v5+/9u4aE3v2PZF3spKq1weh/nzp1j5MiRPPDAA5SWljJl\nyhTi439lyVOz8DMGUZzSlYrS2l9loyjg0SqZ4spCPtpyxOmxCXEtkH2uhBDiGlFSXsmdC9dxKvMc\nlY5KTHo3/v39Qe67tS+PjR+IotT+mpr60jSN1atX89e//pWioiL8/PxYsWIFkydPBmDs9T58u/sk\n3+wtI/dEH1r13oOqq/mqGc/gNIqSu/DrmUwy84sJ8fNsUFxCXGtk5EoIIa4RK78/xJnsDEp0Kbi0\n2UOxy3FO5Z5k6WfbeXTZRmy2y1/jlJ6ezpgxY7j33nspKipizJgxHD16tCqxgvP7Sb3+0C10DAlH\nb2lN3pnOtbalM9gxeOVRbi1lU+yZy45JiGtVvZKrHTt2MHbsWMLCwlBVlTVr1lSV2Ww25s6dS+/e\nvfHw8KB169ZMnTqVc+fONVrQQgjREh1PycViK8OjVTI+oedo3Wcv3h33k21J4ctdh/nLa99ecoKl\naRobN26kR48efPvtt/j4+LBmzRq++uorQkJqvlPQy92VNx+5hWD3VlRkdaA4J6DWdo0+uZTbS9l1\nVL4LRMtTr+SqpKSEnj17snz5ctzc3KqVlZWVcfjwYebPn8+hQ4f45ptvOHfuHKNGjcLhcDRK0EII\n0RKl5hRh06wY3EqrjnkGZxHYYw951jR+OHCUJ//xU73by8rKYs6cOSxYsICCggJGjRrFkSNH+POf\n/3zRKcb+XUJ55I6BBJhCKEjsQ0VZzfVXRq8CKu0VnDyXd2kXKUQzUK81V6NGjWLUqFEATJ8+vVqZ\nl5cXP/74Y7Vj7777Lt27dychIYHu3bs7KVQhhGjZ3IwGFBQcdl214yZvM4Hd95Jz5Dq+3uXCdd3D\nmHJTz4u2tW7dOh566CHy8vJwd3dn+fLl3HvvvfVet/XoHQPZl5DG5rgKso8MIKjnHlxN/11c7+pe\njI1KzuUUUWm142LQXaQ1IZqXRllzZTabURQFX1/fxmheCCFapGBfD3SKAZul5kiRyduMV+QRcsoz\nWPLBdk7VMWKUm5vLpEmTmDRpEnl5eQwYMIBPPvmEmTNnXtKCeFVVeG/27Qzs2BEvLZzs+IFUlBn/\nW0HnAMWBpmloWs1F70I0Z4p2iZ96T09PVqxYwbRp02ott1qtDB06lKCgINavX1+j3Gw2V/351KlT\nlxiuEEK0XJ/tSuZfWw5T6fMrvh0O1ijXNCg41R/V3IkercJ5bUZ01YiRpmn89NNPLF26lMLCQkwm\nE48//jh33HFHg54yLC63Mv+jQxzLyKREycSzXSwmnxwcdoWcA2MJc2vDuqdiGvwkoxBXm44dO1b9\n2dvbu1qZU7disNvtTJ06laKiIr799ltnNi2EEC1e51BPXFQjpSX+aNr5PaV+S1HAu91hco/4cCrL\nyPu/nOYvIzqRlZXFSy+9xH/+8x8AoqOjmTdvHqGhoQ2OydNk4IV7+rLks3gOp+gpOuVGmUcGisGC\nQXEhwNMoiZVocZyWXNntdiZPnszRo0fZtm1bvaYEo6OjndX9VSc2NhZo3tfoDHKf6k/uVf0113vV\np4+DdzYlY87IQ6sIweRTWGs9pUs8eUe82JqQQ4Quk1eeX0RxcTHe3t689tpr1aYAnXWvvh0wgHc3\nxLJy4yEyzYHYrJV4efrwzLSbiI7u2qC2rwbN9TPVGFrKvfrtTNzvOSW5stlsTJo0iWPHjrFt2zYC\nAwOd0awQQojf0OtVbopqy+kfz1Ga3Rq3OpIrN59CzPoEzv6wnvkfpgAwduxY/vGPf9C6detGic3F\noOPR8QOZfksfvtyRQGZ+CTG923Bd9/BG6U+Iq1m9kqvS0lISExPRNA2Hw0FKSgpxcXH4+fnRunVr\n7rzzTg4cOMCGDRvQNI2srCzg/Byk0Wj8g9aFEELU18Sh3fn4lzgy8lrhsCfU2CG9oKgMDlZQ9tMm\nNJuG6urBS6++zlOPzLoi03Ne7q7MGNmn0fsR4mpWr6cFY2Nj6du3L/369cNisbBw4UKioqJYuHAh\nqampfPPNN6Snp9OvXz9at25d9bNu3brGjl8IIVqUqE6taN8qAL3dk9L8oGplFekV5P8rm7zv89Bs\nGoaOYXjcdD9HSgJk3ZMQV1C9Rq5iYmIuuiGobBYqhBBXzujrOnP03DmKUtviEZCFZnOQsTGH8l3F\n4AC8VLxG++LbxZuMA5Vsj0/idFo+7UP9mjp0IVoEebegEEJcY+67tQ+tfQLRSgMpOGTg3BvnKP9P\nMWig62ui3VORBPXxxWCswNUvg5LKIj795WhThy1EiyHJlRBCXGO83I2MHRAGcb+Q/0kC1lwrhiAD\nof8Tiu/tfqjG//7V7hGUTpm1mB/2JcpmnkJcIU7d50oIIUTj0jSNVatWsfzp/4clPx9UHe6DwgkZ\nrUPRK/x+73aTby75+mKSs/PYcyxVnt4T4gqQkSshhLhGJCQkMHToUO677z7y8/Pp1mcgwbc8gS1k\nBHa7S63nqCoYA9IpqTTz2bZjVzhiIVomSa6EEOIqV15ezvz58+nduzfbt28nMDCQDz/8kF9jdzIo\nqh9uWiA5J3tR16yfe0Am5fYyDp3KvLKBC9FCSXIlhBBO4HA4SMosJD232Kntbt68mV69erFkyRKs\nViv3338/x48fZ+rUqeh0Ot58ZCQRfmFo5jAKz0XW2oarhxkblaTmmCkpr3RqfEKImmTNlRBCNNCv\np7N4YsUPnMnIQ1EUukYEcWdMd2aM7H3Z+0tlZWUxe/Zs1q5dC0D37t155513GDJkSLV6kSE+LJo+\nlMf/UUpGSiUm7wKM3tVfy6HTa+hcS6mwVXAqNY++HVtd3oUKIepFRq6EEKIBLBVWHl72PQfOniDd\nkkhaWSLbjsex4P2fuPflrykuq7ik9mw2G2+//TadO3dm7dq1GI1GXnjhBQ4ePFgjsbpg3J+6MPGG\nnvi5BJNzPIrKst8vawedazk2h5Vz2UWXdZ1CiPqT5EoIIRpga1wyZ7OyseizCR2whdCBm3Fru5/s\nymQ2xv7K5Gc/J7ewrF5t7dy5k+joaB599FHMZjMjR47k6NGjPPPMM7i41L5g/YLnZg6jf6d2eBFG\nVvwgKko8qpVrDh2goNfJTu1CNDZJroQQogG2xSVRbi3B5J+JTu9Ap3fg3TqV4N7/wayksO/UKWYt\n/Qa7ve43WWRlZTFjxgyGDBlCXFwcERERrF+/nu+//5527drVKw6jq4EP/3YHgzp3xJtwsn8dTFFm\nazRNwWFXsJV54qJzpVtk0B83JoRoEEmuhBCiAYrLKrFrdvTG6qNTru5lBPfaQzEZ7D95luc+2F7j\nXJvNxltvvUXnzp1ZvXo1Li4uzJs3j4SEBMaNG3fJ67W83I18PG8Co/r1JMAQTklif1L3xZBxeDAu\nmhcRgb6EB3o16HqFEH9MFrQLIUQDuBr0KCj/N+1WnYuxAv9Oh8k7ZmT1TwcZ2DWUUQM7AuenAB9+\n+GHi4uIAGDVqFMuWLaNjx44Nisfd5MLKuWN4d0MoazfHk5ydi91uw9fHmwXTY9Dp5N/UQjQ2Sa6E\nEKIBAn3c0Kl67BXGWsvd/PKxhJ0gJ82Fv//vFtr5G3hxySJWr14NQJs2bVi2bBljxoy57CcLf09V\nVR4c25/7b+vH1rgkikoruK57GK38PZ3SvhDi4iS5EkKIBugQ6oeL6oq5xLvOOj4RiWTk+XFy/1F6\n93qKivJSXFxcmDt3Lk8//TRubm6NEpter3Jzv/qt2RJCOI8kV0II0QA39W2Lh9GDvCI/bBUG9K7W\nGnUsieVYt6zHlmsBYNhNw3nvnX/QoUOHKx2uEOIKkORKCCEawNfLRO92IWTGpVGWH4hXq/Sqssqc\nSjK/zqby5PmkSvFwx6PHaAZOmiWJlRDNmKxsFEKIBhrWNxKT3oOyvBAA7OV2cr/NJeX1FCpPWlBc\nFPxv9af1w52oDGzFhl0nKZXX0AjRbElyJYQQDXT74M54Gb2oKAgkf0c5Ka+kULi9EOxANxdc7vND\niTZi8i9Gdc+noNTMptjTTR22EKKRSHIlhBANFB7kTVfvchzbPyd/Qxr2UjvGSCNhj4VhvM2H8La+\n+HicfyWNyS+LMlsJmw6caeKohRCNpV7J1Y4dOxg7dixhYWGoqsqaNWtq1Fm0aBGhoaG4ubkxbNgw\njh075vRghRDiapOUlMTEiRPZ8I9nsJuzwOSB/4QIQh8MxRhmxMNkqFbfzT8bi72MvQlp2Gx179ou\nhLh21WtBe0lJCT179mT69OlMmzatRvnLL7/MG2+8werVq+nUqROLFy9m+PDhnDx5End3d6cHLURL\nkZBgITn5/J+Li9sAkPt/T5wBtGkDXbvWvr+SaFxms5mXXnqJN954g4qKCkwmEz1jxpPoEoHF7SwQ\nC1A1YnWBq0cxmqGEbLOZQ4kZ9O8S2gTRCyEaU72Sq1GjRjFq1CgApk+fXqN82bJlPPPMM4wbNw6A\n1atXExQUxEcffcT999/vxHCFaFmSk2HUqAvJU80kauNGC127XtmYWjqr1cq7777L4sWLyc3NBeDu\nu+/mpZdeAlcvbn16LWfyKik8l4tvRFKN8xUFDG7FVJZXcjajUJIrIZqhBq+5Onv2LJmZmQwfPrzq\nmNFo5IYbbmDXrl0NbV4IIa4Kmqaxfv16unfvzqOPPkpubi5Dhgxhz549rF27lvDwcMKDvFk0YygB\nbq0oTulKeaFPrW3pXC3YHTayCkqu8FUIIa6EBu9zlZmZiaIoBAcHVzseHBxMenp6HWedFxsb29Du\nr3ot4RqdQe5T7c5PBdY97VdcXExs7JErF9A15suNW0nLK6NLmDe+Hq6X3U58fDzLli2reg9gREQE\njz76KDExMSiKUu3z28YNYroE8f2hYnISeuPXbTt61/Jq7dkdVrBZOXM2mdjYmu8kbAry/2D9yH2q\nv+Z+ry72HlDZRFQI0ezkF1fw5rcJHE7KxeaoxEXnSoCnibuuj2R471b1fodfamoqK1asYPPmzQD4\n+Phw//33M378ePT6uv/6fGBEJ05nFnM03Ur+sRvw7bwbg1tRVbmtzAtXRd+ghE8IcfVqcHIVEhKC\npmlkZWURFhZWdTwrK4uQkJCLnhsdHd3Q7q9aFzL25nyNziD36eJ+u3i9Np6ennLvajFp3vvsOZ1C\nqZKLzliCvdyDggJ33tlcQbJZ4c2HR2IyGuo8Py8vjyVLlrBixQqsVitGo5Enn3ySuXPn4uXlVa8Y\nvuragxkvfU1sopGCBCMeYafwDMzAWmHCURaIj4cvf5l4EyF+Hs667Msi/w/Wj9yn+msp98psNtdZ\n1uDkqm3btoSEhLBp0yb69esHgMViYceOHbz22msNbV4IIS5JWm4Re05mU2IvJKjPHkxexTgcGsUZ\n4WQld+PrPRXkmsv4ZP6dGAzVp+TKy8t5++23ef755zGbzSiKwvTp03nuuecIDw+/pDgCfdz5dMEE\nnvznT/yw/zjmNE8yUspQUPB1CWB4v/ZNnlgJIRpHvZKr0tJSEhMT0TQNh8NBSkoKcXFx+Pn5ER4e\nzuOPP86LL75I586d6dixI0uWLMHT05MpU6Y0dvxCCFHN59uOUVxRjN47HZNXMQCqquAdmorRq5Ds\nowPYfVxl3sqfefmB8w/i2Gw2Vq1axeLFi0lLSwPg5ptv5tVXX6VPnz6XHYuHmyvvPjmar3d24Mvt\nxzl4KgO9TiWmdxuem3ljwy9WCHFVqldyFRsby7Bhw6rWKSxcuJCFCxcyffp0Vq5cyZw5c7BYLDzy\nyCMUFBQwcOBAfvrpJ9njSogGatPm/HYLcH7xOpyfCvxtuaguz1yOTbNhcK85ZO/qWYJ/50PkHnXl\nk1/i6BLuj3tJIvPmzePUqVMA9OnThxdffJFbbrml3muzLkZRFMYN6cq4IV2x2uwoioJeJy/HEKI5\nq1dyFRMTg8Nx8Z2EFyxYwIIFC5wSlBDivK5djVX7WF14KrC5r2NoKPv//V2loNVa7uZbgGdkPJn7\n0nho2nIseecA6NChA8899xx33XUXqto4yY9Bf3U8GSiEaFzytKAQolnxMLmgomK31r6FhSXZQunG\nvVSeOb89gru3H6+9/AIzZ87EYKh7kbsQQtSXJFdCiGalb8dWuKhGior9qx2vyKwg67scKk+cn2ZV\njDrUtoMI7TueMXfeLYmVEMJpZOJfCNGsXNctDDcXIw6LNzaLC9Z8K1mfZnHujXNUnrCgGBR8b/Ql\n8pkITP3CKbCUsOanuKYOWwjRjMjIlRCiWfH2MBIZ5EnmcQuZ6wqwHMsAB+f/KdnTFZfrPdAFGtGZ\ndLgHp1GaGM7eY2lNHbYQohmR5EoI0aykpqZiPvwVFbs2geYABTyjPPEb7keWo5ywwP9uAmr0zqfA\nUcHxlByKSivwcpcd04UQDSfTgkKIZiEjI4PHHnuM9u3bc3jnj6Bp6EI7EzAjiuDJwRj8DXiYqq+r\nMhgr0JmKKSovYc+xc00UuRCiuZGRKyHENS0rK4uXX36Zf/7zn1gs5xer33zzzbTqO5JNZywUFp/F\ny7oL1WDFx8NU43yDWzGVRZUkZdb9KgshhLgUklyJFs/h0CgoLsdcWoG51EKpxYrd7sBmd6AoCq4G\nHa4uetyNBvw8Tfh5mWS/oqtATk4Or776Km+//Tbl5ee3VRg/fjwLFy6ksrKSsgob5z47zsGkUnJO\n9Caoeyy17QmqqHY0NCpt9it8BUKI5kqSK9Fi5ZnLSMk2k5FXjLmomNLSUkpLy7BUWHDY7VWbURoM\nBgwGAyaTCS9PTzw8PfH1MOHvZaJNiA8eJpcmvpJrg93uwKFpDU5Mc3Nzef3111m+fDmlpaUAjBkz\nhkWLFtG3b1/g/Fsl3Fz1LH1oBDNeLOVMfiUFZ4vxa3eiZlxWV1wVVX6PQginkeRKtDj5ReUcT8kl\nLbuA7Ows8vLyMCgO3I06PFx1BHjq0Ks6VFWHpoHVrmG1WygvKyM1L4vySgcmNzd8fHw4ERREm2Bf\nOob5y2LoOlgqbcSfyWLDrhMcT8nF39uN1v6ejBncmd4dQurdTkZGBq+99hr//Oc/KSsrA+DWW29l\n8eLFde5a369TaxZMH8qcdyrITHegOXT4tTuOop5PnG0WE5XmQPxNbnSNCGj4xQohBJJciRbEZncQ\nfyaL02m5pKelUZCfR5CXC11bGTEa6h5N+f0qHbtDo7TCTl5RNvGZmWQEBpKUEUJ4sC8dw/zw9ay5\nrqelqrTa+WzrUd5c9x9ScnOp0MpRFBWDamD1j4cYM7gri6bH4OVR+27qACkpKbz66qv861//oqKi\nAjifVM2fP59Bgwb9YQx3xnQjNaeYt9fvJitTT3qhP+6BGRhM5RRnhGNUPBjUrQ1RnVo57bqFEC2b\nJFeiRSgoLufgyQySzqWTmppCkKeBXuGe6HWX/mJenargZdLjZdITanOQWZhPfHwW6emBpGSGEBrk\nS692wbjLNBNHk7L54IcDnMlNp9KYiUdIMg67jsoSL1LzW7P2lyIOnEznkwV30srfs9q5p0+f5qWX\nXmL16tVYrVYA7rjjDv7+97/Tr1+/esegKAqP3zmQ9q19efGjHZzJ9KIiNYRyzYqLYiTEO4h7R/WR\ndXRCCKeR5Eo0e1n5JexNOEdi4mkqyoro2soNk4tzvkhd9CoRASZa+biSVWTmyJEcMgMCyTWX0bt9\nCBHB3k7p51qUX1TO1sNn+PVsBhbVTKuee9G5VFSVW4rOkHuiN0dSbdz78td8vuguPNxcSEhI4MUX\nX+Sjjz7CbrejqipTpkzhb3/7Gz169LisWBRFYcz1nRnQJZTPtx3jaHI2Z9MLaBfqx/QRvenfJdRZ\nly2EEJJcieYtPbeYfQnnOH78BG66StqHeqDW9shYAxn0KmF+RkK8XUnOLSA+voiysjKyCoLo0yGk\nRY6K5JrL2B1/lkrKcA9OqZZYARi9igjptZeMOJVDZ/VMeGo5Xjl7+eKLL9A0DZ1Ox4wZM3jmmWfo\n1KmTU2IK8ffgkfEDACivsOJq0KOqzv88CCFaNkmuRLOVZy5j77EUEhIS8HF1EO7v1uh96nUK7YPd\nyCuu5HhCAsXFxRSXVTKga2iLexqtpLySAnMZDmwYPWrfQ0rvWom31y/kfG/jp8wUAFxcXJg5cyZz\n584lMjKy0eIzucqLmoUQjUOSK9EsWSptxJ5IJ/H0abxdHYT7X9lF5v6eLngY9ZzKSKW0tIzyCiv9\nOrcmxM/jisbRlCqsNqx2Oxrn95L6Lc2hUXa8jIKtBViSzm/8iU5PYNcb2LH+X3Tu0O7KByyEEE4i\nyZVodhwOjdgT6ZxJSobKUsJbuTdJHK4Gla6hHpzNMRN/5CiVVivX/f/27jy6ruq+//77DHeer65m\nWbJky7YsGzO4YAwxkEASJyXp04Q8JJRfICsNSSBh+D3JSutQoKwU8vsDVgkNJXnaJKRtCGQ9CW2A\ntJjtUngAACAASURBVLSYYmaMa2w8yPJsWbN0defpDM8fwrKFZVnGV5Zkf19reS353Hv32Xev46uP\n99n3u5c1nTMBy6FruJ06KipmYTTc2oZNanOKkf8eodhXBED1qARXBSlErkTTLuI/tgxIuBJCzGkS\nrsRZZ/uBAfYe7Gawv5f2Bj/KNKyxmipNVVhY7eXQUI6dHR1omsrqZU3EQtN/i3KmBTxOmmsibNrv\nJD8UwNgTJ7EhgZEwAFACKtErIoQuDqG6VZJDh0nuXMBvXt7Bt/70khnuvRBCfHgSrsRZJZMrsrtr\nkH379rGo2otDmx17k8+r8GAN5tixswNFUbl8eeOM1cOybZtUtkgmX0TXVIJeFy5n+T8KAl4X9SGV\n3Lb/Jr3vdSiNzlTplQ6cq3xkGxWsiIu8YuJFxRseZkTN0D00WjX/g6UZhBBirijLJ6plWdxzzz38\n8z//Mz09PdTW1nLDDTdw3333oaqz45ebODfsPjxMb28fYY+K3z27/u/QWOFm70COjo5daKrC5cub\nznhV9+7BFLu6hhgYTpLLZdF0Ha/HS31liEXzKghPUszzVOzevZsHHvwhv3ziCUrvhypnfYCKa/zQ\n7CBfMsgm8+Neo6ng8A+RLWZ5Z1c3f3zp4rL0RQghzrSy/PZ58MEHeeyxx3jiiSdYtmwZW7Zs4ctf\n/jJut5t169aV4xRCnFQ2X2J/b5y+vl6W1s2+KumKotBS6WF3X4aOXbvR1NEZrGOLjRqmRSKdJ1c0\nyBVK6NronnenG3ps22bnwUE27exia8dusuk0DVE3NpArWhyKxTg80MCKhXW01EU+9Dk2bNjAww8/\nzDPPPINt2wA0LL6ATM35lOotvG2voijg8zgxTIuK4NHbo4qi4AgMU+jLsXl3n4QrIcScVZZw9frr\nr3PttdfyqU99CoDGxkauvfZa3nzzzXI0L8SUjM5a9RLyqJNuZzOTFGW0VMOuniQdnbvRNJU15zWR\nyRc52Jfg0ECCZDJNsVigUCyiaRoetxt/IEB6MEFj5YdbnL/9wCA/eGI9G97dh6UY6KqC3+mktcbH\nFUsiaIUE772XoFgsUigZtDVVTrntYrHI008/zUMPPcSmTZuA0c2ub7jhBr781W9yIGHzgyf+m95s\nH5neRvy1oyUXAt7jZ+1U3cDColAyj3tMCCHmirKEq8svv5zHHnuMjo4OFi9ezPbt23nxxRdl1kqc\nMblCif29o7cE22rLc2truqiKQmuNl53dcTr3HqA/nsGpQ39fP4ODAzhUC49Dw6ErFCyboaJF3oBc\nLk/PcAWVDYMsnlcx5YX6fcNpbvvbZ9mybx9ZO4HmSQEwkA7Qu8/D1q4E17RXcfGCIDt37kRVNYJe\nF/WVwUnbHR4e5vHHH+fRRx+lu7sbgFgsxje+8Q2++c1vUlNTg23b/Pe7B7hqRT3/trHAyL52dE8G\nd3gI7wR1pizDgaao51xNMCHE2UWxj8zdn6bvf//7PPDAA2iahmmarFu3jr/+678+7nmJxNFigp2d\nneU4tRDs7k2xpeMguUQ/88Kzc9bqg0ayFm91lUiWHBjFAn6XQkNIY35UI+RWxoWngmEzlLFIlVTm\nzZtHU20Fi+uCU6ou/sjvd/D7TbvIOLqJLHoDhzcJgFnwkO1vId/XSogwS2IeVjU6SJtOFi5cwMqF\nMTwTLHQ/cOAAv/rVr3j22WfJ50fXTTU3N/PFL36RtWvX4naPD7fJbIlNewb4/17eQedQmpQ6SHjJ\nBhy+8YVFLRuGdnyEYGExd336Aq5eUXfKYyqEEGdKa2vr2M+h0Pitzsoyc/Xkk0/yy1/+kieffJKl\nS5eyefNmvv3tb9Pc3MzNN99cjlMIcUK2bTOYyBMfidPgL98XKEqmzVDWwrBABVwOBb9TwaWffmmH\n4azJf3YW6ejNk7eLaA4bXVPYOqDjVJzMDzu4YoGTmG/0/bh0hbqQRrpgcejgAQzDwLJs2hvDk57n\n4GCGl7b1kLYTRBZuHAtWAJorR2DeNlyhXhK7L2H7YAyPw09bFfT1DXAo7GVR3ejslW3bbNy4kX/5\nl3/hlVdeGWtj1apVfOlLX2LVqlUnnEkLeh0smRfhjy9t5emXd3IoWcHIzjX46rfjqdqLoo7+/y43\nVAuZaipCQS5rqzqt8RVCiJlUlnD13e9+l+9+97tcd911ALS3t7N//34eeOCBScPVypUry3H6WWnj\nxo3A2f0ey6Ec4zSSzrMv1UE8Psx5TZPfypqMZdtsP5xmV0+W/YM5uoZzFK0SNqO//FVUHKpOc6WX\n9gY/S+v8VIecp1xHqyee5+cvHGT/cIaCI43i60cJDqI4FEr5CJlEjEIqTN+2EH98foyPtVcAozO9\nfpfKRy9qYWdPBqc/QkV9C821J16A/vJTr5O3c7hjPQRjWeD4W6Zudwa3720G3r2MncM+Llpcg8vp\nIFhZT+uiOp5+6tf86Ec/YsuWLQC4XC5uvPFG7rjjDtrb26f8vpv39TOvsZF/+Nc32NXrIdPtZ7hv\nMbo3g41FKVFJpbeG/339FXxk9YWnNKYfJP/+pk7GampknKbuXBmrY+/EfVBZwlU2mz2u5IKqqliW\nVY7mhZhU33CakfgIYe+H2yvOsm22Hkrx71sGORBPkzOzFKwCJbuI7k2haAbYCpbhwCz4GDjsZkuP\nG4/mYWFlgD/9o2oaolNb5zWSKfHQ8/vpSg1ScvcTbH4b3TdE0bBxOB24nQ5U203yYCs9fc38bpNJ\nrmjy6fOPLjD3ujSaKz3s2bMHn89LRdB7wpIOW/b2kTdyuMODk/bL6UsRat7O0D4nz2xyckUTPPp/\n/pUb1j9H8v0PkOrqam699Va+/vWvU1k59QXvR7Q3V+FxOQgFfKx/awcvbNrPQCqIlTRBhSpfkBuu\nPp8vf2LFKbcthBCzSVnC1bXXXsuDDz7I/PnzaW9vZ9OmTTz88MPcdNNN5WheiEkNJLIkEiPU+E79\nct43kOU3b/WxfzhF0khQ0kfw1R0iFIzjDIygauO/tWYZOvmRGLnhKpLxKpI9YfY+l2Z1awWfWhGb\ntLaWbdv87OXDdKfjlLyHCS98Fc1ZABR0DUqlEoqi4nUViSzYjjMYp7/zAv7wno3LoTL/mPwU8TkY\nyZY4cOAQOyIBLlnaMOE5e4fSmLaBw5s+6Vh4qw6Q3Gqw641utvXugfdn7C655BJuu+02rrvuOlyu\n06vL1VIXoTrioz4W4pOXncfB/hGGE1lsReVTl7SyvKVqRivqCyFEOZQlXD366KPcfffd3HrrrfT3\n91NbW8stt9zC3XffXY7mhTgh07SIp3JkMhkCFae2Z9+be0b49ZvdDBaGKepxgvP3EKvuQlFPPOOq\n6gbeWC/eWC+WoZM8tJCenhZe2Jll66Ekt3y08YSzWOu3D7Hl8DA5dZhI85vvB6tRmqpgWTaGYVDQ\nFDxOB77KHhTFYrDjj3j2XY3PLtZoCB1drN8QdbPl0ACH+uMsaYwRmqAWVjydw7RNHMec64PMnElq\nY4rEawlKQ3uOvFHazr+EG7/6Tb5x45+WrbgojNa4umjx6GJ1w7QoFI1xtb6EEGKuK0u48vl8PPTQ\nQzz00EPlaE6IKRtJ50mn07i00YAyFaZl86+b+nlxRz+DpUHc1Xuobd45aaiaiKobhJt34qs+RHzP\nMg6k6nn0BZs/v2oeC6rG7x1YKFk89+4gaXMEX+MWdE/muPZ0TaFomJimhmlZaKqKN9ZHMb2LoR4n\n/9ER5H+tPBpyHJpKpd/BQH8/+3srWbGwZlx7hmnhcTlQUbEMF5Ab36eeAonXEqQ2pbBLo7NUeljH\nuXgh7tgnaWxZSHV9E8lMoazhavx7VtElWAkhzjKza38QIU7RcCpHKpWe8lY3lm3zxCuHeWv/IMPG\nAKGWrfhruk6rDw5vhsr2txjatYKuuMXf/5fFV66YR1vd0Zm0DR3DDKTT2O44nsr9E7ajKAqaOjp7\nVdRUPM7RdYyhxk764lX0Zxxs7dFpO6ZweWXQyc6+QXqG05xn2+NuqeWLBhGfC03RMfJeXMERbMMm\nvTVN4o0E+X1Ht5/xLPQQWh3C1+bDKDrp32Szpz9DMpkmkckD479mLIQQ4sQkXIk5LZsvkS/k8bmm\nVoLh3zb18/aBQYatHmLLNuIKxsvSD0W1qVi8mfgeg+5+m//3Jbjzk800RN2Yls1rnSPk7DSeqt1M\ntqRIUxWKhoVpWJj66OyVotqEGncxvD3MW4fc/F+GhUMffb8ep4ZqGyRTaRIfmGHSNZWKkBcNjXyP\nTe6tQZIbk1jZ0Rk6xakQXBkkt0Sjfkl07HUOTxbdP0wmH2XHwUEuvbBUljESQohzhYQrMacVSiZG\nqYRjCuFq494E/7m9n6HSABVL3ylbsDpCUSCy4D3itsLAoMbPNzj532vn058qcmgog6EUCEUnnyUb\nm70yDYrG0dkrd7QfxTtIPOfjzT0JLl98tPxC0KOTTCYZTGTH376zDAZ3v03mtX/BGDwwdthZ6yS0\nKoS5SCdrmRQLBl0DSfweB2H/6J6M7sgAxcPz6I1nZSsaIYQ4RRKuxJxWNExKpRK6Z/L1Vn2JAk+9\n1cNQaYhQy3u4w8PT0p/RgLWNvkyQgyNunnnHS8CjkTfy6IFhVL140jYmnL1SwFvTSXZvFRv3fSBc\nuXWGUymGkzmoH62H9ZOf/ISf//znDA6+X4JB0wlc4CW0Kohrnmvs9mEU6BpI0vCBrW50d5YcBvFM\ngZIh4UoIIU6FhCsxpxWKBqVSCYc++aLoZ97pZyAfxxE7gK/60LT2SVEtKhZtpv/dAK/udlHpc1Oi\ngDPYN7XXH7v26pjZK1e4l5SaZd9ghqFUkYrA6Ht2OVQyiTTP/utv+YvbfsuLL7441tbCRW0UK5Yx\nHK3B3/Yu7qru487n9xxfH0x3ZzEsk3Tewj3BFjhCCCFOTD41xZxWKJmUSgYO7cTfZtvVk2Hr4RGy\njFDTvGPSNU/l4vBmCDTsIn7ARzJVwtJMdO/IlF9/ZPbKOHb2SjNxRnrIpir5nwMprl5WwcGDB/n3\n/3iBF19cTyY9urWNx+Ph+uuv55ZbbiFY08LfPvkSv31zG+me+Xgru497/0duBR5Ld2cx7BKpvIFn\ngg2WhRBCnJiEKzFnGaZF0TDAtk5YhsGyR8suJIwEgYY9aI6T35YrF3/dfhIHF2HlNfAZaK6TF/I8\n4sjslWmaGIaGNjZ71UNuoIkX//Pfef5n74zb/LypZRH/z53f4sYbbxzbRDSZKbDmolb+/Z19ZNIV\n5Ier8FT0n/z8qoUN2LaCxyUfE0IIcSrkU1PMWYWiMbqYfZKNlDftS7JvOElRj1NRt//MdQ5QNQtX\npJ/USADFNtFcx9e2mvT1qkLJNDEsC4dpkd+TJ71xB/kd7/CeNboOyuv1smbNGurbLuFTn72Oay9b\ngkM/Wmg06HPRVB1l9ZJq1m8rMLx7OTWBV8YVMJ2IWXCjohH0ufDKzJUQQpwSCVdizjJMC8Mw0Sa5\nz/dq5whJI0mwpRNFO7N7XdqWgts/TJJmbLWEaRvoTK1kRKFk4HLoWCMGia1x+rfkMEeMscfdVQu4\n8XOf5uMf/Qgul4u39ybQNA1NPb79+TVhPnlpG7u74xjxGMOd5xFb+vakt0cL6SAaOvWVoRPuWyiE\nEGJiEq7EnKVrKpqmYdoTPz6UKrJ3IE2BDBWxnjPbOcAydWzbRFENbCzyJQu/dvJwZZdsMpuzpLeX\nKO4/ehtTC2v4LvBhR9cQUFYyb+lCXC4Xtj06AKqqoE5we7S2IkB1rIKrl9fw27cMuhJ1JA+2Emzs\nnDBg2TZkBupwqm6WNVcTCRy/JksIIcSJSbgSc9ZouFIxrYnT1aYDSbJmFk+077gNmM8E29KwS6Co\nJrZiUTpRCgRsy6a4v0jyfzIYHQU4UrdTB+diN/6VQdzNDlRVIdetYA6YxDOjT7JsUBR1wlkrGA1d\nC+ujDLW10jOcYf0Og8HDbZhFN+GW7ceNTXaomtJILbWBCq67sr0sYyGEEOcSCVdiznLoGpqmTxiu\nbNtm0/7RcBWsPL78wBlhK4A9umehrWBYNqZlj1t8X+otkduSI/deDit19LalWqvhv9CHZ5kHQwdN\n1znyLjVnAdM2SeVHQ1HBsHA4HZOWTGiuDTOYqCFzfiuKYrOhQ2Vw0EFfIoq/9iCu0CCKZpIfrmLk\nwBLCepTrrlrOigXV0zEyQghxVpNwJeYsVVXQNRUU5bjQMpgqcXgki6FlcIcHZ6R/tq2gKO/PClkO\nLMumZFqQhtzWHLktOYz+o+uolLCK3arhXeFFi+r43t/QWDVtLNMCVUFTFVS9iIFFpjDadr5o4XG7\n8blPvPBcURQuaK0hWyhhWhY+137e3uuka8RH7lAV6QN5bBs0HITVIFdfsIQ7PrcKbQq3MYUQQown\n4UrMaQ5dQ9e048JV13CeolXEGYijqCe+HTe9RmeuVMXALJWwthokOlNYB4/u1ad4FDztHjzneXA0\nOEjnigS84xeQa+ro7BTvL4ZXFBvbtsfWWmWLJl7vyReeO3SN1e3zcDk0/D4fVdGDdHYN05co0DVc\nwLBsKsM+Pr6qjZs/eQGxsLesoyGEEOcKCVdiTnPo6oS3Bg/H85SsEk5fcoZ6BrZhUNw/iLnleeg/\nCJaJBaCBe7Ebz3keXAtdKNrRUOh0aMe1oygKCjaWPfrHtlUU5eji9XTeoDrmI+Q7cSHVY9tftbSB\n6oifqliUhS1JcrkcigJ+v5/aWJi2pkqiQVnELoQQH5aEKzGnOXQNXdeOC1fd8QJFu4TvDIcr27DJ\ndmZJv5smvS2DXTim/EO1H22FTewCP6p74tttLsfE/yRVBUzbwrY1sBUURm8RGqZNpmgTCoeJhaY2\n06QoCi11EebXhElk8qRzRRRFIeh1SdkFIYQoAwlXYk5z6hoOh4OCUcB/zPHD8QIlq4jTl5r2Ptim\nTW5PbjRQvZfGyh0NVHqVHyU2D7PyIqzaAZS6jSiuU99/R1EUbMvCsmxsw4GCgktXGcmWCAaDVIV9\nE856TUZVFSIBj5RaEEKIMpNwJea0kM+F1+sjm8lS8X66KpQsErkillJCc2en5by2ZTOyK01pe47M\n1gxm5mg5A2eNE/8KP77zApTM+WQP6GTTQay8BdiYFuinloNQFbCs0duCZt6LU9GJBRzEMyXC1TXU\nRP0nb0QIIcQZUbZw1dvby/e+9z2ee+45UqkUCxYs4LHHHuMjH/lIuU4hxHFCfjc+v4/e4d6xY7mS\niY2NopfKtklztlDC49DJH8iT3pom/W4aM3U0UDliDvzn+wm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KJum8iYFGRUUF7U1VzKuO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e87445c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.0205  0.0457  0.000224]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:2], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimate quickly diverges from the robot's path after passing the landmarks. The covariance also grows quickly. Let's see what happens with only one landmark:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tQDAYijqmXCrEH24dBI04Ds6yXggFIwuLCqUeyBKKYfXW46VPtsYUm5DujpIr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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e88c3470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.285  0.759  0.00353]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:1], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you probably suspected, one landmark produces a very bad result. Conversely, a large number of landmarks allows us to make very accurate estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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rs2bVMruygLqynLF/UAsh3h9ZW1AIIc5BXZ11SuaxiieSHGrp41hbD3/eeYh9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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e862d668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.00842  0.00879  0.000761]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10,  5], [15, 15], [20,  5], [15, 10], \n",
    "                   [10,14], [23, 14], [25, 20], [10, 20]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1, ylim=(0, 21))\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "I said that this was a real problem, and in some ways it is. I've seen alternative presentations that used robot motion models that led to simpler Jacobians. On the other hand, my model of the movement is also simplistic in several ways. First, it uses a bicycle model. A real car has two sets of tires, and each travels on a different radius. The wheels do not grip the surface perfectly. I also assumed that the robot responds instantaneously to the control input. Sebastian Thrun writes in *Probabilistic Robots* that this simplified model is justified because the filters perform well when used to track real vehicles. The lesson here is that while you have to have a reasonably accurate nonlinear model, it does not need to be perfect to operate well. As a designer you will need to balance the fidelity of your model with the difficulty of the math and the CPU time required to perform the linear algebra. \n",
    "\n",
    "Another way in which this problem was simplistic is that we assumed that we knew the correspondance between the landmarks and measurements. But suppose we are using radar - how would we know that a specific signal return corresponded to a specific building in the local scene? This question hints at SLAM algorithms - simultaneous localization and mapping. SLAM is not the point of this book, so I will not elaborate on this topic. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## UKF vs EKF\n",
    "\n",
    "\n",
    "In the last chapter I used the UKF to solve this problem. The difference in implementation should be very clear. Computing the Jacobians for the state and measurement models was not trivial despite a rudimentary motion model. A different problem could result in a Jacobian which is difficult or impossible to derive analytically. In contrast, the UKF only requires you to provide a function that computes the system motion model and another for the measurement model. \n",
    "\n",
    "There are many cases where the Jacobian cannot be found analytically. The details are beyond the scope of this book, but you will have to use numerical methods to compute the Jacobian. That undertaking is not trivial, and you will spend a significant portion of a master's degree at a STEM school learning techniques to handle such situations. Even then you'll likely only be able to solve problems related to your field - an aeronautical engineer learns a lot about Navier Stokes equations, but not much about modelling chemical reaction rates. \n",
    "\n",
    "So, UKFs are easy. Are they accurate? In practice they often perform better than the EKF. You can find plenty of research papers that prove that the UKF outperforms the EKF in various problem domains. It's not hard to understand why this would be true. The EKF works by linearizing the system model and measurement model at a single point, and the UKF uses $2n+1$ points.\n",
    "\n",
    "Let's look at a specific example. Take $f(x) = x^3$ and pass a Gaussian distribution through it. I will compute an accurate answer using a monte carlo simulation. I generate 50,000 points randomly distributed according to the Gaussian, pass each through $f(x)$, then compute the mean and variance of the result. \n",
    "\n",
    "The EKF linearizes the function by taking the derivative to find the slope at the evaluation point $x$. This slope becomes the linear function that we use to transform the Gaussian. Here is a plot of that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wtnjnWq9LF/Dzg19+sU/hofnLRETkWqmnTNzSqlX2hKxFC+MSMoDUl1JJfSmV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\niAxQUUYIIYQQIgNUlBFCCCGEyMA/af5IBqTIDSwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e8685a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.29, std=1.12\n",
      "EKF    mean=1.00, std=0.95\n"
     ]
    }
   ],
   "source": [
    "import code.nonlinear_plots as nonlinear_plots\n",
    "nonlinear_plots.plot_ekf_vs_mc()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The EKF computation is rather inaccurate. In contrast, here is the performance of the UKF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jy330ESQkQOPG0KmT0dF4p549bZcvt22zXT4WERHPpzll4lJZWfCv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\ni/sWp3zx8teNU0QKnzyTsvT0dOLj4xk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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1e8724940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.13\n",
      "UKF    mean=1.30, std=1.08\n"
     ]
    }
   ],
   "source": [
    "nonlinear_plots.plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that the computation of the UKF's mean is accurate to 2 decimal places. The standard deviation is slightly off, but you can also fine tune how the UKF computes the distribution by using the $\\alpha$, $\\beta$, and $\\gamma$ parameters for generating the sigma points. Here I used $\\alpha=0.001$, $\\beta=3$, and $\\gamma=1$. Feel free to modify them to see the result. You should be able to get better results than I did. However, avoid over-tuning the UKF for a specific test. It may perform better for your test case, but worse in general."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}