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 0x1c0ee9fbc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.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": {
    "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 0x1c0f1a2c588>"
      ]
     },
     "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": {},
   "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
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RKRV//PEHy5cv5+mnRxB7Anb+7s2UD88wYwsc/hMgLyx6usHnEyC8sQ0mky0A7Zvetm7L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\nxKH/B3zyhlKhtn9eAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f2b2b4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yioIFC+Lv759mXckaNSsarJposjocTBO6tQSPQqnH/11TLcWvZ58SQBERkTzD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\nIYQQomKoACSEEEIIUTH/H3Wc+6Ks+YeYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f2b8b518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YmJjo1Rs/fny7NpCIiIiIOp/BIbG6uhrV1dWIjY1FbGys3nIhBBQKBc9uJiIiIroFGBwS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\nIiIiCywSiYiIiMjC/wFzzcvzysl3TAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f2bdab00>"
      ]
     },
     "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": {
    "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3Ol8bhqHgYGvCDEoWAQNAmVTamyvLkmrVKuvUqYIf7X47qwJG48buz0Hp2LGj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\njoABAAAsR8AAAACW+780ZYQOic7fMwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f2b26470>"
      ]
     },
     "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": {
    "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": {},
   "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": {},
   "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": {},
   "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": {
    "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": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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leZcrzh4SXAkhhDhtDIzE2dc6QE/fAG0dnbzaEuK1pm4S0QFMM0JWZdFsOWzO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f39d9da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.0244  0.0406  0.0022]\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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2hikrn0DluBxyJKeVOEmyt6AQQogzqqHdS1VdG1V79+PUY+w62MvOA72EYiH0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f397ec18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.0198  0.0211  0.00154]\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": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LKdt+Tr7o9sW1Q5IrIYQQl5ROpzL2ps54OHlRnNa23nqewSnovVNIK8rgyUXf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\nQyX2KhulFTJyJa5NzbLmqqi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DuanAX5eLc1yMBhRFwWZxQlfHMwCqzo5/p4Nkxrnz09Fk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\nCSGEOBMkXAlxksp8LsoWVgOQyxcZHc8wlsiQzhbIFYrkCjoAmqpg01R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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f39d9e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.0214  0.0457  0.000228]\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": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KEQtJroQQ4jgwJuhQNK2/cj0tlSz/Zhevfbol7jjnDO9OXloKumYHgZr09nat\nvgVr1m484Roee3NtXIVFR/fLYsKg7pgVJ57inh36XbkFNKhu1nxbyGcb98Y9ZiFON5JcCSHEcdAr\n04XVaEKDgjVzN7XBSh55I5/yWl9ccRRF4fKJrecN+sq6R/U5MvfRqLj5tricBau2xRX3d1eOw2VM\noqEqN2o/F3xXmiFzN+7vSjPEk7gJcTqS5EoIIY4Do0FP75wkEhQDCeYAGlsZxXXl3PHcp3HHuu78\nIaTak4gEkgnWO9rbtToVW3YB7lANTy/8kubm2OtTDe2VzsQheVgUB+59vTr0O7ILaVTq2LqvlDeW\nxT/jJsTpRJIrIYQ4Tob2SidBayTkdZLUezO+lho+/bqAt1d8G1ccu8XI9HF9sOoc1JdEb0K3Z5TQ\noq+loLyCV5bGdyzO72eNI9GUTKi6G+GAJapPq4tg77YTd7iGpxZ8SSjcHFdsIU4nklwJIcRxMrpv\nFkatmUafiwRTCHvudupCVfz9zbWEG+NLVm6cNgKXOZFGdwaNDab2dkUL9m4FeMI1PLt4fVxx+3dP\n5cIz+2DTuXAX9u7Qb0svpcVQw97qSiksKsRhSHIlhBDHyZj+2Zj0JpoCDlqatNgzi2gx1FBYVcmz\nizfEFSs7xcGU4T2xaO3Ul0YfX2NNLSNirKGopor/vL8xrri3XzWOFGsyTXWZUUuOAIoCzu478IRr\n+O+Sr3D7gnHFFuJ0IcmVEEIcJy6biX65qRg0JgK1qa3JSu7+ZMUTZ7Lyi0tGYDe4CFbl0Ny4vwCo\nomhwdtuJJ1zL80u+xt/QGHPMnFQHl08ciD0hEXdhH75fLcKSVI1iq6TMU81j8+M7zxDA4/Hwox/9\niPz8/LhfK8TJQpIrIYQ4jqYMz8OksxKsTQPAklyNxlpFuaeKx978PK5YQ3qlM6ZfN4waW9SROADm\npCo0lipK3VX8450v44o79/IxZDhSiPjSaKhLjurTaMDVfTvexjrmr9jKvkpPzHFLS0s5++yzWbJk\nCb/4xS+IRCJxjUuIk4UkV0IIcRxNH98Hi95G2JNKS7PSmqzkbae+yc385VsoqqqPK94NPxqOw5CI\nvzyXSLOmvV1RNDhyd1LfWMcrn3xDnTf2WbFEu4lrzxuCMyEJT2GfqNILDeEmTA4vCUnF1ASq+VuM\nhUW3bdvG2LFj2bx5M3379uW9995DUeRPkDg1yU+2EEIcR3kZLvp2S0GPmaA7BQCTox69q4SaQA1/\nfyO+pbYPq+YbAAAgAElEQVQpI/Lom5NOQsSBryorqs+SWIfWXk6lt4b/fTu+WbFfTh9Ft+RUNMFk\n/FWZ7e3BcBMN4SZc3QvwN7v5eH0Bm3ZXHDZWfn4+48ePp7i4mHHjxrF69Wpyc3PjGo8QJxNJroQQ\n4jibPDQPs85KoHp/hXVXbgG+Zg8ffLGD3aV1McfSaDRcd94Q7AkufKV5HfZIOXN34m1y8+byrVTU\nxV6w1GTUc+MlI3Aakqkv6k0g2EKttwG3N0SdN0iz1ospbR/uUA0PzTv0/ql33nmHc889F7fbzfTp\n0/nkk09ISkqKeRxCnIwkuRJCiONsxlnfLQ2602hpbv01bLAGMCQVUxes5dE4N4pfOWkAOckpaMIu\nArUpUX0mhxe9s5SaQA2Pxjkrdu15Q+mdmY6+KZGmmh6YDHqMBh2hcDPBcBPG9O00RDys+baQlZsK\nO7z+2WefZebMmYRCIW688UbeeustTCZTxxsJcYqR5EoIIY6z3jnJ9O2Wih4LDbWp7e2u3F34mz18\nvL6AbfuqY46n12uZNXkA9gQX3pK8Dv3O7jvxNblZtGY7e8rdMcfV6RRunnkmLmMyvpJeGBQjiXYT\nLruRJLsZm01tPc8wVMP/vL6m/SDqSCTCnXfeyU033UQkEuH+++/nmWeeQafTxXxvIU5mklwJIUQX\nOG9kTyw6K4Hq/fuZEsxBTClFuIO1PPL6mrjiXX/hMFJsibT4Uwl9rz6V0RogIamY2oYaHnk9vhII\nM87qy9CeORhUF57iHpgNekyG/WUfHNl7CSl1fLO3hHfzdxAOh7nrrrt48MEH0Wq1PPfcc9x9991o\nNJrD3EWIU4skV0II0QUun9gfq8FOoyeVlsb9MzqO3F0EIh6Wb9rDN7srY47nsBqZPq4vNp0DT2nH\n2StXbsF3s2K74poV02g0/PHqs3AZkwmU96ApZMB8QHKl1UWwZ+3CHarhkZc+5qabfsnSpUux2Wy8\n//773HDDDTHfS4hThSRXQgjRBXJSHQzukUGCxoy/Jq29PcEYxpS6D0+olqcXxlef6ueXjMBpctFY\nF30kDkCCOYQxdR/uYC3/+1Z8Tw6OG5jDpCE9sSgu3IVndOi3ZxYTDu7hi3l/ZvPmb0hLSyM/P5/z\nzz8/rvsIcaqQ5EoIIY7QQ/NWc/bN/+Vfi47snL0fndkLi95GwwFLg9C61BZo8fLZV7vZXRb7k4Pd\n0g48Eqd7h35nzh4CLfV8snE3O4tr4hrrn35yFknmZMI13Qj7rFF9ocIAzSveoSVQhzExm2f//R8G\nDRoUV3whTiWSXAkhxBFoCDXx/JKNbCz+lr+9voLn3ovvbECAS8/qi8PkoMmXQmPQ2N6eYAphSCrB\nE6rjH++siyvmL6aNxG5IJFjVLepInLa4xpQiPKHauKvB98lJZtq4vt8d6tynvd273kvZf8pQwy0o\nWTmYx/6U5QUNccUW4lQjyZUQQhyBak+AppYmGltCVAZK+PubaygoqY0rRrLTwlkDu2FSrPgqoguA\nOnP24G/y8sHnO6mo9cccc+h3R+KYNHbqS7p36Hfm7MbfXM8nG3bFPd7fzxpHmj2F5voMArUuaj+q\npWp+FbSAc4KTlKsz8Wsa+GBDSdznJApxKokpuVq1ahXTp08nOzsbRVF46aWXovrnzJmDoihRX+PG\njTsmAxZCiBOBQa9Fg4JG34g+qZAqXyV3/uez9nIEsZo1eSC2BAcNVTlRx8wYrAH0rjLqGup4ZlF8\ns1e/nD4KhzGRQEV3Wpq0UX0J5hDG5GLcobq4916lJ9n4ybmDsSs2ql6rwv2pGzSQcmkKyZckY02p\nRbFWUNPg4ek4Z9yEOJXElFz5/X4GDRrEk08+idlsPug1U6dOpbKykoqKCioqKvjggw86daBCCHEi\nSXVZMSUkQJOh9Qk/avh8eyFvLNsaV5wpw/PolpKE0mRvPw6njSNnD94mDwtWbaPeH4o55tlDchne\nKwcjDupLOx4z4+y2G3+zh4/WFcRV9wrg0tGZ+Fe/SEvRPjQJWjLmZOAY21r6QaMBa/Z2Ai31vLFs\nS1znGQpxKokpubrwwgt54IEHuOyyyw5Zq8RgMJCSkkJqaiqpqak4nc5OHagQQpxIFEVDqsuKVqNH\nbdFhz91GbaiSR95Yg7+hMeY4Wq3CRWN6Y9Xb8VXkRPWZHPVobVVU+2rj3tN107SR3x3onNdeBb5N\ngjmIIbkEd6iOx+PYe7VmzRomTRhPQ00RWksiuknTMZ0RvbndaK9FsVVQ6a3hyQVfxDVmIU4Vnbbn\navXq1aSlpdGnTx9+/vOfU10dex0VIYQ4GWUl29AqOpqCZuzppajmCkrrqnh2cXxPD/70vMHYDQ4a\n3Wk0h6M3oduz9+BtdPP6sq2Ews0xx5w6sgcDczMxRJx4y7t16HfltFaD//DLneyNYfbqv//9L5Mn\nT6ayspJzzpnC2Gvvx2Dqhecg+7ps2dvbzzOs9gRiHrMQp4pOOYvgwgsvZObMmeTl5VFYWMidd97J\nlClT2LBhA3q9/pCvW7/+yB5fFvGRz7nryGfftY71558QaUCJKATrTSTYw5gzvsWzM5nnFn3B6GwF\nsyH2X7E9U81U+Ey4S9OwZe5qb9eaS4gYqimstHP/v9/lsrEdl/kO5dz+DjbstOIu7o4xaScaJQKA\nL9iEzRRC59xHtcfKHf9cxO+mDzhojObmZp566inmzZsHwKxZs/jtb3/Lut117Hq7ntriniS49qBL\nCLe/xmCrQ7GWUOa28IenFvLLC/vGPGbROeR3z7F3xhkda7616ZSZqyuvvJKLL76YAQMGcNFFF7Fk\nyRK2b9/O+++/3xnhhRDihNQv20mCYqTJnwSA0VENlmpqAx7e+bIorlhTh2Rg1toIVudy4J54jQYs\nGQUEWry8v7GU5pZIzDHP6pdK92QnumYHgar9SVmwsQUAa+ZOGiJ+1uyopNLTcX+U1+tl7ty5zJs3\nD51Oxx133MFtt92GTqdjbJ9UhuSmYFSd+Ir7d3itNXs7gYiPz7aUU+uLfb+YEKeCY3KKZkZGBtnZ\n2RQUFBz2upEjRx6L24vvtP3LRT7n408++651vD7/3J4Bnl26i/qGZBL0RhQtuHL3UL89nRXbPPz1\npiGYjIeevT/QkCEtvLG2nC0VbtRQBibX/qW6hMxaGsrrqW1oYK/fxNVTYi/QeWvAzO+efZ+ayj4o\nrr00NDbS2BShxteI1eTDkFxGgy+RVXvCPPTzCe2v2759Oz/+8Y8pKCggJSWFt99+mwkTJkTF/t+U\nXKbdNY+iuiBqTikmu5dQqDWRciSHaEgsJxBwsawgxEM/PyvmMYsjJ797jp/6+vpD9h2TOlfV1dWU\nlpaSkZFxLMILIcQJIcVlISfViU41EvK3PjFnTqwGczVlnmpe/HhTzLH0ei0XnHkGFp0Nf0V2VJ+i\ngC1rD/XhOv7vg6/iKvdw+dn96Zmehq7ZiTbQk+wUO0aDjuwUO06rCWfObnyNHt7N306Vu7We1oIF\nCxg9ejQFBQUMGTKEdevWdUisAPrmpjBzwgAcCYm49/Tj+8Ny5Rbga/TwzuptlFZ7Yx6zECe7mJKr\nQCDApk2b+Prrr4lEIhQVFbFp0yaKi4sJBAL8/ve/5/PPP2ffvn0sX76c6dOnk56ezqWXXnqsxy+E\nEF1qSM80DFojoXoX0PoUoS2rdRP6K0u/oSWOZbyfTh2MzeAkVJfZoT6VLa2UJq2HnaUVfPDF4VcF\nDqTVKtxw0TAcCUl4S3oRaQGraf9smtHmR+cspzZQy1Nvf8Ef//hHZs6cic/n48orryQ/P5/c3EPv\n87r96vFkJaai+tPwV6VF9RltfvSJpdQEauKuCC/EySym5Gr9+vUMGzaMESNGEAqFuPfeexk+fDj3\n3nsvWq2WzZs3M2PGDPr06cOcOXPo168fa9aswWKxHOvxCyFElxrbPwejzkzYk9zeZk2pJKJ3U1hV\nzcJV22KO1TsniaE9MzFgxVcVfd6golWxZO7FE67j34vjK8tw9TmD6JGehq7Jhb8qE6c1+lBnZ7fd\n1PvLePyeX/Hwww+j1Wp57LHHeP3113/w97jLZuKmaaNwGVPwFPZDbYlOCp25BfibPSz+fDv7Kjxx\njVuIk1VMydXEiROJRCK0tLREfT3//PMYjUY+/PBDKioqCIVC7N27l//7v/8jKyvrhwMLIcRJ7pzh\neZh1Fhp9iURaWusAKgpYM/dSH67jP3Ev4/XDmmAnUJnToc+RUUwYL5v2lLFhR1nMMXU6hZ9dOBRH\nQmLr7NX3JtM03kqaVr1CoHwHFruLTz/9lLlz5x6yruH3XX/hMPplZ5LQnISvvFdUn9EaICGxhLpA\nLY+9uTbmMQtxMpOzBYUQ4iikuiz0yExCj4mgx9XebksvoVGpZ1tRBSs2FcYc77IJ/UixuYg0JBLy\n2qL6tPoWzKlFeMNunnt/Y1zj/Mm5g8lLS0MJJ+I/YFas/ot6Sv5ZgtrQgMaVQe6Pbmf4yDFxxdZq\nFe74yQQSTSkEK3rT3Pj9mbFd+JrdfPDFzrgrwgtxMpLkSgghjtKoPpkYtSaCnqT2Nq1OxZJeSH1j\nHS98GPvGdpNRz3kje2LR2fAdpPinPWsfgRYfy77aE9eBznq9ljkXDsVhSMRb3JPmcISqN6uofrsa\nWsA+1oFx6kRqm5v5d5zV4KF1Bm/i4B6YVAfeoujSDAZrA4akEuqCtfz9jTVxxxbiZCPJlRBCHKWJ\nQ3Mx6SyE65Oj2u0ZJQRb/ORv2UdZTexPy117/hDsCU6CNVm0NEZXzEkwhUhwluMOunnu/fiSoGun\nDqF7SirUKZQ8XYV3nReNTkPqrFRSL03B0b3wiKrBt7nn2ok4jS6a6nIJ1jui+lzddrWfZ1hQUht3\nbCFOJpJcCSHEUTp7cC52k42WgIumkKG9XW8Mk+CqoD7k4cWPYp+9GtQjjeFnZGHQ2PBWdty/as8q\nxNdUzzurt8eVBOn1WgbbawmveIXmSj+6RB3Zv87GPsIOtJaRUE21lNZV8/pnm2OO26ZnViLnDcnC\nqnVQt7s/kcj+vWYJliDG5GLcoVoeldkrcYqT5EoIIYBXl37DqBv/zYy7XqfO27Fa+eGYDHqGn5GB\nUWsmUJMa1WfLKMLf5OXd/B1xlWW4Zupg7AkuAuW5UUkKgMnpRmOqpdxTy/zlW2KKFw6Hufnmm/nX\nQ39AbQ6jTe+F6+qRGDL3J4MHlpF48aNNcW3Eb/OTs3uQbnOhaUjt8MSjs9su/M31fLJxN9v2yfmz\n4tQlyZUQQgDPL/mK7ZW7yN+2nWv+uiCuRAhg6siemPVWgnXRtZ5MzhrUBA8ltbVx1aeaNq4POclJ\naBqdBN0pUX0aDVgzC/E1enh56eYfTIL27NnD+PHjeeqpp9Dr9Vxxw+9IOWs2vqp+HZ4ctKWU06zz\nsKuiiiVf7jp4wMOwmvRcOa47LmMK3sK+tDTv/zOTYA5hTN2HOyizV+LUJsmVEOK05w2EKaz0EI4E\n8aoVbNpbzP998FVcMS4Z2xtrgo0mb3LUPilF0WBOL8LX6GHep7HNMkHrE3iXTuiHTe/AVxZdxNPj\nD2JLLadRW8+OkgqWf114yDhvv/02w4YNY8OGDeTl5ZGfn8/L/3iIvLR0lHAS/srv19MCS0Yh3rCb\n/7wX3xOJbS4cnsXA3CwMkUQ8RT2j+pzddhOIeFj29R627Kk6ovhCnOgkuRJCnPZaIhFUVUWjbcHV\nYyvucDX/fHcdNZ6GmGMk2k0M7pFGgsZMoC56psmeXkpI9fHltmL2lMVeimD2+UNwml00etJobNhf\n3sAfbGotKppWhLfx4Pu52pYBL7/8crxeL5deeikbN25k1KhRGBJ03HjxCJyGJOqLerfX52rjyCgm\nRD0bd5XEVU+rjVarcNc1E3AZUwiU96AxaGzvSzCGMaXuwxOq5ckFX8QdW4iTgSRXQojTnlZR0ACq\nCtbUCjS2Cso8lTz02uq44kwZ3gOz3kpDbfTSoC6hCUNiOd6whxc++jrmeKkuK1OG9cCis1FflovH\nH6Sk2kso3ExJtRfsBQRbfKzeso+iqv2HyO7evTtqGfCJJ57g7bffxul0tl/zk3MH0zsrA32zC295\ndMHSA+tpPbtofVyfQZuzBudy7rAzsGoTce/tG9XnyN5DoMXLZ1/tZldp3RHFF+JEJsmVEOK0p9Mq\ngAbQoNFAYo9vqW90897nO+KavZo2rg8WvY1GTyotzdGzQbaMIvzNXt5fW0BjU0vMMa//0TDsBhfB\nqhxsBmvUwctJSRoMiWXUhzw8/10l+BdffJGhQ4dGLQPefPPNHaqt63QKv54xCqchGW9Jr6i9UQD2\n7EICLV6WbdpD4REeW3P3dWeTYk2hsS6bBvf+AqsJpjDG5GI8oTqeXvjlEcUW4kQmyZUQ4rSXoFPQ\nKgpEFCItmtYDh50VuANunv8w9r1X2al2+mQno8dMgzu65pXJ4QGjmwpPLQtXx37e4Mg+mQzukYlB\nteP7rizDgQcv2zL34W+qZ+Gyr7hy1lXMnj0bv9/PrFmz2pcBD+XSCX0Z2D0TQ4sLb2n3qL4EYxhD\nUime4JHPXuWmObl26lBcCcnU7R5A5ICc0p69B39zPUu+LIirBpgQJwNJroQQpz2dTkuyw4xWo6M5\n1Lo/yJ65D19TPQtWbqMpjpmmycPyMOs6Lg1qNGBNL8LXVM8bn22Na3w/nToYu8GJv7w7kYgadfCy\nyeEh4t/G1rfu560352O1WnnhhRd47bXXopYBD0ZRFH47cwxOYxK+0h4dCpbas/bib67nvbU7cPvi\nK0/R5tYrxnJGRia6cAqekrz2dqO1Ab2rjLqGWp5euO6IYgtxopLkSgghgPREK1qNnsagBQCTqxrV\n4Ka4toZ312yPOc60cb0x622E3WlRMzUAtrRSwqqPr3aXsq0w9jpPl03oR05yCpqwi4a6/XW01BaV\nuo9raVz2IS0NHhzpPfjqq6+47rrrYj50+fzRvRh5RjeMuPCU9IjqM9l96GxVVPvr4n56so3RoOOu\nn04g0ZSGv6R31OZ2R85ufE31vJu/Pe7aYkKcyCS5EkIIIDPZhk6joznUOiukKBqs6UX4Gz3MX/Zt\nzHH65qbQPS0RXYuVoCcxqk+rb8GYVIYvXM8rn8ReAV2rVbhiUn9sCY725bum2iZKninB/Wnr04dK\n72HYz76R2kbjYSId3G2zxuIyJhEoz6M5nBDVZ8vai6/Rw/xlWwk3xn8kDsB5o3oxZVgvbNpE6nb3\na2832X3o7BXUBGp55giXHoU4EUlyJYQQQPd0J3olgabvZq4ArGmlhCJ+NuwsjauEwsQhrWcNNnyv\noGhbzECzj6Xrd8dVqHTOBUNJtiTSXJ9C3epGih4vIlwURufQkfXzLOyTM/A3eXnhw9ifRmwzbmA3\nxg/Iw6w4OtSlajsSp6SuhjeWxV6n6/vunz2JNHsazZ5s/NX7S1XYs3fjbfTw5vKtBIKNRxxfiBOJ\nJFdCCAH0yUlCr02gOWhtb9MlNGNIrMDb6OGVpd/EHOvisb2xJNgI1aYf9OgaNcFLubuOpRv2xBzT\nZTMxoV8y6saPqFtUhNqoYh1sJWduDqaeJuzpxTQ0+1nxTSH1/lDMcdv8/qpxuIzJNFTmRi3dKYoG\nW+beozoSByA71cEvLhlJoiEF957+7U8nmpx1aCzVVHpreenj2M9fFOJEJsmVEEIAA/JSSdAaaG6w\nRbXbMooJNPn44IuCmGeaRvbJJDvJhdJsI+hJiurTaMCcUoK/ycuClbE/Nbhw4ULefOTXNJXtAJ2e\npEszSPtJGlqzFmg9GFlrr8Yd8PD6svg2zAMM7ZXOlOG9sGideArPiOqzpZbTrPVQUFbFR+t2xx27\nzU3TRtI/JwtDSwrufb2A6PMMX1n6TdzHDglxIpLkSgghgO5pTiwGE2qTKeqpOZOzjojeS1mdm7Vb\nS2KKpdFomDqyJxadlcD3Di8GsKWV0dAcYPWWoh+cZfJ4PFx33XVcdtll1NXWkJo3ANs5/49I+pAO\nm9atacX4m7wsXBV70nag388aS5I5mVBtDuHA/uVRRatiydhLfbiO/7x/ZEfiQOtTmX+5/hySTKk0\nlPck5GudJbQmVxLRu9lXXcPC1bE/PCDEiUqSKyGEoHUGJSfVjk6jJxzYP3ul0YApqZxAo5dFa3fE\nHO/KSf2xJDgI1aV3OF4mwRxEZ6vBHfCwYNWhk4mlS5cyaNAgXnrpJYxGI0888QSvv7UIlyuPQHl3\nWpq0Uddbkyto1PjYXlzJxoLymMfapndOMheN6YNN58Rd2Duqz5HZeiTO+p3FfHUEsduMGZDNZRMG\n4NQnU1swiEhEbX14IHMv3nDrU4lHuvQoxIlCkishxCnF4w/xTaGbrUWeuCqhA/TPTSFBayTkja4P\nZUmpoKElwMpN+4hEYlu26t89ld7ZKehVK4Ha6LMGG8JNWFJLCTR5WbymY8IWCAT41a9+xXnnnUdJ\nSQlnnnkmX3/9NTfffDOTh/dgcI8sDKqjw7E1ik7FlFKKr7GeV+PYI3agW68YS7Ilmaa6TEL19vZ2\nrb4FU0oJ3rCH/x7BpvkD3XvtRLqnZKAE06gvbT2U2pZeQlip59uiclZ9U3RU8YXoapJcCSFOGaqq\nsuqbfTzz/jc8/s4m3l7xbYcN5YczvHcGBq2RsC86uTLa61H1vriWBgEuHN0Li85GoDp6adDXEMaa\nUk6YAJv2lLPvgONl8vPzGTp0KP/85z/R6/X89a9/ZfXq1fTp06f9mv938XAchkT8ZXkdZsVs6cWt\nTyNu2EMw1BTzWNt0S3Nw6YT+2BNcuPf15sBJJHtGEQ3NPj7dsAfPEWyabx+jxcCd10wgyZSGr7gv\njSEDWp2KJb2Q+nAd/35vwxHHFuJEIMmVEOKUEQg18crHX7OjuoaCugr+8vKyuJbHxvTPxqgz0+Rz\nRSVlGg0YkyoINPlYvHZnzPEun9gfq8FOoyeNliYtDeEmar0N+AKNeII+tPYKfGEvb6/8Fr/fz29+\n8xsmTJjArl27GDRoEOvWreOOO+5Ap4uunH7xmDPonZWGrsWJrzI6cTPa/CjmWmp8bt4+wr1Xt14+\nhlR7Ci3eDBrq9h/jY7AG0NqrqA24eWXp0T3ZN218XyYP6YVNSaK2YACqCvbMIoIRL2u27qOwIvbS\nF0KcaCS5EkKcMuq8QTbsLCek8dNirKXcW8VTC76I+Qm0npkukmxWNC1mmoPmqD5LcgXBZj/Lvy6M\neWkwJ9XBkB4ZGLDgr07v0G9MKqGh2cer899h4MCBPP3002i1Wu68807WrVvHkCFDDhpXURTmXDgM\nR0IivtKeHWbnrOnF+BvreWtF7MVPD5TisnDd1CE4E5Jw7+0bVWneltF6LNCbK7Yd9d6oB2+YQoYj\nnUh9Fr6qNPSGJgyJZfgbvcz75MhragnR1SS5EkKcMnYU1RBsCqExBHD1WUMw4mXFpj2s3hzbHh6N\nRkO/3GQSFAOhDkuDbiLfLQ1+sa005jFNG98Hi95OoCoLs0FPkt2MzZJAkt2M3V5N8KvFbHz7Efbt\n28fw4cNZt24dDzzwAAaD4bBxZ00aQG5qCkrYRaA6I6qvdcnRz6Y9Zewoqol5rAf61aWjyUtLRxtK\nxluxf2+XJamKFp2HvRXVfLpx7xHFbpOZbOOWmWNIMqXj2TOIxqABS1prmYr3Pt8Z15KuECcSSa6E\nEKeMHSW1NEUa0Zvq0RkDmNMK8YTr4tqAPaRneuu+K68rql1RNBgTKwk0+ViUH/tTgzMn9MNlcdDs\nS24vzmkzG/Bv8VPy+D4iRTtA0XLOzBv44osvGDp0aExx9Xot10wdjD3Bhbe0R9TeqKhjdo5wY7vZ\nqOeWy87EZUzBW9S7vTyFogVLWjHesJuXPjr6op8/+9Ewzh7YE5uSSs2OIZgdbiIJ9ZTU1LFiU+FR\nxxeiK0hyJYQ4ZdR4GmhRm9AaAwDYswoJtvj5clsJtfUNMcUY3TcTo9ZE4/dmrgAsKeUEmwMsj+Op\nQZvFwFmDcjHrrPgrs2j2NVM/v4aKlypo8bWQkG3FMOmnhNLHoCjx/Uqec/5QMlzJ0JBEQ110sVJr\negmBZh9LvtxFU3N8T022uWJSf4b2zMGoJuI+4FgcW0YxwYiPNVuLKK6qP6LYbTQaDU/8+gJ6JGej\nCWThLuqJOaUEX6OH1z+LvxiqECcCSa6EEKeMppaW1n1ASmsyoTcH0VnrcDfUs+ggJQ8OZlTfLEwJ\nJpqD9vYjWtoY7W4iOh9ltW7W7SiLeVwzz+6HRWfD+2WAor8XEdgcQJOgIXl6Mlm/TAWnnuKaOj7/\nNvYnEQFMRj2zJg/ApndRX9Ijus/hAaObck8d78WxCf9AiqJw5zUTSDQl01CRR2ND66HWekMjCa4K\nvOH4jgU6lGSnhYdvnEqqJYOG0j5ojQ00NPtZeYRH+QjR1SS5EkKcMppbVFRAo9k/q2ROKSfQ5Iv5\nHD+zUU+PjET0mo77rg5cGvx4XeznAmYaQ3hXP0/z+tVEGiKYepvo9rtuOMc70eoUTEkVBBp9vP95\nQcwx2/z84hGk2JJo8aURrHe0t2s0rct3/sZ65i8/so3t0PoE5Xkje2PTuajb06+93Zreujdq8Zqd\nnXJkzeRh3Zl9/nASDen4ivqgmD14gvW8E8cSrBAnCkmuhBCnjIja8Y+8JbmCcCTIVwXl+ALhmOIM\nzEvFoBgJ13dcGjQlVhNqaWDN1uIfjBMMBrnzzjsZMWI4vvICNAYzxonDyfxZJnqXvv06c1IlwZYA\nqzYXxf0EnstmYsZZfbHpHNQXR89e2dLKCEX8rNtefFTLd3f8+CxSbak0ezIJ1LaWZjC7qono6ymu\nqeWTOA6gPux9fjKB4T1zMatptDTYCTYHWLc99ocHhDhRSHIlhDhl6LQKGg2g7i+sqTeG0Vo81Ad9\nfBxjEjD2u3pXofqkDn0mZy2NapCdJdVUuf2HjPHRRx8xcOBAHnzwQZqamrji6p+SfdGfiDjPJNIc\nXTGJ3z0AACAASURBVLfK5HTTog1QVFnH5r1Vsb3ZA/xy+igSLUk0ujMJ+/efCahLaCLB9V0trRVH\nVvMKIDfdyXXnD8OZkIx7Tz8iLRoURYMlrW1vVOeUTdBpFf5xy4/omdINk85KUyTMt/uqOyW2EMeT\nJFdCiFOGTqsAGlQ1+lebKfH/t3fn8XVV9733P3vvM8+D5sHybMsDxsQGDwViwCSQEChJKSRPCKG9\nCU1oQ+iTNKRpgNLelLS9tNwSbtM2aXiekpJApoaZFILBTDYYPOFZlmTpHA3nHJ152MP9Q7ZsYdmW\n5GNkm9/79dLrBfvss/Y6S5b89dpr/1acgp7l+bfGVzpgzdIZeOxeKpnIUeuuNJuJIzBIvpzjmTf2\nHPXe3t5err/+ej760Y+yd+9eFi9ezMsvv8xPHn6IpfNn4cRP5j2bOSuqhSvcR66S4dfrJ74+qqnG\nzxXL5+CzB46avfLW9pDTMzz1xu4Jt3ukP7n2fGY3NKKVa0a2rPE1dFMws7y8tZN44thBcyLaGkL8\nx59/klk10wk4IygostegOONIuBJCnDWcNhuKMka4Cg9QMops3ju+WaFIwM3s5ih2xU0hFRk5ni8N\nbyfjCvdT0HP89u39I68ZhsEDDzzA/PnzeeSRR/B4PHz3u99l48aNrFq1CoDfX7MIvyNELjaN9+YF\nTzR+8EnEjkl8crj1d5cTdkUoDraMLDwH8Eb6qSg5dnT18e5JzAK5nXa+dv1qoq46Mt1zqRSdOFwl\nHME4Q4Whqs1eAcxtjfLY3dfxFzdczt/eshZFUU78JiFOIxKuhBBnjUjAhYqGqdtHHXf60uiU6OpP\n0Z/KjautC9pbcGluiqnDtwYLpQr5UgVPZICiWWDjrl5M02T9+vUsX76cW2+9lXQ6zcc//nG2bdvG\n1772Nez2w3355EXtNIQiWIUIxXRw1PXc4X4qSp5d3QPs7UlM+LPPbony0fPn4rOFSHbMHTmu2iyc\n4RjZSnrS2+Ec8onV81i9cAZeJUxi3/Beh57aXvJ6huc3dZxU2+81ozHMl65ZznlzG098shCnGQlX\nQoizRm3Yh021YVZGVzdXNQu7N0VRL4x74+WLl7ThtnkpDtWM7AmYTBdJpAvoWgrsWeLxbq669jpW\nr17NW2+9RWtrK4899hi/+tWvaGtrO6pNp8PGFRfMwWvzk+mZNuo1zWbhDPWTn+D+hUf60+tWEvXU\nUBpsoZTxjRz31vWSr2R5ZsPek77FdufnLqbWW0dlcBrZ/jq80T5KVoEt++LEj7MGTYgPEglXQoiz\nRl3Ig6ZqmBXXUa85AklKeoE3dozv6bNVC1sJun2Y+SB2y4vbacfltFEs6RQKZcyOV+h94rs88cvH\ncDqdfOtb32L79u1ce+21x72NddNHlhBwhigmmtDL71nYHo2T13M8/1bHhD73ITMaw1y1ch4Be4hk\n55yR457QALqWoSM+wFu7YpNq+5B502r4w48tI+KsJ7lnMZap4ggMkC1neOKViZeSEOJsJOFKCHFa\niiWy/HZTB69s7aJwcK3TiTRGfGiKDaty9L58rkCKklnknT3xcbXlcto4Z1YDTs1NPlmDx2knEnDj\n64fcvw5Q2bgVSy/TOPdDbN26lXvuuQev13vCdme3RFk2twWX4icTax71mjfSR/nQLNAkF4jfft1K\not4olUQTxXQAGN6y5lAtrV9WoW7UVz+1guVzp+O2ahjYtfhgKMzy3EnuNSjE2ULClRDitJNIF/jJ\nf2/mm//ncb79L0/z+Cvj28S3Keofvi2oO49aMO4KJKmYJXZ1JyiX9XH148LF03BrHgrJWiqJCkOP\nDJD9cYJKfwVb1IHt/E8QXHETjc3TTtzYEW64dDF+R5BcfPTCds2hYw/0ky1nJl1VvbkmwO/+TjsB\nR3jU2itPzcktmD+Szabyd7dcTnOwESPVgllxUDIKvLmrh1xxfEFYiLPZuMLVunXruPrqq2lpaUFV\nVR566KGjzrnrrrtobm7G4/GwZs0atm2bfEVgIcQH22/e3Mv/+unLbIl18UbHXv7qoRfY1T14wvf5\nPE48LieKpWEZoxe125wVVFeWTDHHxp294+rHR86fhUuxkV+/j86/6yS3ZXjbmugVUdr+tBX7jDCZ\nYpaXNndO6PNdtXIuzZEoSilMIRkZ9ZonGidfyfKbk5gFuv26ldQHajHSDeQTw+27g4PoWpb98cFx\nz94dz+yWCLf/3iqirnqyPbNAq5AuZNm0L3nSbQtxphtXuMpmsyxevJj7778fj8dz1Ov33nsv9913\nHw888AAbNmygrq6OtWvXksuN76kcIcTU2769yFNPHftr+/b3Z4+3RLrAQ09vIlkcRAntp+LupTvV\nzw+f2jSuxdghnwsFDaM8xrorf5KSMb51V4Zh8N+PP0bvE/di7nwTS7fwneuj7WtthNeEUWwKzuAg\nRT3PKxPcE9BmU7lq5Tx89gDp2OhZL0+0j5JZ4M1dvaTHWVH+vWpDXj5z2TkEHVGSHfOxrOFbg65w\nnFw5w3+Nc5/FE7npo0tYs2QOQbUOy9ComGV6k+PbIFuIs9m4wtUVV1zBX/3VXx1zoeY//uM/cscd\nd3DNNdewYMECfvSjH5HJZHj44Yer3mEhxKmxfz9ccYXrmF/795+4jWpY985+3trdTUlNE5nzDuHp\n28kZaZ54dee4yiiE/cPlGIyxFrX7U5SNEu92Hn8W7Nlnn2Xp0qV84QtfoJJPo4Wb8V2zgoZPN2AL\nHl6E7gykKBkltuyd+EzQjR85h4AzSDnRgF5yjBwfriifJF3M8N9vTX5bmT/53fOZFq1HydeSiTcA\n4KmJkTey/Pc4i6meiKqq3Pflj7BszmyC9ihYkMzJbUEhTnrN1b59+4jFYqxdu3bkmMvl4qKLLmL9\n+vUn27wQ4gPm2Y17yVXSeOs70RxlXOFBFHeCgcwQ67eceD+/upAXTdEwSu6jXnN4slTMMvt6x751\ntW3bNj72sY9x+eWXs3nzZtra2rjjr/6B+stuRbe3j7mOq2wW2dE1iK5PbPPiafUhVi6chlv1k+5t\nHd1uaICinmPdOxO73Xgkj9vBFz7+IULOGoY652EaCp7wIDp59sUSHBhIT7rtI0WDHh76xjWsXbqY\nFfNmc+nihqq0K8SZzHbiU44vFouhKAr19fWjjtfX19PT03Pc927YsOFkLy/GQcZ56pxJY5/JtAFH\nz/Ycfj3Dhg3Vq8I9lopusu6tXRSMPEF/F8Xi8K1Iuy9Grq+JXzy/kRb38WevbEYOTbGhF30Ui6PD\niWUbpGKW2dkZ57XXXkfThv99mUgk+P73v88vfvELDMPA6/Xy+c9/nuuvvx7NZuexbS8zkPaTSThw\neI8MJUWwZelLJXjk8eeZ1zy6MOiJXDDdzbMbvCR6WnHXbUdRhwOazRsjXcnx2zd38sYbkUlXKF9c\na9Lo95LsCzHQ0UqgeSead5B0ro6HfvECa89tOnEj4/Qna1vRDQuXQwPOrD/7ZyMZ/1Nvzpw5x3xN\nnhYUQpw2DiTz9A3lMdUidt/hKuV2/yAVq8TeWOaEbbREPNgUO0ZxdFmETKGCZi+DrUChXKYnmadQ\nKPDDH/6Qa6+9lsceewyAT37yk/zsZz/jc5/7HE6nE5umcu70ME7FTSFxdBix+ZKUjRJbu4Ym/HnP\nnx1lWjSITQ+SGzi89srhH8RQS/QkcvQmChNu9xBNU7lxzSyC9giFnvlU8j7svkHKZolt3RPv7/HY\nNHUkWAnxQXfSM1cNDQ1YlkU8HqelpWXkeDwep6Hh+NPDy5YtO9nLi+M49C8XGef335k49gMDx1+w\n7vf7T/nn2fncO1iaicOXxu05XKtKixTIKDqpIpx77lJstuP8Je5r5H8/tRmj6MflOjwTN5ApU+ty\n4fDlsAo6Tz/3PL/8j+8Tiw0X1bzyyiv527/9WxYsWHBUk583Q7y8O87gUAvO2R0cOZHkDqXRMzqJ\nsmNS4/PHKSff+NcMifhcoq2xkbZdgSRmoYkBw88nli2dcLuHLFsG2/stHn25Qmb/MoLTdjEUq9CX\nU07J9/NM/LN/NpHxf/8MDR37HygnPXM1Y8YMGhoaePbZZ0eOFYtF1q1bx+rVq0+2eSHEB8g7e/oo\nmwUcvtSo4zZnCWwl0oU8HbHjz7jMba3BrtoxSl5ME1LZAt39aYolna6+Icqd2+l76j7++e//klgs\nxvLly3nuued4/PHHxwxWAJeeN4MafxCrGKKcGz0j5gqkKJsltk9yU+Tr1yxiWk0tailMbuDw8gpX\naICikef1d8dXUf54/voPLmF6TSNKroFSJkSFEnt7E2Tyk3saUQhxfOMKV7lcjrfffptNmzZhmiad\nnZ28/fbbdHUNLy697bbbuPfee/n5z3/Oli1buOmmm/D7/dxwww2ntPNCiNNbrlBmy74+Xnx7P2/u\n7CVXKB/3/K7+ISpm5T3rmkBRwObKUjEq7I+njvHuYQGvk7DXhWrZ0QtuQj43zTV+7D0G1sNDVF7c\nhJlLEqpr4dFHH+W1117j0ksvPW6bdpvG6kWtuDUP2f7RM/KHN4Ueom8Se+vZ7RrXX7oIvyPEUNfM\nkUXzrlCSkllk8974uAqoHk8k4OZbn72IqLue7IHZYEGxUmTLvskFQiHE8Y3rtuCGDRtYs2bNyKLK\nO++8kzvvvJPPfe5z/OAHP+DrX/86xWKRW2+9lWQyyQUXXMAzzzwzrq0ghBCnh7Y2ePLJY98aHGMf\n4uPqS+bYsOMAnV0HGEoPEfD7GUxP53cWT8PttI/5noGhPKZlYHMd3Q/VXsao6AymT1xHqTHsZk/S\nTinnxxhIMPjkIJW9w22qPge22R/moitu5JOf/OS4P8/HVszll69sZnCwEWbsOdwvzcLuS1GsFHh1\n2wE+sXreuNs85OYrlvLDJzcx1J8gn4jijQ7i9KUxlRIHBofoiCWZ2RQ5cUPHcfXq+Tzx6i5++WqR\nRCmOaZmUKuOrVC+EmJhxhauLL74Y0zz+Y8bf/va3+fa3v12VTgkh3n/t7S7a26vT1oH+NK9t62TX\n7t3YjCLNQQcHEn3s02w0Rf0snFE35vsG0wUMS8fmGDtcmZbBYPrEC7xboh6UtxIkHt1FpWN4dkZ1\nq4QvCeM+t4H+zQvoTUys2OVlH5pJ1BdiYCBIKevF6Tv81KLDn6LUV2Djzt5JhSu/x8l1H17IP/6i\nn6Gu2Xgigyiqhd2fpFjI8/KWrpMOVwD3ffmjpLJF1m3VcNldBDxH78EohDh58rSgEKKqcoUym3bH\n2LFjBwFbhTkNHoIeO9OiLvr6++juT495m6tQqpDKFjExhtdYvYdmL2NYBsnM8cPVO++8wys/+yfy\nL/6QSkc/il0hfEmYtm+0Eb44jMNXwrR0ktnChGpTOeyHbg16yQ2MvjXo8qcom0W2dvSNu733uuUT\ny6gP1mBm6yikhoOUK5CgZBTYsOP4ZW3Gy+Oy88M/u4ZvXn8p//uPP8Z5cxur0q4QYjQJV0KIEzJN\ni97BDG/vjvHK1i5e2NTBG+8eYFf3IBXdGDnPsize2h1jX0cHLlWnJeIaWU7gc9lQzQqJ1BCJMQLS\ngf40ullBdZRQ1KPD16GZq2Rm7FuXmzdv5lOf+hRLlizh3U2vgWpDm72Qtm+0Ef1oFM09/IShqoFi\nK6MbOrHkiUs7HOljK+bgtfvJDzSOKijq8GaomBU6+4bGtUXPWCIBN7938QL89hCp/XOwLHD40lTM\n8gkX8U+Ex2Xn1mvP58oVx67RI4Q4OSddikEIceqZpkVfKkc8kSWdL6EbJoZpoRsmTrtGxO8m7HcT\n9rvwV/FWT0U32H0gQWd8iIFEkkQiSbFURK9UcLncBIMB9jTWs2xeMzVBD119abp6+0kM9jOz1sNL\nO5L0pEo0hZ0snxHE49AoFksUSkdvkXJgMDMcruxjhyfNVqZsGaSyo1/funUrd999Nz/96U8BcDqd\nXH311bxanE/MSmE5ngNGL6TX7GV0UyeWyNFSO/7Cn2uXzaI2EGKwL0QpHcAVHF54b/cUMJUKA0M5\nBlJ5asOTW2/6pWuW89PfbmP3wBC5vkacvgyGpRNPZiiVdZwO+ZUtxJlAflKFOI0ZhsmuAwn2x1IM\nJFOkkkmy2Sy6bmCaJqZp4nDY8fn8+Hw+/H4fdZEgc1oiNER8k67sDdDdn2bLvjg793azbU8X6VyB\nqM9Ba8RJW8RNWS/QFxticHAQ07S4aMl0tnb00dHRQbFk8PdP7iOeS1M2y7hUFxv3RbhySQ3lSpli\n+eiF1PFEFt3U0cZYzA6g2nUsyyR9sHzA9u3b+cu//EseeeQRLMvC4XDwhS98gW984xv09vbyZw9t\nJNFZpDgUwl43+nad6ihilHRiiYk93eewa6xdNovOZ3rIxFtxBbcCoCgWNneWsl5iW+cAF08yXEUD\nHr7w8Q/xnYdTDO5rp+HclzExGBjKk8mXJVwJcYaQn1QhTlPpXIk3d/XS0d1Ld3c3mlkh4rPTGrCh\naTY0RUFVoKSbZItpUn1JOvfr7PcHOBBvoqE2wpyWKM01/gmFLMMweXNnL/+1fhvPvb6DzoEMllLB\nxEBRVByKncagh08ub2B+o5edsTydXQf4jWGSTCbZ0jHI+t2DJCoJLF8Md6SPZG8b2+MW9R0OfidU\nhzHWmquyjmVZKJoxRq+GA4wFJHr2cd111/Hoo4+OhKo//MM/5I477hgpZNzb28ucxgBvH3BRSofx\nvydcafYyRsGYVOmEz1y6mJ+8sJnegSaMmdvRbAe3rPFkKadL7Ojs5+IlE3y08ghf+Ph5PPHqLl7e\nkSbVORvFUaSsl9nfl6Im5Jl0u0KI94+EKyFOQx2xFO/s6WXvvg5yQ0lm1rrxu8fe989uU/G5hn+U\nTcuiP11i98536e72Eetvoa2pjqVzGo5Z/uBI+WKFn6/bzoO/fJWd3XHKSo4SORz+JDZXHtOwMZQJ\nkRoM8b3fFPkfH57G3AYv73T1MFDU6D3Qxcu7EvRX+vG1bcXfvBdFGX6aLrnVx5v7vFyw0BhzXVK5\nYmBhoaijw1UqWyDkc1PuTlN85VGe69s3/Lntdm6++Wb+/M//nNbW1qPaWzgtxK83uUlkwke9pjpK\nGJZOX2piTwwCLJndwKLpDQxuj5PtayTYNFzk0+7Ooacq7I+f3Pooh93Gt2+8iM/8z34OxAuYGBhO\ng4FJ9FUIMTUkXAlxmunqG+KNbZ3s2LmDgMNkYYsPTR3fzJOqKNQHndQGHAxmK+zauYNkMkUqW2DZ\nvGbqjnO7Kp0r8j//Yx0//s0mksVBdEeSQPNeInUH0OyH10hZpsJQ51wGeubz/72s8fUrZ2KaJvu7\ne3luYxdJcxBP8w4CLXtH3uMMJFDcCVKlEPv7M2POpJUOhSvl8BN8lmUxtC1LduMgxX3Dtws1u5M/\nufVL/Omf/inNzc3H/DyL20K47R70TAhTV1BthwOddjBcDQxNLrB86qJ23tzdQaq3jUDjARQF7K4C\nebNCd3/6xA2cwIqFrXz60iX82xMFEuU+VDQCXimbIMSZQsKVEKeRZKbAW7t62LlzJw0+hfrg5G4D\nqYpCrd9ByG1jX38/m7dmKJbKnDO7idnNR9dLSmeL3PbA0zz5+lZSej+ehr3UTt+Bajv6Fp2iWgTb\ndjBY8DKYdvPSziRhr52XN+9nSM+AP0awbefo9xycvaoUKmRLJu4x1g7phgmWBaqFZVr0bUySfTGN\nFdepADg17G3nc+XVf8D/+u4fnHAMfC470+tD9GScFDMhPOHkyGuavUTZNBicZLi6bs0i7v/Z6yT7\nohRTYdzh4Zk93dLpneA6rmP5xg2ryeSL/HLdNhZOr6F2kn8WhBDvPwlXQpwmimWd17cfYOfO3QSd\nJvVB90m3abepzGnw0JMqsWXrVnR9eCH5kQErmy9x89/+inVbdjBk9BGZuwlvXey47SoKBFr2MPhO\nM6/tTtHe5KE7maPsGqJxzjuMtcTL5ipQsgzyJROPa+xblJahU97RRecvOqn0HZwt8yhEL46gzp5N\nofNC/KGjb/Mdy+KZ9WzY56KYfm+4qmByeHH8RHlcdj6+ai5dv+4l3dM2Eq5MS2cglUc3TGzayVW6\n8bod3HPzJVy1ch6aptIY9Z9Ue0KI94+EKyFOE9s6+tm3vwurnKW1sXpbRymKQnPYhctW5t0dO1BV\nFZumMr0hRLFU4Sv/9BQvbd3JkNVD7aI3cAXHt2bI7hvCcmZI5Eu83VFCVwu4a/djc489G6RqOqZl\nYlgKnves/0okEjz7s38n8dR/YJWGZ35sIRuhD4ew2h2Ewx7SMQcKCk77+H9tLZ/fxI9/6yadqoG2\nfUeMiYllDZeymKw/uGIpP/7NO3QmGylnd6E5y1hYVHSDUlnH5nZMuu1D/B4nl35o5km3I4R4f0m4\nEuI0kC2U6YgliMdjLGzyoE6ihEIqX2F3LM9AtkK6oFMoGzhtKiGvjaDbTnPYSVNA5d1330VRVFRF\n4YFfvM6Tb2wjpccmFKxgePbK7s5RKOgMZU10Z4FI497jvGF4TZWJMrK4fs+ePfzDP/wDP/jBD8jn\nh0OZGvFTc5kb/1I/inZ4HCxDQ1FU7LbxzwhdvmwWvh/6SWRqMMo2NId+sO8WYKEbk98Qua0hxEeW\nz+E/f5tgcO8C6ts3AcMPFZzcNstCiDOdhCshTgO7ugeJx2KEPSpO+/jDQyxV4o29Q7zbm+NAskDR\nLFKxKhjW8BN5iqKgKRoaGk7VSb3fw4xaN+nCZp7esIfHX3uXRDlGdP5bEwpWh6j2EoWiiaHksUe6\nsLuLHGvjB6PiQFU0wn4Xr732Kn/3d3/Hz3/+85EnBxedt5IuzxyM2RkCCzaP8X4XmqIRDYx/7VE0\n6GHxjHpimw+QS9QQaDh4u1M1seCkZq4A/uyG1fx2Uwe7Exlyg8P7JVqWNekq7UKIs4OEKyGmWK5Q\nZn8sSTweZ1Hz+G4HdieKPLtlgE2dQ+SMHAWjQEUp4AwO4vBmcDiKKLYKlmHDKLkoldykh6IMJvx0\nDHnQdrhJFw3KtkFCszbjqZncnnhmxU5FN7FcRYKNu0fNuOVLlVG3/8p5F2bvLh7/3q/4P7cPF9+0\n2+185jOf4fbbb6cz6+R/3Pcoaf3oYAVglFw4FBsNYd+E+njxuW28vH0H+cGGw+HKUlAAdZxPYR5L\na12Qm644l7//aYqBXYtRD86sSbYS4oNNwpUQU+zAQIb+/n5CHu2Es1a5ksFjb8TY0JEko2fImxnc\ndV0Ea2I4A0kU9dgzMZYF5XSYdO80Mp3zsZQ8SngXtugeYHLrg8rZEKZaQfPFcXgzqOrhdgoHw5WR\nM0i/nib94m+wcnmyQDgc5pZbbuHWW2+lqalp+LNt60ZTNEx97MXuesmNW7XRVDOxhd2/e2E79z/2\nKqlUPUZFQ7MbWJYKKNhOMlwBfPnq8/nNxn28vrOEburMbanBaddOul0hxJlLwpUQUyyezJJMpmjw\nHr/I57s9OX78Sg892RRpM4G3YT8NzfvQHON74k1RwBlMYk/WglbAcgxh1W5gcMhCU1Vck9hapZzz\ng1bGHu5BU4eDYb5UoVCqkNydJbc9SXlrEfThqRzNF+W2r3yFu77xVXy+0TNQtUEPmmrDrIwd9Iyy\nE5tqp3mC4WpaXZDFMxvo29JLdqCeYGMPmCoKYJvA+q1jcTltPPjVj/GN7ztIDGW59sJ22aZGiA84\n+Q0gxBSq6AaDQzlyuSyBY4QGy7J48u0BntoSH95Sxhujfu7b2FyFCV9PL7pId83CUguozeux7Hkq\npo3+oRxNET/aBMoH6CUbRtkFziSeSBxNU7F0C2N7kexLKegsjWyX7J7noRxew7QZl3LnHV/CN0ZB\nzNqQ9+DM1dHhyrLALLuxuWy01AYm/Lk/tmIOr+3Yw1DPDAINPVQKXjTFRl2oOk9ltjWEeOC2j5PI\nFCbVPyHE2UXClRBTKJEukM3m8DjUMauwm5bFo6/H+O3OPgYq/fhbd+Bv2TNmHanxSO1rR68o4I+j\nhvYAYJShoqsks0VqJlCoMtfXiqIY4BxCMwoM/SZP+rU0Rma48KjiVAgsDxBcGaTiiJLaMo/W2hD+\nY1Qa93scOOx2MG0YujqyZx+ApdvBsOF2OIgGJl7/69OXLuZfHn+TdE+STLyJcs6PQ3Myp+XogqqT\nFQm4iUyib0KIs4+EKyGmUCpbJJvN4ncdvUbHtCx++lqM3+7qY1CPE5m/EXekf9LXKud85OJNWGoZ\ntfH1kYCm2ssYZY1soYzf4xxZL/TeBenvlY21YiV3oexaR9+v4nAwC6k1NszFDoLLA3j8ThxOO5n9\nUVyam+Xzj71djaIo1AQ9dKRswzNL/syovmuKnbqwb1K33LxuB1/42Hnc+dAAgx3zsQwbXoeT9mm1\nE25LCCFORMKVEFOoWNYpl0t4x1jI/vy2BC8eDFbR9tdxhRInda3MgRkYpgmhTlRvfOS4qlpYWgXT\nUEllC9SHfSPrpsYKV3paJ/1GmsKLj0IhPVzTSQXvQi/B1UHcs9wkMoWRkgmWZVFK1hKyebl4yfTj\n9nFGQ4i3Ox2UcwFcR4SrYiaEXXEytyU65r6E43HTR5fykxe2sXFvgbJVoiVaw4oFLZNqSwghjkfC\nlRBTqFQxqFQq2F2jw9W+/jy/3hRnsDxIpP3Nkw5WpqFRGGjAUgzU6PajXldtFXTdTrGskyuWSWaK\nFEvDBTfdTjtuu438ruHbfrltuZFZKlx+PMs91F3kxhY8/OvEfUQoKxVt6LlagiE/Hz637bj9nNsa\nxbHRSTkTgIYDh9tIh3BpThbOmPxMk82m8m9f/wS3f+9pEuk8N1/5IaKyX58Q4hSQcCXEFCpVdCoV\nHbv38GxMrmTw0LoeBsqDeJp24Y5MrgbVkYqDdVSKLrCnUHwHjnpdUUBRDQxTI50rUSzpuJw2HCWF\n4hsZ+l5PoyeHwxYq2Kc3ogfXQHOI8AXPYXOPLgFxaMbLsizyiTrcmpcV7a34PWOvtzpk6ZxGml2z\n+QAAFRJJREFUnJqbZPrwWijLVCgP1RCye1h5kjNNrXVB/v9vXkupYhA4xtovIYQ4WRKuhJhCIzNX\n2uG/6J96p5/uTBLTEyPYtvOkr2FZCtm+ZixLRwl2HLMWlqIZWLqFYoC300Tfkia+p8ihvVxsERuB\n8wN4l0SJv3s5arYGxR7D7jCAsW/V6QYU+qYTdQT4+Mq5J+zrivZmvE4PA+kARtmJ5ihRSkdQTTfN\nNSHmV2GNlNNhk1IJQohTSn7DCDGFKrqBYRojTwomshXW70qS1tPUzt6Mop58qW+j7KSUjGCpOmp4\nz5jnWJYFPQbW2zmyO1NQPnhdDbwLvAQvCOKe7UZRFRJ75mPTA2gOBctVPO6Ti/lUGKVQx7TmWq5c\nMeeEfY0E3Jwzs4HY272kD0wnNH0HQ52zcStezm9vwe85+c2QhRDiVJNwJcQUsmkqqqpiWhag8Mzm\nAYYqGVw13Ti82apco5LzoZedWPYMijc26jVryMLcYmJuNiF5+Lij2UFweRDfuT40z+EnGSsFF9lY\nGyF7EEvTyR+ngKlhWuR7ZhFwhLnx8iXjKlKqKAo3XLKIV7ftY6C3DQUFPV1Hoy/M769ZNOnF7EII\n8X6ScCXEFLJpKjZNQzctykWd1/amyOhp6qbtqto1SukIlmWiuBIoioVVtLB2WphbTayOI2bGfMB8\nB/ZFbqIzg3ic9lFhxrJgcM9CvEqI8+a2sL27h7w19j56lmWRG/JhZJpoqI1y/SWLxt3ftctmsWzu\nNNZtzVPq9eBXAly5aj7nzKo/iVEQQoj3j4QrIaaQ3aah2WwYhsW2niwFo4Aj1I/dna9K+6ahUsl5\nscwy9L2LvlnH2m2BcfAEDZS5CupiFdo0TN2DomqYpolpWmja4XCV7WtATzXRFmng1muW8yff+y8s\n04bF8KzbkSqGRf7APILOMJ++dDFBn2vcfQ54nfy/v78K9T8r7D0wwMpFbfw/ly3B55ZbgkKIM4OE\nKyGmkF1T0VQN3aywuWs4XLmjsRO/8RiOLPxpGRa57UVyL76B1XUAjMrIeco0BXWBitKuoLiGg5Fp\nDO+3p6kKpmlhWBaHbghWSnZS+xZQ46zjlk8sZ9m8JhyaA7PgxjAtjtyn2DQtMvEmrMw02hoauPHy\nJRP+HOe3t/DV6y8mkS5QF/ayZHbDZIdECCHedxKuhJhCDruG3W6nWC6yozdL0SwQisRP/MZjSOeK\nKD06mU0Zsu9kMXNHPBlY40ZdUkJtV1H8R69dsiwVUNBUBevgzBWAoav0bV2Gl3rOm9PGLVctQ1UV\nAm43DLkpF104bGVURcEwLXJpN4WuJTR7G7nj0xdSH/Edda0Tcdg1LjynDcMwJ7TfoRBCnA4kXAkx\nhfweJx6Pm87OAYp6BdWVRXOUT/zGI1iGRWpnluzmDKXtBbK5w4ug7DVOqJuLHl2MOm87au2W47Sj\noqJg1xRMazhcmQb0bVuKo9RCe/N0vn/7Vdhsw2FnzdLpdPymm8rATIrObaiKQjnvJrvnAqKOJq5Z\ntYirV8+b3MAcJMFKCHEmknAlxBQK+Vx4vT7iQyV0S8fmzo3rfZZukd+dJ7c5R3bb6BkqNajhWewl\nvCyIEgyT3DmHXCKMVfYfuz1LAUtDVRQcNpWybmKYJv27FqJk25hZ28YP/+waGqKHZ6E+feliHn/t\nXfbGZ2FzlTAqdgo9s4k6G7iwfR733LxGnu4TQnwgSbgSYgoFvcMzV8m8jmEZaMcpbWBWTPI78uS2\n5Mhty2EWDwcqe40d72Iv5TaNxvbQSKipFEC1l1AsBbMQPWbblqGhMBysVGU4aA3tORd1aDZt4Vb+\n+faPM6clMuo9i2fW8fsfPoeHnzfoPxDArmg0BKP87uqFfP361aO2wBFCiA8SCVdCTCG7TSPgdaNp\ntoO1ro5dNLT7n7op9x6+ZehocOBb7MO72Iuj3oGiKORLlVGzRapNxxnIku1VIV+HVQqgONOj2rUA\n07ChKioOm4JedpDdcwFafhpNoVbu/+MrWT6/+aj+KIrCNz9zIQvaanlpcychn4sPnzudi5Ycf/9A\nIYQ420m4EmKKhXwuwgEvoGLqxy434JnnQdGU4UC1yIuj9uhzPe+ZLVJtZTS3gcM5SEkPYPasQJ3+\nzKiq6pahgaWhKSpmehrJ7nNxVKLU+er4hy99lMs+NPOYfVJVhWsvaufai9on/LmFEOJsJeFKiClW\nG/JQFw2BqWBWjh2uoh+NoqgTW8OkKGBz5XHX91LpCmGkWzE716A2vgH2LChglHyo6ZmY6dkUirUE\ntTCtUT+/v6ad2c2RE19ECCHEKBKuhJhi9WEf01vqUbBRzvmxTGXMPQUnGqwOcXjTGFE3RmEP2f45\nWInZGKkZYCsNl1/QXWA68Nv9hL0+rlpaR3uTF91ho2KMvcmzEEKIY5NwJcQUc9g12ttqaQj5ySY9\nlNJhXKFE1dpXVAtXaAAUC7t3O7n+JiqFEGbZB4YDm+pkXqOPNe0RLpwfxmXX6M+UKeoGFd048QWE\nEEKMUpUiMnfffTeqqo76ampqqkbTQnwgtNQGWDyzHjsuCoONVW9ftem4I3F8LX3ULNpGZP4WbC6d\nuoCbWy5p5a9/bw5rF9fgOlRq3Rq+pSilFIQQYuKqVqFv/vz5xONxYrEYsViMzZs3V6tpIc56jREf\nF507C5fqJRefRqXgqfo1FAVs7jyqTSfTPYcaV5gL59Vy2aKao0JUxTCx2+04j9zXRgghxLhULVzZ\nbDZqa2upq6ujrq6OaPTYNXWEEKNpmsqqRdM4f24zHgKk9rVjHbsqw6SV0iH6Nq8grDRyXkstN6xs\nHHN2qmJYB8OVrBwQQoiJqlq42rt3L83NzcycOZMbbriBffv2VatpIT4QZjdHuH7tUny2AHqymUz3\nsUsgTJRlQbp7JgNbVhJRGlk+rY7PX9SM/Rjby1QMC5vNJjNXQggxCVUJVytWrODf//3fefrpp/nX\nf/1XYrEYq1atIplMVqN5IT4QnA4b58xs4FMXziWoRsl2LiTdNfOkZ7D0gof+LRdQ7DqHekcja9ub\nuOmiZuy2Y//4l3UTu8OB0yEzV0IIMVGKZVX/5kM+n2fGjBnccccd3HbbbaNeGxoaGvnvXbt2VfvS\nQpzRyrrBazv7eWr9Vt7pLZK2Uij+GP62Tdjc2Qm1pRd85HrnUk5Mw4uPWqeXtXOdzIgcfzbKsize\n7TOYO38+q9vrcdhk9koIId5rzpw5I/8dDAZHvXZK/lnq8XhYuHChhCchJshh02iOermgvRmX1sW2\nvgiJrIvk1iiOSDeu8AEcwT4Udez6U0bJQylVT3mogcpQAx7FQ0DxsLDezkUzHbjtJ376r6iDw+nE\n53ZIsBJCiEk4JeGqWCzy7rvvcskllxz3vGXLlp2Ky4uDNmzYAMg4T4WTGftzDZPopg5CoW1cXM7y\n1v40L+9KkM9EKKTmkFHy2Fx5NEcRzVHCMjWMigO96MEq+XBrLgKqC6/XzQWzwly6IELUf+zK7+/V\nkywStAdZtewclsxumHD/TwfyZ3/qyNhPLRn/98+Rd+Leqyrh6mtf+xpXXXUV06ZNIx6Pc88995DP\n5/nc5z5XjeaF+ECxaSpL5zQylM2zZcsWrlxSy5oFUd7en2HT/jTdyQK6rmNUDIysgaKoaKhoiobf\n72Reo5f5TV4WNPnwuyf+I57K6zS3hamP+E7BpxNCiLNfVcJVd3c3n/70pxkYGKC2tpYVK1bw6quv\n0traWo3mhfjAiQTctE+vJ5vNsqdjL4tafFy2KMpli6JkizqpvE4qXyFTMHDYFLxOjYjPTtTnQJvk\nNjkA2aJOyVQJhQLUBKtfa0sIIT4IqhKufvzjH1ejGSHEEea11tCXzDE0lGZXLMHcRg+qouBz2fC5\nbLREXFW/Zk+yRFNjE7OaItiOUaZBCCHE8clvTyFOU6qqsGxeE3Nnz8TmDrAnnucUPNw7IlcyyOkK\nDQ31zGwMn7LrCCHE2U7ClRCnMa/bwcqFrcybOxvT5mVvf+GUBCzLsugaLNLY0MCMhrDUtxJCiJMg\n4UqI01zA6xwOWPPmUsbF3v4ChlndgNWdKILdTUtzE7OaI1VtWwghPmgkXAlxBgj73axc2Ep7+3ws\nu593e3KUKmPXupqowUyZRAFmz57N8vnNuGTWSgghTor8FhXiDFET9HDxkul4nHb27u9i64EDTIs6\nqZlADav36kuX6E5WaG9v59w5TfKEoBBCVIGEKyHOIAGvkwvPaSPgdRIIBNi7bx+xVIbGsJOI146i\njK8MQ8Uw6egvUMJB+4IFLJjRyAxZxC6EEFUh4UqIM4zDrrF8fjP1YR/hYIB4/wA9PT0cSGSpDzrw\nu2y4HeqYQatQNhjMVuhPl4nW1TNv2jTOnd1Ac21gCj6JEEKcnSRcCXGGmlYfpKU2QGdflN31tcT7\nBxkYGCQ2kEEvl/A6bWgqmBYYpkXFMDEVG9FIhPkL62iuDbN0TiMel32qP4oQQpxVJFwJcQZTVYXp\nDSGm1QXpGRwuOprIFEjnCuRyOUzDRNVUVFXFbrcT8HmpD3tpqw8RCbinuvtCCHFWknAlxFlAVRVa\nagO0HLy9VyzrpLJFTNPCpqloqoLdpuH3OMa9LksIIcTkSLgS4izkcthokI2XhRBiSkidKyGEEEKI\nKpJwJYQQQghRRRKuhBBCCCGqSMKVEEIIIUQVSbgSQgghhKgiCVdCCCGEEFUk4UoIIYQQoookXAkh\nhBBCVJGEKyGEEEKIKpJwJYQQQghRRRKuhBBCCCGqSMKVEEIIIUQVSbgSQgghhKgiCVdCCCGEEFUk\n4UoIIYQQoookXAkhhBBCVJGEKyGEEEKIKpJwJYQQQghRRRKuhBBCCCGqSMKVEEIIIUQVSbgSQggh\nhKgiCVdCCCGEEFUk4UoIIYQQoookXAkhhBBCVJGEKyGEEEKIKpJwJYQQQghRRVUNV9/73veYOXMm\nbrebZcuW8dJLL1WzeSGEEEKI017VwtUjjzzCbbfdxre+9S02bdrEqlWruOKKK+ju7q7WJYQQQggh\nTntVC1f33XcfN998MzfffDPz5s3j/vvvp7GxkQcffLBalxBCCCGEOO1VJVxVKhU2btzI2rVrRx2/\n/PLLWb9+fTUuIYQQQghxRqhKuBoYGMAwDOrr60cdr6+vJxaLVeMSQgghhBBnBNtUXnxoaGgqL3/W\nmzNnDiDjPBVk7KeWjP/UkbGfWjL+p4eqzFzV1NSgaRrxeHzU8Xg8TkNDQzUuIYQQQghxRqhKuLLb\n7XzoQx/i2WefHXX82WefZfXq1dW4hBBCCCHEGaFqtwVvv/12brzxRpYvX87q1at58MEH6e3t5Ytf\n/OKo84LBYLUuKYQQQghx2qlauLruuutIJBL89V//Nb29vSxatIgnn3yS1tbWal1CCCGEEOK0p1iW\nZU11J4QQQgghzhayt+BZ6F/+5V+45JJLCIfDqKpKZ2fnUeekUik++9nPEgqFCIVC3HjjjfJ0SRXJ\nVlDvj3Xr1nH11VfT0tKCqqo89NBDR51z11130dzcjMfjYc2aNWzbtm0Kenr2+c53vsP5559PMBik\nrq6OT3ziE2zduvWo82T8q+973/seS5YsIRgMEgwGWbVqFU888cSoc2Tcp5aEq7NQPp/nIx/5CHff\nfTeKoox5zg033MCmTZt45plnePrpp3nzzTe58cYb3+eenp1kK6j3TzabZfHixdx///14PJ6jXr/3\n3nu57777eOCBB9iwYQN1dXWsXbuWXC43Bb09u7z44ovceuutvPLKKzz//PPYbDYuu+wyUqnUyDky\n/qdGa2sr3/3ud3nrrbfYuHEjl1xyCddccw1btmwBZNxPC5Y4a23YsMFSVdXav3//qOPbt2+3FEWx\nXnnllZFjL730kqUoirVz5873u5tnnQsuuMD64he/OOrYnDlzrG9+85tT1KMPBp/PZ/3oRz8adayx\nsdH6zne+M/L/hULB8vv91ve///33u3tnvWw2a2maZv36178eOSbj//6JRCIj4yrjPvVk5uoD6JVX\nXsHv97NixYqRY6tXr8br9cp2RSdJtoI6fezbt49YLDbqe+Fyubjooovke3EKpNNpTNMkHA4DMv7v\nF9M0+c///E9yuRyrV6+WcT9NSLj6AIrFYtTW1h51vK6uTrYrOkmyFdTpIxaLoSiKfC/eJ1/5ylc4\n77zzWLlyJSDjf6pt2bIFv9+P0+nkS1/6Ej//+c9ZsGCBjPtpQsLVGeIv/uIvUFX1mF+apvHiiy9O\ndTeFEB9At99+O+vXr+exxx475jpPUV3z58/n7bff5vXXX+eP/uiPuPHGG2XR+mlkSvcWFOP31a9+\nlc9+9rPHPWfatGnjaquhoYH+/v6jjvf19cl2RSdJtoI6fTQ0NGBZFvF4nJaWlpHj8r2orq9+9av8\n5Cc/4YUXXqCtrW3kuIz/qWWz2Zg5cyYAS5cu5fXXX+e+++7jm9/8poz7aUBmrs4QkUiEuXPnHvfL\n5XKNq62VK1eSzWZ59dVXR46tX7+efD7PqlWrTtVH+ECQraBOHzNmzKChoWHU96JYLLJu3Tr5XlTJ\nV77yFR555BGef/75kQ2DD5Hxf3+ZpkmpVJJxP01od911111T3QlRXfF4nD179rB9+3Z+9rOfsXbt\nWvL5PE6nE7fbTU1NDa+99hoPP/wwS5cupauri1tuuYUVK1bw5S9/eaq7f8YLBALceeedNDY24vF4\nuOeee1i3bh0/+MEPZPunKsvlcmzfvp1YLMa//du/cc455xAMBqlUKgSDQQzD4G/+5m+YN28ehmFw\n++23E4/H+ed//mccDsdUd/+M9uUvf5mHHnqIRx99lJaWFnK5HLlcDkVRRsZWxv/UuOOOO3C5XFiW\nRXd3N/fddx8PP/ww9957L7NmzZJxPx1M7cOK4lS46667LEVRLFVVR30d+Zh6KpWyPvvZz1rBYNAK\nBoPWjTfeaA0NDU1hr88uDz74oDVjxgzL5XJZy5Yts1566aWp7tJZ6YUXXhjzz/rnP//5kXPuvvtu\nq6mpyXK73daHP/xha+vWrVPY47PHWOOuqqp19913jzpPxr/6brrpJmv69OmWy+Wy6uvrrbVr11rP\nPvvsqHNk3KeWbH8jhBBCCFFFsuZKCCGEEKKKJFwJIYQQQlSRhCshhBBCiCqScCWEEEIIUUUSroQQ\nQgghqkjClRBCCCFEFUm4EkIIIYSoIglXQgghhBBVJOFKCCGEEKKK/i+rDeffpbx3rQAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f3a26d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.269  0.829  0.00361]\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": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OM7GwwsXBA2/z/PPPk06nKSsr44477sDlcgGgZ5IUOWF+cSFWu5OiohJqqqtY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f393e390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [ 0.00856  0.00863  0.000762]\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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ODsaqVasQEhKC1NRUeHp6VniMSCTC4cOH1VaEr1ePvRdU3qOiR6j/Wc2XEXnJ8yVM6zQN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\nIoqBX4fI2z7W8kDUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f3a2de48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.31, std=1.13\n",
      "EKF    mean=1.00, std=0.95\n"
     ]
    }
   ],
   "source": [
    "import kf_book.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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VsbGxTJo0qcD2DRs2pGHDho7nderU4cEHH2TTpk0lFFvkkqQkuOUW++z9JV33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\nbt2Ijy/8f6E//PADt9xyCz4+Po627t2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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0f3afca20>"
      ]
     },
     "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}