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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   "source": [
    "## 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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f12ef42e8>"
      ]
     },
     "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 $\\mathbf F$ 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 discrete state transition matrix and measurement model matrix:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf F \n",
    "&= {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}} \\\\\n",
    "\\mathbf H &= \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t} \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "This leads to the following equations for the EKF. I put boxes around the differences from the linear filter:\n",
    "\n",
    "$$\\begin{array}{l|l}\n",
    "\\text{linear Kalman filter} & \\text{EKF} \\\\\n",
    "\\hline \n",
    "& \\boxed{\\mathbf F = {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}}} \\\\\n",
    "\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu} & \\boxed{\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)}  \\\\\n",
    "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q  & \\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q \\\\\n",
    "\\hline\n",
    "& \\boxed{\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}} \\\\\n",
    "\\textbf{y} = \\mathbf z - \\mathbf{H \\bar{x}} & \\textbf{y} = \\mathbf z - \\boxed{h(\\bar{x})}\\\\\n",
    "\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} & \\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} \\\\\n",
    "\\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} & \\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} \\\\\n",
    "\\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}} & \\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}}\n",
    "\\end{array}$$\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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f15cd6978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.show_radar_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives us the equalities:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\epsilon &= \\tan^{-1} \\frac y x\\\\\n",
    "r^2 &= x^2 + y^2\n",
    "\\end{aligned}$$ "
   ]
  },
  {
   "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 matrices. We model 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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f154194a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f16d4a588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f16d8bba8>"
      ]
     },
     "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": "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\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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f16d15198>"
      ]
     },
     "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",
    "$$\\bar x = f(x, u) + \\mathcal{N}(0, Q)$$\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",
    "$$\\mathbf F = \\frac{\\partial f(x, u)}{\\partial x} =\\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial x} & \n",
    "\\frac{\\partial f_1}{\\partial y} &\n",
    "\\frac{\\partial f_1}{\\partial \\theta}\\\\\n",
    "\\frac{\\partial f_2}{\\partial x} & \n",
    "\\frac{\\partial f_2}{\\partial y} &\n",
    "\\frac{\\partial f_2}{\\partial \\theta} \\\\\n",
    "\\frac{\\partial f_3}{\\partial x} & \n",
    "\\frac{\\partial f_3}{\\partial y} &\n",
    "\\frac{\\partial f_3}{\\partial \\theta}\n",
    "\\end{bmatrix}\n",
    "$$\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",
    "$$\\mathbf{V} = \\frac{\\partial f(x, u)}{\\partial u} \\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial v} & \\frac{\\partial f_1}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial f_2}{\\partial v} & \\frac{\\partial f_2}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial f_3}{\\partial v} & \\frac{\\partial f_3}{\\partial \\alpha}\n",
    "\\end{bmatrix}$$\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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {
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Yhoa+Re3DKTgs/b9LWMsWWsjE9+jPUIxcOZx4K56UZEoWY/t72NW7dcf+3eRGA8uXgXcC3xFC7AN8QHbHcqUoirLDLizkmJpfYS2zwqH+MLNrVU4vFKl5FXzRWRoNC096yHZQEUIgAEnrfxLQdR3H0TEMDb9pbNRgGgsNlv/rMm7Rxew06f2VflbGk6xWXMp1h2jw6q/aXMUmGIrQ1ZGgM3H1SZZ3g+sZbvx54GkgLYRYAP4Q+AzwGSHEKcACfnm7ZjBFUZQ3W65U5/T0CpOTkyT8knNzaxy9UKBsldGS8zhuHV0DXQg0TdCqpVza7CWlxPFcLMvF8wwkEDANqqeqZP4qg7QlgdEAvb/cix7SMZfWscopJlZrPDIcu2r+VgpNBkYH2d2XuqtHg110zcAipfzwNqc+ssN5URRF2XFStpbAP37yHIVcnqJXJ5fLMbXk4WDhj63hN689jkkIgakLspUaEkEyFqbyXInis3kAokeidH2wC2G0AoMvmsUqDzN1jcBSqjt4mo/udAcDnVcPQHcLNfNeUZR7lpSS50/N8+wLZ7gwPknQLSKdJqmwiS18eKKKL5x/Q2kKQDoexb9dxzrZAAEdP9lB4u2JS2oberCMLV0K1e2Xv5dSMrdep39ghJGeRLu2dPdTgUVRlHtSqdrk2Pkl/vvRs7x2/GWiokxH3CASCGB7grIFrmahB8vXld5KrgKArLrw9w1Y8cCE7g/3ED0UueJ63Wzg4VGqbx9Y1soWui/MQF8Pu/vu/k77i1RgURTlnuK4HufnsozPr/HCq+c4Nz5J0mywp8O/UaOo2+DhoZkNhLj+7mG57sJX61CWEBUYz8QI7N96IqNmNq8aWGzXYyHXZP+B3Tww0ol+ncvu3w1UYFEU5Z6xkqtwcirD/OIyF6ZmWS9UCFFlOKmzuU/cctuBRbeumeZ6sbUQpZy24R8aYAPdGqkPp9BjV5nIqLlIJO4245oWcg060p0M9abp7Yi+kR/zjqcCi6Iodz3X9Tg9s8b52QxT01Ng1wn7BOtWmaTfw6dfer1z8V2vXXtNMCkl3nELvtdojTnea8BPBBDhVrDadhSXpyNodfhfrtJwKNQlh/cO8OCu7jf2w94FVGBRFOUN+f2/PsF0tgpAudzqn4i+fHTj/Gg6zB//zOHblp9K3eLl80tMzy8xOztLX8IkEvPz/fM5Lixk6fbbVKqCcECnI2KiCYFPb014lO7VX4HSkRjP2dSPt5Z60d/ip/PdSYQQWI5HK5WteY4PDY3QZVHN9SRTq3WGhkbYN9hJJOjbgVK4s6jAoijKGzKdrfLidO7Sg9nc1hffYvOrRV6dWGF6eppifh1dCJ49meWVmRKFfBantoYhm4BAExph06Q/FWBfbxQNP569/UrDbtkl/8U89oINBujvCqKP+RBCtCdRgiaunO+ycX8jjIZOInTpviqz2TqReIrhgV7GBjt2sjjuGCqwKIpy1/E8yYmpDOOzK0xMTFCp1Tl6Ic90tkLZqVBuWMjGIqZ/BVezkFLDbQYp1YPkln1MrFapBwaRAT/S0xCXNYlZixb5L+Txyh5aTCP18ynM3tcDhJSAEGiatu0QYbuaxBQGA6nXg1e2bFGxdQ4fGOXIWN891WG/mQosiqLcVSzb5YfnFpmYXWJqepLJTJUXJvLk7QJ1LUcgvUrMLUJ9HZ//0uULXctHPd9FIdeN1DrxTA27FsMXKWxcU3u1RvFrRXDBN+Qj8aEEevjS5ixPSnRNR9+i/+Qiu5okgslQuhVY6pbLXK7JgQMHeWh3D9HQ3b2C8dWowKIoyl2jWrd48ewiF6ZmWFxc5OXpIicWc+TsdYK9U/QOj9PId9JYdDGNK+en6D6LSPcC/tg6+cUuPDtKOddBKpwHCeVny1RfbPUfhY6EiL0nhtgieLgSTEPD2GYpfNc2caopfMJkqCOI60kmMzUGB4fYM9jNUHd8y/vuFSqwKIpyVyhUGrxwZp7xC5MUclmOXihwOrNOQa7QcegVAvEcrm3iNjRwGojA9nurmME6ka5zFAtPYJe7qBXP0fhKCWvaAg3i740TemzrxSA9rzWk7GrNYLW1PvwEGEkZhHwak6t1grEkI4P9HN59740Cu5wKLIqi3PHWClVeOLPA+Pg4XrPCyYUKpzNZiizTdeglzHBrVrzbDOLWXTS9zrXWcgyEF6mUHNwVg9KzeSi5aGGN5IeS+Ia2H6nleBJdNzB1fcuOeymhujpAiCAHuwzmcw1sEeCB3bs5MtaHcY/2q2ymAouiKHe0tUKVo6fnOHvuPAGazJcsXppep+Bm6XroJcxQZeNa1/LjNTwMvXbNdDXdwiwexX3lBLgueo9Bx4dT6DF923s8KZGAoeuYxtYBop7rhloHUdNHMigoNDQeeGAvTx4cIBa+d/tVNlOBRVGUN2Q0Hd74vDGPJRrd8vzNWi/WeOHMAmfPnSckLMJ+g6+8kiFrrZMce+2SoCI9gWv5kFYDLdC8arrSk5SPl2mcXG4d6N+D/oE6euzqEyYdt1VbMYxtaiueRmH6ACkjwUO9JgVL58j+MY7sHyAdv/v3WbleKrAoivKGbJ78eCu3Js6X6xw9M8+5c+cIiibD6SCf+e4ieatIoGuGUHoFYGNTLs/xIZsemrCuuv6X23ApfLeAtWyBAPPAg9i9T2OvzeImX9p2pJfrtWsrho5vm9pKcW4PPjtFXzJKR8RleGSER/cN3DPL4V8vFVgURbnjFCoNfnBqnrPnzmN6DUa6gsxm6xyfy1PxCqT6TlNv2u0thEEI8BoGTcsBz9oINpez1izy/5THq3loAY3E2xMYnTXWFnQoDlFbyxLtmb7iPikljisxTRNzm9pKba2X2uI+0maCR0cTDHZG2NufYtc9tGrx9VKBRVGUO0q1bvGDU3OcHx9Hs2ukozozywW+fHyNfLOI3jWB5VWQjfY2wkhA4DUCOHUb3CbYDoamYejaxkz52vkapZdK4IHZaZJ8Otmen1LDp0/iNPfTWHgUQ4dg56XBxfEkmq5hGDrmFp3vtbVe8hceJql38MTuNO9826OIRo6RriuX078fqMCiKModw3E9fnh+ifPjk2RWMgQNh+WVOoVSiVNzDg2tRiQ5iZAeutZaAFIIDSkltjBwpaTarCKbVXTdIBkNYQDFo0Xqk3UAQgdCxI5cOj/F1NfQGz2YTif1ucfwrBCh3nMIzcX1JJ4En2less89tPp1CjP7aSzvIaGneGS4k59/z1t4bP8g2YVrr5x8r1KBRVGUO0Jrt8c5vvPD00xOTBDX6ywVC0jXoWSbuJrAiOQIhGtw2dKPQgiQOsITaLi4gJQezZJF4XtlnLwDOsTfFie0+8pOdCkFfllmfyLJVDVBZeVB8vkBgj1nEOElzCD4TH1j3orn6lQzA5QXd+FzkqSMBE8d7OVD736CJw4M0tsRJbtwGwrtDnXNwCKE+Azw08CqlPLQZed+B/iPQKeUMntrsqgoyr2uVG3yDz+c4PnXJpg4d5KQU6Tmg66IScgX5IdLAkfUMWOZbdMoVms4dcAFNIm3bFN+tQo26FGd5DuSmClzy3ulpyPQ2JVwOdQneX4+SqYRoDqdwNEtfNECVqBVA3FqUZx6hIAWJKVHSYSDvOexYZ5+8jBPHry/Rn9t53pqLJ8FPg38xeaDQohB4F3A3M5nS1GU+0HDcjg3l+Xlc/M8f/wc0+NnGYg69KV9l4y8Wq8LXFz8wcK2aQnNAUNAw4BxGy64reM9Bul3dKD5t5+Y6DRCGEInFTaJh+ADYx7HFmC2HKXk+tCsHqTlIQFTGPiDPnrifnZ3hXjrw3vZNTzI42N9xCPbr5Z8P7lmYJFSPieEGNni1P8B/C7wdzucJ0VR7nGu6zG5lGd8IcvM3CJHT0xQyS4x1ino3GISYakJDg6hYGnbNJNxg3pBo3wsD9lWUPEdChA+HEHzbR9UPMcAx48/YBANtiZHVhsOnUGPx8b6GelLU25Kyg0HKSEVMXE9j5prsGf3HvYMdfPQ7m5MY/uJlfcbIbfZNvOSi1qB5WsXm8KEEO8HflxK+VtCiBngyOVNYcVicSPhCxcu7GCWFUW5m60VG0xlyqxm82QyKxRrFrVKCVnL0xnYusP72eVOMlqFyP6/Q/PVt7ymOQXVrxSRdQd8IB71EewPYBoGxlVWIW4Wu3DXxhiJRnjrsA/LkaxVobO7i6HuOB2R1wNdzZIslVyCkQR9fb3s7YvTl7r/mr727t278Tkej19RuG+4814IEQL+HfDum8qZoij3FctxmVgus5gtsbS4iGfXiZiCKg7Naolu//ajqDbmw28x8VFKSf0Hderfq4MELR3GfySMFq6DJq65ZphV7iSAyUBcx3Ela1WPZEea7mRkI6jYriRT9qi5Ot09A/R2pdg/ECcS2LrP5n53I6PCdgOjwGvtYXcDwCtCiCeklCtb3XArZuXeqFs5U/hup8pme6pstna95bKULXNiaoW6V8dqNHh4by+JoMHJhQqrxVn2DSSJ+7efSBguaKxbNUw9hO57fdkVt+pS+NsC1mQrKIXemsQ4sBsv30SKeUxDx28aaNssb2/Xg9BMEAtEeHBPDyuFJnv7uxjs7WRsMI0ElgtNymWbvSM99Pf1sW8wzd7+1DU36bqXf2eKxeJVz7/hwCKlPAl0Xfx+u6YwRVEUy3Y5MZVhanGN6akpNLfBA/1h/KbGRKZGZm0dz64TC8PlQ4g3i/lBt3ScRhQ90FofzJq1yP91a5dHERQkPpjAvzuAVYBm1YdndSB8xW23DpYSamv9hLQg+3pCZIoWyVSagZ5OdvWmyJQsVopNYvEkDxwaZLS3gwPDnYRULeWarme48eeBp4G0EGIB+EMp5Z/f6owpinJ3Wy/WOHZ+iZn5BVaWlhhI+TB1P89fyHNqvsz4cony2iKmrOHXNRIhg9HOEGO9rcCzWUdQYpRN7EoaX3yJ6vNVyt8ugwRz0CT5s8mNVYnNyDq2lYZcAs8JgFlgU2PaBqucwK0mifhDdER9xBJJkqkOzECQU0tVEskU+8Z209eV4oGRTjrUMOLrdj2jwj58jfMjO5YbRVHuelJKJhZznJpaYWJyEmlV6YmbfPt0jpemClScKmWrSbOcQ9p5NGoIWyfbNFgo+nl5JsBb9iTY3xveqG2MxCWvrvrJL3difTdPc6K1enH4R8JE3xG9ZBa9MOpokTV0owe96qdZi6BpdXS9itBsBBLH9lFeHiWiJ+hORXD8SRp6HF8kSbSji5GODvo6E4z2JOhKhret9ShbUzPvFUXZMbbjcvzCChNzK0xMTtAREkwWmvyX78xTsEtUnDJmIoOp1TH9a/hDcwjhIV0dux6hke+iVk3w3fMOlYbD47sSAHSGIFCaw3np75CNZqvp6wMJAvuunDfieBIzaOGLZNFiHTh1P17dxK1FkI6HdDUqmQFMI04sEmfP3hFGhod4aN8gnakYA50xBjtjhIPbb/alXJ0KLIqi7IhyrckPzy0xNTvP0uICPXGTL7+8yqmlPOtWDn/nLF2DE7jNII0VHeEroGmtJiphuPijRfzRIo1iitLSKMdnBemon+EOP8899xxzzz8PUiJSXXR82MRMX9m85UmJ54HPr+P3e+ihdWRUw2mGcBpBXMtPYWY/gUgHCV+UD/7YAR4aG+apw0N0JyOEAqaqnewAFVgURblpFzfkmpicolbKMZTy89nvLXJuLUuJVVIHThJMreK5Gs1CErfawB/YerJjIJ5DugbljMF3XmvA/FEWF1sLb/Uc/FGqI49TXV8ilvwBmu5s3HdxaXvdMDANHb09EkzoHmaognR1CtMHCcs0nbEE//L9R3jywT33zXbBt5MKLIqi3JRsqcHSqVnOnRvH8OqMdAb5v745x/j6GjVjme5DL2H4GwC4VhCv7qJpdYTYfrfGQHKV2oTD0vlxpGsTjUZ55pln6Ogd4asTGmuVAYrjP0Zs9EX0QLWVtgcgMA0d36ZZ8J5jUJrfQ3V5F1GRpDsa5zd/5q0cOTDMQ7t7NhaWVHaOCiyKotywpVyNs/M5PDdD1HQZSAf58+8sMrG+Tt1couvQi+i+1yc+us0Abt1Dv8qe9J7tUXqphHWhtW1wvHuYX/uFnyEUao3Ket8ej29Mhlmt9VNiWehJAAAgAElEQVQ48278HTMY8UUIrOEL6vhMA8/2Y1Vj1Ne7qa/1EyBGSovyyGiaD7/nCR7fP8jegY5bWzj3MRVYFEW5IefmspyZXWd2doaH9w3Qlwzy7TPrvLqYo8Qa3QePXRJUpCdwGn68hoUZ2HpZFjtnk/9uHrfoggb60IMkR49sBBWAqB/et8/jpcUA43k/9WyY2upeXM1F0z2KmkR4PkzNJKAF6NRDdEcDvPvxXbz14QM8uq+X3o7oLS+f+5kKLIqivGEnpzKcmlxkenqKrrCkLxmgULP5+1dXWbfWie17BVcr41i0dniU4Fp+mjUHz2vgSQcNsdFRLqWkdrZG6Vhrh0cjYRD/sQSl1UHqtkvT9i6Z2xI04O3DHg92SV5Z1Fm3k9RcE7+v1QQWMA0Gkn4SYYOeRJDHHhxjdLCXx/b1qQmOt4EKLIqivCFnZtY4NbnI+Pnz9EYkQrpML+X5m1eyrFTziMQsXnCRetOjtcZtO7A0DeyGTb1WpmLViIX96JqOsDxKPyjRXGjNTQntCxF7IoYwBKK9SrHjefi5soPdc2zG0gYjIz0cHO7E0HVsTyKA2WwDzwiwe/duDo70sH8orfpTbhMVWBRFuW7j8+u8Nj7Py6+dJG66zGVL1OpNRKbBiTmHmlEk2v0q0nMQQnDxPS4ECKHhSvA8G1wH29ZprjSov1RFNiXCJ4j/SJzgcHDjedLTQGPLfebLdYdSUzI81MeevhRBv4knJWtli5WSTU9PL8NDAzyyp5fu1P259/ybRQUWRVGuy2uTGZ598RyvnThFSNQp2VXm5xfRcakE+nF1G39qnkC4AVvULnIVC6/eBFywPaony8jZVo3E6DZJPpXAiLz+SnJtEyEN/LqOedmy95WGw2rZZmBggJHeJPFIgFLdYWatTiAc5YEHxtjV38nBkU4CPvWau91UiSuKsi0pJZl8laOn53n+tSnOnzmB3syj+zwiAZ2usMTQdMYLBpaoEEnPbpuW7dmtdSbzHpywkDUJGvgeDBA8EEJcthmXUw9jCIN0zHfJpMWa5ZIp2fT1DzDcmyYZCzGZqVG2BMMjuxjo7ebBXV10JsK3qliUa1CBRVGUK7iux2ymyPRynqmFDC+cmGB64jxdQYfhLnNj2+BGSVBzdEq2h2fUMSLbL3JuGHXccxnkiQxIICbQH/UT6ArgSfA8yeYWL6sawxQm3bHXl1apWy7LBYvevj6600lsTM4s1enu7mFXXy/7hzrZ059SfSlvMhVYFEXZIKVkfrXE+fksy5k1ZucXmVhcp5pfY3cKeiJXjqjKWyYODkY4t+2mWs66g/jbCnLJbh3YFSLxmA+hCzwpkVKyeQsvz9NoFjtIGQF2dbWGGjdsj+WCRaKzB+mLUPP89CS7Ge3uZqQnyd6BDjXi6w6hAouiKEgpWV6vcG4uy/JqloWFBZxmjabtEZJVhN6gO7x11Kg4Oi4uRvDKzZ+klNRerlF+toy0JVrMgCeHwQwiySO4OFFSsjm0NAsdmATojgVIhk0KNYeZdQd/LI30J9i/by89Pd2M9ibZ09/quFfuHCqwKMp9br1Y4/TMGkurOeYX5mnWKgwk/ZQ0g2w+T6mQZyjO9rURqSGRCP3SrYXdikvxK0WaF1rDiAMPBoi/N47r+nGKIZy8H9dqgCiCZiOkQErwXJ3q2iARvbXS8NlVl/WGxsDQXsZ2jfLYwRGGuxPs6kuqjvk7lPpXUZT7VNNyODO7xuRilvm5ecqlPP1JP+mOCPmqzcRSicWFJYbiLsY2W/u2tGsasnWNlJLGqQbFbxSRdYkICOI/FSd4qDWMWCOPEB7CH8Wrh7DKATRP4Do6niNo5DsxzF66Uh2kOtPUpY8nH9nNo2NDG6sQqz6UO5sKLIpyH5rLFDk1nWF+cYnlpSWCpqDadPnq8TWW8g0Wcw3qxRV0u4KBS9hv0Jvw05/0s6srhL7pxR42XPSmjt2M4FZdSl8v0TjbWnTSv8dP/H3xjd0dLzJCRfRgCbcRwguGMIwgAcOkWU7hlfeR6kjy1OEuouEgDxwc48cOj7J3UK3tdbdQgUVR7iPVusWJqQwzS2tMTk6ylC1zYaXK5FqVhteg4Tao2w5OrQrNLEKWkZ5O3jbI1EzOLvtJzQR5bDTGnu7WcN6o4aCjUzlfpvqlLLLmIXyC2D+LEXwkuO3+JkJI8JXx+6r4Az50K0Vh6jDpYIwf3dvBnsE0+/bu5fEDgwx0xm5nMSk3SQUWRblPzGWKvDa5wtzcHK+en+O12RKZSo2yU6ZBGX8iiy+aQ7c1nPUS/sAimuYgZWtVYrsWpZLvpFaOUTjTJFex6Q9Igl6Z+vHvYy+eBsA36iP+/jhG4uqvFykljgd+vwH1DtbOPklCdLErHedth0bYs3uUx/f3q/kod6FrBhYhxGeAnwZWpZSH2sf+I/A+wAImgV+VUhZuZUYVRbkxjutxYjLDhbkVTp0d58XxNcYzJQpOAdsoEB2aIdk9j2Y41HOdNFcEhlFE01qbaAkBRqCBEWgQSK7RyKcpZoZ5ZU4y01hk/syL1Ot10E3Mhx8i+d5FrtolczFfnkTTdOz8EMXZh4mLTkZTCT7y7ofZt2uIx8f61PbAd6nrqbF8Fvg08Bebjv0j8G+llI4Q4n8H/i3wezufPUVRbkax0uDl8WWm5xY5eX6C587mWKoUKHl5ooPnSffNILRW57trmzh1E7fWwL/F0GFoBZlgKgvUyf2gTja7CMDA4BDagWfI+nRq8+OEh45vO4oMWpMhnUYQe/VhKI6S0FKM9Sb59fe/lbGRXg7v7la7Ot7FrhlYpJTPCSFGLjv27KZvXwB+dmezpSjKzZpeznNicoWpqWkm51f4p7M5VurrWP5luvYfxwxeutmWXYvilh10o9zq/9hGY75B6WgGr+aBptO39xF++Wf/GZmq4OuTgmJ2H8VGjFDvWczo6iUBRkqwqwlqqyM4hV2EtSgxI867HhnkfW9/hIf29DHSk7hVRaLcJkLK7X+BNi5qBZavXWwKu+zcV4EvSCk/t/l4sVjcSPjChQs3nVFFUa6P50kuLJeYXckzMztHvdHkuWmbrFtAJGaJjR5DMzw2Vyikq1Nf78NZsTHMOYRwr0y34VF9uYo125qvoneY0PcjpCN9/OR+P5oQZJsmx3IJytKhqTWRZg3NX0ZoNtL14zYjCCeI4fkJiDDDST/veGiAfUNd7O+PEwmqiY53g7179258jsfjV9RNb6rzXgjx7wAH+MubSUdRlJvnuB65SpNXp/NML66ytLiILh2OLQvysgypCYKDP6TpgvAEmmhttGXoAs8K4dU8BNUrgoqUEmvWovpya3l7dAgdDhEYC1Ce02m6LuUmxAOQ9tu8szvLTCXETDVMrRHBbXYgAU0KpKdhCkhHfTyxN82D+4YZ7ooy3KnmptxLbjiwCCF+mVan/o/La1R7jhw5cqOP2XHHjh0D7qw83SlU2WzvTi2bhuWQyVVYyVVYWCtyfDLH3OwKaysLRLUmL2cMirKBjC0QHnx5o1nK8zykEGiahoeOdIPono7mdzDM1zvM3apL8WhxYxMuX6+P+NviGNHWq6Ni2OBAqiNNd9y/cd8IrWavqg3FpoHjgWW5rNVc0p29/MgTD/PgvmEe3tNDMvr6/iv3kjv1d2YnFItb98FddEOBRQjxHlqd9W+XUtaudb2iKDvHsl3mV4ss5yqs5SsUiwWWMlnOzGQo57N4zRK747BQ8VH2PFx/kcTul9AMuLhPysVFHz3Pw2pauA1BuVBHk0WE1kRKSWgFyi+31vgSpiD2eIzg3ivnpUgk3hZ/WgoBER+ETVgoumSqktE9+3n88EGefnQXY4NqR8d71fUMN/488DSQFkIsAH9IaxSYH/jH9i/ZC1LKf3kL86ko971CpcH0cp6FtRJr2Szr6+tUy2UMDbIVC6OZI2nU6Eu0agjHJzUqokR48FU0w74kLSEEAtB0gRASy9LBdpBmEyou7it1SuutJjH/kJ/4W+LooUtnz0sJXjOILnRiwUvPXVRuwnzRo+IFeeixB3nr4T289y17iYb8W16v3BuuZ1TYh7c4/Oe3IC+KolzG8ySL2RIzKwUy60Uyq6tk17KEfdAV9eGLhDi/XKWcW0O3K/RGWzWFM1lBxWuiRVfwJ5eu+oxCuY5r1fFcCZNNGG+AB/gF+kNBkgdiW86ed60AwjMJ+jTC/tdfJVJC2YJ8A5qeDxmO8cTBA7z7iTGeOjy800Wk3IHUzHtFuQN5nmRutciFhXVW1tbJrGSolIt0xnwc7AsQMHUatsvZxQoLS8tIq0xf5PUViMdzggYNgl0T1/fAXBmOrkCxtcYXAwbG4SDCr227JEujmMIUJp2RVvOa60GxCYWmwPQF8cejSAK87cEx3vHYXg7v7rnZYlHuEiqwKModxPMkC2slxhfWN/ZFwW7QnfCzJxXbWPyxaXucW6qysLSCWy/RF309qDQcyDUkjtbEF1+5+vOaHsZRG+ulmdYixUED7WEfeo9JOh7a/j5Xo5nvJCT89MVNVqtQtgShSJS+dBJXGKAZvPOhgxza08+h0a4dKiHlbqACi6LcAaSULGbLjM+vs5TJsri4gGvV6U8GSIYjl9QaXE8yvlJlcTlDs1pkIAab+8CzNVo7OoYK2050lFLSPNek+I0iXtlr7UX/QBqxqw9BA+ltv0KT9HTKmVF00UEkGEL6QhiRNEPRGMmoH9uVaIafsbH9PLy3j939qZ0qJuUuoQKLorzJ8uU6p6ZXWVjJMj+/gNWoMpD0k+p6PaBUGg6L+SZL+QZz6w0y2Ty1whp9EQ9pG3TFfAR9rQ70mi3w8NB91S2f5xZdin9fpDneGkJs9ptEfyqGlwgh6hH0RhSvmqJZtxHCAdGaTCmlgeeZOFYYqz5KMtrN47uCdMX9HNzVSzJkslxoovlDjO3by5GxAfrS0dtShsqdRQUWRXmTWLbL2fZGW3Pz85QKOQZSAdKdEQCWC01enSvz6myJ1VITS1o0bJtms4lTyqJ7VSaR6MLAp5kMpILs6wmhGSEEAikvXWtLepLqC1Uq36m0hhD7BdF3RgkdCeFKiSYc/OEMuhvHroXxmiZ4rfuQIAyB6wWpzu8nmergXQd7OBgvEzCgI+JjIlMjluxg355dPLF/gFTs3pyfolybCiyK8iaYXy1yemaV+YUllpaW6IoaHB6Mogk4u1TlH0+tM7lWpubWqLt1bFHDCFbA9PDsAkY8i6Y38WwTqxmkXItRXvUxsx4iFU8AUTzr9eXmrUWL4teKOCutFYsDBwPE3hNDj+pIKXE9MHUN0ycx9BJmuIznmOC1ApSUAs8xyZ4do8Of5ImhTn7uyR6mJius1zwqK3WGh0cYHezjiFqV+L6nAoui3EYNy+HViRVmFteYnpnG8Joc7AsSMHVWCk2++OIK46slSk6RplYi2LFCPL2MP56jkU/TzAiIFzF9uUvS9RydZilFaa2PRt7C9kfwtCRO2aT6vSy1H7bmMetxndhPxQjsDWzc68rWvBZd1zcGBwgh0c3X97BvlhJkzz5GjC4O9nTwiz/ah5QwV3CxhZ+nDz7A2HA3D4x0oqtVie97KrAoym2ykqtw/MIyM7NzrK2uMJgKkI5G8KTkn86s8/XXVsk289RFntjQJKmeeTS9NUnRaQRxqgZerYEvkL8ibc1wCabW8MfylBZHca1O3JkJst9aQdYtEBB+a5jI2yNovtdf/FJKXFdi+kx8pn7lrHoJleVhSjMHSRlpHupP80tP9dGwPaZWa/jCSUZ6e/mRw6OqP0XZoAKLotxirutxemaN8bkMk5OT6F6TQ/0RdE2QLzf43A+WObmUp+AW8KWnSA6fQeg2livQpEAgsCox7KKDbm4/0gtAMxyCkXM0vnsSWWoFIL0nSvIDfszuK1cObm22pWHo+hX7nzTLcQrTB6DSTZeZ4umxTt73aBeL+QaFBozu2kOjUuTAQFwFFeUSKrAoyi1UrDR45cIyM/PLzM7MEA+AKRzG56vkKw2+carIXLlCTV8nNPJDzNgKTRuwWyOAhabhNaM4BQ9Zb2IGy8DWExY9y6N8vEztXK01J8UIoO15J/ruXTStC+j2ObRNzVueJ/E88PkNfGZrRJn0BI1CJ+XFUZxSJzEjRk88zs8+3sNgR4DTixUSyQ4e2jfM/qFOiivTar0v5QoqsCjKLbK4VuLFs/OcOH2e1dVV4n7JYqFJtVqhUq3z/Dys2TbNwDrR3c+hBytXhAzPc7BrfuxCE4M1bMfFNHW0TU1WUkrqk3XKx8p4jdaclNCBEG7yMXzaID4vgbV6iPz6CL74EmZ0DS1QxJE2hmHiWTFq+QjNUopGIY3phYgaURKRMD+6L8lTY0lWihYLRY/de8cY6u3kod09xMJ+jq3O3NYyVe4OKrAoyg7zPI8XzizyvVenOHnmLDSKBKgzV6uiCUnErzNd9FF0HezgOsmx76D76mxVE9E8HccNoFlNPKOC4wqEJvAZrRqGnbMpvlDEXm0tMml2mcSfjGN2mJSXbPRygUdSYYpehNlyEDuXwMrZ2NIBAbqm4dNNdKET1PwkjQC98SBv2ZPgsdEo+YrDxGqD3r4+Bvv7ODjSxXB3fNtlXhQFVGBRlB3TsByml/P806sznL0wy+SFs+hWiXRIEvAbpJM+TENjKi8YL3hU9CKxXUfbQWVrnh1ANj00rYmuSxxP4noeTgOqr1U2mr20gEb0SJTg7teXtRdaq+M/pLu8ZdQj34ClkslETqfmmvj8QeJhP6mIj1TEpD/pZ39fmER7ouOFlQYd6TSHd/Ux2tfBweFO/D71ylCuTf2WKMpNKlQaXFhYZ3Ylz0unp5mamiG3usBwHHo6fJd0ijsevLgkqFAhNPAaZnjrpVPWi63hwTEjgbSh1iwjHIuAz6Q5Uad4oo7c1OwVfTiK5r+0891zDQwhCLZHgSX8kqbPIt5rMjjYzQMj3YQCr3foe1KyWrQ4MV8mlkjxwKF+hno62D+UJhZWy9wr108FFkW5QblSnfGFdRZW88zPL/Lq+ALVUg6aRR7rNwmYVzYXja8L8raFDGUJpKev+QwhvI3Pct2ldrqJV2jVRMwuk/hb4pipK0d7SQl2PUJQGMSCBlJKMkULR5gMDAywf6hzI6hYjsdqyWK1ZBGNxdl/YA/9XSkODHeq2fPKDVGBRVHeoLVCtbVY5FqB5eUlVteylOs2PqeElGX6OzSMbeYITuZby9mHusfZqpviYk3FclrBY61ehqyAV3Kw0lrbi4AgdiRKaHdo274OpxEEO0g07KMzarJasrAxGWwHlWjIT6XhkClaFOou6XSagw/00N0RZ2ywg+5U5KbLSbl/qcCiKNepVLN5/uQci6s5lpaWKBbyJEMGPl1gVQs0q3kGorDdxPOqDSu161vOHgBbwrECvLrcmh6vAXtM9H1+Qh3bBxWARr6LgOZnuCPAasnGwmRocIDR3g6qNswvVHCEQXdXD6NdXQx0xhntTaoairIjVGBRlGuoNWzOLhRZWi8T8BcpFtbpjvno7wszvlJjeXWNail31aACkKu3l7MPryN0Z8trOuIhpJSsvVjEfb4BlfZkyME4Yk+CcGcVv2/7zbcA7HoQq9hJ0gySjvpoEiCa6gQjxHzRI5mMMTDSQUcqwUhP6yvov7I5TVFulAosirIN1/WYWMxxfj7L6Qtz5HLrPLJ/mAcHoggBZ5cqLKysUinkGIxdPagANJ3Wcvaa2dj2GmvRovTfS7gL7eHDvSbRdyUp6D1QEUgnjdSruKKJJuyNkV9Aa6FI16C0uA+/liAZjVI3kgSjaYZGhhno7SIRj9PbEaW3I0JXIqzW9VJuCRVY7nO//9cnmM629u0ol8sARF8+unF+NB3mj3/m8JuStzfTar7KiakMC0srzM3PY5Wz7E5pDKRaizdOZmqsrOUpF3IMxuQ1gwq0WrNarlySxS26lL9dpn6iNfRYi2hE3xkl+HBr+HDSyuLWO9DsAFrdj+NIsCXSvdi5ryEF1LJ96FqaSCTB44+PsXtkmEf2DTDYFaO3I0pnPKSCiXLLXTOwCCE+A/w0sCqlPNQ+lgK+AIwAM8CHpJRXroyn3PGms1VenL50pVyyua0vvg/YjsvpmTUm5leZnp7GaVTZkw6y0mgtL79Wtnh1psRrM+tkM0uEaHBOSoI+jYhfpzPmoz/lx9CufHknAhIdnXo9vnHMa3pUvv//s3dnMZJl+X3fv+euETf2PSP3rKqsrKqu6n2mZ3o4w+EibqAtSxRpCSSgxQb8YMiEF9jUg03AgAA+WoABA4IE0DIN2yQlwIJJyJRpDkfmcGbY3TPdXd1de2ZVLpGZse9x1+OHyK6la8tautbzaWR1Vd6IGzcvMuOXZ/ufAcPvDyEAdEh8LUHym8nr04ejSCK1iFiugy0CIt8hCkyiwEQG08dIBIOdFTS7TCaV4e/+whu8e2aFnzizSDYZUwsalSfqMC2W3wX+R+Bf3PS53wL+VEr5O0KI3zr493/z+C9PUZ6cvdaAj67scXVzm62tLWazFqV8gk+2h/zbTybs9CJczjOYTJh0a+D3EfhM39Y1dKFhaiZx3eZIOc7bRzI4B7s6AuRjYAmDaJwhGDq4n9QZ/PmAaDRtdcReiZH6mRRG7saPpZQSP5QYpoFlGJimD7HujeORRuibNM6/hjYpUk4V+E//xtf5pa+tcWKxqAJFeSqElHevlHr9QUIsA//XTS2W88C3pZQ1IUQV+I6Ucu3m53S73esnvnjx4uO8ZuUx+u++0+LThn/X46eKJv/9t1/sPcuDMOLybp+teo9rm1u44wFZGy40Qj7Zi+j6HhMm+NJDigjh7aGzg2E1p2McWoQMTCI/jj/MErlJbGGT1G1emzWZz9wIlw9aKT67to538U+R/WkXpDFv4Py0gzl3p+rD00KUpmFgm/ptxyftKr2N1zG9HOV4jl//qeN881SFfFItaFS+PKurq9f/nslkbvvt5WHHWCpSyhrAQbiUH/I8ivJU1Xtj3rvU5Or2PrVaDVv47A8iLnd0BpGHq40h1sEqXMaO9YgGcWi7WPGtWwpBfi5W2CT0Y0zqi7SHRd7bSiKwmMvo7O/vs/XDP8Ld3wNApBwSP6thrVl3bFmEESAEhm5crw32uWCcYrB9Er81T0JmODZT5Ne/fZSvHCve9lhFedKeyOD922+//SRe5lDee+894Nm6pqcp9f5f3nNMJZVKvXD3ajD22Gn0+eDiDj++0GDjyhbDTgMzGvPBvkE7kLhaD1J1EtVPMVK7+F6E351DdkM0o4kUGrqho99hLAUrIp7YYFh3GTUW+NE1l/XeZ1w4/xkAsbiDffRbeIurhFYDLfjxbaVdgjBCagLLsojbBrqmEYUak3aZ4f4cbmuGmEhScLL86k+d4T/55a9wdC73xLu+1M/T3b3I96bb7d7z+MMGy54QonpTV9j+Q55HUZ6IseuzVe+x3eiz3+pz9uI1Ll/dprZ9lawV4OgaP9iP0ZIjPKdBYu5jrOzOwep4DX+QQowFmhwjtCGBD4ORhxCCYsa542vGktuMPq6xv7nHvowwDIOvfvWrvPvuuzT9GN+9ptEaOvTPFRHxNnZ2Bz3eRRpDIikwdBvpOgzqGbxBGrdbwJIOJnFSZoJvnF7i7/zs6/zUGyuqlpfyTHnYYPnXwN8Ffufg///nY7siRXmMGt0R67U22/UujUaD3f0Gl7ebeJMh426DV8qC3YHNv9uCLj1Ib5Nd+QGacWPcSUqIvCTRQGKZbTRNEIQSKeUd99yK/Ijhp0OGZ4dIfzrUmKoe4+/9rV8kk5nOCJuLwa+ciPjRrsWFls1wnMIbzzCSwXSti6YRajqBpmMJk4RmktIsCgmbN1ar/LWvvcI7J+c5MvvkWymKcj+HmW78vwHfBopCiC3gt5kGyu8LIf4j4Brwq1/mRSpfnpVi4vrfr69jSaXuePx5EYYRW/Ue67sd9psddvf2aDWbxAzoD33MoI8/7nAsL7jaFXx3S9Kli105jzN39ratf2VoIT0dQhfNdumPXCIgigSEgsZBfa9CMs7o/IjBR4PphluANWsT5r9KMnuEROrW7XstHd6Zk7xdlWz2NC42THp+HM1yyCRsHNvENjUycQNTFyxW85w5scrybIHTK2W1Wl55Zt03WKSUf+cuh37mMV+L8hTcvPjxee8TDsKI9VqbS9st6o0me3t7jIcDyhmLlaLNlf0RzcY+wbjHYhp2BvDdTejSJb7wAfHylTueN/LiyEmE0IZ3PC6lRF7zqZ8fEA4PKg+XTFJvpbAqNs3zKSIkYcgdi1MKJEbk8kolztzcLGsLRVKORXsYsN2eoFtx5ubmma0UOXOkTCn7/IW98nJRK++V514YRmzsdri43WR3r8729g4GPpW0Ra6Yoj8OOL8zYHtnB+EPmUvB2Ic/u6pNWyozn941VACiwEL6MPYHeJFLMm4RRDDyAsRuBOcnhJ1p7S8ja5B6M4W9YCOEIAoMhNSxDR3LuL3Lyg0idtouTjLNXLXC2kIRLxJ8sjUAM8bCyjGq5SLH5wvMl9Jqf3nluaCCRXluhWHE1b0ul7Zb7Ozts7O9jS59FnM2vbHOR5t9Gn2fnfaITmOPOBNW8hqubfH9bZNOOEZktnBmP73n6wgRgdD5fEBFAmE9IPpwDO1pC0VP6iTfSBJfiSNuevP3hikMYZB1zNvGQvrjgP2+T6lUplzMkc+kWG+4YNjMLR2hWimxOl9gsZxRgaI8V1SwKM+l7XqPT6/W2dmts7OzzWA4YuSGbLYmXNgd0pu4jIIJrhcS9BsQDDGkz2dbBkKLM4qV8Z0+ucUP7rgvys06wxGRn0RGgqAd0L04gfp0DEWLaSRfS+IcdxD67SeadIrEtRirlRszxyIpafR9hj6Uq3PYThJPxBlrSRZWKpSLeY7N5VmqZFRdL+W5pIJFea50BxPOru+zudvk6rWrbO+1+RT6/bwAACAASURBVGR7wHpjyCRycaMJk3CCNIfo8QkyaKMnu+h6jzAwGY0TeP4xIsaI1CV8MUTn3gsKheYjByP4UR/q3vSTBiTPJEmcSqCZd37z94ZJwlGWuG1z5CBYvCBiu+3iaw7xTAEtlmF5eYFSucxMIcPyTJbZQkq1UJTnmgoW5bngByHnrjW4uNVga3OTy5u7fHStz3pjQD/sMZI97EyTWK5OMtXCHyfx6hEi2cewGtdbJVJCs3aCUHeRmQv0JwECgX2XcPBrPtp3WsgLB7s36gJ7LU76dALDufuPTxRpDGpLJPUkry+mAcFGK6DWi4inCszPz3Hm+BKLczMslKaBkknGHvNdU5SnQwXLU+YHIb2hy8j1GU18Rq6P64eEYUQkJVE0nfpqmTqmoWPqGjHLIOXYpByLRMx64X+73Wn0+ejKLls7u1zZuMa5rR4fbvboBl1GdEhWN5id3UAzfaSESbuE35YwGWHYjVu6uqIohkRHmEO0RJ0wsBm4IZYhbhkD8fd8+t/p4547CBRDwIkiYqWCbcfAHBCGt+6JMi27J5CRRm97FT0skUlmiSeS/KgmcZIFTr6+zLGlOd5em2OhnKFaSGKqEizKC0YFyxPm+SH7nSGt3phWf0xnMGY0HOG67vUPz/eIoggZSaSMDupF6eiGgaHr2LZNPB4nHneIxWxyqTjFjEM5myCbjL0wQeP5IR9f2ePydp0rl6/QH/T5f8422ex26IYdnMoG1cWLaOaNxYzBOEEwMIj6Y6xY/bbxkyh0pmPw1gBhBBAahFLDDyWWIfD3fQZ/PmDy6cFmXAY4bzvob9tojokZxdC9OOHQJvIlvhdBFDE9qUAKcNsVoqBMPpvnzbUSGDFOnZhjbXmWb5xe5JWVMoYaO1FeYCpYngA/CNltDdhp9NltD+i0O/T7PQaDIePxiLipETM1bFMjZWiYjkATAk2AJvTpLKQowg8nhJHEHfSotyLGfogXQiqZJJ1Ok8lkyaSTVHJJFsppipl774v+LNttDfjw0i5XN7fZ2dnC1OGPftxga9DAtWuUVj/ESvZveU4U6rj9NH7LxzBb09lcXyDEQQiF1jQKtBBCA7fuM/zeiMnZg0DRwXnLIfGNBNLR8MMI05SkE20if0yYid26J4oAGen0d1YQVpFiIsNPnsizVM1zcvUIp4/OcnqlrFonyktBBcuXqDd0uVJrs7nfpdVq02q16HY7JCyNdFxnMWOQqKTuWCX3sMJI0hsH9Pt1Lu/VCKRGPp+nWCpSymdZqkz775+XNzQ/CDm7vs+lzTpX1q8ggjExQ+Nf/MUWtVGDKLVF+cT7aEZ423O9Xo6gE6HJIboxvuP5dWM4nS/spZCBjWwERN8bMLhwEDgaOG86JL+ZRE/r+GGElALTMLAMDU0TaLaLYbvXzykjgT9O0Dz3JnG/TD6R42fOlPnaa2vMVcucWSlTySe/jNulKM8kFSxfgnZ/zIXNJlv7Hfb29qjX6zimJJ80WVpIYD7GbhBdE+QSJrmEySLg+hHNQZfLF+psmDGuVSpcKJc5Opfn6GzumQ6Y3tDlr85ts765zfbWJrMZi91xxP/yF9vsTepo+Q1Kxz9CaLe3RCLfxB9bhP0Jdvzu1ZqFiLDsPcZNSfB/mHBtMD2ggfO6Q/JbSfSMfrDBVkQkpxWGNcI7/gIQhdNB+v7mKkmKVJIZfuOnT3Hq+AprC0WOzubUlGHlpaOC5TGaeAGfbtRZ32myvbNNq9mgmDQ5NRsjdodNmr4Mtqkxm4tRzdr0xgG13S12dnbY25/lyk6Z1fkCR2fzz9w4zOZ+lx9d3OHy5XUmww6nZh06w4Df+942tcke9swlsiuf3nXNydaOxNvvY7hdYs7twfM5b8/D//H/jawdBIouEGcsct9MYeentbeklNMik0xDJWYZBP6t54xCndH+HN3Noxh+lhRpXluu8A9++ascXyxzcqmoankpLy0VLI9BFEku77Q4v9lge3uHWq1GOWXw6kLysbZOHoQQgoxjknFM+uOA7YOAabaW2G5UePVIhXw6/lSu7WZRJDm7vs+5q7tcuniRmOYznzVp9Ub88z+vsTtqohUuYc9+yMQDBIiDFfC6JtA0gUAg/QSMQzD6fPHbWkqJt+sx+HCAt3uwDkXXEPOvIY+8hlZpYiQ+A4bXtwJGaFiWScw00HWNwJ9uA+z2M4wbVYZ78xhhiiRJFot5/uZPnuYnXz/CKytlsmrasPKSU8HyiIZjjw8u1tjY3uPqxgaOEXF6LnHXdRFPQypucCJu0BsHrK9fpt5o0OwMOL5Y4tRS6al11YwmPn/2o3U+vbzJ5UuXSVoRthayvePy8faEi/UhE3ufZOVHuO7BGIiY/jEdeNfoDF18T4dhBgKPgDG7LYGhaxTScdxtl8GHA/z69PnCFCROJnBOJGjVTkBYxuwW6JxdQou30ZJ76LERph0RaSYjaRKME4w7KYJRFlPEMIVNWjosV/L8/Dtr/PxXj7O2UKBwl31ZFOVlo4LlEVzb6/LRlV3W16/SadU5UnZIx5/dW5qOG5xZSLLTHnH27Mf0+0u0emO+cmIOJ/Zkum1cL2CvPeTqXofvfnSVy5ev0NrfIWN4DIMJvu9j6IKzO3FG9Eks/AjD8K9veyJv+jMKA2QYQCimnzuYBSalJNr2aXx3SNCcFocUtiBxKkHiRALN1hjszmP7HrPpDuVChY1ugn4/iRzNgQ6hBlIINKGhCx3HAyFNSpkER2bz/OxX1nj3zBKr8wXVQlGUL3h23wWfYVJKPr6yz7mNGpcuXcLRQ07PpzDuUCvqWaMJwXw+Rj4RcvHaBoPBgOHE463js1/aaw7GHtv1HnvtIc3ukNp+gw8vbnNtY51o0mU+JXEMjVhcxzIMrnY1PBGgOS1i2X3uuJsW066wUiaO7xm0ehAFEq0WIC77hP3prDEtppE4ncBZc66XXnF7Wdx2lbyZ4GdOZtE1j7l4AIkyoRbDNG3cMEITNzb0snA5MlfkG1/7CvOlDMfm8mrXRkW5CxUsDygIIz64UOPCxg6XL19iIW9RSj1/XSCOrfPKXJL1eouPPxkxnnhY/ohq7vF8LX4Qst3os1Xvsd/q0Ww2abc77Le6tAcu/fY+JXPMQsnii/MINjoCF5dY/tqhXksLfOSnNTjbIPKmLRQ9qU8D5ZiDuKlc/bhVYrS3RNpI8/ZyFj+UDAONlaVFFip58pkE3XFAZxjghoJisUCpXKa1X2MmG+cXvrqK9YQmYijK80oFywPw/JDvf7rFpY1Ntjavslp2SD3DXV/3Y+iCYxWHnY7LZ+c+wzQMwlDysNt8SSnZbw/ZrPeoNfs0m00ajSaDQY+cYxDXwNQigkGdtD5hJi3uOMur50FISCzRvufrhb2Q4V8OGX0wQnrT7jGRieO8kiF5FLSbWpBSwqhexW3OkzUyvLGUIeMYRIZDIV8imUrRnAjaQUAum2WhnCWbyTBbTLFUyXLlYJ2LChVFub/n913xCfODaah8dvEK9b0dTs4mntgU4i+TEIK5XAxDc3nvs3UiKTm12eT4QuHQ5/CDkGt7XdZ3O9Sbber1Oq12G50IP4xwA8l+12WzOaLX2CVreRwtGAhx5/s3CSAiQhjuHY/7dZ/h94aMPxrDwSxga8XCeG0Wo1JBHwl8L0Ro01peiIBhfY6wVyZppjhWTRLpFkMzh5nMUZqZoZjPkc1lyaWTlLMJZvJJihnn+sSGu28DpijKF6lgOYQwjPjhZ9tcuHKV+l6Nk7NJrDvtMfscq2RsSk7E1Y0NfnzxKLapszSTvedzRhOfK7U2G7tt6vUm2zs1Lm632O24tIY+raGHJ328wMf1JcGgjuaNMAn4gWZQzcQ4WnFYm0ncsq4mbYHu6YSTFEZsut5ESol/zWfwvQHu55WGBcReiZF8N4lRNXCDEYZoYfhlItdC+jZeL85ov4Lmp0ilUqxVk1SLWapzcxyZL7O6UKaQccin4pRzCTIJ+7ktg6Moz4pHChYhxH8O/MdMp+l8DPx9KeXkcVzYs0JKyXvndzi/vsnO9ianXsBQ+VwurgERF86fxzQM4rZJOXf7/uqDsceFzSbX9trs7e+zfm2Hz7a6XNob0nXHjMIhnvQI8TCcPpgRkT+EWJfIGjL2YvTHCfpNm812nHM7CX7yRI580gKg6EjMgYXbXMRK7TD5ZMLw+0P82sGUY2O6Sj7x9QRGfvotHIQRuqZj2R6x9B7+MEn32nEmnXnS8RSZrMNbR7K8trbMwmyFr6zNsljJPrHZcIryMnnoYBFCzAH/GXBKSjkWQvw+8LeB331M1/ZMOHetwcWrNbaubXCi+mytT/ky5OIacUdw4cIFTNPgW68uX5/9NHZ9Lmw2Wa+12NmpcXVrh/O1AZ9u9+n5AwbBAOG0SCxskkq3MOJD3E4Rt64hoyGmvXd9TCWKNLx+ln59Frfr8kc/Dvj33iiTTZicKko+3pHsv7fP6F+1kaNpC0VzNJy3HJx3HPTEjW40KSVhBIZpwCRP+9oy4/o8SS1NwUlxai7FuyfnWF09wtpimZNLJVVdWFG+RI/aFWYAcTEtGesAO49+Sc+O3daAT9Z3uXLlMkfLDnHr+R9TOYz5fIzLeyMuXbpMImbxzok5rux2uLLTpFbbZXd3l8HY49+ebbA77NIL+tj5HfJzV7BSnevh4Q2TBH2DaHB7CXtNi4hlWlipDv3tFRpD+JOzGt8+YvL+e3/F3ocfEQYHixrTaeJv5Um8JTES3i3XGrgxJp0ywWCGcDiDJRPE9ThVK8mxSpIziznOnDjKwmyFM0fKlLK3t8AURXm8hJzuTvRwTxbiN4F/DIyBP5FS/vrnx7rd7vUTX7x48VGu8amYeCHvX25w6fIVUrpLMfFy/YbrhxEX6gEyXsKKxTCjMe1WC0cL2B1K3tsO6MkeMlkjtfgRZqJ7y/OjwMRtVfD2AgythqbfvYc0CgX9swuwvUvQqV3/fHFmgWj+a/iFRXzdJxQhGGPQfJA6MtIhiKFLE0vYJIwY+bhBOaFRzegsVsuUy0WWyikWColnrj6aojyvVldXr/89k8nc9oP1KF1hOeCvAytAB/gDIcRvSCl/72HP+Sy5sNNjp7aLHk0opl/MloqUEi+ESSCZ+JKxD2447VYaTgJ2+yG11gUM6ZN3BIW44IOOxfYYxnofs3KO+OynSA2CUKBpXK8A7A/yBJ0Qjd5dQ0WGEveqy+TchLDTAKZlWlaPHeOVV14hl8sRSrg6dNmd2HQ8By9IIT9ffx9NS7vMZqaFPmdSBpNAkkhmmJmpUC2kOFJJEXtJWpqK8qx4lK6wnwXWpZR1ACHEvwLeBW4LlrffftiVEY/fe++9B9z7mrbqPS61L5Nw9nnn+PGnVkjycZNSMnRDOqOA/iRg5IZMIp9JNMENXLa2t5h4PsLOMJyEjAddtPEAExcnlmG9n2dnIhlbLeKLP0RP7yClIIo0pCZAaghNQ4viaIGD7k+wnAFCWLdcRzgIGZ4fMr4wJnKn84WFraMXV1k98Ta/8vXlWx6/cP36YeRDEMHQDeiOQ5bnZ6mUC0xCjXgizdz8HLOlPKdXyo+1dtdhvm9eRuq+3N2LfG+63e49jz9KsFwDviaEcJh2hf0M8N4jnO+Z4PkhZ9f32NjYYD4fe+5DJQgl3bFPdxTQHQUMRmOGoxGj4RDX9RAyxDYkMR2ENyAMdGytjzHpM2NOSNgezYHP9qjEVigZmx0yx/8/zEQbKTUkB7W5ogAvAE3T6DQcotaQnDFCiIPWhZR4NY/huSHupvt5uS+MvEHiZAKjmme4uYYw7l5xWQhIWNAa+ow9SakyS2gmIJbh2Nwc1XKBtYUCM/mkmjKsKE/RQweLlPIHQog/BD4AAuBHwD99XBf2tFzYarK1XUOPJpRSz+euf2Ek6Qx9GgOfztBjNBoxGA4ZDUfIyCdpSrImxNJgaBBGsDeE3kTSH7TJJUyKhoshJCCQVpL1QQw33iN95HuYByvihRCfFxtGRyA1SRBCMDahHxBlOwRuhHtlwujciKA7LbeCBrGVGIkTCcySiRCCSSeBLgyyibt/S0opqXV8mhOdWKZItjjDmZOrVMt51haKVAsqUBTlWfBIs8KklL8N/PZjupanbuIFXNlpsbOzw1rl6e9V8qCGbsjlvSFntwbstofUu2P6Ix9NSHQN4gYU4pCNCapJScKcdi3tDgSdXp9et02SIQXzRqBKCZfcMr41wSidRUvsAnces2j1xgcD6kB/QPtcEzb96b85mC685uCsOujOredwezlszaScsm4/MTBwIy41fFziLK0c4c3Tq5xYrnJ8vsBsMaUCRVGeIWrl/U0ubbfY3d0jaU2LND4PIinZ67h851ybj6/1qHVHeNGYkAApQqQ42Bs+BOELNsYGBjqmtEgaGqV4SCJsgT8kSxdd3LpTYjOI04s0IqeHmT9LGGkYUrvjG7nnhXA5hA+vwO7g+ueNsknyVILYYgxxh5lZgWsTDLPk7BjHZm5MB/ZDGPiw3w9pjAWzc0c5cvQY33p9hdeOVtTUYUV5RqlgOfB5a2V3t8Za5dnfXyOSkt3OhD/9tMUPL7ZpuwNcRoT6BCuzj5loo8f66Pbw+j4lUWARjtP4owyD1hKdocHu/oiU8Didc9HE7Vv6brspPN3DKlxC0yPCEAItwjRuBG/QCRi9P4IPRjA6GDzRBcwbiBWD1GwC2zTuGEZSwqC2hKM5rM4kMHSN9gQGHkxCnUDYkEjyldeO8sbxBX7+K8fIPQM7XyqKcncqWA5c2+uyX68/862VMJLU+x5nN/v88Y/32B/0mYgBItHAKV/EztUQWnjX58tEC71XRhd1vP0Y/jhGx4vz/n6MOSvGbPzWqcG9wCY0Jljpzen+JFFEGEn0IMK76DF6f4R7+UaxSKNoEBzLQHmGpK4TiRZRNEZKecdgGe4vIMdlnHiWciHLRlcnmUzi5OJEvkG1kOPM2lF+4tXpplqqy0tRnn0qWJgOCl/d61Df32cx++ibN/lBxMW9Ec2Bx9ANGU5CbFOjkLQopkxmczESDxheUk4DZbvl8lcX63z/Soeh7BPFGyTnzmJla3csQX/LOUIdr1ch6GhEfZdY8iqkArzOLMPWEldHMSIJ+fz08aEUTCKDSIRo1gAhQHZDRmdduh+7RIODFo4O8VfiOG85mAsmza6LHIChxXA7ZXwXtEiiaREIOV3cKHXcXh6vVyWVzPP1V6osVnNYts3EDxG6wVvHlllZmOPN41W1S6OiPEdUsACN7ohmu0foT0jFUg91Dikl52pDfni5y6fbA/r+GD/yiYiIZITGdItbQzOxNYtj5QRvraR5Yyl93/pjg0nA1caERqfP98/t8UndY6x3MUuXySx8dM8WyvXrizS83gx+G+RwjGHtIg7GX+zcNsJwmeytsjmOMzeeDvJrSAQSGUq8Cz7eh2OC9eD6OfWiTuKtBPFX42jOja+hmI0hMy0izyW00mjSxtD1aY+cBITGuDWLzzz5YpZffr3CV45k8IKI5tCnOjPL4uICxxdKrM7lr5euVxTl+aCCBdhu9Gk2GxSS1kN1tTQHHn/wg10+2enSD/uMwzF6ooOd6qCZHobhEYUm7thhOHHwB1kaWw4f1xL86w8cfv7VEj9xPIf+hYFtP4zYak2otcfU63XOb/c535KM9S7O0nvEihuHuj4pwe+XCDoCORxhmLuIL4ynWKkGgWvitY/wWSPB1+clw34P79KfEdU+YeSOpg/UwThuEnvTIXEkhqbd+U1fCNCsAWamj2naxE0HpEHoWXSuvIIYzzCfyvNr78zy6kKKzdaEULNZO7HKUrXEmSNlUo7a+ldRnkcqWID99pB2u81q+c5TXe/ls50Bv/vvtqiPOwxpk5q7TKVUw4iN7/qcKDAYNyv09xboDkr87z8c85cXO/wHb1U4MTud6dTse2w0xjSabVqtJkEYcrEj6Gtd4ovvHzpUAIJBgaBnEvU9DGvvtlD5nJnZYtzL0azV+JPPNuh3mtePiVQS++0Q+4xFZAs0Ted+ZeYiOV3rohsCzQgYNyp0N06QkEXmM3l+7Z0ZTF3jUt1nbm6B2WqFV5bLLJQzh/7aFEV59rz0wdIbunT7Q6LQx7EebLbRxd0h//zPN6mN99Hz15g5+gm66d33eZoRkKhs45S3mbTLdNZPMGgU2Pl/R/zCmQonqg47zSG12i5aNKHqwB9f1hjQx66cI15aP/Q1BpMkwcAh7PgHLZXbu82klAT1gMnlCeHW9whDiQsYhsHs/CLd4juMinkoXkTY76OJkCiKCKW8y4qWqTCSaJqN31yiWzuG7uUpGBnWZrJ8+0QeL9IoVKqsVWc4Nlfg6GzultlmiqI8n176YKl3hnR7XTIPuHf9ZnPMP/vOJrvjOmb5Ermjn9x38PyLhIB4fp9YtkF/e4W9ayf4l+8FLCY1jmZcKo4kE4PPGoK66xPGmqRmPz30+aUUBMMMQTtE1+sI7dbQi4YR7oaLd8UjGt7UiknlSRSP8XOvz2GaJm3f5P2Bw7C5xnBYxip9AolNpHHnJkvkx/AGGSbdCmF3mbhIkzNSzGSTvLGUppqPU6xUqVZnODJbYHUuj2299N+KivLCeOl/mhvdEb1ul/wDBEskJb//g112x0304pWHCpWbCS3CKe0QeCbtC33GDfAyJkdeLyClxmcNwZgxTvUzhHbnbqw7ae6bRB0fJwzQrCEAMpD42z7uukuwe2MgXsQF5pKJuWwyaX0VU2bQDoIjZ054K7nLZ6MS3WEFb5zD1z28eBc3PkJoETLSkZFBMMqCH0dEOpZmkzdTrJTSHJ9xWCglqM7MUKlUWK7mWVsoELfVDo6K8qJ56YOlN3IZDkcszBx+fOX7lzpcbvZwjRYzjxgqAN4ghdtNwaBJslBjWCuw1Snw559pnF7O05hEBGYfK/tg+6hJL4McSIZyB2ojjJrE2/Kul1hBA3PexF6xMSoGYTTtJhOdEBlK/BD0g++QnOnyTnqLmpti10tSH6eRfhpjpCE0EAf/6ehokSDr6MwVUpxeylHOp5iZmaFcLrFUyXKkmiMRf/DxLEVRng8vdbD4Qchw7BL4HrZxuHUSfhjxRz+u0/HbZI9/hqbff6rvvbj9DF7HwW946FoTOznAWGjRu2pwYV9jKON4GFiZ3UO3VprdEVGoEeyN4ZMm1NrgwucdYXpBx1q2sBYtNPumWV3RtPtMhiYCganf2tWlC5iP9ZmP9WmNIkZammy+QDIeQ9fAEJIgCOhOBOlSgVdXl1lcmKVUyLM8k2V5JotlqjEURXnRvdTB0h95jMdjYtada1/dycXdEe3JGOIt4oXdR3p9t5/Bazt4DQ/TaKAb0ym9ZmxCav4S/WvHudTMI1Ngx3qHOmfYCwnfcwk/9aHVvnHAEYh5HW3eIF2++yQF6cfR0HCMaZDcTcyQiGhENZ6ikLXpubDXj+j5JkdW13j79HFeWamwPJOlWkip3RsV5SXyUgfLYOwxnkweaC/7D6/1GYcjnJn7r3S/F2+QvhEq5j76F3ZZtBJ9nMomg+YiUahhm6O7niuaREw+mzD+aIy3cdMAva1DJQ1zQ8gJ9EPMuApGRQwM0vdYQiIlhBj0fJ3NnsbYMNAsBy0d52trx/nGqyt869Ul1d2lKC+plzpYvCDE933Me/1qfpNISs5uTRdAlh6htRK4MdxuEq/hYpr120Llc7HcPoPeEBllmEx0bm5nRF6Ee95l/MkY95ILn/fI6RBbixF/NU4vNoPsmAi/C1qDlHPvN3opIejPkMBkLiVv/bwU+FJnEhm4kY7QTSLbJFWYoTRTwo00fvLMCd59dYVTy+WHvjeKojz/Xu5g8UPCIMQ4ZDdNdxQwcH2kOcJ0hg/1mlGo43Zz+E0fQ2+j63dfSNnsjYisHWSUwZvECdwI/7LL5JMJkwuTG4PwgLVsET8TJ3YqhhabjpuY3gTPSdHbBSZxwmCCpo1BeHdsbQX9KiKIk7AM4qagF2h4UsePNDTdxLJMYrZNJhbDNjSaPZeUEyefcTh54iSvrc5xfKHwUPdFUZQXx0sdLH4QEgQ+sUPWomr0PXwZYMTu3i11L1KC283jtyNEOMSw+/d/kr4JuzbRuXXqe3vg3zhkLpjET0/DRE/e3s2lWxPs3C5Zs0g4tInGSQJXQhgC0fRDSAQQBTG83jEs3aGctxibOpZpkrQsLNPCMjRihiRuQsKcfjG7HYkWS/LqmTO8vjrL8kz2oe6Loigvlpc7WMKIMIzQDrmUYjAJiWSIbrn3f/AdBJMEQd8gGoyxYs27Pq7eHiLrAeE1D3bPQXDu+jFz1iR2Okb8VBw9c/8xE83wsTI1oniCyI8dfNgcbFYPEqLAxN07hZXMMGMLTi/HsAyJrUPMmH4Y2o2usYEHe0ONWLrI0vIK33x1mULGeah7oijKi+elDhZNiGmX0H1qXn0ujCQSeddaW/fjj5L4/QDDbN92DhlI3G2XydUJweb4lpYJ6QQUX4MjJZy3foATe7BZA0KAbg+nm34xrXQspQZSEPkxepe/jkOWggXfKLZYzlXveJ5IQnME/cBgdq5KfKJxcqmoStorinKLRwoWIUQW+GfAaaZvz/9ASvmXj+PCngRNEwihcdiYcGwdDY0oePDV4qFnE451uq0ewmhQyjrTAfitaZi42y4yuJFwRtYgmtHR5k2KcxmaOycJSDDc0Igf/+EDrcD/IqFFCCK8XonBxleJ+Tlm43HeTGxj6XdO2b4L9ZHASaZZmiuyVEqw1Zpgm4aaSqwoyi0etcXyT4B/I6X8W0IIC3iu+kMEIDSBvF+Z3gNxS0MTDxcs/jhBOAjAbyO3PVrvTXB3XG5ONbNoEluKEVuMYWQMGt3pWI4QEancD2jXfo6ovUj3oklq+X10++HGeiI/xqi2hlc/RpIUiwmTn16OaNdvvw9eCPtDCLUY1bkSxWyK5VIc29CodX1MQ1e7OiqKcouHzzYGogAAERJJREFUDhYhRBr4FvD3AKSUHjcWdz8XDF1D1zRC//6PBUjaBjo6offgXT+7n7UJv1tDNgbAjdnBVsWahslSDD1x65hJ8aZxC9tpYsiLMDmB3luk82me+Mw5YqUraMbhvoBgkmTSWMGtH8WOHHI4vDkDb1QihID2zY+NoD2BnqeTzxcoFnIsFuIUUyZCCCZ+iGEYWKoasaIoXyAO+9v6bU8U4nXgnwKfAq8B7wO/KaUcAnS73esnvnjx4qNf6Zdgqznirz5Zx+vtU03f/w0ykpL/6Xtjtv198q/9G3Tr7lOFv6j2cZLwD85Nm0lFHW3OQFQNsrnDh9Ro7yhaf4VifoaejDHRJvi6i5GqYSQaaHYXzR7w+aCRDGwiN004yRAMZpCTLFZkYUc2szGPtfSAjBnc8hpBBP3AZBgYJJJJ0ukMxaRBOaXdMi177Et2RiavvbLGm0fUFGNFeZmsrq5e/3smk7mty+JRusIM4E3gH0opfyCE+CfAbwH/7SOc84mKmRqmZTE8ZLkvTQjmMhr7DQu/X0AvbB36tbKzWYZfP4qXq6NZksx9Five8fUNDwhYMNtkUw6XBgn23Th+O0nYOUIgQqKb+tYEAk1q6Og4kYEtNGbjE1YSLbLWFwNF0AsMRqFJIplkJpUi55iUkhpx8/auLi+Q2JaFrWp/KYryBY8SLFvAlpTyBwf//kOmwXKbt99++xFe5vF67733gOk1dQcTulGCK5pkdeFwe92/6TW50Jvgj2eIxRqHfl0Z05DHygS9IUKMsawHD5bAgkjXiCXSvH4ky+vA0IfNrklrAp2JYHDQGSkAQ4dcDLK2pJSQzCRA15JA8vo5xz50XfADHc31qKZSvHpihblcDMe+e2hstSZUnSJfe+sMa4vFB/5anjc3f98oN6j7cncv8r3pdrv3PP7QwSKl3BVCbAoh1qSU54GfYdot9txwYiZ2LMYkkERSoh1iEPrkbIK4HqfXqBKtHL66sW6P0Z0EmaCCZe8/1PVqekBIhBfcaJUkTDhR/LzX8XDdmkEEfQ+6EwG6SSaTpZxJM+7sU0xqrM4k7nuOsRdSKMTVvvSKotzmUWeF/UPgfz2YEXYF+PuPfklPjmnoZBIxYrEYIzckGbv/7ZjNxThWStHZSTHanyVZ3TzcazlDvGSScODgezlMq33/J33BQw6HARBG09ZN34NxoJFIJilXM2RSCUppi1LK4trG3RdtftHQDVlwnPvWH1MU5eXzSMEipfwx8Fy383KpOIlkksGkf6hgAfjmWo5ze206tWUSM5uHqnIstIhYtg0yj7efwXc1DOv2hZL3Mt0nRSNmHq4EjRtMw2TogxfpxOMOqXyCajJFPmlRTFlkE8ahWmq3nNePkEInlXRIqgrGiqJ8wUu98h4gn4qTSqbo7HcO/ZwzCylKiSTdbp5Ro0qiVDvU8wx7QjzXBAoE7TTuyEHXBxhGD6Hdv0st9GwMNFJ32EY5ktMgmYTT/498gdBNkskE+XyChBMnHZ8GSSFhYhqHC6c76Y590pkMxYyj1rAoinKblz5YCuk46XSaqxv+ocdZDF3wS68X+RffG9LcOEE8V0czgvs+D0C3XeKFOr6dwR/HCPsm7jCNkD6a5iE0F03zQIQIJAgJSKQUeKM0lmZjmRadybR7y4tgEggCKbBtG9u2iSdj5J04ibhN1jHIOibpuIH+mFbId0cBuUqGcvb+YzGKorx8XvpgScQtitkk8USS3jgg6xxuVf1XjmT4/qUMP6oV6KyfJL/68aFfUzd99FwDK2niJVIEkxjSt4i8ONKL8H0JwbRApJzmCpFvEckqVjyPncrjGjq6YZAwTfK2Tcy2ids6iYOPpG3cc1bXwwojSW8SspxJ37KAU1EU5XMvfbAAVAsp8rkcrfbuoYNFE4L/8J0q1/54zM7+MoNkl2T12gO9rmb6xDItZHpaYTgKzGmABCYy0kFq03leUjCsz+L485xZmuHM8SKGLjB1DdvQcGz9oNzMl98t1Rn5JJIpSrkUTuzBS9soivLiU8ECVAtJ8vkC21ubh+4OA5jJ2vzaO1V+73sh++un0e0x8Xz9gV9fiINWjOlD/Pb6X5Fv0lk/RSnm8HNnioeaDvxlafR9ijNV5kvpp3YNiqI821SwACnHppRLkUxlaA48SqnDz3R652iW5sDnjz4KaZx/k+KpH2JnHnwq8b10r63iyBwnZzIcn3l63U+uHzHwJGvFwksRLL/1Lz9ivTHdaqDfn27Klnr/RvHulWKC3/mVV5/KtSnKs0wFy4GVaparMxW21i89ULAA/OKrRdoDn7+4LGl88jWyRz8mUTl8uZd7mbSLjPaWmbUz/M2vVJ7qLKxax6VcKjNfSmO+BMUn1xtDfrDeuvWTjdadH6woynUPP+f0BTNXTFMpFpC6RXd0yHLHB4QQ/O2vV/lrp6qUzRl6l96gfeUkMny02zvp5mmee5uiWeJnXylRzT69Ve5eENEcBsxUZzg2l39q16EoyrNPtVgOaJpgpZplZ3aWra2rpOPGA7UOdE3wN96uUMlY/MEPdZp7JrVWhezyOeKF3UMtovyclDCqz9K5fIaCUeZbq2V+8bWnW49rp+1SLldYquRUGRdFUe5JBctNVqo5NnYr7O7u0Rz4FB+wSwzg3dUc1azNH/4wznorRedCmn5yn2T1KvH8Hpp+95X2UoLby9PbPErUq1Iy87x7tMivvjPzRGZ83c3ED2mNQs4cm+H4giqRryjKvalguYmha5xYLFJvLnLp4jlyCfOhFhWulBz+y19a5vuXOvzRj+M0x2mGl6q0GWFnmpjxPkZshG67RIFB5Fv44wTjVgU9SJLQE5SSaf76WxW+eiTz1Fe3b9THzM7OslLNq9aKoij3pYLlC+ZLaeZniuzv59hpD1goxB/qPJoQvLua483lNB9s9Pjh5S4bjRGTQYmgH+DJgFCGaEy3OzaFQUqLUck7vL6U4qdOFUh8CQscH1Sj7xFoNvNzs7yyXH7al6MoynNABcsXCCE4vVKm2R3w8ccfk3WCO9bmOqyYqfPuao53V3N0Rj7r+2MaA49m36c3DohbGgnbIB03ODGbYC5nP/UWyuf8IGKzNWF17SSnV8pYalMvRVEOQQXLHeTTcU4uVxgMBly+conT8ykM/dHf7LOOyRvLz8dqdSkll/dHlCpVlmdLLJQzT/uSnriV4o2FqNfXsaRSdzyuKMoNKlju4vh8gXpnSKfTZaPR5mg5/sy0JJ6ErdYErARHlhZ5Y7X6tC/nqbh58eOLvBugojxuah3LXWia4M3VKkdWlvGEzXbbfdqX9MS0Bj7NERw7epS312aJWer3D0VRDk8Fyz0k4hZfOTHH8dVVmmOo97ynfUlfuoEbsdF0WV1d5dWjVQqqgrGiKA9IBct9lHMJ3jw+x9rxNTbbHu3hg63Kf56MPMl2D1ZXj3P62BxH1Qp7RVEegurjOISlmSwj1ycMQy5cOE8USQoPsXjyWdYfB2x2I+bmFzh5ZJZXlktP+5IURXlOqWA5pJNLJYQQaJrg3PnzhFJSTr8YiwVbA5+Npsvc/ALLs0VePzbzUk1UUBTl8XrkYBFC6MB7wLaU8pcf/ZKeXScWixi6hhAa5y+cZ+KNmS/Enmq5lUe123Gp9UNOnDhBNGpzrJpSoaIoyiN5HC2W3wQ+A178DTqAY3N5TF3DskwuXbrEuZ0BxyoOlvF8DVcFoWS9PsKVJqdOneL11Tk6tfBpX5aiKC8AIaV8+CcLMQ/8z8A/Bv6Lm1ss3W73+okvXrz4KNf4TOqNfD7b6rBV26PdqDOTEqRjz0e4DNyI7V5EJptntlplbS5DKRN72pelKMpzYnV19frfM5nMbV0cj9pi+R+A/xpI3e+BL5q0Y/LGkTxxy2DHcajVanQmHtWUhvkYVul/GYJQsj+I6Ps6cwsLzJZynJjLELNUqRZFUR6fhw4WIcQvA/tSyveFEN++12OfpdXKj3sF9del5Opel0/W99nc2mZvt0YmY1JJ24+lDMzjEEnJXtej1vFYWSwzPzfHicUSxxcKt4ynqNXld6fuzZ2p+3J3L/K96Xa79zz+KC2WbwD/vhDil4AYkBZC/J6U8jce4ZzPHSEEyzNZZvJJzuaTrBcKbO9s89Fmi0rGeqoBE0aSet9jt+PiJNOceuU4S9UCp5ZLJOMv1nRpRVGeHQ8dLFLKfwT8I4CDFst/9bKFys1ilsHba7OszGQ5X86xvd9me2ebDzdb5BMG5bT9xMrgj9yQRt+jMfBJZbIcWztCtZTn1FKJck4VTlQU5cul1rE8ZoWMw7sZh2a3wPlyjlqjS71e51K9jogC8kmTdNwgGdMf2zRlKSUjL6I99GkNfKRmkM8XeGWlzEwhw7G5PJVcQk0jVhTliXgswSKl/A7wncdxrhfF5wHTH5W5uldmu96j2e7S7Xa41u3i7vVJ2TqOrRO3NOKWTszU7hs2YSRxgwjXjxh5If1xyNANMCybXC7Hkdk8+UyaaiHFYiVDNqlmeymK8mSpFsuXLOXYnF4pc2qpRKM7ot4ZUu+OaPWG9Ht9RuMRrdGIUXeM57poAgxdoGvTDykhiiSRnIZKIMG2bGzbxnEyVAoJkqkU6UScUsZhtpiimHFU60RRlKdGBcsTommCci5xfYxj4gU0uyN6I5f+yKM/chlOPMIwIggCgjAgiiI0IRBCQ9M1dE0nZlvEbRMnZpKKW+RScfLpuCptryjKM0O9Gz0lMctgrpRm7qbPSSnxgwg/CPHDiCCcBouuTWuUmYaObeqqNaIoyjNNBcszRAiBZepqb3lFUZ5rz0cNEkVRFOW5oYJFURRFeaxUsCiKoiiPlQoWRVEU5bFSwaIoiqL8/+3dO4hVVxjF8f/CRxNTKKIENSQRC61GCSGgiDZibEyKQKzstDBgwEZskiZlEptgIYoWiSL4iIVFRARThTwQHwyiBFHjMFNYaCeJK8XdQy7qaOEZ99G9fs05Z18ufGw+zuLscy+7UwmWiIjoVIIlIiI69UI7SD7L8A6SERHxenraDpJ5YomIiE4lWCIiolPTthQWERFtyhNLRER0qrlgkbRR0jVJNyTtrl1PX0i6KemypIuSfq9dT02SDkqakHRlaGyepLOSrpfj3Jo11jLF3Hwl6e/SOxclbapZYy2Slkg6L2lU0lVJO8t4c73TVLBImgF8D3wErAC2SFpRt6peWW97xPb7tQup7BCw8bGx3cA528uAc+W6RYd4cm4Aviu9M2L7zEuuqS/+AXbZXg58COwo95fmeqepYAE+AG7Y/sv2Q+AosLlyTdEzti8A9x4b3gwcLueHgY9falE9McXcBGB7zPaf5fwBMAososHeaS1YFgG3h67vlLEAAz9L+kPSttrF9NBC22MwuIEACyrX0zefS7pUlspe+6We55H0DrAS+JUGe6e1YHna1ov5WdzAaturGCwT7pC0tnZB8crYBywFRoAx4Ju65dQlaQ5wHPjC9v3a9dTQWrDcAZYMXS8G7laqpVds3y3HCeAkg2XD+N+4pLcAynGicj29YXvc9r+2HwH7abh3JM1iECo/2D5RhpvrndaC5TdgmaR3Jc0GPgNOV66pOklvSHpz8hzYAFx59reacxrYWs63Aj9VrKVXJm+axSc02juSBBwARm1/O/RRc73T3B8ky08h9wIzgIO2v65cUnWS3mPwlAIwE/ix5XmRdARYB8wHxoEvgVPAMeBt4Bbwqe3mXmJPMTfrGCyDGbgJbJ98p9ASSWuAX4DLwKMyvIfBe5ameqe5YImIiOnV2lJYRERMswRLRER0KsESERGdSrBERESnEiwREdGpBEtERHQqwRIREZ1KsERERKf+A2PDujuDiFPmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f17cf84e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.023 0.043 0.002]\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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f17e4d630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.02  0.02  0.002]\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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f17cf86a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.019 0.047 0.   ]\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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f17f691d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.262 0.805 0.004]\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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f17fd27f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.008 0.009 0.001]\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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f17cf8da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.12\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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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24f18194f28>"
      ]
     },
     "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}