{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Adaptive Filtering" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "%matplotlib inline\n", "from __future__ import division, print_function\n", "import book_format\n", "book_format.load_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So far we have considered the problem of tracking objects that are well behaved in relation to our process model. For example, we can use a constant velocity model track an object moving in a straight line. So long as the object moves in a straight line at a reasonably constant speed, or varies it's track and/or velocity very slowly this filter will perform very well. Suppose instead that we are trying to track a maneuvering target, by which I mean an object with control inputs, such as a car along a road, an aircraft in flight, and so on. In these situations the filters perform quite poorly. Alternatively, consider a situation such as tracking a sailboat in the ocean. Even if we model the control inputs we have no way to model the wind or the ocean currents. \n", "\n", "A first order approach to this problem is to make the process noise $\\mathbf{Q}$ larger to account for the unpredictability of the system dynamics. While this can *work* in the sense of providing a non-diverging filter, the result is typically far from optimal. The larger $\\mathbf{Q}$ results in the filter giving more emphasis to the noise in the measurements. We will see an example of this shortly.\n", "\n", "So in this chapter we will discuss the concept of an *adaptive filter*. This means about what it sounds like. The filter will *adapt* itself when it detects dynamics that the process model cannot account for. I will start with an example of the problem, and then discuss and implement various adaptive filters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Maneuvering Targets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So let's begin by writing a simulation of a maneuvering target. We are not interested in modeling anything with high fidelity, nor do we really care about 3 dimensions, so I will implement a simple 2D model that you can provide steering inputs into. You can provide a new speed and/or direction, and it will modify its state to match." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from math import sin, cos, radians\n", "\n", "def angle_between(x,y):\n", " return min(y-x, y-x+360, y-x-360, key=abs)\n", "\n", "class ManeuveringTarget(object): \n", " def __init__(self, x0, y0, v0, heading):\n", " self.x = x0\n", " self.y = y0\n", " self.vel = v0\n", " self.hdg = heading\n", " \n", " self.cmd_vel = v0\n", " self.cmd_hdg = heading\n", " self.vel_step = 0\n", " self.hdg_step = 0\n", " self.vel_delta = 0\n", " self.hdg_delta = 0\n", " \n", " \n", " def update(self):\n", " vx = self.vel * cos(radians(90-self.hdg))\n", " vy = self.vel * sin(radians(90-self.hdg))\n", " self.x += vx\n", " self.y += vy\n", " \n", " if self.hdg_step > 0:\n", " self.hdg_step -= 1\n", " self.hdg += self.hdg_delta\n", "\n", " if self.vel_step > 0:\n", " self.vel_step -= 1\n", " self.vel += self.vel_delta\n", " return (self.x, self.y)\n", " \n", "\n", " def set_commanded_heading(self, hdg_degrees, steps):\n", " self.cmd_hdg = hdg_degrees\n", " self.hdg_delta = angle_between(self.cmd_hdg, self.hdg) / steps\n", " if abs(self.hdg_delta) > 0:\n", " self.hdg_step = steps\n", " else:\n", " self.hdg_step = 0\n", " \n", " \n", " def set_commanded_speed(self, speed, steps):\n", " self.cmd_vel = speed\n", " self.vel_delta = (self.cmd_vel - self.vel) / steps\n", " if abs(self.vel_delta) > 0:\n", " self.vel_step = steps\n", " else:\n", " self.vel_step = 0 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's implement a simulated sensor with noise." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from numpy.random import randn\n", "\n", "class NoisySensor(object):\n", " def __init__(self, noise_factor=1):\n", " self.noise_factor = noise_factor\n", "\n", " def sense(self, pos):\n", " return (pos[0] + randn()*self.noise_factor, \n", " pos[1] + randn()*self.noise_factor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's generate a track and plot it to test that everything is working and to see what we will be trying to track. I'll put the data generation in a function so we can create paths of different lengths (why will be clear soon)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy import array\n", "import matplotlib.pyplot as plt\n", "\n", "import book_plots as bp\n", "\n", "noise_factor = 2.\n", "\n", "def generate_data(steady_count, noise_factor):\n", " t = ManeuveringTarget(x0=0, y0=0, v0=0.3, heading=0)\n", " xs = []\n", " ys = []\n", "\n", " for i in range(30):\n", " x, y = t.update()\n", " xs.append(x)\n", " ys.append(y)\n", "\n", " t.set_commanded_heading(310, 25)\n", " t.set_commanded_speed(1, 15)\n", "\n", " for i in range(steady_count):\n", " x, y = t.update()\n", " xs.append(x)\n", " ys.append(y)\n", "\n", " ns = NoisySensor(noise_factor=noise_factor)\n", " pos = array(list(zip(xs, ys)))\n", " zs = array([ns.sense(p) for p in pos])\n", " return pos, zs\n", "\n", "pos, zs = generate_data(50, noise_factor)\n", "bp.plot_track(*zip(*pos))\n", "plt.axis('equal')\n", "bp.set_labels(title='2D Track', x='X', y='Y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here is the track vs the simulated sensor readings." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fPrhw4fb7ennB449nfYwiItlI5TciIuJYwsMxmjWDGjVwOn+ej/r2BeB6mTJ2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\n+y4//PBDNgYmIiI5xS2T+v3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WDW5zI5WIiOROSupFRLLSyZNm6c3ixfDhh3D4MNSpY47E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\nrjGempqKixcvwszMDBKn6ukUm3oiItLq3jPPAKm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bp.plot_track(*zip(*pos))\n", "bp.plot_measurements(*zip(*zs))\n", "plt.axis('equal')\n", "plt.legend(loc=4)\n", "bp.set_labels(title='Track vs Measurements', x='X', y='Y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This may appear to be an extreme amount of noise, but it will allow us to see the effect of various design choices more easily.\n", "\n", "Now we can implement a Kalman filter to track this object. First let's implement a constant velocity filter. But let's make a simplification first. The *x* and *y* coordinates are independent, so we can track each independently. In the remainder of this chapter we will only track the *x* coordinate to keep the code and matrices as small as possible. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from filterpy.kalman import KalmanFilter\n", "from filterpy.common import Q_discrete_white_noise\n", "\n", "def make_cv_filter(dt):\n", " cvfilter = KalmanFilter(dim_x = 2, dim_z=1)\n", " cvfilter.x = array([0., 0.])\n", " cvfilter.P *= 3\n", " cvfilter.R *= noise_factor\n", " cvfilter.F = array([[1, dt],\n", " [0, 1]], dtype=float)\n", " cvfilter.H = array([[1, 0]], dtype=float)\n", " cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n", " \n", " return cvfilter\n", "\n", "def initialize_filter(kf):\n", " \"\"\" helper function - we will be reinitialing the filter\n", " many times.\n", " \"\"\"\n", " \n", " kf.x.fill(0)\n", " kf.P = np.eye(kf.x.shape[0]) * .1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To be clear about the dimension reduction, if we wanted to track both *x* and *y* we would have written\n", "\n", " cvfilter = KalmanFilter(dim_x = 4, dim_z=2)\n", " cvfilter.x = array([0., 0., 0., 0.])\n", " cvfilter.P *= 300\n", " cvfilter.R *= 1\n", " cvfilter.F = array([[1, dt, 0, 0],\n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]], dtype=float)\n", " cvfilter.H = array([[1, 0, 0, 0],\n", " [0, 0, 1, 0]], dtype=float)\n", "\n", " q = Q_discrete_white_noise(dim=2, dt=dt, var=0.020)\n", " cvfilter.Q[0:2, 0:2] = q\n", " cvfilter.Q[2:4, 2:4] = q" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HEiVKcPjwYf73v/+RmprK1q1b8fDwsJ134cIF2/0DBw5kad0iIiKSPaSmpjJn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\n5swZfqvZCF566SWcP38e7du3h1qtRmVlJebNm4fp06fXeYx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# extract the x coordinates\n", "import numpy as np\n", "\n", "dt = 0.1\n", "# initialize filter\n", "cvfilter= make_cv_filter(dt)\n", "initialize_filter(cvfilter)\n", "\n", "xs = pos[:, 0]\n", "z_xs = zs[:, 0]\n", "# plot the results\n", "kxs, _, _, _ = cvfilter.batch_filter(z_xs)\n", "t = np.arange(0, len(z_xs) * dt, dt)\n", "bp.plot_track(t, xs)\n", "bp.plot_filter(t, kxs[:, 0], label='KF')\n", "bp.set_labels(title='Track vs KF', x='time (sec)', y='X');\n", "plt.legend(loc=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see from the plot that the Kalman filter was unable to track the change in heading. Recall from the **g-h Filter** chapter that this is because the filter is not modeling acceleration, hence it will always lag the input. The filter will eventually catch up with the signal if the signal enters a steady state. Let's look at that." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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iNzHGEBYWhr+/PwAlS5akb9++9O/fH5vNRqtWrVLd5+k/DdM/h7mhcOWac1sF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\nFevWraNWrVqXrTc3N5d169YxdOjQQtt69erFtm3bePrpp6lSpQrHjh0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# reinitialize filter\n", "initialize_filter(cvfilter)\n", "\n", "pos2, zs2 = generate_data(120, noise_factor)\n", "xs2 = pos2[:, 0]\n", "z_xs2 = zs2[:, 0]\n", "t = np.arange(0, len(xs2) * dt, dt)\n", "# plot the results\n", "kxs2, _, _, _ = cvfilter.batch_filter(z_xs2)\n", "\n", "bp.plot_track(t, xs2)\n", "bp.plot_filter(t, kxs2[:, 0], label='KF')\n", "plt.legend(loc=4)\n", "bp.set_labels(title='Effects of Acceleration', x='time (sec)', y='X')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The underlying problem is that our process model is correct for the steady state sections, but incorrect for when the object is maneuvering. We can try to account for this by increasing the size of Q, like so." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2fdXLQp2HlhBQyqJyqVYAPPLII+lfpEgG4PAgLyIiInLsjCH4O/h2C4TuS74G\n3tmKYkp/D3o0B5uttWOKFMlgFORFRETEIWJjDd/8BB+ugFXbUt6BBqBp7TheqL2bZ5tUT98CRTI4\nBXkRERFJV/HxhlkrYUwwnDqfvN9mM7jF7uSVDo/QpoEnFUo4AwrxIv+mIC8iIiLpZtdhQ/d3YOue\n5H2Vi/3FwI55aVjVIqdXBT38UeQ2FORFREQkVcXFGdb/BufCIacn5PQCbw+YtwreXQCxcTfG+uSC\nFxtB+fzbeLSEJ+XK5XNc4SKZjIK8iIiIpIroa4ZP/wnrB0/+91hnWzx+Lov5/Yu2uGa30NIZkbun\nIC8iIiL3JSLS8P4XMG0phP19+/G1H4X3B0LJh57FxUXLZ0TulYK8iIiI3JPoa4YPlsPYT+FChH1f\nTk+DU+QGKgbU5dIVG+GX4NLFMwzqkpNXWrlhszkBTg6pW+RBoSAvIiIid8QYw7UYuHoNVvwIwz6C\nk2H2Ywrmjad/Oxtdm1g822IsL1Y/S7t27RJ7071mkQeZgryIiIik6Oo1w7xVMHM57D8B0TG33uvd\nvyD4XJtFizrR9G/bF4BPP/2UvHnzpmPFIlmLgryIiIjYCfvb8MEymLEc/rr432M9s19hdE93ujeH\n37ZX5Pvvv0/q8/X1TeNKRbI2BXkREREB4Hy4YcynMHMFXItJeYyLs8E1u0Veb3imygXmv1uFrk3+\nwCWbK9WqVaNatWrpW7RIFqYgLyIiksVdjjJMWgTvzofIq/Z9RXyhdyvo+DTEx4RTokQxDh8+TO7c\nuYG8tKszn2zZsjmkbpGszuboAkRERMQx4uMNM5cbHmkNwz+yD/FVSsPCEdC7znRa1jhBHm+LfPly\n065dO3777bekcTVq1MDJSbvPiDiCgryIiEgWdOCEIegVeHkinL9pHXxZf1g6Kpats6H14xYnjh9h\nxowZSf0ffPABjz/+uAMqFpF/09IaERGRLCQ21vDuwoStI29eB/9wfhj+P4g5NZdvP99Cy6A5APTp\n04djx445plgR+U8K8iIiIg+48+GGjTtg/W8Q8jMcPHmjz9nJ0KjCHhZMKIdrdotz5xozduwoYmJi\ncHFxwc/PDz8/P4fVLiK3piAvIiLygPpqk2HIbNh5KOX+SiVhWt9omtQP4mz/UPz8/PDx8eHAgQM4\nOysiiGR0+r9URETkAXMu3NBnMixak3K/E9H0bHqBSQMK4ezszqRJk4iJubHORiFeJHPQ/6kiIiIP\nCGMMn333bidaAAAgAElEQVQP/abC35dutGdzMpT3j+bJmm4EVoAtIe9z/sRRnJ3fB6Bjx44OqlhE\n7oeCvIiISCZ3LcawZB1MXwo/77Xv6/gUPJbzM9atXsro7l8CULNsD111F3kA6P9iERGRTOr0ecOM\n5TD7SzgXbt/n4fwXS8fn5clqFleuPMeenRuJi4vDyckJT09PxxQsIqlK+8iLiIhkMtdjDePmGYq3\ngdHB9iHeJRu8+lw8OY/XJa/zdgDc3d2ZM2eOHtwk8oDRFXkREZFMZMsuQ4/xsPuIfXs2c5b29S/z\nzoDi+ORyosdTyyhWrJhjihSRdKEgLyIikgkcOGGYMB8++sq+/dFH4O3OcPnEGiIuXsAnVwkASpcu\nnf5Fiki6UpAXERHJoK5eMyxdlxDeN+6w78ueLRafax8Q+lFvnJ0toINDahQRx1GQFxERyWD+vmSY\nOB9mLIeIyOT9TWvD5D42dv5cBC17F8m6FORFREQyiEtRhsmLYPJCuBRl3+fkBN5xPzK690N0b+MP\nOOHfvLlD6hSRjEFBXkRExMHCLyVsIzlpof2DnAB8clymb3svOj0N+XPXxmbThnMikkBBXkRExEHO\n/p2N/u8Z5nwJkVft+0o+DO3rHKBOmTDq1av7T6uV7jWKSMalIC8iIpLOTpw1DPvMj+9/zUVcvH2f\nS/xJPhzyEO0bgLNzSaCkQ2oUkYxPQV5ERCSdXIsxvLsAxnwKV6Lz2PWV9YcB7aFpjVzkzqUr7yJy\newryIiIiacwYw3c/Qd+phkN/2of0IrmOMry7Fy80zotlWYCXY4oUkUxHQV5ERCQNREQa1v4Ky9dd\nYcPO7Jw858TNa9yLF7rCgJYn6da2lOOKFJFMTUFeREQkFR360/DmLFi2AeLiANzt+r094nm783Vq\nFvsDZ+0BLyL3QUFeREQkFVy8bBj5CUxbEk9sXPItIr3coV0DGNnVRr5croSGpn+NIvJgUZAXERG5\nDyfDDMFfX2XqF25ciAC4EeIrlYQnqyV81CgH2Zx1E6uIpJ4M81SJsWPHYrPZePXVV+3ahw0bRqFC\nhXB3dycoKIi9e/c6qEIREZEEv+4zDJltqNTZUKQlDPk4McQnKFckgg3vxxD6scXo7hZ1K1gK8SKS\n6v4zyM+bN++OT3T+/Hk6dux4T0Vs3bqV2bNn8+ijj/5zx36Cd955h0mTJjF9+nR++eUXfHx8aNCg\nAZGRkff0OiIiIvfjXLjh2UGGKi/BqE9gx0H7fr8CsGgk7PzcmzoVsjukRhHJOv4zyHfq1IkGDRpw\n+PDh/zzJ7NmzKVWqFIsXL77rAiIiIujQoQNz584lV65cSe3GGKZMmcKgQYNo0aIFZcuWJTg4mMuX\nLzN//vy7fh0REZH7sXRtHOU6wPKN9u3ZnKFBVZjxf7D3c2hV37K7KCUiklb+M8jPmjWL0NBQypcv\nz+jRo4mNjbXr3717N7Vr16Z79+6UL1+eHTt23HUB3bp1o1WrVgQGBmKMSWo/evQoYWFhNGzYMKnN\n1dWVunXrsmXLlrt+HRERkXsR9rfh8R6naP22jb8u3mivUeIES0bBX9/C95Mtuje3cM2uAC8i6ccy\nN6fnFJw9e5bevXuzdOlSypQpw6xZs6hUqRLDhg1j8uTJ5MyZkwkTJtCpU6e7fvHZs2fz4YcfsnXr\nVpycnAgKCqJ8+fK89957bNmyhdq1a3PixAkKFy6cdEyXLl04ffo0q1atSmqLiLixMPHgwX/9nlNE\nROQuxMbBbwddWbw6grDox9j3p4ddv493DG+1P0b1UpcdVKGIPCiKFy+e9Lm3t/ddH3/bXWt8fX1Z\nvHgxX3/9NS+//DKBgYHkzZuX8+fP8+KLLzJ+/Hhy58591y+8f/9+3nzzTTZt2oSTU8JGusYYbvNz\nBYB+ZSkiIqnOGFi7MyeTlz3EuQiXFMc8XeUCA1qeJId7XDpXJyKS3B1vP1m1alWqVKnC8uXLOXfu\nHOXKlePNN9+8pxAP8NNPP/HXX39RtmzZpLa4uDh+/PFHZs2axe7duwEICwuzuyIfFhaGr6/vLc8b\nEBBwT/VIcqH/bHKsOU19mtu0oXlNG1lhXo+fNQR12cOxiGLJ+pycoEZZGNAemtXJC+RNldfMCvPq\nCJrXtKF5TRs3ryq5F3e0/eScOXMoXbo03377LcOGDWPatGkcP36c8uXL88477xAXd/dXJlq0aMHu\n3bvZuXMnO3fuZMeOHQQEBNCuXTt27NhB8eLF8fX1JSQkJOmY6OhoNm3aRM2aNe/69URERG4WERHB\nrzv28+4CQ9nn4VjEjQtL+XJCt2bwxZiENfAbZ1g0q6PfBotIxvKfV+T37dtHt27d2LRpE0FBQcyc\nOTNpLU+LFi3o3bs3gwYNYv78+cyaNYvq1avf8Qt7e3snWwvk7u5Orly5KFOmDAB9+/ZlzJgxlCpV\niuLFizNq1Ci8vLxo37793b5PERERAGKuG1ZthYmfXGLLHw8Tf1M+tyxD9+YWY3uAt6eCu4hkbP8Z\n5CtUqICXlxdz585NdjNrwYIFWbp0KV999RW9evWiVq1adO/enQ8++OCei7Es+y27XnvtNa5evUqv\nXr0IDw+nevXqhISE4OHh8R9nERERuSE+3rD7CHy/9SofzNvFJasK4ZctoDDclNXLFYVZr1vUKKcA\nLyKZw38G+bZt2/Luu++SJ0+eW45p0qQJQUFBvP3220yfPv2+gvy6deuStQ0dOpShQ4fe8zlFRCTr\nMcawZRdMXXiNNdtd/gnubkDVZGPLFYWXmsDLLdHTV0UkU/nPIP/JJ5/c0Uk8PT2ZPHkyHTp0SI2a\nRERE7knkFcPnITBjOfx+CCDlp6sW8YV2DRI+yhdTeBeRzOmOd625E5UrV07N04mIiNxSfLxh4w7Y\nfgB2HYJdR2D34XhiYpPv4+CTCwIrQp3HoG6FhKvwNpsCvIhkbqka5EVERNLD2QuG596ELbv+3XMj\nxLu7wvNPQvdmULGEnkEiIg8eBXkREclUfjtgaPY6/Hku5f6CuSLo396TLk2cyOml8C4iDy4FeRER\nyTSWrDW8MDyWmNiEb182G/g6/UDzJx6iVaOSlC8GuXPkdHCVIiLpQ0FeREQyJGMMZy/AnqMJH6F/\nwOchkPity9sTFgyHJwKCcHbWtzMRyXr0L5+IiGQo12MNc7+BcfPg2JmUxxTIeZm1H3hRsoiFvpWJ\nSFalf/1ERCRDiI83LFoDQ2bHc/hU8p1nEjWoAgtHeJErh9a/i0jWpiAvIiIOtybUMGBa4t7vN0K8\nhxuU84dHCkZTqbQrlUombB+pHWhERBTkRUTEgc78ZRg4HRastm93y3aV7o0vMbJXfjzcEp/KKiIi\nN1OQFxGRdHcxIpL3v4hn/AIvLl+50e7hBn1aw8B2buT0cndcgSIimYCCvIiIpKutuw3P/l8kZy7l\nt2tvUfsq0//PjQJ5tWxGROROKMiLiEiaO3nyJDPnLOG8ez/mfAlwI8SXfBjeHwj1K+sKvIjI3VCQ\nFxGRNBEVFYWHhwcx1w0rt+Zj3KqOmJu+67hlh7c6Q/+2kN1FV+FFRO6WgryIiKQ6YwyVqz9DvTbz\n+fLngpy9kB2csyf1N6kFU/uBXwEFeBGRe6UgLyIiqWLDhg1kc3En0hbA/BA4nPMHDnxn/23m4fzw\nXj9oWkcBXkTkfinIi4jIPTPGcD0Wvt8G4z72JfRwAa6bxN4b32IK5oWXWybsSJOwnaSIiNwvBXkR\nEbknO3fupHPf+UT5jOPQnwAlko2pXhZ6t4Zn60E2ZwV4EZHUpCAvIiJ3xBjDN998wzPPPMPpvyxG\nLynPzphx8Kf9uIfyQ8tAaNcAqpZReBcRSSsK8iIickeMgYFDPmXR5pKs/OURIq/eCOnentCtWcKV\n9yqlwbIU4EVE0pqCvIiI3NKEiZPZcfxhIrPVJXQEnHFbxIGN9mNeeArG94L8uRXeRUTSk4K8iIgk\niYmJ4dixY5QoUYJ1vxpmbHqRY+e9Uxxbxi/hQU6BFRXgRUQcQUFeRESSbN++nbad3iDg2bUs22AB\n9iE+lxc0rArP1IS2T+gGVhERR1KQFxHJwmJjY+nVqxdTp07lz7+ys+CnavyZ73tObLgR0F1d4mhd\n5zw9WvtSpTQ4OSm8i4hkBAryIiJZTHR0NPHx8bi7u+Pk5MSvh3JR48Xz/H6yMMYAuCSN7fAktK25\nB5+c1wkoV8BhNYuISHIK8iIiWUzv3r0p7F8RD78efPQV7IseCyfsx1QpDVP6Qo1yFqGh1x1TqIiI\n/CcFeRGRB9z+/fvZvn07bdq0ZU0oHHEew0df58CkMLZRTXj1OWhQVVtIiohkdAryIiIPoLi4OJyc\nnAA4d9GZrsOO8uYXhmNnLCCP3Vgvd+j0TEKAL/6QwruISGahIC8i8oCJjo6mdLkA3n73J1Zu9uSb\nn4oSn3cQx87Yj6teFv7XFFrXB093BXgRkcxGQV5E5AGwfv16Cj1UnN+OFWTpuuz86RvK/8ZnTzYu\nl1fCA5z+1xTKFVV4FxHJzBTkRUQyOWMME+ceZ8OJikTFJLbah/h6FRPCe8tAcM2uAC8i8iBQkBcR\nyYRCQkL47rvveHXgJF6ZBKsOdUw2pqw/PFcf2jfQ2ncRkQeRgryISCYQHx/Pr7/+SpUqVQDwKVyZ\nmV+HMmuHITrmRkj3zQPdm0OrICjjr/AuIvIgU5AXEckErl69SsMmXXn57TWs25mbrXtyg88g+Gcp\njWVBzxYwujt4eyrAi4hkBQryIiIZ1PDhw2natCl+xSowYLo7EcV+Y+z85OMqFIeZr0HVMgrwIiJZ\niYK8iEgGERsby99//42Pjw8A2bNnZ8DozfxxrQJhf9uPdXKC+pWgbQN44UlwdlaIFxHJahTkRUQy\niM8//5ylS5fy5ZdfcvAkbPmrH+vPuNiNeTwA2jWAZnUgj7fCu4hIVmZz5IuPHTuWKlWq4O3tjY+P\nD02bNmXPnj3Jxg0bNoxChQrh7u5OUFAQe/fudUC1IiKp6+LFi4waNQqAM38ZYnO25ecL3fFraSjV\nDr7+6UaIL5AHlo2F1VMtujS2FOJFRMSxQX7Dhg288sor/PTTT6xduxZnZ2eeeOIJwsPDk8a88847\nTJo0ienTp/PLL7/g4+NDgwYNiIyMdGDlIiL35vr168THxwNw6m8v3l3oTPn2kRRqBl3Hu3DeasTJ\nc/Yh/aUmsOdzaF5X4V1ERG5w6NKaVatW2X09b948vL292bJlC40aNcIYw5QpUxg0aBAtWrQAIDg4\nGB8fH+bPn0+3bt0cUbaIyD1r2rQZj9Yfy9c7HuWPYzbwfp2I48nHebpBvUrQtw3Ur6wALyIiyWWo\nNfKXLl0iPj6eXLlyAXD06FHCwsJo2LBh0hhXV1fq1q3Lli1bFORFJMPbvXs3Fy9epHbt2uw8aDji\n9hHfr/BNNs7JCeo8Ck9UgfqVoXIpyKYbWEVE5D9Yxhjj6CIStW7dmsOHDxMaGoplWWzZsoXatWtz\n4sQJChcunDSuS5cunD59OumKfkRERFLfwYMH071uEZFb2bBhAx9+8jWPPbOQZZvzEW9uhHNXlzhq\nlr5EYPmL1CwTgbdHnAMrFRGR9Fa8ePGkz729ve/6+AxzRb5///5s2bKFTZs2YVm3vwp1J2NERNLb\n+fPnef2NN3h9+Gds2pOLjbu6cTBHfw5uujHGyWZoGxjGS0+dwdM13nHFiohIppYhgny/fv1YvHgx\n69atw8/PL6nd1zfh189hYWF2V+TDwsKS+v4tICAgTWvNSkJDQwHNaVrQ3KYNR83rpk2bCAgIwNXV\nlY07DIfci/HChOIpjm1QBab0tSjtVwAokK513iv9fU0bmte0oXlNG5rXtHHzqpJ74dBdawD69OnD\nokWLWLt2LSVKlLDr8/f3x9fXl5CQkKS26OhoNm3aRM2aNdO7VBGRFI0cOZK585bTfbyhXi+IttmH\neCcnCKqUsH3kqslQ2k+/URQRkfvn0CvyvXr14rPPPmPFihV4e3tz9uxZALy8vPDw8MCyLPr27cuY\nMWMoVaoUxYsXZ9SoUXh5edG+fXtHli4iWdiiRYu4dOkSXbt2xRhDtWcmMGhRMS5dvTHG3RWa1IIm\nteHp6pArh8K7iIikLocG+RkzZmBZFo8//rhd+7BhwxgyZAgAr732GlevXqVXr16Eh4dTvXp1QkJC\n8PDwcETJIpIFGWM4duwY/v7+ABQpUoTnn3+e4pVfYshsi02/l7cb37Q2TOsPD+VXeBcRkbTj0CCf\n+FCU2xk6dChDhw5N42pERFJ25MgRatSowYkTJ3B1dcXJuxoF6v9G/Vftg3qBPPBeP2hZTzfki4hI\n2ssQN7uKiGQ0gwcPZuDAgeTOnZtixYrRuHFjlqz6k6VbivHVZgCvpLHZnKFbMxjZFXJ6KcCLSPqL\nj48nJiYmzc5fpEgRIOFeRblzLi4u2Gxpd0uqgryICAnfBKOjo3F3dwfg5MmTfPzxxwwYMIDVP8Mx\n94/oNMH+GJsNOj4FQ7qAXwEFeBFxjPj4eK5du4arq2ua/TbQ1dU1Tc77IDPGEB0dTfbs2dMszCvI\ni4gAo0aN4sqVK4wbNw6AV/oOZdmPblTsDL8fSj7+uSAY/j/tQCMijhcTE5OmIV7ujWVZuLq6Jv2Q\nlRYU5EUkSzpz5gxr1qyhQ4cOALRv35627drx3U+Gj76CrzYX43qs/TFOTvB8A3itA5Tx1zdMEck4\nFOIzprT+c1GQF5EswxiT9I+qk5MTr776Kk8//TR58uQhV75iFGmwjUYDkx/nlh26NIaB7aGIr75Z\niohIxqAgLyJZgjGGqlWrsmTJEvz8/PDx8WHKlClcv36dNaGGTiPh9F/2Ib1GOejcCFrXB29PBXgR\nEclYHP5kVxGRtLJ7924OHz4MJPx6s27dunz22WdJ/W3aduTdpflp0AdO/3XjuJeawN75sHmWRdem\nlkK8iIhkSLoiLyIPrK+++oqDBw/y8ccfAzBixAjc3Ny4EGGYuQKmL4Wwv2+Mz5cTPhoMjWspuIuI\nSIL169dTv359Fi5cSOvWrR1djh1dkReRB8b+/fsZM2ZM0tddu3bFx8cn6evj59zpM8WiSEt4+0P7\nEP9Uddj5qUK8iEhGYLPZ7ugjODjY0aU6lK7Ii0imtmfPHsqWLQskPLBk7dq1HDt2DD8/P/LkyUOr\nzmN5c5Zh+QbYdzz58YXyweBO0KO5dn0QEckobl4GCTBr1iy2bt3K3Llz7dpr1qyZnmVlOAryIpJp\nxcXF0ahRI7744gsqV66Mq6src+fOpVChIsz9xjD2Uzj0Z8rHPvYIDGifcCOrSzYFeBGRjKR9+/Z2\nX4eEhPDzzz8na/+3qKgoPDw80rK0DEVLa0QkU5kzZw7r168HEraQfP3115NuaI2Lh11nH6NsB3hp\nTPIQ7+4Kz9aDkCmw/RPo8KSlEC8ikkl17twZNzc3jh8/TtOmTfH29qZx48YA/P7777z44osUK1YM\nNzc38uXLR7t27Th58mSy80RERPB///d/FC1aFFdXVwoXLszzzz/P6dOnb/na169fp1WrVnh6erJm\nzZo0e4+3oyvyIpKhGWMIDw8nd+7cQMLyl4kTJ1KvXj0Aevbsyckww7sLDNMXl+X4Ofun53l7QtPa\n0CIQGlYFd1cFdxGRB0V8fDwNGzakWrVqTJw4EWfnhGj7ww8/cODAATp37kzBggU5dOgQM2fO5Oef\nf2b37t24ubkBCVfwAwMD2bNnDy+++CIBAQH89ddffPfddxw+fJiCBQsme81r167x3HPP8eOPP/L9\n999Tq1atdH3PN1OQF5EMbc2aNbz11lts3boVSPh1a/HixQm/ZFi4Bhauhh93Jo6+EeJzecGAdvDq\nc+DlofAuIgIJF0OMMWn2dXq7fv06TZo0YeLEiXbtPXv2pH///nZtTZs2pVatWixbtoznn38egAkT\nJvD777+zZMkSnn322aSxgwcPTvH1rly5QrNmzdi+fTurV6+mSpUqqfyO7o6W1ohIhhITE8PYsWOJ\nj48HICgoiPj4eM6cOQPA5WhXvt1ThyItodfEm0N8Ag/XOIa+BEeWwuBOlkK8iMgD7uWXX07WlnjF\nHSAyMpILFy5QvHhxcubMyfbt25P6li5dSrly5exC/K1cunSJp556it9//51169Y5PMSDrsiLSAZg\njCE+Ph4nJyeyZcvGkiVLqFChAk8//TROTk5s27aNM39Bv6mGD1fC1Wv2x9ts8HhlqPbIMeo/Fk69\nOpUc80ZERDK4f189T+2v05vNZsPPzy9Ze3h4OG+88QZLly4lPDzcri8iIiLp88OHD9OiRYs7eq3+\n/ftz9epVtm/fTvny5e+r7tSiIC8iDtezZ09q1qxJx44dsSyLyZMnkydPHgCOnzW88xl8/DXEXLc/\nrqw/9GgBzwVB/twWoaEXHFC9iIg4iouLCzZb8gUmrVu3ZsuWLQwcOJCKFSvi5eUFQNu2bZN+4wt3\nt+1w8+bNWbhwIaNHj2b+/Pkpvm56U5AXkXR38uRJjhw5QmBgIACNGjVi5syZdOzYEYDAwEAO/Wl4\naaxh3ncQG2d/fMUS8GYnaF4XbDYtnRERyapS+o1AeHg4a9asYfjw4bz99ttJ7dHR0fz99992Y4sV\nK8auXbvu6LUaN27MM888Q4cOHfDw8OCjjz66v+JTgeN/lBCRLOfUqVN06dKFuLiEhN6oUSOWL18O\nwKUoQ98phtLtYe7X9iG+Whn4agKEfgwt61kK8SIiWUhKV89TanNycgKwu/IOMHny5GTB/7nnnmPP\nnj0sXbr0jmpo27Yts2bNYu7cufTp0+dOS08zuiIvImkuKiqKp556itWrV+Pq6kq1atXo0KEDkZGR\neHt7Y7PZyJYtG0vXGfpOgdN/2R9ftwK81RkeD9DTV0VEsqqUrr6n1JYjRw7q1avH+PHjiYmJ4eGH\nH2bTpk1s3LiRPHny2B3zf//3f3zxxRe0a9eOkJAQKlWqxMWLF1m1ahUjRoygbt26yc7/0ksvERkZ\nSb9+/fD09GT06NGp+0bvgoK8iKSJ0NBQihYtSu7cufHw8MDT05MvvviC559/HsuyGD58eNLY3w8Z\nBs2A77ban6NeRRj2P6hbQeFdRCQrsywr2YWclNoSzZ8/nz59+jBr1iyuX79OYGAga9eu5YknnrA7\nxt3dnY0bNzJs2DCWLVtGcHAw+fPnJzAwkBIlSti91s369OnD5cuXGTJkCF5eXrzxxhup+G7vnGUc\nfbtxKrj57mNvb28HVvJgCQ0NBSAgIMDBlTx4ssLcdurUiUcffZQBAwYAEBYWRp48eZIe1nH2gmHB\napi3CnYctD82f26Y1BvaPnF3V+Czwrw6guY1bWhe00ZWnNfo6GhcXV1vP1Ac4r/+fO43w2qNvIik\niuXLlzNixIikr1955RW7EJ4/f36cnZ05csrQ6k3DQy1gwDT7EG9Z0LMl/DEf2jW49ZUWERERUZAX\nkXsUFRXF6tWrk74uX74806dPJyYmBoAqVarYPVXv6jXD8I8NZTvAF+sh7qabWF1dEq6+b50N7w+w\nyOmlAC8iInI7WiMvInfMGJN0lfzatWu0atWKo0ePkitXLh555BG2bduGi4tLsmO+3gx9p8LR0/bn\nq1sBXngqYR94b0+FdxERkbuhIC8id8QYQ9WqVVmwYAGPPPIIuXPn5rXXXuP8+fPkypULAH9//6Tx\n4ZcMn66CD1fCH8fszxVQCqYPgKplFN5FRETulYK8iNzSihUrKFy4MAEBAViWRZ06dVi6dGnS3fmD\nBw+2Gx9z3bB+O8wPgcVrITrG/ny5c8Do7vC/JuDkpBAvIiJyPxTkRSRJZGQk58+fT7qyfujQIb7+\n+mvmzJkDwMiRI3Fzc7M/5orh259g5Y/wzRa4FJX8vJ5u0OkZGNoF8uZUgBcREUkNCvIiWdzN696/\n/fZbPvroI77//nsA2rdvz+bNm5PGenh4JH2+67BhxnL4bBVEXk353BVLQLdm0L4BeHkowIuIiKQm\n7VojkoUdPXqUOnXqJD3lrnHjxliWRWxsLAAFCxakVatWSeNjrhsWrDYEvmx4rCPMXJ48xPsVgL5t\nYNscCP0Yuje3FOJFRETSgK7Ii2QhcXFxvPTSS8yaNYvs2bPj5+fHqVOn2LdvH6VLl8bd3Z1Vq1Yl\nO+74WcOHK+Gjr+BcePLzlvaDNo9D87pQvtjdPcRJRERE7o2CvMgDbsGCBQQFBeHr64uTkxOHDh1i\nzZo1PPPMM1iWxa+//kru3LmTHWeMYU0oTFsC3/wE8fH2/c5O0DIw4QFOdSsovIuIiKQ3BXmRB8ze\nvXtxc3NLumH166+/5uLFi/Ts2ROAqVOnUrBgwaTx/w7xV68ZPv8epi6GPf/f3r2HVVnl/R9/781m\nszlsNqgggiJoiop5SKUSDXWUxBq1Gu3Cw2Q546GmNGvs0WrGpsQOj51Myrpm0vn5K63pVz1jPo2O\nkofU0vEwouMpQc0URAFFOXP//thBbUXUlG42fl7XdV+41n1YXxbI/d1rr3vtrAuv3zLcPe/9N7+E\niKZK3kVERMyiRF7Ey+Xn51NYWEhMTAzgHoEvLy/n+eefB2Dy5MmcOXOm5vgePXpccI3cfIM12+CL\nbfDhasgruLCd5AT36Psdt4LNpgReRETEbHrYVcTLlJaWcujQoZryxx9/XLOuO8Dw4cMJDg6uKffp\n04eUlBSPa+ScMvhglcGD/20QP9og4k6492l48/95JvFB/vDwCNi7BD5/xcKwvhYl8SIiUu8WLlyI\n1Wrl66+/9qgvKiqib9++2O12PvroI2bNmoXVaq11e/nll02K/uejEXmRBq6kpIQ9e/bQrVs3AL76\n6isef/zxmj9ut99+O5999lnN8T169KgZdS8uNTh4FL45CgeOwp5DsH6H+2tdWke4E/jxd4IrSIm7\niIiY7+zZswwZMoSvv/6aJUuWcPfdd7Nz504A5s+fj8vl8ji+tnegGxuvSOTT09N56aWXOH78OPHx\n8VSfArwAABrWSURBVLz66qv06dPH7LBE6kVpaSkffvghY8aMAeDkyZMMGjSI3NxcLBYLCQkJNUtE\n2mw2oqKi+Oijj2rOLywy+HA1/J/PYf2/4fuVJevka4Nb4t0Prfa7CZK6afqMiIg0HNVJ/FdffcX7\n77/P3Xff7bH/nnvuITw83KTozNPgE/mlS5cydepU3nzzTfr06cP8+fNJSUlh9+7dtGrVyuzwRH4S\n40fZdVVVFaNGjWLx4sXYbDZsNhsTJ05k6NChBAcHExUVxa233kp+fj7O4FBWb/Uj7o5NNL8TLBaD\nG1pC2yhoE+keef9kLZSU1d2+3deduCd1d2+3xEOAQ4m7iIg0POfOneOOO+5g06ZNtSbx17MGn8i/\n/PLL3H///YwfPx6A119/nc8//5w333yTtLQ0k6MTb1VWbrDsS9j8H2jqcn+IUesI9xYW8tOWUqyq\nMsg5BUdPQHAgtGv1w3X++te/MmzYMFwuF3sOGaSM+4hfjfw1674xqKy08M//9OChF/Lx8WtG/mkr\nLQbsYPBjfoSFGoQ6IXbApzzxtjtJP1no2e7Xu91bbaxWiIlwJ/ptv0/4b2oPt3QGfz8l7iIi0rCd\nPXuWO+64g40bN9aZxJ88eRKr9YdHP61Wa61LKzc2DTqRLysrY+vWrUyfPt2jPjk5mQ0bNpgUlXgr\nwzDYuhcWLof3V8Kp07Uf1ywEEjoaJHSCm+MhPtb90GeAA+y+FsrKDdZvzWf/d0HsPOjLzm9g9zdF\nFBYHUlH5Q3IcHlJOyq2+DOwFafM3sGLvL9jyTTD7jgAhc3h7BbDi+4ODHued5T+Ooi0HT/3077Vb\nO/h1CqQOguZNlLCLiIh3uv/++/nuu+9q5sRfTHx8vEe5WbNm5Obm1nd4pmvQiXxeXh6VlZU0b97c\noz48PJzjx4/Xek7qH9yjojmnKqgy3E8tW4Cqqgrsvlb8/aw4/MBKGUEBPoQ38aGpC/xtZ2ne1Bd/\nhx2AM2fO4Ofnh93+Q9lutxPWxI/ELkD5CQIDAwkMDAQgNzfXo5yTk0NQUJBHuZJAjuUHciQX8k4W\n4OvrwNfuoMqAc0UFhLocNA11EOAHJefyiG7hT6sWgfjaLBw7dgyn00lQUBAA3333HcHBwR5lp9OJ\n0+kE4OjRowQHB1+0/O233+JyuTzKwcHBNaudHDlyhKKioprrHzlyBJfLVbP/8OHDhISEeJRdLlfN\ngybnlw8dOkRISEhNOTs7m9DQ0DrLISEhhISEAJCVlUVoaOgF5eBgF5VVcOBANn4BTfj2VDD/PgAb\ntp/m4PEAzhTbKC6FonMVlJT5UFR86aQ2rwCWb3Rv57P5uKfEVFSGnrcn6IJjcwt8WfS/sOh/Adub\n7Pvikk1flpbh7k9RdSfp3z/I+q37q90X7roNutyg5F1ERC40688Gf/pL/V3/Dw/ArPHX7h6Um5uL\nw+EgOjq6zuM+/PBDQkN/uDdX52+NXYNO5H+Kpauq/3X+t3Z++fwfcOB5ZWed5QDLWbq0/pY7k1yE\nu8p4+82XGNS/J4N+cQsnC3155sUlRMcNxB4cz+ETDjIPWCnzaCPkvOufX25W868g/3KqSkrp0DKP\nlMQgurUt4o2XppB8+xDa3Xg7Wcf9eWvRatq3j6NXt2iaOMtZ/O7LDOzXjf633YKfvYpZTz/BkJRB\nDBgwAIDp06czePDgOsvJtw+mQ9fBfLV4L/Pe+YwWMb2xO9tRWmFl167DhIWV0rRpJaXlVvYcKMHm\nCKbcqKCi0oKtoox2Ud/S56bTtI0oZtG7b3DzzTfTvXsPDAPmvbWEmLjbCGoaz7FTdv69q4CWEaV0\nbFtCE2cFGSs/pl1cV8IjO1B41sb6Tdm4mljwcfhy+pwPuafCqPToz5jz+i/4vPKFv+oh/qe545Zz\nlFdaWbXuAHbnDZwubcrZUp8Ljq1WUXnRXQC4AisICy7jWL4vZ0t8az3G315JQtxpmoeWY7UY+FgN\nrFbwt1cRHFBBcEAFrsBKbD4GRcU+FBX7cKbYh7IKK11ii+jWpgirFarOwLEzEAB0iXBvAGUFsGVL\n3XE2dluu9w6oJ+rX+qF+rR/XU7+2bt0ah8Nhdhj1YsGCBTz++OOkpKSwZs0aOnXqVOtxffv2bbAP\nu545c4bMzMxa97Vr1+6qrt2gE/lmzZrh4+NDTk6OR31OTg4tWrQwKSq3c0YMm7Jj2JRdXfNntqyA\nOdVTJXiOzF0/PuP8FwaXr6jYBrRm6xHYusRdZ7d8wrplAVT9vTrpbEvWf+Af/6k+6022roQXV1aX\nV7D+fyoJWVVFSFAFZ3idgq12thcEE9mkjHJnCvmlLdmZHcj2b4LYZ3mRrz+P59z/VP9haM++Az+O\nKpGTOUDNjyYYin/YW0pbtn8L27+trnmN7euB9dX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# reinitialize filter\n", "initialize_filter(cvfilter)\n", "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=2.0) # var was 0.02\n", "\n", "# recompute track\n", "kxs2, _, _, _ = cvfilter.batch_filter(z_xs2)\n", "\n", "bp.plot_track(t, xs2)\n", "bp.plot_filter(t, kxs2[:, 0], label='KF')\n", "plt.legend(loc=4)\n", "bp.set_labels(title='Large Q (var=2.0)', x='time (sec)', y='X')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the filter reacquired the track more quickly, but at the cost of a lot of noise in the output. Furthermore, many tracking situations could not tolerate the amount of lag shown between seconds 4 and 8. We could reduce it further at the cost of very noisy output, like so:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fWu/evTl16hRLly4FIDIyMqnv4MGDWf46RERExPli4iz2Hfdm9c58rNyen1Pn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\nvdH1HHkhhBBCCCHuV5LICyGEEEIIoUOSyAshhBBCCKFDksg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# reinitialize filter\n", "initialize_filter(cvfilter)\n", "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=20.0) # var was 0.02\n", "\n", "# recompute track\n", "cvfilter.x = array([0., 0.])\n", "kxs2, _, _, _ = cvfilter.batch_filter(z_xs2)\n", "\n", "bp.plot_track(t, xs2)\n", "bp.plot_filter(t, kxs2[:, 0], label='KF')\n", "plt.legend(loc=4)\n", "bp.set_labels(title='Huge Q (var=20.0)', x='time (sec)', y='X')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maneuvers imply acceleration, so let's implement a constant acceleration Kalman filter and see how it fairs with the same data." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def make_ca_filter(dt):\n", " cafilter = KalmanFilter(dim_x=3, dim_z=1)\n", " cafilter.x = array([0., 0., 0.])\n", " cafilter.P *= 3\n", " cafilter.R *= 1\n", " cafilter.Q = Q_discrete_white_noise(dim=3, dt=dt, var=0.02)\n", " cafilter.F = array([[1, dt, 0.5*dt*dt],\n", " [0, 1, dt], \n", " [0, 0, 1]], dtype=float)\n", " cafilter.H = array([[1, 0, 0]], dtype=float)\n", " return cafilter\n", "\n", "def initialize_const_accel(f):\n", " f.x = array([0., 0., 0.])\n", " f.P = np.eye(3) * 3" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Vien6vuMKluumIC8iIiJyh4g7n3ajpj+OwPFTcPw07DkMh2Mvj/H2MNQo8Dnf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\n4u/vT+vWrdm9e7e9wypwRo4cidls5s0337R3KA7v1KlTdOv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utVsMqampBAUFMXjwYN56\n6y27xSEiYi+qkRcRkXv2wQcfsH379jvOO5+Xvv/+e9zc3OjTp4/dYhARsSeNyIuIiIiIOCCNyIuI\niIiIOCAl8iIiIiIiDkiJvIiIiIiIA1IiLyIiIiLigJTIi4iIiIg4ICXyIiIiIiIOSIm8iIiIiIgD\nUiIvIiIiIuKA/j+aw56k9fgYzgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cafilter = make_ca_filter(dt)\n", "initialize_const_accel(cafilter)\n", "\n", "kxs2, _, _, _ = cafilter.batch_filter(z_xs2)\n", "bp.plot_track(t, xs2)\n", "bp.plot_filter(t, kxs2[:, 0], label='KF')\n", "plt.legend(loc=4)\n", "bp.set_labels(title='Constant Acceration Kalman Filter', x='time (sec)', y='X')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The constant acceleration model is able to track the maneuver with no lag, but at the cost of very noisy output during the steady state behavior. The noisy output is due to the filter being unable to distinguish between the beginning of an maneuver and noise in the signal. Noise in the signal implies an acceleration, and so the acceleration term of the filter tracks it. \n", "\n", "It seems we cannot win. A constant velocity filter cannot react quickly when the target is accelerating, but a constant acceleration filter misinterprets noise during zero acceleration regimes as legitimate acceleration.\n", "\n", "Yet there is an important insight here that will lead us to a solution. When the target is not maneuvering (the acceleration is zero) the constant velocity filter performs optimally. When the target is maneuvering the constant acceleration filter performs well, as does the constant velocity filter with an artificially large process noise $\\mathbf{Q}$. If we make a filter that adapts itself to the behavior of the tracked object we could have the best of both worlds." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Detecting a Maneuver" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we discuss how to create an adaptive filter we have to ask *how do we detect a maneuver?* We cannot reasonably adapt a filter to respond to maneuvers if we do not know when a maneuver is happening.\n", "\n", "We have been defining *maneuver* as the time when the tracked object is accelerating, but in general we can say that the object is maneuvering with respect to the Kalman filter if its behavior is different than the process model being used by the filter. \n", "\n", "What is the mathematical consequence of a maneuvering object for the filter? The object will be behaving differently than predicted by the filter, so the *residual* will be large. Recall that the residual is the difference between the current prediction of the filter and the measurement. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KS+np6W6vL1++rPbt2yspKUnPP/+8mjVrprJly8rHx0eTJ0/Wpk2bbBkTCofD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\nbLwzZpjzjRsnvfGG+z5n2Ue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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mkf_internal import show_residual_chart\n", "show_residual_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To confirm this, let's plot the residual for the filter during the maneuver. I will reduce the amount of noise in the data to make it easier to see the residual." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GIWi1WpRSgIxsIIR4tp27rOg0DK7EmTsSIYQQhZFZW+Q7dOjAhAkT8PX1JTAw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from adaptive_internal import plot_track_and_residuals\n", "\n", "def show_residual_chart():\n", " dt = 0.1\n", " # initialize filter\n", " cvfilter= make_cv_filter(dt)\n", " initialize_filter(cvfilter)\n", " pos2, zs2 = generate_data(120, noise_factor=0.2)\n", " xs2 = pos2[:, 0]\n", " z_xs2 = zs2[:, 0]\n", "\n", " cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n", " xs = []\n", " res = []\n", " for z in z_xs2:\n", " cvfilter.predict()\n", " cvfilter.update([z])\n", " xs.append(cvfilter.x[0])\n", " res.append(cvfilter.y[0])\n", " \n", " xs = np.asarray(xs)\n", " plot_track_and_residuals(t, xs, z_xs2, res)\n", " \n", "show_residual_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the left I have plotted the noisy measurements (not the track!) against the Kalman filter output. On the right I display the residuals computed by the filter - the difference between the measurement and the predictions made by the Kalman filter. Let me emphasize this to make this clear. The plot on the right is not merely the difference between the two lines in the left plot. The left plot shows the difference between the measurements and the final Kalman filter output, whereas the right plot shows us the difference between the plot and the *predictions of the process model*. \n", "\n", "That may seem like a subtle distinction, but from the plots you see it is not. The amount of deviation in the left plot when the maneuver starts is small, but the deviation in the right tells a very different story. If the tracked object was moving according to the process model the residual plot should bounce around 0.0. This is because the measurements will be obeying the equation \n", "\n", "$$measurement = process\\_model(t) + noise(t)$$.\n", "\n", "Once the target starts maneuvering the predictions of the target behavior will not match the behavior as the equation will be \n", "\n", "$$measurement = process\\_model(t) + maneuver\\_delta(t) + noise(t)$$.\n", "\n", "Therefore if the residuals diverge from a mean of 0.0 we know that a maneuver has commenced.\n", "\n", "We can see from the residual plot that we have our work cut out for us. We can clearly see the result of the maneuver in the residual plot, but the amount of noise in the signal obscures the start of the maneuver. This is our age old problem of extracting the signal from the noise. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adjustable Process Noise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first approach we will consider will use a lower order model and adjust the process noise based on whether a maneuver is occurring or not. When the residual gets *large* (for some reasonable definition of large) we will increase the process noise. This will cause the filter to favor the measurement over the process prediction and the filter will track the signal closely. When the residual is small we will then scale back the process noise.\n", "\n", "There are many ways of doing this in the literature, I will consider a couple of choices." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Continuous Adjustment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first method (from Bar-Shalom [1]) normalizes the square of the residual using the following equation:\n", "\n", "$$ \\epsilon = \\mathbf{y^\\mathsf{T}S}^{-1}\\mathbf{y}$$\n", "\n", "where $\\mathbf{y}$ is the residual and $\\mathbf{S}$ is the measurement covariance, which has the equation\n", "\n", "$$\\mathbf{S} = \\mathbf{HPH^\\mathsf{T}} + \\mathbf{R}$$\n", "\n", "If the linear algebra used to compute this confuses you, recall that we can think of matrix inverses as division, so $\\epsilon = \\mathbf{y^\\mathsf{T}S}^{-1}\\mathbf{y}$ can be thought of as computing\n", "\n", "$$\\epsilon=\\frac{\\mathbf{y}^2}{\\mathbf{S}}$$\n", "\n", "Both $\\mathbf{y}$ and $\\mathbf{S}$ are attributes of `filterpy.KalmanFilter` so implementation is of this computation will be straightforward.\n", "\n", "Let's look at a plot of $\\epsilon$ against time." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/uroaU6ZMMd1GcXFxzPY91QXP3nlMYyvVj+uuL94CGgK3nS6H4TjYPmsH/h66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\n86d8D/MmL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.common import dot3\n", "from numpy.linalg import inv\n", "\n", "# reinitialize filter\n", "initialize_filter(cvfilter)\n", "\n", "cvfilter.R = np.eye(1)*0.2\n", "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n", "epss = []\n", "for z in z_xs2:\n", " cvfilter.predict()\n", " cvfilter.update([z])\n", " y = cvfilter.y\n", " S = cvfilter.S\n", " eps = dot3(y.T, inv(cvfilter.S), y)\n", " epss.append(eps)\n", "\n", "plt.plot(t, epss)\n", "bp.set_labels(title='Epsilon vs time', x='time (sec)', y='$\\epsilon$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plot should make clear the effect of normalizing the residual. Squaring the residual ensures that the signal is always greater than zero, and normalizing by the measurement covariance scales the signal so that we can distinguish when the residual is markedly changed relative to the measurement noise. The maneuver starts at t=3 seconds, and we can see that $\\epsilon$ starts to increase rapidly not long after that. \n", "\n", "We will want to start scaling $\\mathbf{Q}$ up once $\\epsilon$ exceeds some limit, and back down once it again falls below that limit. We multiply $\\mathbf{Q}$ by a scaling factor. Perhaps there is literature on choosing this factor analytically; I derive it experimentally. We can be somewhat more analytical about choosing the limit for $\\epsilon$ (named $\\epsilon_{max}$) - generally speaking once the residual is greater than 3 standard deviations or so we can assume the difference is due to a real change and not to noise. However, sensors are rarely truly Gaussian and so a larger number, such as 5-6 standard deviations is used in practice.\n", "\n", "I have implemented this algorithm using reasonable values for $\\epsilon_{max}$ and the $\\mathbf{Q}$ scaling factor. To make inspection of the result easier I have limited the plot to the first 10 seconds of simulation. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bqpfaSf6Kt/Ca35iR89MH6cU8YeoA1OUwuXK93gcS2YZJA/V79+5RtWpVNBoN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.common import dot3\n", "from numpy.linalg import inv\n", "\n", "# reinitialize filter\n", "initialize_filter(cvfilter)\n", "cvfilter.R = np.eye(1)*0.2\n", "\n", "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n", "\n", "Q_scale_factor = 1000.\n", "eps_max = 4.\n", "\n", "epss = []\n", "xs = []\n", "count = 0\n", "for i, z in zip(t, z_xs2):\n", " cvfilter.predict()\n", " cvfilter.update([z])\n", " y = cvfilter.y\n", " S = cvfilter.S\n", " eps = dot3(y.T, inv(cvfilter.S), y)\n", " epss.append(eps)\n", " xs.append(cvfilter.x[0])\n", "\n", " if eps > eps_max:\n", " cvfilter.Q *= Q_scale_factor\n", " count += 1\n", " elif count > 0:\n", " cvfilter.Q /= Q_scale_factor\n", " count -= 1\n", " \n", "bp.plot_measurements(t, z_xs2, lw=6, label='z')\n", "bp.plot_filter(t, xs, label='filter')\n", "plt.legend(loc=4)\n", "bp.set_labels(title='epsilon=4', x='time (sec)', y='$\\epsilon$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The performance of this filter is markedly better than the constant velocity filter. The constant velocity filter took roughly 10 seconds to reacquire the signal after the start of the maneuver. The adaptive filter takes under a second to do the same. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Continuous Adjustment - Standard Deviation Version" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another, very similar method from Zarchan [2] sets the limit based on the standard deviation of the measurement error covariance. Here the equations are:\n", "\n", "$$ \\begin{aligned}\n", "std &= \\sqrt{\\mathbf{HPH}^\\mathsf{T} + \\mathbf{R}} \\\\\n", "&= \\sqrt{\\mathbf{S}}\n", "\\end{aligned}\n", "$$\n", "\n", "If the absolute value of the residual is more than some multiple of the standard deviation computed above we increase the process noise by a fixed amount, recompute Q, and continue." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bp7ebjJqfnx/8/PzKfD7GGPLy8mBqaqr3YdmKpG9INUNT0XEyxpCbmyvY74EQ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\nkZ2dXeM+Pj4+0P96vlF+fj6GDRsGhUKBf/7zn9Uuq2F/J6KmoiG9XfZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.common import dot3\n", "from numpy.linalg import inv\n", "from math import sqrt\n", "\n", "def zarchan_adaptive_filter(Q_scale_factor, std_scale, \n", " std_title=False,\n", " Q_title=False):\n", " pos2, zs2 = generate_data(120, noise_factor=0.2)\n", " xs2 = pos2[:,0]\n", " z_xs2 = zs2[:,0]\n", "\n", " # reinitialize filter\n", " initialize_filter(cvfilter)\n", "\n", " cvfilter.R = np.eye(1)*0.2\n", "\n", " phi = 0.02\n", " cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=phi)\n", " xs = []\n", " ys = []\n", " count = 0\n", " for i,z in zip(t,z_xs2):\n", " cvfilter.predict()\n", " cvfilter.update([z])\n", " y = cvfilter.y\n", " S = cvfilter.S\n", " std = sqrt(S)\n", "\n", " xs.append(cvfilter.x)\n", " ys.append(y)\n", "\n", " if abs(y[0]) > std_scale*std:\n", " phi += Q_scale_factor\n", " cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=phi)\n", " count += 1\n", " elif count > 0:\n", " phi -= Q_scale_factor\n", " cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=phi)\n", " count -= 1\n", "\n", " xs = np.asarray(xs)\n", " plt.subplot(121)\n", " bp.plot_measurements(t, z_xs2, label='z')\n", " bp.plot_filter(t, xs[:, 0])\n", " bp.set_labels(x='time (sec)', y='$\\epsilon$')\n", " plt.legend(loc=2)\n", " if std_title:\n", " plt.title('position(std={})'.format(std_scale))\n", " elif Q_title:\n", " plt.title('position(Q scale={})'.format(Q_scale_factor))\n", " else:\n", " plt.title('position')\n", " \n", " plt.subplot(122)\n", " plt.plot(t, xs[:, 1])\n", " plt.xlabel('time (sec)')\n", " if std_title:\n", " plt.title('velocity(std={})'.format(std_scale))\n", " elif Q_title:\n", " plt.title('velocity(Q scale={})'.format(Q_scale_factor))\n", " else:\n", " plt.title('velocity') \n", " plt.show()\n", " \n", "zarchan_adaptive_filter(1000, 2, std_title=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So I chose to use 1000 as the scaling factor for the noise, and 2 as the standard deviation limit. Why these numbers? Well, first, let's look at the difference between 2 and 3 standard deviations. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Two Standard Deviations**" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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C108LU1NTbNiwocxuMkVCQkIQEhJS7fMxxqBQKCCVSsu8WbY2lTWkmrGp7TgZ\nYygoKODtfSDEGGhUGkybcheH7r2gK1s+MB7BI914jIoQQkh90qiaRJVKJcRiMSWPPOM4DmKxmLdf\nRgjhG2MM7711GbtLJPFzu8Tiw49ceYyKEEJIfdOoEnnGGIRCYcUbklonFAp1NzUT0tis+BrYctdP\ntzzpJYYNG9ypkYEQQkiVNKpEnhBC+PbpQYalXxYvvxYIfPYBR0k8IYSQKqNEnhBC6sieEwxzNhcv\nD+gE7AsBhEJK4gkhhFQdJfKEEFIHjvzJMGVN8XLX1sAPqwGJmJJ4Qgghz4cSeUIIqWW/nc3ByIWF\nUKu1y21bAMc/BkxllMQTQgh5fpTIE0JILbpxV4RXFnFQMhMAQAsX4JeNgLUFJfGEEEKqhxJ5Qgip\nJdEPpZi7wxO5kAMAnG1UCN8MONpSEk8IIaT6KJEnhJBacD+R4d1P3ZGuMQcA2JqqEL5VBHcnSuIJ\nqQoN0yArN4PvMAgxSpTINwACgaDMR3x8PN/hEdLoJD1hGDBbg8f5pgAAc6ECJ7aI0MqdknhCqoIx\nhq0/fITFX0zEiX++5TscQoyOiO8ASPXt27dPb5kxhg8//BBPnjyBmZkZT1ER0jilZTEMnAvcT9K2\nk0iYAkc2iNChFSXxhFRVcloCohOvAwBOXNiPgZ3egICjNkhCilAi3wCMGTNGb3n16tWIj4/H3r17\nYWNjw1NUhDQ+OXkML70HXLuvXRYKGNaOuoXATu35DYyQekqlVuotP0pPhKNNM56iIcT40NfasnCc\n4UdNbV9LTpw4gSVLluDdd9/F2LFj6/z8hDRWBQqG4QuBf25olzkOCBkbi+6dVfwGRkg9piws0FuO\nSbrNUySEGCdK5BuQu3fvYsyYMejZsyc2btzIdziENBoqFcOYj9Q4fbG4bOs8YFCHNP6CIqQBUDyT\nyMclUyJPSEmUyJeFMcOPmtq+huXk5GDYsGGwsLDAd999B4GA3lpC6oJGwzB1ViIO/yXUla2YBsx8\nlfrEE1JdikKF3jK1yBOij/rINwCMMYwfPx4xMTH4448/YGdnx3dIhDQKjDHM+0SJ0CvOurJ5o4FF\n43kMipAG5NmuNcmpD5CvyIVMYspTRIQYF2q2bQBWrVqFw4cPY/v27ejQoQPf4RDSaCzfnodPD4t1\ny5Nf0uDjYIDj4f4YQhqiZxN5Boa45Ls8RUOI8aEW+Xru2rVrCAkJgY+PD8RicamhKF999VXI5XKe\noiOk4dox6h06AAAgAElEQVSy4haW/dJSt/y6fyZ2fWBJSTwhNejZPvIAEJN8G95uNBIUIQC1yNd7\nqampYIzh5s2bePPNNzF+/HjdY8KECXjy5AnfIRLS4IT+zDC3RBI/oE0+9n5iCaGQkvgif/zxB15+\n+WW4uLhAIBAgNDS01DZLly6Fs7Mz5HI5+vTpgxs3bvAQKTFmymf6yANATNItHiIhxDjxmsi7u7sb\nnI10yJAhALT9T6miL1/v3r2h0WigVquh0Wj0Hmq1Gq6urnyHSEiDcvgPhrfWFi93a83wwyYZJGJK\n4kvKzc1F27ZtsWXLFshkslK/VKxbtw4bN27Etm3bEBERAXt7e/Tv3x85OTk8RUyMkVJVukU+OvG6\nwQSfkMaI10T+v//+Q3Jysu5x6dIlcByHkSNHAgDWr19PFT0hxGicvsgwagmgVmuX27YAjn3MwVRG\nSfyzgoKCsHLlSrz22mulRtFijGHz5s1YuHAhhg8fDl9fX4SGhiI7OxthYWE8RUyMkUJZOpEvVClx\n+0EUD9EQYnx4TeRtbW1hb2+ve/z000+wtLTEiBEjqKInhBiVf64zDFsAKAu1yy1cgJObAGsLSuKr\nKiYmBikpKRgwYICuTCqVolevXjh//jyPkRFjoyjRIm9pWjxT+dX7//IRDiFGx2j6yDPG8OWXX2Lc\nuHGQSCRU0RNCjMbVaIbB8zTIzdcuO9sBp7YADjaUxD+P5ORkAICDg4Neub29vW4dIYB+H/mAlr10\nz6/fj4BGo+YjJEKMitGMWnPq1CnExsZi6tSpAMqv6B8+fFjmcS5evFjmOjc3N0il0hqIltSE7Oxs\nXLt2rdrHKe89Nyb1JU6g/sRaF3HGJEsxY3NzpOdr6w4r00JsfOsOHicU4HFC5Y5RE3F6eXlV+xj1\nQXmj/hjr36WxxgUYd2xAxfE9Tk0pXsiXQmpiioLCXGTnZ+Lk78dgZ+HCW2x8otiejzHGVt263Wha\n5D///HN06tQJbdq0qXBbGt6NEFIXHjyWIHibF9KeJvHmXB62zLgHD8fS/XZJ5Tk6OgIAUlJS9MpT\nUlJ06wgBAJW6UPfcRCSGi3Vx0vMg7Q4fIRFiVIyiRf7Ro0c4evQoduzYoSsrWdG7uBR/466ooi9v\nQqSCAvrwNSbm5ubVmsCq6Ju1sU+CVV/iBOpPrHURZ2wSw2urgSfZ2mVTlosTm0Xo1tGn0seoyTgz\nMzOrfQxj4eHhAUdHR4SHhyMgIACAtn4+d+4cNmzYUOZ+xvZ3acz/X4w5NqDy8Z2+vQ94+n+wbev2\ncHV3wb1jlwEAWarHtXJ9xvzaUWzPx5hjq27dbhQt8rt374ZUKsXo0aN1ZSUr+iJFFX23bt34CJMQ\n0kgkPGLo+y7w4GmDsUydh+PvJqBbR+qaV1m5ubm4fPkyLl++DI1Gg7i4OFy+fBkPHjwAx3GYM2cO\n1q1bh0OHDuHatWuYOHEizM3NMWbMGL5DJ0akZB95iYkE7o4v6JaT0x5AwzR8hEWI0eA9kWeM4Ysv\nvsCoUaP0ZiClip4QwoekJ9okPubprTgSTQEO9/wJvUd58xtYPRMREQF/f3/4+/ujoKAAISEh8Pf3\nR0hICABg/vz5mDt3LoKDg9GxY0ekpKQgPDwcpqamPEdOjEnJmV0lJjKYy61gKrMAACgLC5CRTZMe\nksaN9641v//+O6Kjow0OKTl//nzk5+cjODgY6enp6NKlC1X0hJBa8zidof9s4O4D7bKJkOFgux/Q\nf/1YfgOrhwIDA6HRlN9aGhISokvsCTGk5PCTYhMJAMDRphmiE68DAJJS42FjYc9LbIQYA94T+T59\n+kCtLnsIKaroCSF1ITOHYdA84EasdlkoBPYv5zAkcByvcRHSWDHG9LrWiE20XducSiTyyWkJ8PUw\nvn7PhNQV3rvWEEII3/IyCjD03QJEPh0EQyAA9i4BXg2kEbII4UuhWgn2tA+8SGgCoUAIAHC0babb\nJjk1npfYCDEWlMgTQho1ZSHD66Ojce528Y2sn30AjOpHSTwhfDLUGg8AjjauuudJaQ/qNCZCjA0l\n8g1YbGwsBAIBQkNDdWW7d++GQCBAfDy1YhCiVjOMn5OGX7KKh5T8ZBYweQgl8YTwTVnyRleRRPfc\n0aZEi3zaAzDG6jQuQowJJfL1XFFibugxa9YscBxX4QRaYWFh2LJlSx1FTIhxYIxh+joNvrtsoytb\nPBGYO4qSeEKMQckRa8Ti4hZ5c7klTKXmALTJfnr24zqPjRBjwfvNrqRmLFu2DM2bN9cra9myJX74\n4QeIROW/zWFhYbh+/Tpmz55dmyESYjQYY5i/SYkvfxLryt55pRDL3jLhMSpCSEn6LfLFiTzHcXC0\ndS1xw+sDGrmGNFqUyDcQAwcORKdOnZ57/4pa7Z9Hfn4+ZDJZjR+XkOpaswf45IfiJH68XzI2v+9Y\nK/8PCCHPR6HXR16it05/CMoH8HEPqNPYCDEW1LWmATPUR/5ZgYGB+Pnnn3XbFj2KMMawdetWtGnT\nBjKZDA4ODnjrrbeQmpqqdxx3d3cEBQXh9OnT6Ny5M2QyGdavX19r10bI89rxI8Piz4qXh/nl4IvN\njhAIKIknxJgon5kMqiQnGrmGEADUIt9gZGRk4MkTwzPcldfKuHjxYsyfPx8JCQnYvHlzqfUzZszA\nV199hYkTJ+Ldd99FfHw8tm7din///RcRERGQSCS6c9y7dw9vvPEGpk2bhqlTp8LV1bXU8Qjh0zcn\nGd75pHi5bwcgbL0ZRCJK4gkxNnp95J9pkW/axF33/GZcJNQatW54SkIaE0rky7D0S4blX9Xe8ZdM\nBpZOqbnkYdCgQXrLHMfhypUrFe7Xr18/NG3aFBkZGRgzZozeuvPnz+Ozzz7D3r17MXZs8cyWgwYN\nQs+ePbFnzx5MnToVgLblPjo6GkePHsWQIUNq4IoIqVlh4QwTVxUvd/YBDq0BpBJK4gkxRkq9RF6q\nt87DyRsWcmtk5aUjKy8dt+IiaWIo0ihRIt9AbN26Fa1atdIrk0qlZWxdOd999x3MzMwwYMAAvdb+\nli1bwt7eHmfOnNEl8gDQrFkzSuKJUQo9WojJ64VgTJu0t/YEfvoEMJNTEk+IsVKqivvIS55pkRcK\nhOjYqjdO/3cYAHDh+q+UyJNGiRL5BqJjx46lbnaNjY2t1jHv3LmDnJwcODg4GFz/+LH+kF+enp7V\nOh8htSHsuAKT14rAnnYx822mQvhmEWwsKIknxJgplPm652KT0gMndPbpq0vkr8VcRE5+FsxkFnUW\nHyHGgBL5MiydwmHpFL6j4JdGo4GtrS2+/fZbg+utra31lmmEGmJsjv+pwYQ1QjBOewN3u9wohKu2\nwU66BYApv8ERQspVXos8oB25xt2xJWKTb0OtUSHi1u/o4/dyXYZICO8okSdl3gzbvHlz/Prrr+jc\nuTNMTSnpIfXL2UiGEYtUUEM7Nrxv0wL8+oEcttwMgP6eCTF6eje7igx3Fe3s8yJik28DAC7dOUeJ\nPGl0aPhJAlNTU6Snp5cqHzVqFDQaDZYvX15qnVqtRkZGRl2ER0iVXbzJ8PJ8oECjTeI9rfNwcocU\nth1eAAJovGlC6gNliXHkJWLDiXx7r24QPB2tJi75DtKzDY/eRkhDRYk8QceOHZGZmYk5c+YgLCwM\nBw4cAAD07NkTwcHB+PjjjxEUFIRNmzZhx44dmDdvHjw9PXH06FGeIyektBsxDEHvAdl52mUni0KE\n75KjqR31iSekPtFvkS/dtQYATKXm8HJprVu+En2h1uMixJhQ15oGoKqzUT67/cyZM3H16lXs27cP\nW7duBaBtjQe0o+H4+/vj//7v/7B48WKIRCK4ublh5MiRePHFF587BkJqw70Ehv6zgdRM7bKNBXBy\nuwk8nenvk5D6przhJ0tq17wrbsdHAQCioi+gd3saPY00HpTI13MTJ07ExIkTDa5zd3eHRqOpcHuZ\nTIbdu3eXeY5JkyZh0qRJ5cYRExNTmXAJqTXxyQz93gWSnk46bCYDfv4EaO1JSTwh9ZH+zK5lJ/Jt\nmnfCwTO7wMAQnXgD2XmZMJdb1kWIhPCOutYQQuq9pCcM/WYD8SnaZZkEOPYx0MmHknhC6itFJVvk\nLU1t4OHkDQBgTEPda0ijwnsin5SUhAkTJsDe3h4ymQy+vr74448/9LZZunQpnJ2dIZfL0adPH9y4\ncYOnaAkhxuZJBsOAOcC9BO2yiUCDH9cAvf0oiSekPqto+MmS2rXoqnt+5FwoHj6Jra2wCDEqvCby\nGRkZ6N69OziOw88//4xbt25h27ZtsLe3122zbt06bNy4Edu2bUNERATs7e3Rv39/5OTk8Bg5IcQY\nZOUyBM0Drj/t2SVkKnzrtAMDO1MST0h9p9DrWlP+PCWdfPrA0swWAFCgzMP2Q0vx5fG1OHjmM/x7\n8wwyc9JqNVZC+MJrH/n169fD2dlZr3+2m5ub7jljDJs3b8bChQsxfPhwAEBoaCjs7e0RFhaGadOm\n1XXIhBAjUaDk8Mp8hv9ua5N2jmmwx+8nDNv2Ds+REUJqgn7XmvJb5E2l5pj+8kfY/P1CKJT5yM7L\nQNTTLjZ/XtGOejMx6H209uxYqzETUtd4bZE/fPgwOnXqhJEjR8LBwQF+fn7Yvn27bn1MTAxSUlIw\nYMAAXZlUKkWvXr1w/vx5PkImhBgBlRpYtNsTZy8Xt7zvHHQVo7cPA2gEJUIahMqOWlPE2c4db720\nACZCceljqRTYc3ITHmck1WiMhPCN1xb5+/fv68YlX7RoESIjIzFr1iwAQHBwMJKTkwEADg4OevvZ\n29vj4cOHBo958eLFMs/n5uYGqbTiyoDUjezsbFy7dq3axynvPTcm9SVOwLhj1WiAZd+449x1K13Z\ne/4X4D/YxGjjrom4vLy8aiAS46FSqbBkyRIcOHAASUlJcHJywtixY7F06VIIhUK+wyM80zANClVK\n3bKJqHRybkhL13b4aOJOPHwShwJlHh6lJ+L8tXBk5KSiQJmHXUdXws+rG5rZN4evR0cIBfS3Ruo3\nXhN5jUaDTp06YdWqVQCAdu3a4e7du9i+fTuCg4PL3ZfGLSek8WEM2PBDM5z8z1ZXNrFXHEa+ZsJj\nVOR5rF69Grt27cKePXvQpk0bREVFYeLEiZBIJFi8eDHf4RGeFZaY1VVsIoWAq3wHAiszW1iZFdcR\nPu4B2HRwAdRqFR6lJ+LkvwcBALYWDujg3RvW5nZwsfNAM/vmlFuQeofXRL5p06bw8fHRK/P29kZ8\nfDwAwNHREQCQkpICFxcX3TYpKSm6dc/q0KFDmecrKCgAY4z+oxoBxhjMzc3Lfb8qUtTKWZ1j1IX6\nEidg/LEu/ozh+3PFy28PA3a87waOc+crpHLV5OuZmZlZ7WMYk4iICLz88st46aWXAACurq4YMmQI\n/v33X54jI8ZA70bXMmZ1rSxXhxYYEfg29p/erleempWCk/9+p1u2sbBHR+/esIQLpCam1TonIXWF\n10S+e/fuuHXrll7ZnTt34O7uDgDw8PCAo6MjwsPDERAQAECbjJ87dw4bNmyo8vnEYjEKCgoglUop\nmecRYwwFBQWQSKpXOZPG5ZM9hVgdWlxlDfBPw7Z5NvR/uZ4KCgrCunXrcPv2bbRs2RI3btzAmTNn\nsGjRIr5DI0Ygt6B4ZDqZ1Kzax+vauj9c7D3x4NF9pKQ9wD83zyCvIFtvm7SsRzj570EIBSI4WXrg\nTvrfMJNZwkxuCVeHFvB08gY4Dtl5GTCTWVK3HGIUeE3k586di27dumH16tUYMWIEIiMjsXXrVqxZ\nswaAtvvMnDlzsHr1anh7e8PLywsrV66Eubk5xowZU+XzCQQCSCQSKBSKijeuBdnZ2krD3Nycl/NX\nVl3EKZFIIBDwPo0BqSe+PJCD/+0qbiHr7pOJpeNiIBTalrMXMWYzZ85EQkICWrVqBZFIBJVKhcWL\nF2P69Ol8h0aMQF5Blu65qbRmPoua2TdHM/vmAIDBXccg6t7fSElLQGrWI9yMu4R8RS4AQK1RISH9\nLhLS7+rtL5eao1ClQKFKCRORGM52Hmje1Actm7WDp3MriKv5ywEhz4PXRL5Dhw44fPgwFi1ahBUr\nVsDNzQ0rV67EjBkzdNvMnz8f+fn5CA4ORnp6Orp06YLw8HCYmj7fz14CgYC3G16Lbuw01m4LRepL\nnKRxOPgbw9tbi8eQ7tmWYdWb0RBRY1i99umnn+Lrr7/GgQMH4Ovri8jISMyePRvu7u6YPHmywX0a\n8s3MtcWYYwPKji8+9bbueWGBulauQwBzOElawcmuFVrZ9sCDtNu4mvAX0nNTDG5fsgW/UKVEbNJt\nxCbdxun/DkHACWFv4QIbU0dYyprAUt4ElrImFY5//7yM+X2l2KqmugMZ8JrIA8DgwYMxePDgcrcJ\nCQlBSEhIHUVECDEWv/ytwbglGmigzdr93RQ4+rEEd28xniMj1bVq1SosXrwYI0aMAAD4+voiLi4O\na9asKTORJ42HQpWne15byXBJQoEQ7k184GbbCmm5ychRZEJRmIuCwjzkFGQgIf0eCgq1LfYmQjEK\n1Uq9/TVMjeTMOCRnxumVW8hs4WDhqn1YusFUYlHr10IaF94TeUIIMeSP4w/w2pomKIT2F7SWlhk4\nsd0KlmbUJ74hYIyV6l4nEAjAWNlf0oztV0JjvjncmGMDKo4v42I8cE/73NXZvU6v4+LFi7A1c9I7\np0ajxuPMZMglZjCXWyIrNwOxybdx58EV3H4QhZS0BIPHyspPRVZ+Ku6mRALQjpTj7tQS1uZ2sJBb\nwcLUGlZmTeBg41ypLkTG/L5SbM+nugMZUCJPCDE6F28yDN3cFPlP56xzs8hF+NdWsLOmJL6hGDZs\nGNauXQsPDw/4+PggMjISmzZtwoQJE/gOjRiBvBI3u9ZUH/nqEAiEcLB21i1bmFqhbfPOaNu8MwAg\nIycVMUm3kJyWgEdpCUhOT0By2gOo1Sq946RmpSA1y3DXHVOpOczlVjCTW8JcZgmBQIj8ghyIRCZo\nYukEOysnpGVkwUQoQXTidShVSqjUhShUKVFY4rlQIITYRAIrsyawt24KC7k1hEJK9xoqemcJIUbl\n+n2GoPeA7HxtEu9orcGp/zNFMwdK4huSTZs2wcLCAsHBwUhJSYGTkxOmTZuGJUuW8B0aMQK5Jfqj\nm8qMvzuKlZkt/Ly665UpVQrEJd9FdOJ1RCfeQEzSLShVZQ+2kVuQrb3utAcVn/BK1eKTiGUwlZpD\nJtHeX6jRqCExkUEqkUMqlkEmNoVMIofERAahUASRUARTqbl21B6ZBcQmMigK85GvyEWBMh8qdSFE\nQhEYY8hX5CJfkYv7cffAGEOq5j7EJlJITWQwlZnDyqwJJGIZGNNAo9GAMQYN04AxDazNm8BcblVB\n9LVLpS7UDXcqE8vBcQJoNGrtFyN1ofbXQ44DxwkgFAghEdd+V6+qoESeEGI0ohMYBswBUp/+0mhj\nAYR/KkALF0riGxpTU1Ns2LDhuYYSJg1fyURebgQt8s9DLJLAy6U1vFxaAwDUahXiH0UjKTUe2Xnp\nyMxNR1ZuOlKzUvAoLbFUv/uapFDmQ6HMr7Xjl3Q98e8qbW9r6QBTqQVUKiUEAiGEQhEUSu2XBnAc\nRAIRzOSWsDK1gdXTxF+bbKug1qihVqugKMyHolABoUAAxrQ3JhcU5oPjBBBwAmRlZgEch8vJv4I9\nnTU4Jz8LqZnJyFfm6cXDcQIwpjEYq4O1Cz4cv+25X5vaQIk8IcQoJDxi6D8HSErVLpvJgBMbgdae\nlMQT0tjotcjXwDjyxkAoFMHDqSU8nFqWWqfRqJGTn4XsvEzk5GciKy8DGo0acqkZlIUFeJyRhCeZ\nyYhJuAuNRg1LCyuYiMQQiUxgIhTDRCSGicgEIqEJ1BoNFMp8PMlKxpOMZOQWZJeZmBqD1MwUpGYa\n7m6k2yYrBXHlblE5CWkVb1Pea2WM85ZQIk8I4d3jdIYBsxlik7SVpFQMHPsY6NjK+CpNQkjty9NL\n5Otni3xVCARCWJhaw8LUutztnuemTQ3ToECRh9yCbOQrcsFxHDiOg0JZgAJlHgqUechXaP9VFOZD\nrdFApVIipyALOflZyMnPhFJZAKlYDqlEDplYDpHQBCqNtv+/TGIKucQUaU8ywHEC2NnbokCZjwJl\nHnLys5CRkwqVSqltHRcIwEF7fgbgUXoiVOrC537daoKAEzzt+sNQ8LR1XsAJIBKJIRKaaGNlDEyj\nNrpuNQAl8oQQnmVkMwyaB9yK1ybtIiHD96s49PajJJ6Qxio3v/53rTEWAk4AudQM8lr+ZeN5vmQU\nqgqRnBYPtUYNE6EJNEyDQlUhJCZSyCSm4DjtNtl56cjISUNGTipy8jMAcBAKRBAIBBAKRJCKZRCL\nJE/73jPIpWaQiuUAtC3sd+7eAWMMzZt7AuBgIhJDJpHD1sIR5nJLXUu7RqMGA+rVrL2UyBNCeJOb\nzzB0PhB5R7ssYGp8MykBg7u58xoXIYQ/jLFnbnalRL6hMhGZ6GbbLY+9ddNqnSf/aZfNdi3K/5Ih\nqEcJfBFBxZsQQkjNUygZXl0I/FVi9IXPOv6GNya58xUSIcQIKAoLoH7abcNEJIZYJOE5IkKMFyXy\nhJA6p1IxjAkBTkUUl210OojJm/vzFxQhxCjkFmTpnjeG/vGEVAcl8oSQOqXRMExZAxz6o7hsqel+\nzNk/HDDCEQEIIXWr5GRQ1D+ekPJRIk8IqTOMMczaBOz9pbhsXvub+OiX0YCJCX+BEUKMRskbXalF\nnpDyUSJPCKkzH+4Cdv5YvPzWy8DH21qBE1BLPCFEK7eRDT1JSHVQIk8IqRNr9zKs3Vu8PKofsPN9\n45xggxDCH0rkCak8SuQJIbVux48Mi/6veHlodyD0I0AopCSeEKKPhp4kpPIokSeE1Ko9Jxje+aR4\nuU/bQny7AjARURJPCCmt5KyudLMrIeWjRJ4QUmt+OMMweRXTLXeW3cfhDSaQSiiJJ4QYpn+za+3O\nRkpIfUeJPCGkVvxygWFMCIOGaZP2tsIY/HzQDeamlMQTQsqWSy3yhFQar4n80qVLIRAI9B5NmzYt\ntY2zszPkcjn69OmDGzdu8BQtIaSy/rjM8OoChkK1Nml/gcXj5H5HWFuLeI6MEGLs8vRudrXgMRJC\njB/vLfLe3t5ITk7WPa5evapbt27dOmzcuBHbtm1DREQE7O3t0b9/f+Tk5JRzREIInyJuMgz9H1BQ\nqE3i3URPcCrUCg7Ocp4jI4TUB3SzKyGVx3siLxQKYW9vr3vY2toC0E4cs3nzZixcuBDDhw+Hr68v\nQkNDkZ2djbCwMJ6jJoQYcu0+Q9A8IDtPu+xow3DqmyZo5mXJb2CEkHqDhp8kpPJ4T+Tv378PZ2dn\neHp6YvTo0YiJiQEAxMTEICUlBQMGDNBtK5VK0atXL5w/f56vcAkhZbgTz9B/NpCWpV22sQBObeHQ\nwoX6xBNiTFTqQuw6shLv7xiFiFtn+Q5HhzGGqHsXkK/IBQBw4CCXmPIcFSHGjdcOq126dEFoaCi8\nvb2RkpKClStXolu3brh+/TqSk5MBAA4ODnr72Nvb4+HDh2Ue8+LFi7Uac02oDzECFGdNqy9xAlWP\nNfGJGG9/2hKPMsUAAFOJGhun3kF+Wh4uptVGhFr15TWtiTi9vLxqIBJCgEt3zuF6rPZv8tvTO/CC\nSxtYmtnwGtOTzGR8//vnuBH7n67MyswWAoGQx6gIMX68JvKDBg3SPW/dujW6du0KDw8PhIaGonPn\nzmXuRzNBEmI8UtJNMHP7C7okXipWY9Pbd+HjmsdzZIQQQ/68ckL3XKlS4Nj5vRg3YDYvsRSqlPj1\nv0M4FfE9VOpCXbmZzBIj+87gJSZC6hOjGkJCLpfD19cX9+7dw7BhwwAAKSkpcHFx0W2TkpICR0fH\nMo/RoUOHWo/zeRW1yhlzjADFWdPqS5xA1WNNesIw5mMg6Wmru5QV4PgaEV7s0qq2QgRQf17Tmowz\nMzOz2scgJD7lHuKS7+iV/XvzDHq1ewmuDi3qNJakjBic2PclHmcm6co4cOjeZiCGdBsHOY0hT0iF\neO8jX1JBQQFu3rwJJycneHh4wNHREeHh4Xrrz507h27duvEYJSEEAB6lM/SbDdxL0C6baJT4ceId\nvNjFhN/ACCFl+jPqZ91zjitOAX7559s6i0FRWICImFM4df0bvSS+mX1zzBu5HiNenE5JPCGVxGuL\n/Pvvv4+XX34ZzZo1w6NHj7BixQrk5+djwoQJAIA5c+Zg9erV8Pb2hpeXF1auXAlzc3OMGTOGz7AJ\nafTSshgGzAFuxmqXhUyFb3ufxqBpg3mNixBStnxFHv6786dueUy/d/DNqU8BADfjIpGvyIWsFm8u\nfZyRhFMR3yPy7l9QFBboymViOYZ0fxPdWw+gPvGEVBGviXxiYiJGjx6NJ0+ewM7ODl27dsWFCxfQ\nrFkzAMD8+fORn5+P4OBgpKeno0uXLggPD4epKd3FTghfMnMYBs0FrtzTLguYGvtst2PYGn762BJC\nKic57YGuH7qDtQs6teqDs5ePI+Hxfag1KlyLuYiO3r1r/LxqjRq/Rx7Fz3/vR6FaqbfOx80fo/u/\nA0tTfm+2JaS+4jWR379/f4XbhISEICQkpA6iIYRUJF/B8MoHwMVb2mUODF9hNUZ+Mwegm9BJFSUl\nJWHBggU4ceIEsrOz4enpiZ07d6JXr158h9YgZeQ80T23s24KjuPQrkVXJDy+DwCIuvd3jSfyD5/E\nIuzUNsQ/uqdXbiG1gY9zF4x+aSoNYEFINRjVza6EEONVqGIY9RHwx+Xisp3vM4x/ZTEgMKrbbUg9\nkJGRge7du6NXr174+eefYWdnh/v378Pe3p7v0BqsjOxU3XNrsyYAgPYtuuKnv78BANyMuwRFYQEk\nJtIaOd+fV07gh7NfQKNR68qc7Tzweu+pSHuYC47jKIknpJookSeEVEijYXhrDXDsr+KydTOBacOp\nP6NfhecAACAASURBVCt5PuvXr4ezszN2796tK3Nzc+MvoEYgvUSLvJWZdhZ1BxsXONo0Q3LaAxSq\nlLgR+x/8vLpX6zyMMfzyz7c48c8BXZlQKEJQp5HoGzAcQqEI6Un1Yw4IQowdNaMRQsrFGMN7i1Ow\n95fisvnjgP+NpZY08vwOHz6MTp06YeTIkXBwcICfnx+2b9/Od1gNWsmuNVbmTXTP27Xoqnv+zamt\nCI/4Hhqmea5zPHwSh51Hlusl8c3sm+ODMZswoNMbEAqp/ZCQmkT/owgh5Vq1PgVbzhbPsDxlKLBm\nOo8BkQbh/v372LFjB+bNm4dFixYhMjISs2bNAgAEBwcb3MdYZ/I11rgA/dgSkuN0zx8lPsHFHO06\nmaoJRAITqDSFUBYW4Pj5fUhIeIC2zXpW6VzRj67g/N1jYGC6MicrT/TwfA0J91OQcD+l3PiMDcX2\nfCi2qqnurN3UIk8IKdPOL1Kx5GhxEv9aLw3+7380uzKpPo1Gg4CAAKxatQrt2rXDxIkT8e6771Kr\nfC3KU2TpnsslFrrnFjIb9PMdAyt58f0JNx9GQK1RVfrYqTnJ+PveT7okngOHlo4BeLHVSJgIxTUQ\nPSHEEGqRJ4QYdOBQNt75ygp4mrP389dg3zIBhEJK4kn1NW3aFD4+Pnpl3t7eiI+PL3MfY5vJ15hn\nGH42NrVGjb3nc3Xre3QJhImo5ORtHTAw8GUs3z0d6dmPoVDlwcRKBf8XupR7HsYY4lPu4adfPoeG\naW9qdbBxwcRB78PZzr3S8RkTiu35UGzPp7qzdlMiTwgp5Ze/GcZvkII9nfmx0wsq/LhOBImYknhS\nM7p3745bt27pld25cwfu7u78BNTAZeWmgT3t924us3wmidcSCoTo4tNX17/9/LVwmErNoVIXwsc9\noNQvcXcTruLArzv0ZmeViGWYOmQh7K2da/FqCCFFKJEnhOi5EmOKWTsB1dPqoZVzIX7abAIzOSXx\npObMnTsX3bp1w+rVqzFixAhERkZi69atWLNmDd+hNUgZOcVDT5a80fVZnX364pd/vgUDw50HV3Dn\nwRUAQBefvhjVLxgCTgC1WoWzUcdx9NwevZtiOXAY228WJfGE1CFK5AkhOncSZJizqwXyFdplVwfg\n5DYT2FpSEk9qVocOHXD48GEsWrQIK1asgJubG1auXIkZM2bwHVqDlJ5dPGKNdTmJvI2FHbzd/HAz\n7pJe+YUbp6FUKWAht0bk3b+QmZumWycVy9G2eWd0az0Qnk29az54QkiZKJEnhAAAbsUxzNrphZx8\nbbVgZwWEbwZc7CmJJ7Vj8ODBGDx4MN9hNAoZBsaQL0vPtkG6RJ7jBLouOZfunCu1rZvjC5jy0gcV\nHpMQUjsokSeEIOYhQ//ZQHqOtt+slbk2iX/BlZJ4QhqCkrO6WpmV3SIPAK09O+LNgXORkZOKjt69\ncfjP3bh050+9bczlVujRNgj9Al412N+eEFI3KJEnpJF7+FibxCc+1i7LxGr8tEGIdl6UxBPSUBia\n1bU8Hb17656/OWA23By8kJqVAgu5FRxtm8HHPQAiISXwhPCNEnlCGrEnGQz95wD3H2qXJVwhNrx1\nH11bUz9XQhqSkje7ltdH3hChUIQ+/i/XdEiEkBpAE0IR0khl5jAMmlmAm7HaZZGmEJ/Z/n97dx4X\ndZ3/Afw1MwwwHCKCA6IokHimZiIalTck5Zpm6nplbv3oMAOppTwK3RCPvPLAzN1cdlt/arub/dZc\nF1OSCGtxPUrNoxWvFBJELhmY4/P7Y3RglFv0+50vr+fjwWPn++E7M69mnTdvPnzm8/0A/buUSJqL\niJrf9ZLqM/KNa+SJSL44I0/UApWVC4yaeAGHrncEAKiEBX/q9ik6vzoE4FVbiRTFbDahuKwQgHWL\nSC+PNhInIqLmwhl5ohamolLgmbcFvrnZxAPAR+PP4tebp7CJJ1Kg4hvXISAAAB5uXlzbTqQgnJEn\nakGMJoFJicCeg1UN+8rXgRcmhkqYiojupUpThe22q7ObhEmIqLlxRp6ohbBYBH6zCNiRUTW28EUg\nbiJn4YmUzGSqtN3WcjaeSFFk08gvXrwYarUas2bNshtfsGAB2rdvDzc3NwwdOhQnTpyQKCGR4xJC\nYOYK4C9pVWNvTALmPy9ZJCK6T4xmo+22k5OzhEmIqLk1upE/efJks4f49ttvsWnTJvTu3Ruqamt0\nly5dipUrV2LdunXIzs6GXq9HZGQkSktLmz0DkVIJIfBWCrBxR9VYzNPAspmwe78RkTIZOSNPpFiN\nbuSTk5Ntt//+97/bbhcUFGDNmjWNDlBUVISpU6di8+bN8Pb2to0LIbB69WrMmTMHY8eORc+ePZGa\nmoqSkhJs2bKl0c9D1FItSgWWV3vLTIkCUt5kE0/UUpjsZuTZyBMpSaMb+fLyctvtf/zjH7bbPj4+\nuHr1aqMDxMTEYPz48Rg8eDCEELbxnJwc5OXlISoqyjbm6uqKQYMGISsrq9HPQ9QSrdoq8O6mquOn\nvY/h43mAWs0mnqilsJ+R59IaIiVpdCPv6emJL774osbvaTSaRj3Wpk2bcPbsWSQlJQGwnyHMzc0F\nAPj5+dndR6/X275HRLVb/zeBN9ZWHUciG1u3doXWiU08UUtSfUZeyzXyRIrS6O0nFy5ciIEDByIi\nIgKFhYW4ePEiXFxckJaWhosXLzb4cU6dOoV58+YhMzPT9guAEMJuVr42dS0JOHjwYIMzSMURMgLM\n2dzuZ87PD/hg0dYg23GE4TssWFCKH05+36D78zVtXs2RMzSUW4RS0xirbT/JRp5IWRo9Ix8YGIj9\n+/ejsLAQ+/btQ6dOneDv74/U1FQsW7aswY9z4MAB5Ofno2fPntBqtdBqtcjIyEBKSgqcnZ3h62u9\nhHReXp7d/fLy8uDv79/Y2EQtxq7sNkje1sl2HGY8iqXzi6Ft11rCVEQkFaOp2hp5ftiVSFGadEGo\nzp0748svv8Tly5dx/vx5BAQEoFOnTvXfsZqxY8ciPDzcdiyEwIwZM9ClSxfMnTsXoaGh8Pf3R1pa\nGvr16wcAMBgMyMzMxPLly2t93LCwsKb8J90Xt2bl5JwRYM7mdj9zbt8r8LstwK0/bD3sk4+0jzqj\ntf9DDbo/X9Pm1Zw5i4qK7voxqGUymqutkeeMPJGi3NWVXQMCAhAQENCk+3p5ecHLy8tuzM3NDd7e\n3ujRowcAIC4uDsnJyejWrRtCQ0ORlJQET09PTJ48+W5iEynSjgyBKQsBi8V63OsB4F9rfdHai2vi\niVoyE2fkiRTrrhr55qZSqezWvyckJKC8vBwzZ85EYWEhBg4ciLS0NLi7u0uYkkh+dmUJTHwHMJut\nx92DgD0fAD5s4olaPLsZee5aQ6Qosmrk09PT7xhLTExEYmKiBGmIHMOX2QLj5gFGk/W4cwfgyw8A\nvTebeCKyn5Hn0hoiZWn0h12JSD4yjgg8/RZQcXPCLcjbgL1rgHa+bOKJyKr6jDwvCEWkLGzkiRzU\ngWMCo94Eym/uLNeh4iL2PrELgX5s4omoCi8IRaRcbOSJHNDBHwWi44HSmxdabld5GXtH/B+CZ42T\nNhgRyY79BaE4I0+kJGzkiRzM0TMCT8wGisusx22Nv+DLHh8hdPFMaYMRkSxVn5F34ow8kaKwkSdy\nICdyBCLjgMIS63EbYwH2dP8I3TcnAnVc8ZhI7hYvXgy1Wo1Zs2ZJHUVxjJyRJ1IsWe1aQ0S1O3NR\nYEQskH/deuzlAaTNuIDeE+eziSeH9u2332LTpk3o3bu33RbE1DxM1dfIO7lImISImhtn5IkcwPlc\naxOfW2A99tABu1cCD//6YTbx5NCKioowdepUbN68Gd7e3lLHUaTqM/K8IBSRsrCRJ5K5K/kCkbHA\nxTzrsc4F+GI5MKAnG3hyfDExMRg/fjwGDx4MIYTUcRTJbtca7iNPpChcWkMkY/nXBaLigJ8uWY+d\ntcBni4HHH2ITT45v06ZNOHv2LLZs2QIA9S6rOXjw4P2I1WhyzQVYsxWXFNmOT586g/xLxRImsif3\n106umK1p5JgtNDT0ru7PRp5IpopKBUbGA8dzrMcaYcK2RBWiBvBtS47v1KlTmDdvHjIzM6HRaAAA\nQgjOyt8DZovJdlujYv0gUhK+o4lkqKxc4Kk3gUOnrMcqYcGfnv4eTw/tJ20womZy4MAB5Ofno2fP\nnrYxs9mMr7/+Ghs3bkRZWRm0Wvv13GFhYfc7Zp1uze7JLRdgn+0fR6tW0fZ9qC/atNJLFcvGUV47\nuWG2ppFztqKiovpPqgMbeSKZMVQIjHkbyPqhauyjPrsx6a2npAtF1MzGjh2L8PBw27EQAjNmzECX\nLl0wd+7cO5p4ajr7D7tyjTyRkrCRJ5IRo0lgwjvA3mrL+Fb5b8cLKROkC0V0D3h5ecHLy8tuzM3N\nDd7e3ujRo4dEqZTJaOaHXYmUirvWEMmE2SwwbSGw85uqsaS2nyH20/HcYpJaBJVKxX3k7wGTiReE\nIlIqzsgTyYDFIvA/S4Dt+6rG3p4GzH35GelCEd1n6enpUkdQHIvFbPuwqwoqaNT8sU+kJJyRJ5KY\nEAKxq4E/7qoae+1ZYNFL0mUiImWwWx/vpOVfPIgUho08kcQWvn8N6/9WdTxjFLA6tv49tYmI6mOq\nfjEoftCVSHHYyBNJKHWXwO8+b2M7njgc+CgBUKvZxBPR3bt9Rp6IlEXSRn79+vXo06ePbfeCiIgI\n7Nq1y+6cBQsWoH379nBzc8PQoUNx4sQJidISNa8vswX+Z7HFdhz1UAX+9C6g0bCJJ6LmYTRxxxoi\nJZO0kQ8MDMSyZctw+PBh/Oc//8GwYcMwZswYHD16FACwdOlSrFy5EuvWrUN2djb0ej0iIyNRWloq\nZWyiu/bdcYGxbwuYLNa3YK9WV7F9mQu0Tmziiaj5mKrNyHNpDZHySNrIjx49Gk888QRCQkLQuXNn\nJCUlwdPTE//+978hhMDq1asxZ84cjB07Fj179kRqaipKSkqwZcsWKWMT3ZUf/ivw5GwzygzWpr29\nORc7P/JCK3c28UTUvKrPyHNpDZHyyGaNvNlsxtatW2EwGDBo0CDk5OQgLy8PUVFRtnNcXV0xaNAg\nZGVlSZiUqOn+e0ngidlAYZkGAOBruYa0xQYEBrpInIyIlMjID7sSKZrkG8r+8MMPeOSRR1BRUQGd\nToft27eja9eutmbdz8/P7ny9Xo/Lly9LEZXorvx8VSAyDsgtsB57ulrwzxVu6P6Qj7TBiEix7JfW\ncEaeSGkkb+S7deuG77//HkVFRfj000/x61//ut6LgtS1Ld/Bgwdr/Z5cOEJGgDmb0/VSDSa+XI5z\nuToAgIvWgvf/5wyEqRRyjO8IrynQsnKGhoY2QxJqaeyX1nBGnkhpJF9ao9VqERISgr59+yI5ORkD\nBw7E+vXr0a5dOwBAXl6e3fl5eXnw9/eXIipRk5Qa1Ij9MBQ5N5t4jVpgyYz/4uHO/NA2Ed1b1bef\n5K41RMoj+Yz87cxmMywWC4KDg+Hv74+0tDT069cPAGAwGJCZmYnly5fXev+wsLD7FbXRbs3KyTkj\nwJzNqbxC4PGYEvx40R0AoFIBnySqMHFEF4mT1cwRXlOgZeYsKiq668eglsdk5hp5IiWTtJF/++23\nMWrUKHTo0MG2G83+/fuxe/duAEBcXBySk5PRrVs3hIaG2na1mTx5spSxiRrEaBKY+A5w6CdP29iG\neAsmjtBImIqIWhKjiReEIlIySRv5vLw8TJ06Fbm5ufDy8kKfPn2we/duREZGAgASEhJQXl6OmTNn\norCwEAMHDkRaWhrc3d2ljE1UL4tFYEYSsPObqrGlnb5AzDOjpAtFRC2O0VRhu80ZeSLlkbSR37x5\nc73nJCYmIjEx8T6kIWoeQgi8thLYsqdq7HX3v+O3f3paulBE1CLZ7VrDGXkixZHdGnkiRzdvI/Dh\nZ1XH03y/xpR5HQEnvt2I6P6y27WGM/JEisPOgqgZrdoqsOTPVceTQ89h5qtuUEm+PxQRtUSckSdS\nNrYXRM3kL/8SeGNt1fGoCIHNvw+Cmu8yIpKI3ZVduf0kkeKwxSBqBru/FZixqOr4sd7AtiQVtE61\nX7yMiOheq76PPJfWECkPG3miu/TdcYFn5wEms/X4wRDg86WAzoVNPBFJy25GXsOlNURKw0ae6C6c\nPC8wKrYSNwzW445+wD9XAt6t2MQTkfRM1T/syqU1RIrDRp6oiS79IjBylgkF5dYfjj4u5di9Cmjf\nlk08EclD9aU1nJEnUh428kRNcK1YIDoeuFBg3fjJTWXAF2t16NaJTTwRyYeJH3YlUjQ28kSNlH9d\nYPgs4HiO9dhJGPG3+QaE92QTT0TyYjcjz0aeSHHYyBM1wtVCgeGvA0d/sh6rhAWbh2ThiZHe0gYj\nckCLFy9G//794eXlBb1ej9GjR+P48eNSx1IUo5kXhCJSMjbyRA10wyDwqwTgh/9aj1Ww4GP97zFl\n0WBpgxE5qP379+O1117DgQMHsG/fPjg5OWHEiBEoLCyUOppimEy8IBSRkvHKrkQNYDYLTF0I/PuE\n9VitBlLftmDKUy9JG4zIge3evdvu+M9//jO8vLyQlZWFp556SqJUylJ9+0nOyBMpD2fkiRrgzXXA\njoyq4zWzgSlPcXaLqDkVFxfDYrHA25tL1ZpL9aU1nJEnUh428kT1WLNd4IPtVcfxk4BXn+EHW4ma\nW2xsLPr27YtHHnlE6iiKYbe0hjPyRIrDpTVEddiRITD7AwHA2riPGwIse1XSSESKFB8fj6ysLGRm\nZkKlqvkX5YMHD97nVA0j11wAYKgot90+duw4XJx0Eqa5k5xfO2ZrGmZrnNDQ0Lu6P2fkiWqx96DA\npHcsEDeb+IF++fjTu4Bazdl4ouY0e/ZsbNu2Dfv27UNQUJDUcRTFLEy22xoV5+6IlIbvaqIafHdc\nYMxbAhUm6++6D2h/wed/0EPnwiaeqDnFxsbi008/RXp6Orp06VLnuWFhYfcpVcPcmt2TWy7Amk0I\nAbOlqpEPDx8AtUoe83dyf+0AZmssZmuaoqKiu7o/G3mi23x9RGDUb4Eyg7Vpb2/Jw56PvdDWm008\nUXOaOXMmPvnkE+zYsQNeXl7Izc0FAHh6esLd3V3idI7PIsy22xqNk2yaeCJqPpK+qxt6MZAFCxag\nffv2cHNzw9ChQ3HixAkJ0lJL8K/vBEbGAyU3rMe+pnykJZUhKERe60qJlGDDhg0oLS3F8OHDERAQ\nYPtasWKF1NEUofpsPD/oSqRMkjbyDbkYyNKlS7Fy5UqsW7cO2dnZ0Ov1iIyMRGlpqYTJSYm+OiQw\n5m2gvMJ67Kcrx77nDqL78AekDUakUBaLBWazGRaLxe7r3XfflTqaIlSaK2y3XbSuEiYhontF0qU1\n9V0MRAiB1atXY86cORg7diwAIDU1FXq9Hlu2bEFMTIwUsUmBsn8UGJ0AVNzccrmjH7DnAx1CA6Ol\nDUZE1ESVxqoda9xdPSVMQkT3iqwWzN1+MZCcnBzk5eUhKirKdo6rqysGDRqErKwsqWKSwhz8UWDk\nbKD05s+8AF8gfR0QGsg18UTkuCpMVY28m6uHhEmI6F6RVSN/+8VAbn3wyc/Pz+48vV5v+x7R3Thw\nTGDE6wKFJdZjHy8gbTUQHMAmnogcW/VGnjPyRMokm11rGnIxkOoc7YIh1TlCRkD5OXNyXfGb5V1Q\nZrRettzLxYBV/3MWNwrKcbCgORNaOcrrCThO1paU824vGkItT0X1pTU6NvJESiSLGfnaLgbi7+8P\nAMjLy7M7Py8vz/Y9oqYoM6jx9kcdbU28r7kAH4/Zi26B5fXck4jIMdgtrXFhI0+kRJLPyNd1MZDg\n4GD4+/sjLS0N/fr1AwAYDAZkZmZi+fLlNT6eHDf7v0XOFySoTuk5hRD49VwTcgqs//x1MGDPHzzR\np+eoZs8IOM7rCThO1paY824vGkItj93SGs7IEymSpI18fRcDUalUiIuLQ3JyMrp164bQ0FAkJSXB\n09MTkydPljI6ObBV24BPM6r+6W98w4w+PblPPBEpS4Xxhu22G9fIEymSpI38hg0boFKpMHz4cLvx\nBQsW2PYRTkhIQHl5OWbOnInCwkIMHDgQaWlpvOofNUnGEYG3UqqOXxlyDVOf8ZEuEBHRPVJpMthu\n88OuRMokaSNvsVgadF5iYiISExPvcRpSutwCgV+/C5hvXrV8QDczVia2kTYUEdE9Yr9rDbefJFIi\nWXzYleh+eDsFyL25G03b1sCnizVwceY2k0SkTPZLa1pJmISI7hU28qR8QuC7o0b8qdqFhFPfATro\n2cQTkXJxH3ki5WMjT8pWXAzLuPGIe+OCbWjsIGDkQDbxRKRcQgi7NfJurvxcGZESsZEn5crPBwYM\nwLoDAfiuPAQA4KwF3n9N4lxERPdYpdkAAQEAcHHWwUmjlTgREd0LbORJmcxmYMoU7Mx7APHBK23D\nsycCIe05G09EymZ3VVcuqyFSLMkvCEV0T7z3Hv7zTT5+3Ws/LCoNAKB/d+CdGRLnIiK6Dyq5Pp6o\nReCMPCmP0YiTO79HdI9/4obaui40qB3wf8sAN1fOxhOR8lX/oKsbt54kUizOyJPinC9wQlT7T5Gf\nb/091dsT+GI54NeGTTwRtQz2S2u49SSRUnFGnhQl75pAZCxw6WYT764Ddq0AugexiSeiloNbTxK1\nDGzkSTGulwiMnA38dMl67KwFdiwBBvRkE09ELQuX1hC1DGzkyfEVF+OGQeBXCcDRn6xDajXwvwuB\n4WFs4omo5eGuNUQtAxt5cmwmEyqHRuLZ6EP45vuq4T/MAcYOZhNPRC1ThemG7ba7jo08kVKxkSeH\n5rP9r5hWGo/dlQ/bxlbFAtOfZBNPRC0X18gTtQxs5Mlhaa/kYtGuHvjUd4Jt7N3fALET2MQTUctW\naTTYbruxkSdSLDby5JDEP3fjTwk5+Nin6gpPs8YDib+RMBQRNVpKSgqCg4Oh0+kQFhaGzMxMqSMp\ngt3SGjbyRIrFRp4cjhAC8R+7Y1Wb12xjz40EVr0OqFScjSdyFNu2bUNcXBzmz5+PI0eOICIiAtHR\n0bh48aLU0RzaDUMpDPywK1GLwAtCkUMRQuC1lcCGy4/ZxsYMAn4/B1Cr2cQTOZKVK1dixowZeOGF\nFwAAa9aswe7du7FhwwYkJydLnM5xVFSW48ylYzhz6Qeczz2D87+cgdliAgCoVGq4urhJnJCI7hU2\n8uQwhBB4fRWw4e9VY8MeKsTW33nDyYlNPJEjqaysxKFDh5CQkGA3HhUVhaysrBrvczznILROztA6\nucBJ44Tv//st/n0iHWaLGb1CwvFQaAQ6+nWGzsX9fvwnNDshBADrXxaFEDBbTDCaKmE0GaFRq6FW\nO+Hq9cu4nH8ehaX5KCz+BZeu5uBywXlYLOYaH7NLh15Qq/jHdyKlkrSRz8jIwPLly3Ho0CFcvnwZ\nmzdvxvTp0+3OWbBgATZt2oTCwkIMGDAA69evR48ePSRKTFIRQuCNtcD6v1WNRT18DQum5sBZGyZd\nMCJqkvz8fJjNZvj5+dmN6/V65Obm1nifjf+XVOvjfXPsX/jm2L8AAN4evvDy8EErd294ubdBR7/O\neCg0Ai5aV5RX3ICL1gVqteau8gshUF5ZBoOxDHnXLsFZ6wovjzZQq9S4UVGK3IKLuFJwAWWGEmg1\nzhAQKK8og6HyBsoryqxfN28bKm7YvmcRFmg0TrBYLBDC0uR8Ph7tENK2FyZE84NDREomaSNfVlaG\n3r17Y/r06XjuuefuWN+8dOlSrFy5EqmpqejSpQt+97vfITIyEqdOnYKHB69U1yIIAfHqTMwJWYrV\nO6r+P584HIh9KgdOd/ezmIgUqLA0H4Wl+XZj2/dthJNai3JjKbQaF/h5dUI7ryD4ewXBSaOFyWyE\np6s3nDRaCCFwo7IY+SWXUWy4BhcnHbQaZ1y/cRWFN66i1FCIUsN1mCxGAMA/jlifw0mthdbJFeWV\nJXeV32w2Nfo+3m56tGsdAr9WHeHrGQCds7Ve/nD02F1ludcOHjwodYRaMVvTMFvjhIaG3tX9JW3k\no6OjER0dDQB4/vnn7b4nhMDq1asxZ84cjB07FgCQmpoKvV6PLVu2ICYm5n7HJSls3IgFX/hhWWBV\nEz9uCPCnd4GjR6SLRUR3x9fXFxqNBnl5eXbjeXl5aNeuXY33CWgdArPFDLPFCJPFCJ3WA6H+faHT\nuuNc/gn8UnIJ18t+gYC4475GcwWM5grb7UvXTuPStdN256hVGrRx90NpRREMxrJG/zeZLEaYKo2N\nvl9tVFBBo9ZCo3aCEBaYhQluzq3Qxt0PnjpvuDl7wkvnCx+PdnB2cm225yUixyHbNfI5OTnIy8tD\nVFSUbczV1RWDBg1CVlYWG/mW4L//RdKyPLwX+K5taPRjwF8WAFquiSdyaM7OzujXrx/S0tIwbtw4\n2/iePXswfvz4Gu/z9vSVdTyi9TGMpkpcLy1Acdk1FJUV4pfCn5H941e4WnQFAKBWa2pdT24RZuSX\nXm7wf4NW4ww3Z0+4uLigzFCCMoN1Jl6jdoJfmw5o59MRrT18YDJbm3udizt0zu7W/3Vxg87FHa7O\nbjeP3aFzdoNKrYbJbIRGpYFG0/Qf0bdmHsPC5Ln0UM75mK1pmK1pioqK7ur+sm3kb62RrGn95OXL\nDS+05ICMRuCzz7B08UW8266qiY8eCGx7D3DWsoknUoL4+HhMmzYN4eHhiIiIwIcffojc3Fy8/PLL\nTX5MrZMz2rZuh7atq2b1o8LHI+/aJWjUGvh6+SO/KBenLhzF6Yvf41zeGahVaqhVahQUV/11wMVZ\nh476zgjw7YTyijLcqCiDn3cA2vsGo23rAPh6+eHEsVNQqVS25qDkxnWUV9yATyv9XTXhzk4uTb4v\nEbUssm3k61LXXuFyXP90O0fICEiXU3P9Ov6Z8D3mt3/PNjagazHmPvsTfvj+zj+Z8/Vsfo6S5Vse\ndAAAGKBJREFUtSXlvNt1lHI0YcIEFBQUICkpCVeuXEGvXr2wa9cuBAYGNuvzqFVqtPPpaDvWe7eH\n3rs9Hu/zpN15RaXX8HP+OXh7toWfd0C9H4i9/WeRp1treLq1br7gRET1kG0j7+/vD8C6XrJDhw62\n8by8PNv3SHmEANZ83QOp7YfbxvqFFuP9F3+Ci/bOJp6IHNsrr7yCV155ReoYAAAvjzbw8mgjdQwi\nogaTbSMfHBwMf39/pKWloV+/fgAAg8GAzMxMLF++vNb7yXH90y1yXqNVnZQ5394gkPpl1fGwfsDn\nS1vBXdfvjnP5ejY/R8naEnPe7TpKIiJSHsm3nzxz5gwAwGKx4Pz58zhy5Ah8fHwQGBiIuLg4JCcn\no1u3bggNDUVSUhI8PT0xefJkKWPTPbLkzwLLPqk6/tWj1jXxri5cE09ERER0O0kb+ezsbAwbNgyA\nda1hYmIiEhMT8fzzz+Pjjz9GQkICysvLMXPmTBQWFmLgwIFIS0uDu7tjXrWPamEyYfmfTZj7+6oP\neP3qUeCvydydhoiIiKg2kjbyQ4YMgcVS95XrbjX3pEyWy7l4c+werHaaahsb+rB1Jp5NPBEREVHt\nZLtGnpSvoqgcM8YdxdZqTfzjfYAdS7ichoiIiKg+aqkDUMtUXGLBU2N/wlZ11QW/nhkM/GsV4OnO\nJp6IiIioPmzk6b7L+VngsTFXsK/iQdvYK8/wg61EREREjcFGnu6rrw4JhL8ocMwQYBtLigHWxQMa\nDZt4IiIioobiGnm6bz78TOD1VYDJbG3YnTUWfDRHjeei2cATERERNRYbebrnSsoE3lgH/P7/qsb8\n2gCfLVZj4INs4omIiIiago083VN7D1TixYWVOF9Stff/w12tO9N00LOJJyIiImoqrpGne2bNdoEn\n3lTbNfEThwMZKWziiYiIiO4WZ+Sp2RWVCry9Adi4AwA0AIA27maseVODSZHWq/gSERER0d1hI0/N\nRgiBjTuAd38P5F+vGh/gV4DPNvnA34cNPBEREVFzYSNPzaK4TGBGEvBZhv34eJdv8Mctj0Lnyiae\niIiIqDlxjTzdte+OCwx40b6J72Q4h0/M72Lrn0PYxBMRERHdA5yRpya7YRCY8yGw7q+AEFXjr48H\nlrzYAa4e70kXjoiIiEjh2MhTk5y7IvBMvAFHLrjaxtx1wEdvAZMiVQC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zarchan_adaptive_filter(1000, 2, std_title=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Three Standard Deviations**" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fLegOe4jKJCU9ibgbF0lIjiMhJZ7ryfGk3UwCTUNDI+8/zbSckpJX2bDn4nco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\n0WD+OwZX/BFW5AR5N53/F7i2s5p4Eam54uJi+vXrx5NPPml2FBERv2X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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zarchan_adaptive_filter(1000, 3, std_title=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see from the charts that the filter output for the position is very similar regardless of weather we use 2 standard deviations or three. But the computation of the velocity is a different matter. Let's explore this further. First, lets make the standard deviation very small." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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NzUWfPn1Qr149/u/LL7/k28ycORMzZsxAeHg4OnTogJSUFBw4cABeXl52jJwg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\nvBxBQUEd2vfFixcRH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I5fE6jjwhhNRVKhXDqq2WuB5dOFZ80GLAvy0l8YQQQqoGtcjXAQKBoNjXkydP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\nH0Y/N8oAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zarchan_adaptive_filter(1000, .1, std_title=True)\n", "zarchan_adaptive_filter(1000, 1, std_title=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the standard deviation limit gets smaller the computation of the velocity gets worse. Think about why this is so. If we start varying the filter so that it prefers the measurement over the prediction as soon as the residual deviates even slightly from the prediction we very quickly be giving almost all the weight towards the measurement. With no weight for the prediction we have no information from which to create the hidden variables. So, when the limit is 0.1 std you can see that the velocity is swamped by the noise in the measurement. On the other hand, because we are favoring the measurements so much the position follows the maneuver almost perfectly.\n", "\n", "Now let's look at the effect of various increments for the process noise. Here I have held the standard deviation limit to 2 std, and varied the increment from 1 to 10,000." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DDz/gyJEj6N+/f6H1bt68iVatWmHevHlYtmxZife/adMmTJ06FY6Ojrh06RKs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MmUKBgYGkUCioVq1aNHr0aLp586bFx9Hr9RQUFEShoaEV/hzsnSAqxaBXZhVx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ejIwMioiIoPr165NarSadTkdDhgyhixcv2t2na9eu5OXlVSVn/nNE2dnZNH/+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\nSUVORK5CYII=\n", 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aPHky9ejRgzw9PeXlbt68SV5eXqRQKGjw4ME0e/ZsevLJJ8nR0VE+5pcmkSci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Rw6B1RT9VZbNmzWjWrFk0YcIEqlevHgUEBFCrVq1ICGEQh7lE/vbt2/Jza968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\nq51mUlxSiKzcTJSaS2C2lCKvKBs5BZeRW3AFuYWXkVNwBQXFudCoNNB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zarchan_adaptive_filter(1, 2, Q_title=True)\n", "zarchan_adaptive_filter(10, 2, Q_title=True)\n", "zarchan_adaptive_filter(100, 2, Q_title=True)\n", "zarchan_adaptive_filter(1000, 2, Q_title=True)\n", "zarchan_adaptive_filter(10000, 2, Q_title=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can see that the position estimate gets marginally better as the increment factor increases, but that the velocity estimate starts to create a large overshoot. \n", "\n", "It isn't possible for me to tell you which of these is 'correct'. You will need to test your filter's performance against real and simulated data, and choose the design that best matches the performance you need for each of the state variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fading Memory Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fading memory filters are not normally classified as an adaptive filter since they do not adapt to the the input, but they do provide good performance with maneuvering targets. They also have the benefit of having a very simple computational form for first, second, and third order kinematic filters (e.g. the filters we are using in this chapter). This simple form does not require the Ricatti equations to compute the gain of the Kalman filter, which drastically reduces the amount of computation. However, there is also a form that works with the standard Kalman filter. I will focus on the latter in this chapter since our focus is more on adaptive filters. Both forms of the fading memory filter are implemented in `FilterPy`.\n", "\n", "The Kalman filter is recursive, but it incorporates all of the previous measurements into the current computation of the filter gain. If the target behavior is consistent with the process model than this allows the Kalman filter to find the optimal estimate for every measurement. Consider a ball in flight - we can clearly estimate the position of the ball at time t better if we take into account all the previous measurement. If we only used some of the measurements we would be less certain about the current position, and thus more influenced by the noise in the measurement. If this is still not clear, consider the worst case. Suppose we forget all but the last measurement and estimates. We would then have no confidence in the position and trajectory of the ball, and would have little choice but to weight the current measurement heavily. If the measurement is noisy, the estimate is noisy. We see this effect every time a Kalman filter is initialized. The early estimates are noisy, but then they settle down as more measurements are acquired.\n", "\n", "However, if the target is maneuvering it is not always behaving like the process model predicts. In this case remembering all of the past measurements and estimates is a liability. We can see this in all of the charts above. The target initiates a turn, and the Kalman filter continues to project movement in a straight line. This is because the filter has built a history of the target's movement, and incorrectly 'feels' confident that the target is moving in a straight line at a given heading and velocity. \n", "\n", "The fading memory filter accounts for this problem by giving less weight to older measurements, and greater weight to the more recent measurements. \n", "\n", "There are many formulations for the fading memory filter; I use the one provided by Dan Simon in *Optimal State Estimation* [3]. I will not go through his derivation, but only provide the results.\n", "\n", "The Kalman filter equation for the covariances of the estimation error is\n", "\n", "$$ \\mathbf{P} = \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}$$\n", "\n", "We can force the filter to forget past measurements by multiplying a term $\\alpha$\n", "\n", "$$ \\tilde{\\mathbf{P}} = \\alpha^2\\mathsf{FPF}^\\mathtt{T} + \\mathbf{Q}$$\n", "\n", "where $\\alpha > 1.0$. If $\\alpha == 1$ then we get the normal Kalman filter performance. $\\alpha$ is an attribute of `FilterPy`s Kalman filter class; its value defaults to 1 so the filter acts like a Kalman filter unless $\\alpha$ is assigned a value other than 1. There is no hard and fast rule for choosing $\\alpha$, but it is typically very close to 1, such as 1.01. You will need to make many runs with either simulated or real data to determine a value that responds to maneuvers without causing the estimate to become too noisy due to overly weighting the noisy measurement.\n", "\n", "Why does this work? If we increase the estimate error covariance the filter becomes more uncertain about it's estimate, hence it gives more weight to the measurement. \n", "\n", "One caveat - if we use $\\alpha$ than we are computing $\\tilde{\\mathbf{P}}$, not $\\mathbf{P}$. In other words, `KalmanFilter.P` *is not* equal to the covariance of the estimation error, so do not treat it as if it is.\n", "\n", "Let's filter our data using the fading memory filter and see the result. I will inject a lot of error into the system so that we can compare various approaches." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GMrDrSCmi6xrJ70LUa2mZyew7uZX9h37mjlprsM3CzJIhPcYyoOtIzE0taijC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# reinitialize filter\n", "\n", "pos2, zs2 = generate_data(70, noise_factor=1.2)\n", "xs2 = pos2[:, 0]\n", "z_xs2 = zs2[:, 0]\n", "\n", "cvfilter.x = array([0., 0.])\n", "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n", "cvfilter.alpha = 1.00\n", "\n", "xs = []\n", "res = []\n", "for z in z_xs2:\n", " cvfilter.predict()\n", " cvfilter.update([z])\n", " xs.append(cvfilter.x[0])\n", " res.append(cvfilter.y[0])\n", "xs = np.asarray(xs)\n", "plt.subplot(221)\n", "bp.plot_measurements(t[0:100], z_xs2, label='z')\n", "plt.plot(t[0:100], xs, label='filter')\n", "plt.legend(loc=2)\n", "plt.title('Standard Kalman Filter')\n", "\n", "cvfilter.x = array([0., 0.])\n", "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=20.)\n", "cvfilter.alpha = 1.00\n", "\n", "xs = []\n", "res = []\n", "for z in z_xs2:\n", " cvfilter.predict()\n", " cvfilter.update([z])\n", " xs.append(cvfilter.x[0])\n", " res.append(cvfilter.y[0])\n", " \n", "xs = np.asarray(xs)\n", "\n", "plt.subplot(222)\n", "bp.plot_measurements(t[0:100], z_xs2, label='z')\n", "plt.plot(t[0:100], xs, label='filter')\n", "plt.legend(loc=2)\n", "plt.title('$\\\\mathbf{Q}=20$')\n", "\n", "cvfilter.x = array([0., 0.])\n", "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n", "cvfilter.alpha = 1.02\n", "\n", "xs = []\n", "res = []\n", "for z in z_xs2:\n", " cvfilter.predict()\n", " cvfilter.update([z])\n", " xs.append(cvfilter.x[0])\n", " res.append(cvfilter.y[0])\n", "xs = np.asarray(xs)\n", "plt.subplot(223)\n", "bp.plot_measurements(t[0:100], z_xs2, label='z')\n", "plt.plot(t[0:100], xs, label='filter')\n", "plt.legend(loc=2)\n", "plt.title('Fading Memory ($\\\\alpha$ = 1.02)')\n", "\n", "cvfilter.x = array([0., 0.])\n", "cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n", "cvfilter.alpha = 1.05\n", "\n", "xs = []\n", "res = []\n", "for z in z_xs2:\n", " cvfilter.predict()\n", " cvfilter.update([z])\n", " xs.append(cvfilter.x[0])\n", " res.append(cvfilter.y[0])\n", "xs = np.asarray(xs)\n", "plt.subplot(224)\n", "bp.plot_measurements(t[0:100], z_xs2, label='z')\n", "plt.plot(t[0:100], xs, label='filter')\n", "plt.legend(loc=2)\n", "plt.title('Fading Memory ($\\\\alpha$ = 1.05)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first plot shows the performance of the Kalman filter. The filter diverges when the maneuver starts and does not reacquire the signal until about 10 seconds. I then made the filter track the maneuver very quickly by making the process noise large, but this has the cost of making the filter estimate very noisy due to unduly weighting the noisy measurements. I then implemented a fading memory filter with $\\alpha=1.02$. The filtered estimate is very smooth, but it does take a few seconds to converge when the target regains steady state behavior. However, the time to do so is considerably smaller than for the Kalman filter, and the amount of lag is much smaller - the estimate for the fading memory is much closer to the actual track than the Kalman filter's track is. Finally, I bumped up $\\alpha$ to 1.05. Here we can see that the filter responds almost instantly to the maneuver, but that the estimate is not as straight during the steady state operation because the filter is forgetting the past measurements. \n", "\n", "This is quite good performance for such a small change in code! Note that there is no 'correct' choice here. You will need to design your filter based on your needs and the characteristics of the measurement noise, process noise, and maneuvering behavior of the target." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Noise Level Switching" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To be written" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variable State Dimension" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To be written - vary state order based on whether a maneuver is happening." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiple Model Estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The example I have been using in this chapter entails a target moving in a steady state, performing a maneuver, and then returning to a steady state. We have been thinking of this as two models - a constant velocity model, and a constant acceleration model. Whenever you can describe the system as obeying one of a finite set of models you can use *Multiple Model (MM) Estimation*. This means what it sounds like. We use a bank of multiple filters, each using a different process to describe the system, and either switch between them or blend them based on the dynamics of the tracked object. \n", "\n", "As you might imagine this is a broad topic, and there are many ways of designing and implementing MM estimators. But consider a simple approach for the target we have been tracking in this chapter. One idea would be to simultaneously run a constant velocity and a constant acceleration filter, and to switch between their outputs when we detect a maneuver by inspecting the residuals. Even this choice gives us many options. Consider the dynamics of a turning object. For example, an automobile turns on a wheelbase - the front wheels turn, and the car pivots around the rear wheels. This is a nonlinear process, so for best results we would want to use some type of nonlinear filter (EKF, UKF, etc) to model the turns. On the other hand, a linear constant velocity filter would perform fine for the steady state portions of the travel. So our bank of filters might consist of a linear KF and an EKF filter for the turns. However, neither is particularly well suited for modeling behaviors such as accelerating and braking. So a highly performing MM estimator might contain a bank of many filters, each designed to perform best for a certain performance envelope of the tracked object.\n", "\n", "Of course, you do not need to base your filters on the order of the model. You can use different noise models, different adapters in each. For example, in the section above I showed many plots depicting the effects of changing parameters on the estimate of the velocity and position. Perhaps one setting works better for position, and a different setting for velocity. Put both in your bank of filters. You could then take the best estimates for the position from one filter, and the best estimate for the velocity from a different filter.\n", "\n", "### A Two Filter Adaptive Filter\n", "\n", "I trust the idea of switching between filters to get the best performance is clear, but what mathematical foundations should we use to implement it? The problem that we face is trying to detect via noisy measurements when a change in regime should result in a change in model. What aspect of the Kalman filter measures how far the measurement deviates from the prediction? Yes, the *residual*.\n", "\n", "Let's say we have a two state (constant velocity) Kalman filter. As long as the target is not maneuvering the filter will track it's behavior closely, and roughly 68% of the measurements should fall within 1$\\sigma$. Furthermore the residual should fluctuate around 0 because as many if the sensor is Gaussian an equal number of measurement should have positive error as have negative errors. If the residual grows and stays beyond predicted bounds then the target must not be performing as predicted by the state model. We saw this earlier in this chart where the residual switched from bouncing around 0 to suddenly jumping and staying above zero once the tracked object began maneuvering." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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QokhRCoYOhT/+gJQUWL4cgE37FcM/M3NsQgghCi2zJvKzZ8+mePHiDB8+nOjo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_residual_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this problem we saw that the constant velocity filter performed better the constant acceleration filter while the object was in steady state, and the opposite was true when the object is maneuvering. In the chart above that transition occurs at 4 seconds. \n", "\n", "So the algorithm is easy. Initialize both a constant velocity and constant acceleration filter and run them together in a predict/update loop. After every update examine the residual of the constant velocity filter. If it falls within theoretical bounds use the estimate from the constant velocity filter as the estimate, otherwise use the estimate from the constant acceleration filter. If you have enough insight into your problem, you can also choose to blend the outputs of the two filters proportional to the size of the residual." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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iIly8eLHSWhx1bP8koc5ttCqiOGtXQ4kTaDixNvo4X5S/dZlh1f7ajoqQxuGr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def run_filter_bank(threshold):\n", " dt = 0.1\n", " cvfilter= make_cv_filter(dt)\n", " cafilter = make_ca_filter(dt)\n", "\n", " pos, zs = generate_data(120, noise_factor=0.2)\n", " z_xs = zs[:, 0]\n", " t = np.arange(0, len(z_xs) * dt, dt)\n", " xs, res = [], []\n", "\n", " for z in z_xs:\n", " cvfilter.predict()\n", " cafilter.predict()\n", " cvfilter.update([z])\n", " cafilter.update([z])\n", " \n", " std = np.sqrt(cvfilter.R[0,0])\n", " if abs(cvfilter.y[0]) < 2 * std:\n", " xs.append(cvfilter.x[0])\n", " else:\n", " xs.append(cafilter.x[0])\n", " res.append(cvfilter.y[0])\n", " xs = np.asarray(xs)\n", " plot_track_and_residuals(t, xs, z_xs, res)\n", "\n", "run_filter_bank(threshold=1.4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we get nearly ideal performance. While the target is not maneuvering our estimate is nearly noise free, and then once it does maneuver we quickly detect that and switch to the constant acceleration filter. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* [1] Bar-Shalom, Yaakov, Xiao-Rong Li, and Thiagalingam Kirubarajan. *Estimation with Applications to Tracking and Navigation*. New York: Wiley, p. 424, 2001. \n", "\n", "* [2] Zarchan, Paul, and Howard Musoff. *Fundamentals of Kalman Filtering: A Practical Approach*. Reston, VA: American Institute of Aeronautics and Astronautics, 2000. Print.\n", "\n", "* [3] Simon, Dan. Optimal State Estimation: Kalman, H and Nonlinear Approaches. Hoboken, NJ: Wiley-Interscience, p. 208-212, 2006" ] } ], "metadata": { "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }