├── .gitmodules
├── EFKSLAM.ipynb
├── EKF.ipynb
├── PF.ipynb
├── POMDP.ipynb
├── README.md
├── UKF.ipynb
└── occupancy-grid
    ├── inverse_range_sensor.m
    ├── main.m
    └── state_meas_data.mat


/.gitmodules:
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1 | [submodule "turtlebot-eif-localization"]
2 | 	path = turtlebot-eif-localization
3 | 	url = https://github.com/plusk01/turtlebot-eif-localization.git
4 | 


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/POMDP.ipynb:
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  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# POMDPs\n",
  8 |     "## Timothy Devon Morris\n",
  9 |     "\n",
 10 |     "A partially observable Markov decision process (POMDP) is a generalization of a Markov decision process (MDP). A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe the underlying state. Instead, it must maintain a probability distribution over the set of possible states, based on a set of observations and observation probabilities, and the underlying MDP.\n",
 11 |     "\n",
 12 |     "In this notebook, we will solve the POMDP presented in Thrun's Probabilistic Robotics P. 515 Figure 15.1."
 13 |    ]
 14 |   },
 15 |   {
 16 |    "cell_type": "code",
 17 |    "execution_count": 1,
 18 |    "metadata": {
 19 |     "collapsed": true
 20 |    },
 21 |    "outputs": [],
 22 |    "source": [
 23 |     "import numpy as np\n",
 24 |     "import itertools\n",
 25 |     "import matplotlib.pyplot as plt"
 26 |    ]
 27 |   },
 28 |   {
 29 |    "cell_type": "code",
 30 |    "execution_count": 2,
 31 |    "metadata": {},
 32 |    "outputs": [],
 33 |    "source": [
 34 |     "class POMDP(object):\n",
 35 |     "    \n",
 36 |     "    def __init__(self, P, R, Z, gam=1.):\n",
 37 |     "        '''\n",
 38 |     "        Constructor for POMDP class:\n",
 39 |     "        P - Array (N_states, N_states, N_Actions)\n",
 40 |     "            describes transition probabilities given actions\n",
 41 |     "            next_state, prev_state, action. \n",
 42 |     "            (Terminal actions have probability 1 to return to themselves under all actions)\n",
 43 |     "        R - Array (N_states, N_actions)\n",
 44 |     "            rewards for state action pairs\n",
 45 |     "        Z - Array (N_states, N_observations)\n",
 46 |     "            measurement probabilities given states\n",
 47 |     "        self.Ups - Constraints presented on the value function\n",
 48 |     "            list of lists. Encodes linear function over belief space \n",
 49 |     "        '''\n",
 50 |     "        self.P = P\n",
 51 |     "        self.R = R\n",
 52 |     "        self.Z = Z\n",
 53 |     "        self.Ups = np.zeros((P.shape[0],1))\n",
 54 |     "        self.Us = np.zeros((1))\n",
 55 |     "        self.gam = gam\n",
 56 |     "    \n",
 57 |     "    def loop(self, T, plot=False):\n",
 58 |     "        for t in xrange(T):\n",
 59 |     "            # Lines 5-13\n",
 60 |     "            # Value of prev_state, kth constraint, action u, measurement z\n",
 61 |     "            v_jkuz = self.gam*np.einsum(\"ik,iz,iju->jkuz\",self.Ups,self.Z,self.P)\n",
 62 |     "            \n",
 63 |     "            # Iterate through all possible combinations of constraints\n",
 64 |     "            Ups = []\n",
 65 |     "            Us = []\n",
 66 |     "            for kz in itertools.product(np.arange(self.Ups.shape[1]), repeat=self.Z.shape[1]):\n",
 67 |     "                Ups.append(self.R + np.einsum(\"ijkj->ik\",v_jkuz[:,kz]))\n",
 68 |     "                Us.append(np.arange(self.P.shape[2]))\n",
 69 |     "                \n",
 70 |     "            self.Ups = np.concatenate(Ups, axis=1)\n",
 71 |     "            self.Us = np.concatenate(Us, axis=0)\n",
 72 |     "            self.prune()\n",
 73 |     "            if plot:\n",
 74 |     "                self.plot(t)\n",
 75 |     "        return self.Ups, self.Us\n",
 76 |     "                \n",
 77 |     "            \n",
 78 |     "    def prune(self):\n",
 79 |     "        # Quick pruning to remove redundant constraints\n",
 80 |     "        self.Ups, idx = np.unique(self.Ups, axis=1, return_index=True)\n",
 81 |     "        self.Us = self.Us[idx]\n",
 82 |     "        \n",
 83 |     "        # Pruning by finding the max for a list of possible probabilities\n",
 84 |     "        # Note this only works in the case of 2 states and does not\n",
 85 |     "        # generalize well to more complex state spaces\n",
 86 |     "        s = []\n",
 87 |     "        for p in np.linspace(0,1,num=100):\n",
 88 |     "            s.append(np.argmax(p*self.Ups[0]+(1-p)*self.Ups[1]))\n",
 89 |     "        \n",
 90 |     "        self.Ups = self.Ups[:,s]\n",
 91 |     "        self.Us = self.Us[s]\n",
 92 |     "        # Once again remove redundant constraints\n",
 93 |     "        self.Ups, idx = np.unique(self.Ups, axis=1, return_index=True)\n",
 94 |     "        self.Us = self.Us[idx]\n",
 95 |     "        \n",
 96 |     "    def plot(self,t):\n",
 97 |     "        fig = plt.figure(t)\n",
 98 |     "        x = np.linspace(0,1, num=1000)\n",
 99 |     "        y = np.max(np.outer(x,self.Ups[0])+np.outer(1-x,self.Ups[1]),axis=1)\n",
100 |     "        plt.plot(x,y)\n",
101 |     "        plt.title(\"Value of b after {} iterations\".format(t+1))\n",
102 |     "        plt.xlim([0, 1])\n",
103 |     "        plt.ylim([-100, 100])\n",
104 |     "        plt.show()\n",
105 |     "        \n",
106 |     "            \n",
107 |     "        \n",
108 |     "                \n",
109 |     "    "
110 |    ]
111 |   },
112 |   {
113 |    "cell_type": "code",
114 |    "execution_count": 3,
115 |    "metadata": {
116 |     "collapsed": true
117 |    },
118 |    "outputs": [],
119 |    "source": [
120 |     "P = np.zeros((3,3,3))\n",
121 |     "# Transition Probabilities between non-terminal states under various actions\n",
122 |     "P[0, 0, 2] = .2\n",
123 |     "P[1, 0, 2] = .8\n",
124 |     "P[1, 1, 2] = .2\n",
125 |     "P[0, 1, 2] = .8\n",
126 |     "\n",
127 |     "# Transition Probabilities to and from terminal state\n",
128 |     "P[2, 0, 0] = 1.\n",
129 |     "P[2, 0, 1] = 1.\n",
130 |     "P[2, 1, 0] = 1.\n",
131 |     "P[2, 1, 1] = 1.\n",
132 |     "P[2, 2, 0] = 1.\n",
133 |     "P[2, 2, 1] = 1.\n",
134 |     "P[2, 2, 2] = 1.\n",
135 |     "\n",
136 |     "# Reward function for state action pairs\n",
137 |     "R = np.zeros((3,3))\n",
138 |     "R[0, 0] = -100\n",
139 |     "R[0, 1] = 100\n",
140 |     "R[0, 2] = -1\n",
141 |     "R[1, 0] = 100\n",
142 |     "R[1, 1] = -50\n",
143 |     "R[1, 2] = -1\n",
144 |     "\n",
145 |     "# Measurement probabilities for states\n",
146 |     "Z = np.zeros((3,3))\n",
147 |     "Z[0, 0] = 0.7\n",
148 |     "Z[0, 1] = 0.3\n",
149 |     "Z[1, 0] = 0.3\n",
150 |     "Z[1, 1] = 0.7\n",
151 |     "Z[2, 2] = 1.0\n",
152 |     "\n",
153 |     "pomdp = POMDP(P,R,Z)"
154 |    ]
155 |   },
156 |   {
157 |    "cell_type": "code",
158 |    "execution_count": 4,
159 |    "metadata": {
160 |     "scrolled": false
161 |    },
162 |    "outputs": [
163 |     {
164 |      "data": {
165 |       "image/png": 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04OZB3blUpTglgSVscjCz2sBbwFR3/1Mxy7sAb7l770PtR8mh+ioocF74LJOx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\nRKL8Pykm6AQQxKGWAAAAAElFTkSuQmCC\n",
166 |       "text/plain": [
167 |        "<matplotlib.figure.Figure at 0x10fdcbb10>"
168 |       ]
169 |      },
170 |      "metadata": {},
171 |      "output_type": "display_data"
172 |     },
173 |     {
174 |      "data": {
175 |       "image/png": 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oHEREJCJp4WBmk8zsCzP7LHyNiZl2s5nlmtlSMzsrWTWIiEjFJKUP6Rj3uPvd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\nAAAASUVORK5CYII=\n",
176 |       "text/plain": [
177 |        "<matplotlib.figure.Figure at 0x10ff21150>"
178 |       ]
179 |      },
180 |      "metadata": {},
181 |      "output_type": "display_data"
182 |     },
183 |     {
184 |      "data": {
185 |       "image/png": 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FROTANToc3P20fc03s8uALwCnuruH6+wCdoXPPzCzZcBBwLzGlkNERJpfXL2V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\nrkJggg==\n",
186 |       "text/plain": [
187 |        "<matplotlib.figure.Figure at 0x110056390>"
188 |       ]
189 |      },
190 |      "metadata": {},
191 |      "output_type": "display_data"
192 |     },
193 |     {
194 |      "data": {
195 |       "image/png": 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z+yh8XRAz7Ydmlm9my83svGTVICIidZOUZ0jH+LW73x07wsyGA1OAEUAv4HUz\nO8bdK5Jci4iIJCgVzUqTgCfdvdTdVwP5wEkpqENERGqQ7HC4wcwWmdkjZtYxHNcbWB8zT0E47hBm\nNtXMFprZwqKioiSXKSIiseoVDmb2upktifOaBDwADAbGAIXAPVWLxVmVR0a4z3D3PHfP69q1a33K\nFBGRI1SvPgd3PyeR+czs98CL4dsCoG/M5D7AxvrUISIiDSuZZyv1jHl7CbAkHJ4JTDGzbDMbCAwF\n3k1WHSIicuSSebbSXWY2hqDJaA1wLYC7LzWzp4FlQDnwbZ2pJCKSXpIWDu5+VS3Tfgb8LFnbFhGR\n+tEV0iIiEqFwEBGRCIWDiIhEKBxERCRC4SAiIhEKBxERiVA4iIhIhMJBREQiFA4iIhKhcBARkQiF\ng4iIRCgcREQkQuEgIiIRCgcREYlQOIiISITCQUREIhQOIiISoXAQEZGIpDwm1MyeAoaFbzsAO9x9\njJkNAD4GlofTFrj7dcmoQURE6i4p4eDuX64aNrN7gJ0xk1e6+5hkbFdERBpGUsKhipkZ8CVgfDK3\nIyIiDSvZfQ5nAJvdfUXMuIFm9qGZvWlmZyR5+yIiUgd1PnIws9eBHnEm3ebuL4TDlwNPxEwrBPq5\ne7GZjQX+amYj3H1XnPVPBaYC9OvXr65liohIHdQ5HNz9nNqmm1kmcCkwNmaZUqA0HH7fzFYCxwAL\n46x/BjADIC8vz+tap4iIHLlkNiudA3zi7gVVI8ysq5llhMODgKHAqiTWICIidZDMDukpHNqkBDAO\nuMPMyoEK4Dp335bEGkREpA6SFg7u/tU4454Fnk3WNkVEpGHoCmkREYlQOIiISITCQUREIhQOIiIS\noXAQEZEIhYOIiEQoHEREJELhICIiEQoHERGJUDiIiEiEwkFERCIUDiIiEqFwEBGRCIWDiIhEKBxE\nRCRC4SAiIhEKBxERiVA4iIhIhMJBREQi6hUOZnaZmS01s0ozy6s27Ydmlm9my83svJjx54fj8s3s\nlvpsX0REkqO+Rw5LgEuBebEjzWw4MAUYAZwP3G9mGWaWAdwHfB4YDlwezisiImkksz4Lu/vHAGZW\nfdIk4El3LwVWm1k+cFI4Ld/dV4XLPRnOu6w+dYiISMOqVzjUojewIOZ9QTgOYH218SfHW4GZTQWm\nhm9LzWxJQxfZRHUBtqa6iDShfXGQ9sVB2hcHDavrgocNBzN7HegRZ9Jt7v5CTYvFGefEb8byeCtw\n9xnAjLBMlukVAAAEFElEQVSGhe6eF2++o432xUHaFwdpXxykfXGQmS2s67KHDQd3P6cO6y0A+sa8\n7wNsDIdrGi8iImkiWaeyzgSmmFm2mQ0EhgLvAu8BQ81soJllEXRaz0xSDSIiUkf16nMws0uA6UBX\n4CUz+8jdz3P3pWb2NEFHcznwbXevCJe5AZgFZACPuPvSBDY1oz51NjPaFwdpXxykfXGQ9sVBdd4X\n5h63yV9ERI5iukJaREQiFA4iIhKRVuFwuFtrhB3cT4XT3zGzAY1fZeNIYF/8u5ktM7NFZjbbzPqn\nos7GkOgtV8xsspl59Vu5NCeJ7Asz+1L4u7HUzP7S2DU2lgT+j/Qzs7lm9mH4/+SCVNSZbGb2iJlt\nqelaMAvcG+6nRWZ2YkIrdve0eBF0UK8EBgFZwD+B4dXmuR54MByeAjyV6rpTuC/OBlqHw986mvdF\nOF9bgtu4LADyUl13Cn8vhgIfAh3D991SXXcK98UM4Fvh8HBgTarrTtK+GAecCCypYfoFwN8Irj87\nBXgnkfWm05HDSYS31nD3MqDq1hqxJgF/CoefASZYnHt3NAOH3RfuPtfd94ZvFxBcM9IcJfJ7AfAT\n4C5gf2MW18gS2RffBO5z9+0A7r6lkWtsLInsCwfahcPtaabXVLn7PGBbLbNMAh71wAKgg5n1PNx6\n0ykcehO9tUbvmuZx93JgJ9C5UaprXInsi1jXEPxl0Bwddl+Y2QlAX3d/sTELS4FEfi+OAY4xs7fN\nbIGZnd9o1TWuRPbFNOBKMysAXgZubJzS0s6Rfp8Aybu3Ul3UdMuNI52nOUj4c5rZlUAecGZSK0qd\nWveFmbUAfg18tbEKSqFEfi8yCZqWziI4mnzLzEa6+44k19bYEtkXlwN/dPd7zOxU4LFwX1Qmv7y0\nUqfvzXQ6cqjtlhuRecwsk+BQsbbDqaYqkX2BmZ0D3AZM9OAOuM3R4fZFW2Ak8IaZrSFoU53ZTDul\nE/0/8oK7H3D31cBygrBobhLZF9cATwO4+z+AHIKb8h1tEvo+qS6dwiGRW2vMBL4SDk8G5njY49LM\nHHZfhE0pvyMIhubargyH2RfuvtPdu7j7AHcfQND/MtHd63zDsTSWyP+RvxKcrICZdSFoZlrVqFU2\njkT2xTpgAoCZHUcQDkWNWmV6mAlcHZ61dAqw090LD7dQ2jQruXt5vFtrmNkdwEJ3nwk8THBomE9w\nxDAldRUnT4L74ldAG+B/wz75de4+MWVFJ0mC++KokOC+mAWca2bLgArg++5enLqqkyPBfXET8Hsz\n+zeCZpSvNsc/Js3sCYJmxC5h/8rtQEsAd3+QoL/lAiAf2At8LaH1NsN9JSIi9ZROzUoiIpImFA4i\nIhKhcBARkQiFg4iIRCgcREQkQuEgIiIRCgcREYn4/8cl132MOpH0AAAAAElFTkSuQmCC\n",
196 |       "text/plain": [
197 |        "<matplotlib.figure.Figure at 0x10ff216d0>"
198 |       ]
199 |      },
200 |      "metadata": {},
201 |      "output_type": "display_data"
202 |     },
203 |     {
204 |      "data": {
205 |       "image/png": 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nYziuDjObaWYLzWxhWVlZiospIiLxmhUOZvacmS1J8JoO3A2MACYAJcAdtYsl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\na+puAAAAAElFTkSuQmCC\n",
206 |       "text/plain": [
207 |        "<matplotlib.figure.Figure at 0x10fff13d0>"
208 |       ]
209 |      },
210 |      "metadata": {},
211 |      "output_type": "display_data"
212 |     },
213 |     {
214 |      "data": {
215 |       "image/png": 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dqSQikl1iCwd3v7qBYXcCd8a1bBERaRpdIS0iIhEKBxERiVA4iIhIhMJBREQi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\niIhIxP8HGrLmK5mjiXYAAAAASUVORK5CYII=\n",
216 |       "text/plain": [
217 |        "<matplotlib.figure.Figure at 0x11000da10>"
218 |       ]
219 |      },
220 |      "metadata": {},
221 |      "output_type": "display_data"
222 |     },
223 |     {
224 |      "data": {
225 |       "image/png": 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OB1a6+2cJ/Qaa2Xtm9rqZHR7z8kVEpAEavOdgZq8APZIMus7dnwm7zwYeTRi2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\n",
226 |       "text/plain": [
227 |        "<matplotlib.figure.Figure at 0x10fe6ef10>"
228 |       ]
229 |      },
230 |      "metadata": {},
231 |      "output_type": "display_data"
232 |     },
233 |     {
234 |      "data": {
235 |       "image/png": 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LW5+ax10vzueZOSv56XmH8ZnBepCfyL4gkXCemRu8inPeik30Lynix2cfyrljy/bqVZwd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\nQmCC\n",
236 |       "text/plain": [
237 |        "<matplotlib.figure.Figure at 0x110284a10>"
238 |       ]
239 |      },
240 |      "metadata": {},
241 |      "output_type": "display_data"
242 |     },
243 |     {
244 |      "data": {
245 |       "image/png": 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fH5LyUZwtWYs9cjCzfYDHk4qGA78EioDvA2Vh+S/c/fk469Icjh/Vh4OHd+fXL8zl3rfn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\nhYOIiET8f4+4mFzOYOHYAAAAAElFTkSuQmCC\n",
246 |       "text/plain": [
247 |        "<matplotlib.figure.Figure at 0x11027afd0>"
248 |       ]
249 |      },
250 |      "metadata": {},
251 |      "output_type": "display_data"
252 |     },
253 |     {
254 |      "data": {
255 |       "image/png": 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mtwGbE0YvcPexcaxXRERaRizhUMfMDPgicHyc6xERkZYV9zGHccAad/8ooWyI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\nOIiISITCQUREIv4f+3C41tAZ+AkAAAAASUVORK5CYII=\n",
256 |       "text/plain": [
257 |        "<matplotlib.figure.Figure at 0x10fe90cd0>"
258 |       ]
259 |      },
260 |      "metadata": {},
261 |      "output_type": "display_data"
262 |     }
263 |    ],
264 |    "source": [
265 |     "pomdp = POMDP(P,R,Z)\n",
266 |     "Ups, Us = pomdp.loop(10,plot=True)"
267 |    ]
268 |   },
269 |   {
270 |    "cell_type": "code",
271 |    "execution_count": 12,
272 |    "metadata": {},
273 |    "outputs": [
274 |     {
275 |      "name": "stdout",
276 |      "output_type": "stream",
277 |      "text": [
278 |       "98.0\n",
279 |       "98.0\n",
280 |       "94.0\n",
281 |       "98.0\n",
282 |       "98.0\n",
283 |       "85.0\n",
284 |       "85.0\n",
285 |       "94.0\n",
286 |       "-53.0\n",
287 |       "96.0\n"
288 |      ]
289 |     }
290 |    ],
291 |    "source": [
292 |     "for t in xrange(10):\n",
293 |     "    r = 0\n",
294 |     "    p = .6\n",
295 |     "    state = 0\n",
296 |     "    while state != 2:\n",
297 |     "        a = Us[np.argmax(p*Ups[0]+(1-p)*Ups[1])]\n",
298 |     "        r += R[state, a]\n",
299 |     "        state = np.random.choice(np.arange(3),p=P[:,state,a])\n",
300 |     "        p = 0.8 - 0.6*p\n",
301 |     "        m = np.random.choice(np.arange(3),p=Z[state,:])\n",
302 |     "        # Bayes Rule\n",
303 |     "        if m == 0:\n",
304 |     "            p = p*Z[0,0]/(p*Z[0,0]+(1-p)*Z[1,0])\n",
305 |     "        if m == 1:\n",
306 |     "            p = p*Z[0,1]/(p*Z[0,1]+(1-p)*Z[1,1])\n",
307 |     "    print r\n",
308 |     "        \n",
309 |     "    "
310 |    ]
311 |   },
312 |   {
313 |    "cell_type": "code",
314 |    "execution_count": null,
315 |    "metadata": {
316 |     "collapsed": true
317 |    },
318 |    "outputs": [],
319 |    "source": []
320 |   }
321 |  ],
322 |  "metadata": {
323 |   "kernelspec": {
324 |    "display_name": "Python 2",
325 |    "language": "python",
326 |    "name": "python2"
327 |   },
328 |   "language_info": {
329 |    "codemirror_mode": {
330 |     "name": "ipython",
331 |     "version": 2
332 |    },
333 |    "file_extension": ".py",
334 |    "mimetype": "text/x-python",
335 |    "name": "python",
336 |    "nbconvert_exporter": "python",
337 |    "pygments_lexer": "ipython2",
338 |    "version": "2.7.13"
339 |   }
340 |  },
341 |  "nbformat": 4,
342 |  "nbformat_minor": 2
343 | }
344 | 


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/README.md:
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 1 | ## Kalman Filter
 2 | 
 3 | ## Extended Kalman Filter
 4 | 
 5 | ## Unscented Kalman Filter
 6 | 
 7 | ## Particle Filter
 8 | 
 9 | ## EKF SLAM
10 | 
11 | ## FAST SLAM
12 | 
13 | ## Occupancy Grid Mapping
14 | 
15 | ## POMDPs
16 | 


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/occupancy-grid/inverse_range_sensor.m:
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 1 | function l = inverse_range_sensor(mi, xt, zt, thk)
 2 |     l0 = log(.5/.5);
 3 |     locc = log(.7/.3);
 4 |     lfree = log(.3/.7);
 5 | 
 6 |     % === Set up params for inverse measurement model =========================
 7 |     alpha = 1.2; % average thickness of obstacles in meters
 8 |     beta = 2*pi/180; % width of the sensor beam
 9 |     z_max = 150; % max distance of sensor
10 | 
11 |     xi = mi(1);
12 |     yi = mi(2);
13 |     
14 |     xb = xt(1);
15 |     yb = xt(2);
16 |     thb = xt(3);
17 | 
18 |     r = sqrt((xi - xb)^2 + (yi - yb)^2);
19 |     phi = atan2(yi-yb, xi-xb) - thb;
20 |     if phi > pi
21 |         phi = phi - 2*pi;
22 |     elseif phi < -pi
23 |         phi = phi + 2*pi;
24 |     end
25 |     [m,k] = min(abs(phi - thk));
26 |     
27 |     ztk = zt(1,k);
28 |     
29 |     if r > (ztk + alpha/2) || m > beta/2
30 |         l = l0;
31 |     elseif abs(r - ztk) < alpha/2
32 |         l = locc;
33 |     else
34 |         l = lfree;
35 | end


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/occupancy-grid/main.m:
--------------------------------------------------------------------------------
 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 2 | % Occupancy Grid Mapping
 3 | %
 4 | % Chapter 9.1, 9.2, Table 9.1, 9.2 (p.286-288)
 5 | % Probabilistic Robotics, Thrun et al.
 6 | %
 7 | % Assumptions:
 8 | %   - Conditional independence of grid cells
 9 | %
10 | % Devon Morris BYU
11 | % 20 Oct 2017
12 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
13 | clear, clc;
14 | 
15 | % === Load the Data =======================================================
16 | load('state_meas_data.mat')
17 | 
18 | 
19 | % === Set up the grid =====================================================
20 | dx = 1;
21 | dy = 1;
22 | 
23 | x_len = 100;
24 | y_len = 100;
25 | x = (0:dx:x_len-dx/2) + dx/2;
26 | y = (0:dy:y_len-dy/2) + dy/2;
27 | 
28 | Grid = zeros(length(x),length(y));
29 | nt = length(X);
30 | 
31 | 
32 | for t = 1:nt
33 |     xt = X(:,t);
34 |     zt = z(:,:,t);
35 |     for i = 1:length(x)
36 |     xi = x(i);
37 |         for j = 1:length(y)
38 |             % inverse sensor model
39 |             yi = y(j);
40 |             mi = [xi yi];
41 |             l = inverse_range_sensor(mi, xt, zt, thk);
42 |             Grid(i,j) = Grid(i,j) + l;
43 |         end
44 |     end
45 | end
46 | probs = 1 - 1./(1+ exp(Grid));
47 | b = bar3(probs);
48 | for k = 1:length(b)
49 |     zdata = b(k).ZData;
50 |     b(k).CData = zdata;
51 |     b(k).FaceColor = 'interp';
52 | end
53 | 


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/occupancy-grid/state_meas_data.mat:
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https://raw.githubusercontent.com/DevonMorris/ProbabilisticRobotics/14300d26ce92ab9c1d9b53d0851a07e0f6b56402/occupancy-grid/state_meas_data.mat


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