1 | // %pacpus:license{
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2 | // This file is part of the PACPUS framework distributed under the
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3 | // CECILL-C License, Version 1.0.
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4 | // %pacpus:license}
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5 | /// @file
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6 | /// @author Firstname Surname <firstname.surname@utc.fr>
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7 | /// @date Month, Year
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8 | /// @version $Id: particle_filtering.hpp 76 2013-01-10 17:05:10Z kurdejma $
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9 | /// @copyright Copyright (c) UTC/CNRS Heudiasyc 2006 - 2013. All rights reserved.
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10 | /// @brief Brief description.
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11 | ///
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12 | /// Detailed description.
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13 |
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14 | #ifndef __PARTICLE_FILTERING_BASE__
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15 | #define __PARTICLE_FILTERING_BASE__
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16 |
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17 | #include "bayes_filtering.hpp"
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18 | #include "../math/ublas.hpp"
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19 | #include "../math/rng.hpp"
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20 | #include "../math/distributions.hpp"
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21 |
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22 | namespace filter{
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23 | namespace particle {
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24 |
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25 | using namespace math;
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26 | using namespace ublas;
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27 | using namespace rng;
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28 | using namespace distributions;
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29 |
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30 |
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31 | /*!
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32 | * \class Particle
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33 | * \brief This class describe a particle \n
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34 | * A particle is constituted by : 1) a state vector and 2) importance weight \n
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35 | */
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36 | class Particle {
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37 | public :
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38 | /*!
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39 | * \brief Constructor
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40 | * \param state_size : the size of the state vector
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41 | * \param weight_ : the initial weight of the particle
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42 | */
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43 | Particle(const size_t state_size, const double & weight_){
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44 | X=ZeroVector(state_size);
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45 | weight=weight_;
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46 | }
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47 |
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48 | Vector X; /*!< state vector */
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49 |
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50 | double weight; /*!< particle weight */
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51 |
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52 | };
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53 |
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54 | /*! \class ParticleSet
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55 | * \brief This class describe a set of particles \n
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56 | * A set of particle is reprented by a vector of particles \n
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57 | * somes methods can be applied to the set of particles like : \n
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58 | * estimate computation, resampling scheme or normalization method \n
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59 | */
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60 |
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61 | template<class P=Particle> class ParticleSet {
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62 | public :
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63 |
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64 | std::vector<P> particles; /*!< vector of particles */
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65 |
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66 |
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67 | std::vector<P> particles_; /*!< temporary vector of particles used in resample scheme */
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68 |
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69 |
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70 | /*!
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71 | * \brief Allocate the set of paticles
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72 | * \param nparticle : number of particles
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73 | */
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74 | void Allocator(const size_t &nparticle);
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75 |
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76 | /*!
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77 | * \brief Resample the set of particles \n
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78 | * \param threshold : threshold parameter \n
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79 | * The resampling scheme is the reasmpling scheme proposed by Kitawaga \n
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80 | * This can be overloaded to use an another resampling scheme \n
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81 | */
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82 | virtual void Resample(const double & threshold=1.0);
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83 |
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84 | /*!
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85 | * \brief Compute the number of effective samples in the particle set
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86 | * \return number of effective samples
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87 | */
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88 | double Ness();
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89 |
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90 | /*!
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91 | * \brief Get the number of particles
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92 | * \return number of particles
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93 | */
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94 | size_t ParticlesNo(){ return particles.size(); }
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95 |
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96 | /*!
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97 | * \brief Compute the estimate
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98 | * \return a vector double describing the estimate
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99 | */
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100 | Vector Estimate ();
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101 |
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102 | /*!
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103 | * \brief Normalize the weights of each particles
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104 | */
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105 | void NormalizeWeights();
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106 |
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107 | /*!
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108 | * \brief Destructor
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109 | */
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110 | virtual ~ParticleSet(){};
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111 |
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112 | protected :
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113 |
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114 | /*!
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115 | * \brief Compute the cumulative sum of the weight of each particles
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116 | * \return a vector of double describing this cumulative sum
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117 | */
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118 | std::vector<double> WeightCumSum();
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119 |
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120 | /*!
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121 | * \brief Create the a random cumulative sum
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122 | * \return a vector of double describing this cumulative sum
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123 | */
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124 | std::vector<double> RandomCumSum();
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125 |
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126 | };
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127 |
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128 |
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129 | //Particle set memeber functions
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130 | template<class P> void ParticleSet<P>::Allocator(const size_t &nparticles){
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131 | particles.resize(nparticles);
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132 | particles_.resize(nparticles);
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133 | }
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134 |
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135 | template<class P> double ParticleSet<P>::Ness(){
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136 | double ness =0;
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137 | for(typename std::vector<P>::iterator I=particles.begin();I!=particles.end();I++)
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138 | ness+=(*I).weight*(*I).weight;
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139 |
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140 | if(ness==0)throw filter_error("In particle filter :: number effective sample computation -> ness is equal to infinity");
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141 |
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142 | return 1/ness;
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143 | }
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144 |
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145 |
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146 | template<class P> std::vector<double> ParticleSet<P>::WeightCumSum(){
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147 | double sum=0;
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148 | std::vector<double> cumsum(particles.size());
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149 | for(size_t i=0;i<particles.size();i++){
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150 | sum+=particles[i].weight;
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151 | cumsum[i]=sum;
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152 | }
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153 | return cumsum;
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154 | }
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155 |
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156 | template<class P> void ParticleSet<P>::NormalizeWeights(){
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157 |
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158 | double sum=0;
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159 | for(typename std::vector<P>::iterator I=particles.begin();I!=particles.end();I++)
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160 | sum+=(*I).weight;
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161 |
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162 |
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163 | if(sum==0) throw filter_error("In particle filter :: normalization of weight -> weight sum is equal to 0");
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164 |
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165 | for(typename std::vector<P>::iterator I=particles.begin();I!=particles.end();I++)
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166 | (*I).weight=(*I).weight/sum;
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167 |
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168 | }
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169 |
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170 | template<class P> std::vector<double> ParticleSet<P>::RandomCumSum(){
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171 | double sum=0;
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172 | std::vector<double> cumsum(particles.size());
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173 | uniform_rng UD;
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174 | for(size_t i=0;i<particles.size();i++){
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175 | sum+=UD();
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176 | cumsum[i]=sum;
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177 | }
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178 |
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179 | //normalization
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180 | for(size_t i=0;i<particles.size();i++)cumsum[i]=cumsum[i]/sum;
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181 |
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182 | return cumsum;
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183 | }
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184 |
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185 |
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186 | template<class P> void ParticleSet<P>::Resample(const double & threshold){
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187 | size_t N=ParticlesNo();
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188 | if(Ness()<=N*threshold){
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189 | // resample method by Carpenter
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190 | std::vector<double> Q=WeightCumSum();
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191 | std::vector<double> T=RandomCumSum();
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192 |
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193 | // select the best particle
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194 | std::vector <size_t> ind(N);
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195 | unsigned int j=0;
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196 | for(unsigned int i=0; i <N; i++){
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197 | do{
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198 | if(T[i] < Q[j]){ind[i] = j;break;}
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199 | j++;
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200 | }while(j<N);
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201 | }
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202 |
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203 | // build the new particle set
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204 | for(unsigned int i=0; i <N; i++){
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205 | particles_[i]=particles[ind[i]];
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206 | particles_[i].weight=1.0/static_cast<double>(N);
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207 | }
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208 |
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209 | // swap the particle set
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210 | particles.swap(particles_);
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211 | }
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212 | }
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213 |
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214 |
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215 |
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216 | template<class P> Vector ParticleSet<P>::Estimate(){
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217 | Vector estimate = ZeroVector(particles[0]->X.size());
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218 | for(typename std::vector<P>::iterator I=particles.begin();I!=particles.end();I++)
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219 | estimate+=(*I).X*(*I).weight;
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220 | return estimate;
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221 | }
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222 |
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223 |
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224 | /*!
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225 | * \class DynamicEquation
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226 | * \brief This class describe a basic dynamic equation for particle filtering \n
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227 | * where : class S is a set particle \n
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228 | * : class I is a particle \n
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229 | * : class D is a random generator used to draw input data \n
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230 | */
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231 | template <class D, template <class> class S=ParticleSet, class P=Particle> class DynamicEquation:public BayesDynamicEquation< S<P>, P >{
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232 | public :
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233 |
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234 | /*!
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235 | * \brief virtual method where matrices of state system must be allocated
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236 | * \param state_size : the size of the state vector of each particle
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237 | * \param data_size : the size of the input vector
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238 | */
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239 | virtual void Allocator(const size_t &state_size,const size_t &data_size)=0;
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240 |
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241 | /*!
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242 | * \brief virtual method where parameters of the dynamic equation must be evaluated
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243 | * \param s : set of particles at time k-1
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244 | *
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245 | */
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246 | virtual void EvaluateParameters( P *s)=0;
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247 |
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248 | /*!
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249 | * \brief virtual method where the a priori state vector must be computed
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250 | * \param in : the set of particles at time k-1
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251 | * \param out : the set of particles at time k
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252 | */
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253 | virtual void Predict(S<P> *in, S<P> *out)=0;
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254 |
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255 |
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256 | /*!
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257 | * \brief Destructor
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258 | */
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259 | virtual ~DynamicEquation(){}
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260 |
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261 | /*!
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262 | * \brief Get/Set random generator used to draw input random U
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263 | */
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264 | D & URNG(){return _URNG;}
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265 |
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266 | protected :
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267 |
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268 | D _URNG; /*!< Random generator used to drawing input data*/
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269 |
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270 | Vector _Urand; /*!< Vector where random input data are stored */
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271 |
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272 | };
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273 |
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274 |
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275 |
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276 |
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277 | /*!
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278 | * \class LinearDynamicEquation
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279 | * \brief This class describe a linear dynamic equation \n
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280 | * X(k+1)(i) =A*X(k)(i)+B*U(k)(i) \n
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281 | * X(.)(i) = the state of the particle i \n
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282 | * A = state matrix \n
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283 | * B = entrie matrix \n
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284 | * U = input random vector \n
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285 | */
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286 | template <class D,template <class> class S=ParticleSet, class P=Particle> class LinearDynamicEquation : public DynamicEquation<D,S,P>{
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287 | public :
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288 | /*!
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289 | * \brief virtual method where matrices of state system must be allocated
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290 | * \param state_size : the size of the state vector of each particle
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291 | * \param data_size : the size of the input vector
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292 | */
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293 | void Allocator(const size_t &state_size,const size_t &data_size);
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294 |
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295 | /*!
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296 | * \brief virtual method where parameters of the dynamic equation must be evaluated
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297 | * \param s : set of particles at time k-1
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298 | */
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299 | virtual void EvaluateParameters(P *s)=0;
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300 |
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301 | /*!
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302 | * \brief virtual method where the a priori state vector must be computed
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303 | * \param in : the set of particles at time k-1
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304 | * \param out : the set of particles at time k
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305 | */
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306 | virtual void Predict(S<P> *in,S<P> *out);
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307 |
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308 | /*!
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309 | * \brief Destructor
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310 | */
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311 | virtual ~LinearDynamicEquation(){}
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312 |
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313 | /*!
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314 | * \brief Get/Set a constant data in A matrix
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315 | */
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316 | double & A(const int &row, const int &column){return _A(row,column);}
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317 |
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318 | /*!
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319 | * \brief Get/Set a constant data in B matrix
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320 | */
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321 | double & B(const int &row, const int &column){return _B(row,column);}
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322 |
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323 | protected :
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324 |
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325 | Matrix _A; /*!< A matrix */
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326 |
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327 | Matrix _B; /*!< A matrix */
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328 |
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329 | };
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330 |
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331 |
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332 | // Particle linear dynamic equation member functions
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333 | template <class D, template <class> class S,class P> void LinearDynamicEquation<D,S,P>::Allocator(const size_t &state_size,const size_t &data_size){
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334 | DynamicEquation<D,S,P>::_Urand=ZeroVector(data_size);
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335 | _A=ZeroMatrix(state_size,state_size);
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336 | _B=ZeroMatrix(state_size,data_size);
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337 | }
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338 |
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339 |
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340 | template <class D, template <class> class S,class P> void LinearDynamicEquation<D,S,P>::Predict(S<P> *in,S<P> *out){
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341 |
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342 | for(size_t i=0;i<in->particles.size();i++){
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343 | EvaluateParameters(&in->particles[i]);
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344 |
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345 | out->particles[i]->X=_A*in->particles[i]->X+_B*DynamicEquation<D,S,P>::_Urand;
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346 | out->particles[i]->weight=in->particles[i]->weight;
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347 | }
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348 | }
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349 |
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350 |
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351 | /*!
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352 | * \class NonLinearDynamicEquation
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353 | * \brief This class describe a linear dynamic equation
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354 | * \n
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355 | * X(k+1)(i) =f(X(k)(i)+U(k)(i)) \n
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356 | * X(.)(i) = the state of the particle i \n
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357 | * A = state matrix \n
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358 | * B = entrie matrix \n
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359 | * U = input random vector \n
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360 | */
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361 | template <class D, template <class> class S,class P> class NonLinearDynamicEquation : public DynamicEquation<D,S,P>{
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362 | public :
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363 | /*!
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364 | * \brief virtual method where matrices of state system must be allocated
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365 | * \param state_size : the size of the state vector of each particle
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366 | * \param data_size : the size of the input vector
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367 | */
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368 | void Allocator(const size_t &state_size,const size_t &data_size);
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369 |
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370 | /*!
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371 | * \brief virtual method where parameters of the dynamic equation must be evaluated
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372 | * \param s : set of particles at time k-1
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373 | * f=
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374 | */
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375 | virtual void EvaluateParameters(P *s)=0;
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376 |
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377 | /*!
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378 | * \brief virtual method where the a priori state vector must be computed
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379 | * \param in : the set of particles at time k-1
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380 | * \param out : the set of particles at time k
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381 | */
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382 | virtual void Predict(S<P> *in,S<P> *out);
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383 |
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384 | /*!
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385 | * \brief Destructor
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386 | */
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387 | virtual ~NonLinearDynamicEquation(){}
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388 |
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389 |
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390 | protected:
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391 |
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392 | Vector _f; /*!< Matrix f where result of (f(X,U)) is stored */
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393 |
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394 | };
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395 |
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396 | // Particle non linear dynamic equation member functions
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397 | template <class D,template <class> class S,class P> void NonLinearDynamicEquation<D,S,P>::Allocator(const size_t &state_size,const size_t &data_size){
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398 | DynamicEquation<D,S,P>::_Urand=ZeroVector(data_size);
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399 | _f=ZeroVector(state_size);
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400 | }
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401 |
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402 |
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403 |
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404 | template <class D,template <class> class S,class P> void NonLinearDynamicEquation<D,S,P>::Predict(S<P> *in,S<P> *out){
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405 | for(size_t i=0;i<in->particles.size();i++){
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406 | EvaluateParameters(&in->particles[i]);
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407 |
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408 | out->particles[i].X=_f;
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409 | out->particles[i].weight=in->particles[i].weight;
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410 |
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411 | }
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412 | }
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413 |
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414 | /*!
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415 | * \class MeasureEquation
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416 | * \brief This clas describe a basic measure equation particle filtering
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417 | * \n
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418 | * where : class S is a set particle \n
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419 | * : class I is a particle \n
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420 | * : class D is the distribution of probability of observation data \n
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421 | */
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422 | template <class D , template <class> class S=ParticleSet, class P=Particle> class MeasureEquation: public BayesMeasureEquation< S<P>, P >{
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423 | public :
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424 |
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425 | /*!
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426 | * \brief virtual method where matrices of state system must be allocated
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427 | * \param state_size : the size of the state vector of each particle
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428 | * \param data_size : the size of the input vector
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429 | */
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430 | virtual void Allocator(const size_t &state_size,const size_t &data_size)=0;
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431 |
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432 |
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433 | /*!
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434 | * \brief virtual method where parameters of the measure equation must be evaluated
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435 | * \param s : set of particles at time k
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436 | */
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437 | virtual void EvaluateParameters(P *s)=0;
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438 |
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439 | /*!
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440 | * \brief virtual method where the a posteriori state vector must be computed
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441 | * \param in : the a priori set of particles at time k
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442 | * \param out : the a posteriori set of particles at time k
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443 | */
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444 | virtual void Update(S<P> *in,S<P> *out)=0;
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445 |
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446 | /*!
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447 | * \brief Destructor
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448 | */
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449 | virtual ~MeasureEquation(){};
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450 |
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451 | /*!
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452 | * \brief Get/Set the distribution of probability of data observation Z
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453 | */
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454 | D & ZDistribution(){return _ZDistribution;}
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455 |
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456 | protected :
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457 |
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458 | D _ZDistribution; /*!< The distribution of probability of observation data Z*/
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459 | };
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460 |
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461 |
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462 |
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463 | /*!
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464 | * \class LinearMeasureEquation
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465 | * \brief This class describe a linear measure equation
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466 | * \n
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467 | * X(k)(i)=H*Z(k) \n
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468 | * Z(k) = observation data \n
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469 | * => weigth update \n
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470 | * w(k+1)(i)=p(Z|HX(i))w(k)(i) \n
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471 | * w(.)(i)= weight of particle i \n
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472 | */
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473 | template <class D, template <class> class S=ParticleSet, class P=Particle> class LinearMeasureEquation : public MeasureEquation< D,S,P >{
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474 | public :
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475 | /*!
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476 | * \brief virtual method where matrices of state system must be allocated
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477 | * \param state_size : the size of the state vector of each particle
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478 | * \param data_size : the size of the input vector
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479 | */
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480 | void Allocator(const size_t &state_size,const size_t &data_size);
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481 |
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482 |
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483 | /*!
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484 | * \brief virtual method where parameters of the measure equation must be evaluated
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485 | * \param s : set of particles at time k
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486 | */
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487 | virtual void EvaluateParameters(P *s)=0;
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488 |
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489 | /*!
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490 | * \brief virtual method where the a posteriori state vector must be computed
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491 | * \param in : the a priori set of particles at time k
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492 | * \param out : the a posteriori set of particles at time k
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493 | */
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494 | virtual void Update(S<P> *in,S<P> *out);
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495 |
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496 | /*!
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497 | * \brief Destructor
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498 | */
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499 | virtual ~LinearMeasureEquation(){}
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500 |
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501 | /*!
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502 | * \brief Get/Set a constant data in observation matrix H
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503 | */
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504 | double & H(int row, int column){return _H(row,column);}
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505 |
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506 | protected:
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507 |
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508 | Matrix _H; /*!< Observation matrix */
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509 | };
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510 |
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511 |
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512 | // Particle linear measure equation member functions
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513 | template <class D,template <class> class S, class P> void LinearMeasureEquation<D,S,P>::Allocator(const size_t &state_size,const size_t &data_size){
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514 | _H=ZeroMatrix(data_size,state_size);
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515 | }
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516 |
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517 | template <class D,template <class> class S, class P> void LinearMeasureEquation<D,S,P>::Update(S<P> *in,S<P> *out){
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518 | for(size_t i=0;i<in->particles.size();i++){
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519 | EvaluateParameters(&in->particles[i]);
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520 |
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521 | out->particles[i].weight=pdf(MeasureEquation<D,S,P>::_ZDistribution, _H*in->particles[i].X)*in->particles[i].weight;
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522 |
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523 | }
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524 | out->NormalizeWeights();
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525 | }
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526 |
|
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527 |
|
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528 |
|
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529 | /*!
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530 | * \class NonLinearMeasureEquation
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531 | * \brief This class describe a non linear measure equation
|
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532 | * \n
|
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533 | * Z(k)=h(X)(i) \n
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534 | * Z = observation data \n
|
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535 | * => weigth update \n
|
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536 | * w(k+1)(i)=p(Z|h(X(k)(i)))w(k)(i) \n
|
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537 | * w(.)(i)= weight of particle i \n
|
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538 | */
|
---|
539 | template <class D,template <class> class S=ParticleSet, class P=Particle> class NonLinearMeasureEquation : public MeasureEquation<D,S,P>{
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540 | public :
|
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541 | /*!
|
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542 | * \brief virtual method where matrices of state system must be allocated
|
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543 | * \param state_size : the size of the state vector of each particle
|
---|
544 | * \param data_size : the size of the input vector
|
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545 | */
|
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546 | void Allocator(const size_t &state_size,const size_t &data_size);
|
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547 |
|
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548 | /*!
|
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549 | * \brief virtual method where parameters of the measure equation must be evaluated
|
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550 | * \param s : set of particles at time k
|
---|
551 | * h=
|
---|
552 | * H=
|
---|
553 | */
|
---|
554 | virtual void EvaluateParameters(P *s )=0;
|
---|
555 |
|
---|
556 | /*!
|
---|
557 | * \brief virtual method where the a posteriori state vector must be computed
|
---|
558 | * \param in : the a priori set of particles at time k
|
---|
559 | * \param out : the a posteriori set of particles at time k
|
---|
560 | */
|
---|
561 | virtual void Update(S<P> *in,S<P> *out);
|
---|
562 |
|
---|
563 | /*!
|
---|
564 | * \brief Destructor
|
---|
565 | */
|
---|
566 | virtual ~NonLinearMeasureEquation(){}
|
---|
567 |
|
---|
568 | protected :
|
---|
569 |
|
---|
570 | Vector _h; /*!< vector where h(X) is stored */
|
---|
571 |
|
---|
572 | };
|
---|
573 |
|
---|
574 | // Particle non linear measure equation member functions
|
---|
575 | template <class D,template <class> class S, class P> void NonLinearMeasureEquation<D,S,P>::Allocator(const size_t &state_size,const size_t &data_size){
|
---|
576 | _h=ZeroVector(data_size);
|
---|
577 | }
|
---|
578 |
|
---|
579 |
|
---|
580 | template <class D,template <class> class S, class P> void NonLinearMeasureEquation<D,S,P>::Update(S<P> *in,S<P> *out){
|
---|
581 |
|
---|
582 | for(size_t i=0;i<in->particles.size();i++){
|
---|
583 | EvaluateParameters(&in->particles[i]);
|
---|
584 |
|
---|
585 | out->particles[i].weight=pdf(MeasureEquation<D,S,P>::_ZDistribution,_h)*in->particles[i].weight;
|
---|
586 |
|
---|
587 | }
|
---|
588 |
|
---|
589 | out->NormalizeWeights();
|
---|
590 | }
|
---|
591 |
|
---|
592 | } // namespace particle
|
---|
593 | } // namespace filter
|
---|
594 |
|
---|
595 |
|
---|
596 | #endif // __PARTICLE_FILTERING_BASE__
|
---|