1 | /************************************ |
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2 | Extended Kalman Filter |
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3 | Matrix operations |
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4 | |
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5 | V. Smidl, Z. Peroutka |
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6 | |
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7 | Rev. 28.10.2010 (ZP) |
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8 | |
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9 | 26.10.2010 Prvni verze (VS) |
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10 | |
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11 | 26.10.2010 Upravena chyba v Thorton_fast - spatne shiftovani o vypoctu SIGMA. |
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12 | 27.10.2010 Pokus o odstraneni problemu v Thorton_fast - potize dela omezovani (orezavani) varianci. |
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13 | 28.10.2010 Drobne upravy v kodu. |
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14 | |
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15 | *************************************/ |
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16 | |
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17 | #include "matrix_vs.h" |
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18 | |
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19 | #define HIGH_PRECISION 0 |
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20 | |
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21 | /* Matrix multiply Full matrix by upper diagonal matrix; */ |
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22 | void mmultAU(int *m1, int *up, int *result, unsigned int rows, unsigned int columns) |
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23 | { |
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24 | unsigned int i, j, k; |
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25 | long tmp_sum=0L; //in 15+qAU |
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26 | int *m2pom; |
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27 | int *m1pom=m1; |
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28 | int *respom=result; |
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29 | |
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30 | for (i=0; i<rows; i++) //rows of result |
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31 | { |
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32 | for (j=0; j<columns; j++) //columns of result |
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33 | { |
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34 | m2pom=up+j; |
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35 | |
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36 | for (k=0; k<j; k++) //inner loop up to "j" - U(j,j)==1; |
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37 | { |
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38 | tmp_sum += ((long)(*(m1pom++))**m2pom)>>(15-qAU); |
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39 | m2pom+=columns; |
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40 | } |
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41 | // add the missing A(i,j) |
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42 | tmp_sum += (long)(*m1pom)<<qAU; // no need to shift |
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43 | m1pom-=j; // shift back to first element |
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44 | |
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45 | *respom++=tmp_sum>>15; |
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46 | |
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47 | tmp_sum=0; |
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48 | } |
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49 | m1pom+=columns; |
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50 | } |
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51 | }; |
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52 | |
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53 | |
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54 | void bierman_fast(int *difz, int *xp, int *U, int *D, int *R, unsigned int dimy, unsigned int dimx ) |
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55 | { |
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56 | int alpha; |
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57 | int beta,lambda; |
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58 | int b[5]; // ok even for 4-dim state |
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59 | int *a; // in [0,1] -> q15 |
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60 | unsigned int iy,j,i; |
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61 | |
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62 | int *b_j,*b_i; |
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63 | int *a_j; |
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64 | int *D_j; |
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65 | int *U_ij; |
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66 | int *x_i; |
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67 | |
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68 | a = U; // iyth row of U |
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69 | for (iy=0; iy<dimy; iy++) |
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70 | { |
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71 | // a is a row |
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72 | a_j=a; |
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73 | b_j=b; |
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74 | D_j=D; |
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75 | |
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76 | for (j=0; j<dimx; j++) |
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77 | { |
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78 | *b_j=((long)(*D_j)*(*a_j))>>15; |
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79 | b_j++; |
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80 | D_j++; |
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81 | a_j++; |
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82 | } |
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83 | |
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84 | alpha = R[iy]; //\alpha = R+vDv = R+a*b |
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85 | // R in q15, a in q15, b=q15 |
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86 | |
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87 | a_j=a; |
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88 | b_j=b; |
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89 | D_j=D; |
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90 | |
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91 | for (j=0; j<dimx; j++) |
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92 | { |
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93 | lambda=alpha; |
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94 | if (HIGH_PRECISION == 0) |
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95 | alpha = alpha + (((long)(*a_j)*(*b_j))>>15); |
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96 | else |
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97 | alpha = (((long)alpha<<15) + (long)(*a_j)*(*b_j))>>15; // xxxx lepsi presnost |
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98 | |
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99 | *D_j = ((long)lambda**D_j)/alpha; |
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100 | |
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101 | if (*D_j==0) *D_j=1; |
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102 | |
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103 | b_i=b; |
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104 | U_ij=U+j; |
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105 | |
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106 | for (i=0; i<j; i++) |
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107 | { |
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108 | beta = *U_ij; |
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109 | if (HIGH_PRECISION == 0) |
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110 | { |
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111 | *U_ij = *U_ij - ((long)(*a_j)*(*b_i))/lambda; |
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112 | *b_i = *b_i + (((long)beta*(*b_j))>>15); |
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113 | } |
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114 | else |
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115 | { |
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116 | *U_ij = ((long)lambda**U_ij - (long)(*a_j)*(*b_i))/lambda; |
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117 | *b_i = (((long)*b_i<<15) + (long)beta**b_j)>>15; |
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118 | } |
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119 | b_i++; |
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120 | U_ij+=dimx; |
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121 | } |
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122 | |
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123 | a_j++; |
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124 | b_j++; |
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125 | D_j++; |
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126 | } |
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127 | |
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128 | x_i=xp; |
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129 | b_i=b; |
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130 | |
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131 | for (i=0; i<dimx; i++) |
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132 | { |
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133 | if (HIGH_PRECISION == 0) |
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134 | *x_i += ((long)difz[iy]**b_i)/alpha; // multiply by unscaled Kalman gain |
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135 | else |
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136 | *x_i = ((long)alpha**x_i + (long)difz[iy]**b_i)/alpha; |
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137 | |
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138 | x_i++; |
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139 | b_i++; |
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140 | } |
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141 | |
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142 | a+=dimx; |
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143 | } |
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144 | } |
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145 | |
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146 | /**/ |
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147 | |
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148 | // Thorton procedure - Kalman predictive variance in UD |
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149 | void thorton_fast(int *U, int *D, int *PSIU, int *Q, int *G, int *Dold, unsigned int rows) { |
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150 | unsigned int i,j,k; |
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151 | // copy D to Dold |
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152 | int *Dold_i,*Dold_k; |
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153 | int *D_i; |
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154 | int *PSIU_ij,*PSIU_ik,*PSIU_jk; |
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155 | int *Q_jj,*Q_ii,*Q_kk; |
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156 | int *U_ji; |
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157 | int *G_ik,*G_jk; |
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158 | int irows,jrows; |
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159 | long sigma; // in qAU+15!! |
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160 | long z; |
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161 | long z_tmp; |
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162 | |
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163 | Dold_i=Dold; |
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164 | D_i=D; |
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165 | |
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166 | for (i=0;i<rows;i++) |
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167 | { |
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168 | *Dold_i=*D_i; |
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169 | Dold_i++; |
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170 | D_i++; |
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171 | } |
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172 | |
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173 | // initialize G = eye() |
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174 | G_ik= G; |
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175 | *G_ik++=32767; |
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176 | for (i=0;i<rows-1;i++) |
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177 | { |
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178 | // clean elem before diag |
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179 | for (k=0; k<rows; k++) |
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180 | { |
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181 | *G_ik++=0; |
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182 | } |
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183 | *G_ik++=32767; |
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184 | } |
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185 | // eye created |
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186 | |
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187 | Dold_i=Dold+rows-1; |
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188 | D_i=D+rows-1; |
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189 | |
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190 | for (i=rows-1; 1; i--) |
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191 | { // stop if i==0 at the END! |
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192 | irows=i*rows; |
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193 | sigma = 0; |
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194 | |
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195 | PSIU_ik=PSIU+irows; |
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196 | Dold_k=Dold; |
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197 | |
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198 | for (k=0;k<rows; k++) |
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199 | { |
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200 | sigma += (((long)(*PSIU_ik)**PSIU_ik)>>(qAU))*(*Dold_k); |
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201 | PSIU_ik++; |
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202 | Dold_k++; |
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203 | } |
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204 | |
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205 | sigma += (long)*(Q+i+irows)<<(qAU+qD-15); |
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206 | |
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207 | G_ik=G+irows+i+1; |
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208 | |
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209 | for (j=i+1; j<rows; j++) |
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210 | { |
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211 | sigma += ((((long)(*G_ik)**G_ik)>>15)**(Q+j+j*rows))>>(30-qAU-qD); |
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212 | G_ik++; |
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213 | } |
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214 | |
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215 | if (sigma>((long)1<<(15+qAU))) |
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216 | { |
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217 | *D_i = 32767; |
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218 | } else |
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219 | { |
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220 | *D_i=sigma>>qAU; |
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221 | } |
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222 | |
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223 | if (*D_i==0) *D_i=1; |
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224 | |
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225 | for (j=0;j<i;j++) |
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226 | { |
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227 | jrows = j*rows; |
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228 | |
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229 | sigma =0; |
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230 | PSIU_ik=PSIU+irows; |
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231 | PSIU_jk=PSIU+jrows; |
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232 | Dold_k=Dold; |
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233 | |
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234 | for (k=0;k<rows; k++) |
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235 | { |
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236 | |
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237 | sigma += (((long)(*PSIU_ik)**PSIU_jk)>>qAU)**Dold_k; |
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238 | PSIU_ik++; |
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239 | PSIU_jk++; |
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240 | Dold_k++; |
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241 | } |
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242 | |
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243 | G_ik=G+irows+i; |
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244 | G_jk=G+jrows+i; |
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245 | Q_kk=Q+i*rows+i; |
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246 | |
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247 | for (k=i;k<rows;k++) |
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248 | { |
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249 | sigma += ((((long)(*G_ik)**G_jk)>>15)**Q_kk)>>(30-qAU-qD); |
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250 | G_ik++; |
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251 | G_jk++; |
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252 | Q_kk+=rows+1; |
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253 | } |
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254 | |
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255 | z=(sigma/(*D_i))<<(15-qAU); // shift to q15 |
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256 | if (z>32767) z=32767; |
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257 | if (z<-32768) z=-32768; |
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258 | |
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259 | U_ji=U+jrows+i; |
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260 | *U_ji = z; |
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261 | |
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262 | |
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263 | PSIU_ik=PSIU+irows; |
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264 | PSIU_jk=PSIU+jrows; |
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265 | |
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266 | for (k=0; k<rows;k++) |
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267 | { |
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268 | if (HIGH_PRECISION == 0) |
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269 | *PSIU_jk -= ((long)*U_ji**PSIU_ik)>>15; |
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270 | else |
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271 | *PSIU_jk = (((long)(*PSIU_jk)<<15) - (long)*U_ji**PSIU_ik)>>15; |
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272 | |
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273 | PSIU_ik++; |
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274 | PSIU_jk++; |
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275 | } |
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276 | |
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277 | G_jk=G+jrows; |
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278 | G_ik=G+irows; |
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279 | |
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280 | for (k=0;k<rows;k++) |
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281 | { |
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282 | if (HIGH_PRECISION == 0) |
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283 | *G_jk -= ((long)*U_ji**G_ik)>>15; |
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284 | else |
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285 | *G_jk = (((long)(*G_jk)<<15) - (long)*U_ji**G_ik)>>15; |
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286 | G_jk++; |
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287 | G_ik++; |
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288 | } |
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289 | } |
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290 | |
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291 | Dold_i--; |
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292 | D_i--; |
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293 | if (i==0) return; |
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294 | } |
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295 | } |
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