| 1 | /************************************ |
|---|
| 2 | Extended Kalman Filter |
|---|
| 3 | Matrix operations |
|---|
| 4 | |
|---|
| 5 | V. Smidl |
|---|
| 6 | |
|---|
| 7 | Rev. 30.8.2010 |
|---|
| 8 | |
|---|
| 9 | 30.8.2010 Prvni verze |
|---|
| 10 | |
|---|
| 11 | *************************************/ |
|---|
| 12 | #include "fixed.h" |
|---|
| 13 | #include "stdio.h" |
|---|
| 14 | /* Matrix multiply Full matrix by upper diagonal matrix; */ |
|---|
| 15 | void mmultAU(int *m1, int *up, int *result, unsigned int rows, unsigned int columns) { |
|---|
| 16 | unsigned int i, j, k; |
|---|
| 17 | long tmp_sum=0L; |
|---|
| 18 | int *m2pom; |
|---|
| 19 | |
|---|
| 20 | for (i=0; i<rows; i++) //rows of result |
|---|
| 21 | { |
|---|
| 22 | for (j=0; j<columns; j++) //columns of result |
|---|
| 23 | { |
|---|
| 24 | m2pom=up+j;//?? |
|---|
| 25 | |
|---|
| 26 | for (k=0; k<j; k++) //inner loop up to "j" - U(j,j)==1; |
|---|
| 27 | { |
|---|
| 28 | tmp_sum+=(long)(*m1++)**m2pom; |
|---|
| 29 | m2pom+=columns; |
|---|
| 30 | } |
|---|
| 31 | // add the missing A(i,j) |
|---|
| 32 | tmp_sum +=(long)(*m1)<<15; // no need to shift |
|---|
| 33 | m1-=(j); // shift back to first element |
|---|
| 34 | |
|---|
| 35 | // saturation effect |
|---|
| 36 | tmp_sum=tmp_sum>>15; |
|---|
| 37 | if (tmp_sum>32767) tmp_sum=32767; |
|---|
| 38 | if (tmp_sum<-32768) tmp_sum=-32768; |
|---|
| 39 | |
|---|
| 40 | *result++=tmp_sum; |
|---|
| 41 | |
|---|
| 42 | tmp_sum=0; |
|---|
| 43 | } |
|---|
| 44 | m1+=(columns); |
|---|
| 45 | } |
|---|
| 46 | }; |
|---|
| 47 | |
|---|
| 48 | void UDprt(int *U, int *D) { |
|---|
| 49 | return; |
|---|
| 50 | for (int i=0;i<5;i++) { |
|---|
| 51 | for (int j=0;j<5;j++) { |
|---|
| 52 | printf("%d,",U[i*5+j]); |
|---|
| 53 | } |
|---|
| 54 | printf("\n"); |
|---|
| 55 | } |
|---|
| 56 | for (int i=0;i<5;i++) { |
|---|
| 57 | printf("%d,",D[i]); |
|---|
| 58 | } |
|---|
| 59 | printf("\n"); |
|---|
| 60 | } |
|---|
| 61 | |
|---|
| 62 | // Thorton procedure - Kalman predictive variance in UD |
|---|
| 63 | void thorton(int *U, int *D, int *PSIU, int *Q, int *G, int *Dold, unsigned int rows) { |
|---|
| 64 | unsigned int i,j,k; |
|---|
| 65 | // copy D to Dold |
|---|
| 66 | int *Dold_pom=Dold; |
|---|
| 67 | for (i=0;i<rows;i++) { |
|---|
| 68 | *Dold_pom++=*D++; |
|---|
| 69 | } |
|---|
| 70 | D-=rows; // back to first D |
|---|
| 71 | |
|---|
| 72 | // initialize G = eye() |
|---|
| 73 | int *G_pom = G; |
|---|
| 74 | *G_pom++=1<<14; |
|---|
| 75 | for (i=0;i<rows-1;i++) { |
|---|
| 76 | // clean elem before diag |
|---|
| 77 | for (j=0; j<rows; j++) { |
|---|
| 78 | *G_pom++=0.0; |
|---|
| 79 | } |
|---|
| 80 | *G_pom++=1<<14; |
|---|
| 81 | } |
|---|
| 82 | // eye created |
|---|
| 83 | |
|---|
| 84 | long sigma; // in q15 |
|---|
| 85 | for (i=rows-1; i>=0;i--) { // check i==0 at the END! |
|---|
| 86 | sigma = 0; |
|---|
| 87 | |
|---|
| 88 | for (j=0;j<rows; j++) { |
|---|
| 89 | sigma += (((long)PSIU[i*rows+j]*PSIU[i*rows+j])>>15)*(Dold[i]); |
|---|
| 90 | } |
|---|
| 91 | sigma += Q[i*rows+i]; |
|---|
| 92 | for (j=i+1;j<rows; j++) { |
|---|
| 93 | sigma += (((long)G[i*rows+j]*G[i*rows+j])>>13)*Q[j*rows+j]; |
|---|
| 94 | } |
|---|
| 95 | |
|---|
| 96 | *(D+i)=sigma>>15; |
|---|
| 97 | if (D[i]==0) D[i]=1; |
|---|
| 98 | |
|---|
| 99 | /* printf("d=sig\n"); |
|---|
| 100 | UDprt(U,D); |
|---|
| 101 | UDprt(G,Dold);*/ |
|---|
| 102 | |
|---|
| 103 | for (j=0;j<i;j++) { |
|---|
| 104 | // printf("\n%d,%d\n",i,j); |
|---|
| 105 | sigma =0; |
|---|
| 106 | for (k=0;k<rows;k++) { |
|---|
| 107 | sigma += ((((long)PSIU[i*rows+k])*PSIU[j*rows+k])>>15)*Dold[k]; |
|---|
| 108 | } |
|---|
| 109 | for (k=0;k<rows;k++) { |
|---|
| 110 | sigma += ((((long)G[i*rows+k])*G[j*rows+k])>>13)*Q[k*rows+k]; |
|---|
| 111 | } |
|---|
| 112 | long z=sigma/D[i]; // shift by 15 |
|---|
| 113 | if (z>32767) z=32767; |
|---|
| 114 | if (z<-32768) z=-32768; |
|---|
| 115 | |
|---|
| 116 | U[j*rows+i] = (int)z; |
|---|
| 117 | |
|---|
| 118 | /* printf("U=sig/D\n"); |
|---|
| 119 | UDprt(U,D); |
|---|
| 120 | UDprt(G,Dold);*/ |
|---|
| 121 | |
|---|
| 122 | for (k=0;k<rows;k++) { |
|---|
| 123 | PSIU[j*rows+k] -= ((long)U[j*rows+i]*PSIU[i*rows+k])>>15; |
|---|
| 124 | } |
|---|
| 125 | |
|---|
| 126 | for (k=0;k<rows;k++) { |
|---|
| 127 | G[j*rows+k] -= ((long)U[j*rows+i]*G[i*rows+k])>>15; |
|---|
| 128 | } |
|---|
| 129 | |
|---|
| 130 | /* printf("end\n"); |
|---|
| 131 | UDprt(U,D); |
|---|
| 132 | UDprt(G,Dold); |
|---|
| 133 | printf("\n"); */ |
|---|
| 134 | } |
|---|
| 135 | if (i==0) return; |
|---|
| 136 | } |
|---|
| 137 | } |
|---|
| 138 | |
|---|
| 139 | void bierman_fast(int *difz, int *xp, int *U, int *D, int *R, unsigned int dimy, unsigned int dimx ) { |
|---|
| 140 | int alpha; |
|---|
| 141 | int beta,lambda; |
|---|
| 142 | int b[5]; // ok even for 4-dim state |
|---|
| 143 | int *a; // in [0,1] -> q15 |
|---|
| 144 | unsigned int iy,j,i; |
|---|
| 145 | |
|---|
| 146 | int *b_j,*b_i; |
|---|
| 147 | int *a_j; |
|---|
| 148 | int *D_j; |
|---|
| 149 | int *U_ij; |
|---|
| 150 | int *x_i; |
|---|
| 151 | a = U; // iyth row of U |
|---|
| 152 | for (iy=0; iy<dimy; iy++, a+=dimx) { |
|---|
| 153 | // a is a row |
|---|
| 154 | for (j=0,a_j=a,b_j=b,D_j=D; j<dimx; j++,b_j++,D_j++,a_j++) |
|---|
| 155 | *b_j=((long)(*D_j)*(*a_j))>>15; |
|---|
| 156 | |
|---|
| 157 | alpha = (long)R[iy]; //\alpha = R+vDv = R+a*b |
|---|
| 158 | // R in q15, a in q15, b=q15 |
|---|
| 159 | // gamma = (1<<15)/alpha; //(in q15) |
|---|
| 160 | //min alpha = R[iy] = 164 |
|---|
| 161 | //max gamma = 0.0061 => gamma_ref = q7 |
|---|
| 162 | for (j=0,a_j=a,b_j=b,D_j=D; j<dimx; j++,a_j++,b_j++,D_j++) { |
|---|
| 163 | beta = alpha; |
|---|
| 164 | lambda = -((long)(*a_j)<<15)/beta; |
|---|
| 165 | alpha += ((long)(*a_j)*(*b_j)>>15); |
|---|
| 166 | D[j] = (((long)beta<<15)/alpha)*(*D_j)>>15; //gamma is long |
|---|
| 167 | if (*D_j==0) *D_j=1; |
|---|
| 168 | |
|---|
| 169 | for (i=0,b_i=b,U_ij=U+j; i<j; i++, b_i++,U_ij+=dimx) { |
|---|
| 170 | beta = *U_ij; |
|---|
| 171 | *U_ij += (lambda*(*b_i))>>15; |
|---|
| 172 | *b_i += ((long)beta*(*b_j))>>15; |
|---|
| 173 | } |
|---|
| 174 | } |
|---|
| 175 | int dzs = (((long)difz[iy])<<15)/alpha; // apply scaling to innovations |
|---|
| 176 | // no shift due to gamma |
|---|
| 177 | for (i=0,x_i=xp,b_i=b; i<dimx; i++,x_i++,b_i++) { |
|---|
| 178 | *x_i += ((long)dzs*(*b_i))>>15; // multiply by unscaled Kalman gain |
|---|
| 179 | } |
|---|
| 180 | |
|---|
| 181 | //cout << "Ub: " << U << endl; |
|---|
| 182 | //cout << "Db: " << D << endl <<endl; |
|---|
| 183 | |
|---|
| 184 | } |
|---|
| 185 | |
|---|
| 186 | } |
|---|
| 187 | |
|---|
| 188 | // Thorton procedure - Kalman predictive variance in UD |
|---|
| 189 | void thorton_fast(int *U, int *D, int *PSIU, int *Q, int *G, int *Dold, unsigned int rows) { |
|---|
| 190 | unsigned int i,j,k; |
|---|
| 191 | // copy D to Dold |
|---|
| 192 | int *Dold_i,*Dold_k; |
|---|
| 193 | int *D_i; |
|---|
| 194 | int *PSIU_ij,*PSIU_ik,*PSIU_jk; |
|---|
| 195 | int *Q_jj,*Q_ii,*Q_kk; |
|---|
| 196 | int *U_ji; |
|---|
| 197 | int *G_ik,*G_jk; |
|---|
| 198 | int irows,jrows; |
|---|
| 199 | long sigma; // in q15 |
|---|
| 200 | |
|---|
| 201 | for (i=0,Dold_i=Dold,D_i=D;i<rows;i++,Dold_i++,D_i++) { |
|---|
| 202 | *Dold_i=*D_i; |
|---|
| 203 | } |
|---|
| 204 | |
|---|
| 205 | // initialize G = eye() |
|---|
| 206 | G_ik= G; |
|---|
| 207 | *G_ik++=1<<14; |
|---|
| 208 | for (i=0;i<rows-1;i++) { |
|---|
| 209 | // clean elem before diag |
|---|
| 210 | for (k=0; k<rows; k++) { |
|---|
| 211 | *G_ik++=0; |
|---|
| 212 | } |
|---|
| 213 | *G_ik++=1<<14; |
|---|
| 214 | } |
|---|
| 215 | // eye created |
|---|
| 216 | |
|---|
| 217 | for (i=rows-1, Dold_i=Dold+i, D_i=D+i; |
|---|
| 218 | true; i--, Dold_i--,D_i--) { // stop if i==0 at the END! |
|---|
| 219 | irows=i*rows; |
|---|
| 220 | sigma = 0; |
|---|
| 221 | for (k=0, PSIU_ik=PSIU+irows; |
|---|
| 222 | k<rows; k++, PSIU_ik++) {//Dold_i= |
|---|
| 223 | sigma += (((long)(*PSIU_ik)**PSIU_ik)>>15)*(*Dold_i); |
|---|
| 224 | } |
|---|
| 225 | sigma += *(Q+i+irows); |
|---|
| 226 | for (j=i+1, G_ik=G+irows+i+1; j<rows; j++,G_ik++) { |
|---|
| 227 | sigma += (((long)(*G_ik)**G_ik)>>13)**(Q+j+j*rows); |
|---|
| 228 | |
|---|
| 229 | } |
|---|
| 230 | |
|---|
| 231 | *D_i=sigma>>15; |
|---|
| 232 | if (*D_i==0) *D_i=1; |
|---|
| 233 | |
|---|
| 234 | |
|---|
| 235 | for (j=0;j<i;j++) { |
|---|
| 236 | jrows = j*rows; |
|---|
| 237 | |
|---|
| 238 | sigma =0; |
|---|
| 239 | for (k=0, PSIU_ik=PSIU+irows, PSIU_jk=PSIU+jrows, Dold_k=Dold; |
|---|
| 240 | k<rows; k++, PSIU_ik++, PSIU_jk++, Dold_k++) { |
|---|
| 241 | |
|---|
| 242 | sigma += ((((long)*PSIU_ik)**PSIU_jk)>>15)**Dold_k; |
|---|
| 243 | } |
|---|
| 244 | |
|---|
| 245 | for (k=i,G_ik=G+irows+i,G_jk=G+jrows+i,Q_kk=Q+k*rows+k; |
|---|
| 246 | k<rows;k++,G_ik++,G_jk++,Q_kk+=rows+1) { |
|---|
| 247 | sigma += ((((long)*G_ik)**G_jk)>>13)**Q_kk; |
|---|
| 248 | } |
|---|
| 249 | |
|---|
| 250 | long z=sigma/(*D_i); // shift by 15 |
|---|
| 251 | if (z>32767) z=32767; |
|---|
| 252 | if (z<-32768) z=-32768; |
|---|
| 253 | |
|---|
| 254 | U_ji=U+jrows+i; |
|---|
| 255 | *U_ji = (int)z; |
|---|
| 256 | |
|---|
| 257 | |
|---|
| 258 | for (k=0,PSIU_ik=PSIU+irows,PSIU_jk=PSIU+jrows; |
|---|
| 259 | k<rows;k++,PSIU_ik++,PSIU_jk++) { |
|---|
| 260 | *PSIU_jk -= ((long)*U_ji**PSIU_ik)>>15; |
|---|
| 261 | } |
|---|
| 262 | |
|---|
| 263 | for (k=0,G_jk=G+jrows,G_ik=G+irows; |
|---|
| 264 | k<rows;k++, G_jk++, G_ik++) { |
|---|
| 265 | *G_jk -= ((long)*U_ji**G_ik)>>15; |
|---|
| 266 | } |
|---|
| 267 | |
|---|
| 268 | } |
|---|
| 269 | if (i==0) return; |
|---|
| 270 | } |
|---|
| 271 | } |
|---|
| 272 | |
|---|
| 273 | void bierman(int *difz, int *xp, int *U, int *D, int *R, unsigned int dimy, unsigned int dimx ) { |
|---|
| 274 | long alpha; |
|---|
| 275 | long gamma,beta,lambda; |
|---|
| 276 | int b[5]; // ok even for 4-dim state |
|---|
| 277 | int *a; // in [0,1] -> q15 |
|---|
| 278 | unsigned int iy,j,i; |
|---|
| 279 | |
|---|
| 280 | for (iy=0; iy<dimy; iy++) { |
|---|
| 281 | // a is a row |
|---|
| 282 | a = U+iy*dimx; // iyth row of U |
|---|
| 283 | for (j=0;j<dimx;j++) |
|---|
| 284 | b[j]=((long)D[j]*a[j])>>15; |
|---|
| 285 | |
|---|
| 286 | alpha = (long)R[iy]; //\alpha = R+vDv = R+a*b |
|---|
| 287 | // R in q15, a in q15, b=q15 |
|---|
| 288 | // gamma = (1<<15)/alpha; //(in q15) |
|---|
| 289 | //min alpha = R[iy] = 164 |
|---|
| 290 | //max gamma = 0.0061 => gamma_ref = q7 |
|---|
| 291 | for (j=0;j<dimx;j++) { |
|---|
| 292 | beta = alpha; |
|---|
| 293 | lambda = -((long)a[j]<<15)/beta; |
|---|
| 294 | alpha += ((long)(a[j])*b[j]>>15); |
|---|
| 295 | D[j] = (((long)beta<<15)/alpha)*D[j]>>15; //gamma is long |
|---|
| 296 | if (D[j]==0) D[j]=1; |
|---|
| 297 | |
|---|
| 298 | // cout << "a: " << alpha << "g: " << gamma << endl; |
|---|
| 299 | for (i=0;i<j;i++) { |
|---|
| 300 | beta = U[i*dimx+j]; |
|---|
| 301 | U[i*dimx+j] += (lambda*b[i])>>15; |
|---|
| 302 | b[i] += (beta*b[j])>>15; |
|---|
| 303 | } |
|---|
| 304 | } |
|---|
| 305 | int dzs = (((long)difz[iy])<<15)/alpha; // apply scaling to innovations |
|---|
| 306 | // no shift due to gamma |
|---|
| 307 | for (i=0; i<dimx; i++) { |
|---|
| 308 | xp[i] += ((long)dzs*b[i])>>15; // multiply by unscaled Kalman gain |
|---|
| 309 | } |
|---|
| 310 | |
|---|
| 311 | //cout << "Ub: " << U << endl; |
|---|
| 312 | //cout << "Db: " << D << endl <<endl; |
|---|
| 313 | |
|---|
| 314 | } |
|---|
| 315 | |
|---|
| 316 | } |
|---|
