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Révision 286

Ajouté par begresset il y a presque 4 ans

TP3 : Implantation des fonctions de calcul matriciel + implantation du filtre de Kalman.

Voir les différences:

branch/gresset/sp4a3/sp4a3_kalman.c
#include "sp4a3_kalman_extra.h"
void Add_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double b[nb][mb], double out[na][ma]){
void Add_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double out[na][ma]){
int i=0, j=0;
for(i=0; i<na; i++){
for(j=0; j<ma; j++){
out[i][j]=A[i][j]+B[i][j];
}
}
}
void Inverse_Mat_22(int n,int m,double A[n][m],double B[n][m]){
double det=A[0][0]*A[1][1]-A[0][1]*A[1][0];
B[0][0]=(A[1][1])/det;
B[0][1]=(-A[0][1])/det;
B[1][0]=(-A[1][0])/det;
B[1][1]=(A[0][0])/det;
}
void Transpose_Mat(int n,int m,double A[n][m],double R[m][n]){
......
R[j][i]=A[i][j];
}
void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double b[nb][mb], double out[na][ma]){
void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double out[na][ma]){
int i=0, j=0;
for(i=0; i<na; i++){
for(j=0; j<ma; j++){
out[i][j]=A[i][j]-B[i][j];
}
}
}
void Mul_Mat_Mat(int na,int ma,double A[na][ma], int nb,int mb,double B[nb][mb], double out[na][mb]){
void Mul_Mat_Mat(int na,int ma,double A[na][ma], int nb,int mb,double B[nb][mb], double out[na][mb]){
int i=0, j=0, k=0;
double sum;
for (i=0; i<na; i++){
for (j=0; j<mb; j++){
out[i][j]=0;
sum=0;
for(k=0; k<ma; k++){
sum= sum+A[i][k]*B[k][j];
}
out[i][j]=sum;
}
}
}
void Init_Mat(int na,int ma,double A[na][ma], double out[na][ma]){
int i=0, j=0;
for (i=0; i<na; i++)
for (j=0; j<ma; j++){
out[i][j]=A[i][j];
}
}
......
double RMT44T42[4][2]={{-308,-268},{-611,-99},{-816,118},{-432,122}};
double RAT44[4][4]={{13,15,21,19},{27,27,30,48},{87,53,19,9},{59,14,15,49}};
double RST44[4][4]={{-11,-11,-7,-11},{-15,-17,-16,-32},{-69,-37,-5,3},{-49,-6,-9,-45}};
double RMT44T44[4][4]={{816,412,192,304},{1155,583,379,687},{1146,668,466,758},{486,308,222,338}};
double RMT44T44[4][4]={{816,412,192,304},{1155,583,379,687},{1146,668,466,758},{486,308,222,338}};
printf("Execution des tests unitaires.\n");
Transpose_Mat(2,4,T24,R42); if (!Equal_Mat_Mat(RTT24,R42)) error("Erreur calcul Transposition 2x4");
Transpose_Mat(4,4,T44a,R44); if (!Equal_Mat_Mat(RTT44,R44)) error("Erreur calcul Transposition 4x4");
......
Mul_Mat_Mat(4,2,T42a,2,4,T24,R44); if (!Equal_Mat_Mat(RMT42T24,R44)) error("Erreur calcul Multiplication 4x2 2x4");
Mul_Mat_Mat(2,4,T24,4,1,T41a,R21); if (!Equal_Mat_Mat(RMT24T41,R21)) error("Erreur calcul Multiplication 2x4 4x1");
Mul_Mat_Mat(2,4,T24,4,2,T42a,R22); if (!Equal_Mat_Mat(RMT24T42,R22)) error("Erreur calcul Multiplication 2x4 4x2");
Mul_Mat_Mat(2,4,T24,4,4,T44a,R24); if (!Equal_Mat_Mat(RMT24T44,R24)) error("Erreur calcul Multiplication 2x4 4x4");
Mul_Mat_Mat(2,4,T24,4,4,T44a,R24); if (!Equal_Mat_Mat(RMT24T44,R24)) error("Erreur calcul Multiplication 2x4 4x4");
Init_Mat(2, 4, T24, R24); if (!Equal_Mat_Mat(T24, R24)) error("Erreur initialisation 2x4");
Init_Mat(4, 4, T44a, R44); if (!Equal_Mat_Mat(T44a, R44)) error("Erreur initialisation 4x4");
printf("Test unitaires OK.\n");
}
......
FILE * Fout = Fout = fopen("output.dat","w");
if (fichier == NULL)
error("Impossible d'ouvrir le fichier output.dat");
error("Impossible d'ouvrir le fichier output.dat");
printf("Kalman\n");
double t = 0;
......
Plot_Mat(R,"R = ");
}
else
{
{
//getchar();
t -= t0;x -= x0;y -= y0;
debug=0; ///Mettre à 1 pour afficher les matrices.
///Ajouter votre code ci-dessous///
// Kalman
// X = F*X
// X = F*X
double matx[4][1];
Init_Mat(4, 1, X, matx);
Mul_Mat_Mat(4, 4, F, 4, 1, matx, X);
Plot_Mat(X," X(k+1|k) = ");
//P = F*P*F'+Q;
//P = F*P*F'+Q;
double out[4][4], out1[4][4];
Mul_Mat_Mat(4, 4, F, 4, 4, P, out);
Mul_Mat_Mat(4, 4, out, 4, 4, FT, out1);
Add_Mat_Mat(4, 4, out1, 4, 4, Q, P);
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
// K = P*H' / ( H*P*H' + R);
Plot_Mat(K,"K = ");
// K = P*H' / ( H*P*H' + R);
double mat[4][2];
Mul_Mat_Mat(4, 4, P, 4, 2, HT, mat);
Plot_Mat(mat,"P(k+1|k).HT = ");
double mat1[2][2], mat2[2][2];
Mul_Mat_Mat(2, 4, H, 4, 2, mat, mat1);
Add_Mat_Mat(2, 2, mat1, 2, 2, R, mat2);
Plot_Mat(mat2, "H.P(k+1|k).HT + R = ");
double mat3[2][2];
Inverse_Mat_22(2, 2, mat2, mat3);
Plot_Mat(mat3, "INV(H.P(k+1|k).HT + R) = ");
Mul_Mat_Mat(4, 2, mat, 2, 2, mat3, K);
Plot_Mat(K, "K = ");
//X = X + K*([xb(i);yb(i)]-H*X);
//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
//X = X + K*([xb(i);yb(i)]-H*X);
double Obs[2][1]={{x}, {y}}, Delta[2][1], mat4[2][1];
Mul_Mat_Mat(2, 4, H, 4, 1, X, mat4);
Sub_Mat_Mat(2, 1, Obs, 2, 1, mat4, Delta);
Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
double mat5[4][1];
Mul_Mat_Mat(4, 2, K, 2, 1, Delta, mat5);
Add_Mat_Mat(4, 1, X, 4, 1, mat5, X);
Plot_Mat(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
// P = P - K*H*P;
// P = P - K*H*P;
double mat6[4][4], mat7[4][4], matp[4][4];
Mul_Mat_Mat(4, 2, K, 2, 4, H, mat6);
Mul_Mat_Mat(4, 4, mat6, 4, 4, P, mat7);
Init_Mat(4, 4, P, matp);
Sub_Mat_Mat(4, 4, matp, 4, 4, mat7, P);
Plot_Mat(P," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
/// La matrice X doit contenir la position filtrée ///
/// La matrice X doit contenir la position filtrée ///
}
t = cpt * dt;
dx = (x - oldx)/dt;

Formats disponibles : Unified diff