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Révision 472

Ajouté par Louis FOUCHER il y a presque 3 ans

Foucher TP 3 SP4a fonctionnel

Voir les différences:

branch/FOUCHER_Louis/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 R[na][ma]){
void Add_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double R[na][ma]){
int i, j;
for(i=0; i<na; i++)
{
for(j=0; j<ma; j++)
{
R[i][j] = A[i][j]+B[i][j];
}
}
}
void Inverse_Mat_22(int n,int m,double A[n][m],double B[n][m]){
void Inverse_Mat_22(int n,int m,double A[n][m],double R[n][m]){
float det;
det = (A[0][0]*A[1][1]) - (A[0][1]*A[1][0]);
R[0][0]= A[1][1] / det ;
R[0][1]= - (A[0][1] / det) ;
R[1][0]= - (A[1][0] / det) ;
R[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 R[na][ma]){
void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double R[na][ma]){
int i,j;
for(i=0; i<na; i++)
{
for(j=0; j<ma; j++)
{
R[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 R[na][mb]){
void Mul_Mat_Mat(int na,int ma,double A[na][ma], int nb,int mb,double B[nb][mb], double R[na][mb]){
int i,j,k;
for(i=0; i<na; i++)
{
for(j=0; j<mb; j++)
{
R[i][j] = 0;
for(k=0; k<ma; k++)
{
R[i][j] += A[i][k] * B[k][j];
}
}
}
}
......
// kalman param
double sigma_etat = 10.0;
double sigma_observation = 2.0;
double X[4][1] = {{0},{0},{0},{0}};
double X[4][1] = {{0},{0},{0},{0}};
double X1[4][1];
double X2[4][1];
double P[4][4] = {{sigma_etat*sigma_etat, 0, 0, 0},
{0, sigma_etat*sigma_etat, 0, 0},
......
double R[2][2] = {{sigma_observation*sigma_observation, 0},
{0 , sigma_observation*sigma_observation}};
double K[4][2];
double K[4][2];
double K1[4][2];
double H[2][4] = {{1, 0, 0, 0},
{0, 1, 0, 0}};
double HT[4][2];
......
{0, 0, 1, 0},
{0, 0, 0, 1}};
double FT[4][4];
Transpose_Mat(4,4,F,FT);
Transpose_Mat(4,4,F,FT);
double P1[4][4];
double P2[4][4];
double DEN[2][2];
double DEN1[2][4];
double IDEN[2][2];
double M4[4][1];
double M5[2][1];
double M6[4][4];
double DELTA[2][1];
while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
printf("-------------%04d--------------\n",cpt);
double Obs[2][1] = {{xobs},{yobs}};
int i, j;
if (cpt ==0)
{
t0=t;x0=xobs;y0=yobs;
......
debug=0; ///Mettre à 1 pour afficher les matrices.
///Ajouter votre code ci-dessous///
// Kalman
// Kalman
double Obs[2][1] = {{xobs},{yobs}};
// X = F*X
Mul_Mat_Mat(4,4,F,4,1,X,X1);
// X = F*X
Plot_Mat(X," X(k+1|k) = ");
Plot_Mat(X1," X(k+1|k) = ");
//P = F*P*F'+Q;
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
//P = F*P*F'+Q;
Mul_Mat_Mat(4,4,F,4,4,P,P1);
Mul_Mat_Mat(4,4,P1,4,4,FT,P);
Add_Mat_Mat(4,4,P,4,4,Q,P1);
// K = P*H' / ( H*P*H' + R);
Plot_Mat(P1,"P(k+1|k) = F.P(k|k).FT + Q = ");
// K = P*H' / ( H*P*H' + R);
Mul_Mat_Mat(4,4,P1,4,2,HT,K1);
Mul_Mat_Mat(2,4,H,4,4,P1,DEN1);
Mul_Mat_Mat(2,4,DEN1,4,2,HT,DEN);
Add_Mat_Mat(2,2,DEN,2,2,R,DEN);
Inverse_Mat_22(2,2,DEN,IDEN);
Mul_Mat_Mat(4,2,K1,2,2,IDEN,K);
Plot_Mat(K,"K = ");
//X = X + K*([xobs(i);yobs(i)]-H*X);
//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
Plot_Mat(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
//X = X + K*([xobs(i);yobs(i)]-H*X);
Mul_Mat_Mat(2,4,H,4,1,X1,M5);
Sub_Mat_Mat(2,1,Obs,2,1,M5,DELTA);
Plot_Mat(DELTA,"DELTA = Obs - H.X(k+1|k)");
Mul_Mat_Mat(4,2,K,2,1,DELTA,M4);
Add_Mat_Mat(4,1,X1,2,1,M4,X2);
// P = P - K*H*P;
Plot_Mat(P," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
Plot_Mat(X2," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
// P = P - K*H*P;
Mul_Mat_Mat(4,2,K,2,4,H,P);
Mul_Mat_Mat(4,4,P,4,4,P1,M6);
Sub_Mat_Mat(4,4,P1,4,4,M6,P2);
Plot_Mat(P2," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
for (i=0;i<4;i++){
for (j=0;j<1;j++){
X[i][j]=X2[i][j];
}
}
for (i=0;i<4;i++){
for (j=0; j<4; j++){
P[i][j]=P2[i][j];
}
}
/// La matrice X doit contenir la position filtrée ///
}
t = cpt * dt;

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