Projet

Général

Profil

« Précédent | Suivant » 

Révision 540

Ajouté par Yannis SENOUCI il y a presque 3 ans

filtre kalma fonctionnel

Voir les différences:

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 B[n][m])
{
double det=1/((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 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];
}
}
}
}
......
double xobs,yobs;
double oldx,oldy;
double dx=0,dy=0,dt=0.1;
int cpt = 0;
int cpt = 0,i,j;
// kalman param
double sigma_etat = 10.0;
......
{0, 0, 1, 0},
{0, 0, 0, 1}};
double FT[4][4];
Transpose_Mat(4,4,F,FT);
Transpose_Mat(4,4,F,FT);
//matrice intermediaire pour calcul
double X1[4][1];
double FP[4][4];
double FPFT[4][4];
double P1[4][4]={{sigma_etat*sigma_etat, 0, 0, 0},
{0, sigma_etat*sigma_etat, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}};
double PHT[4][2];
double HP1[2][4];
double HPHT[2][2];
double HPHT_R[2][2];
double HPHT_R_inv[2][2];
double HX1[2][1];
double Delta[2][1];
double KXY_HX1[4][1];
double X2[4][1];
double KH[4][4];
double KHP1[4][4];
double P2[4][4]={{sigma_etat*sigma_etat, 0, 0, 0},
{0, sigma_etat*sigma_etat, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}};
while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
printf("-------------%04d--------------\n",cpt);
......
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
Plot_Mat(X," X(k+1|k) = ");
// X = F*X
Mul_Mat_Mat(4,4,F,4,1,X,X1);
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,FP);
Mul_Mat_Mat(4,4,FP,4,4,FT,FPFT);
Add_Mat_Mat(4,4,FPFT,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,PHT);
Mul_Mat_Mat(2,4,H,4,4,P1,HP1);
Mul_Mat_Mat(2,4,HP1,4,2,HT,HPHT);
Add_Mat_Mat(2,2,HPHT,2,2,R,HPHT_R);
Inverse_Mat_22(2,2,HPHT_R,HPHT_R_inv);
Mul_Mat_Mat(4,2,PHT,2,2,HPHT_R_inv,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,HX1);
Sub_Mat_Mat(2,1,Obs,2,1,HX1,Delta);
Mul_Mat_Mat(4,2,K,2,1,Delta,KXY_HX1);
Add_Mat_Mat(4,1,X1,4,1,KXY_HX1,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(Delta,"DELTA = Obs - H.X(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,KH);
Mul_Mat_Mat(4,4,KH,4,4,P1,KHP1);
Sub_Mat_Mat(4,4,P1,4,4,KHP1,P2);
Plot_Mat(P2," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
//la position change donc : X(k+1|k) prend la valeur de X(k+1|k+1)
for(i=0;i<4;i++)
{
for(j=0;j<1;j++)
{
X[i][j]=X2[i][j];
}
}
//la variance du vecteur d'état change à chaque iteration de X : P(k+1|k) prend la valeur de P(k+1|k+1)
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;

Formats disponibles : Unified diff