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Révision 476

Ajouté par Awa Semou FAYE il y a presque 3 ans

Filtre kalmann

Voir les différences:

branch/faye_awasemou/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;//i=variable permettant de parcourir les lignes et j=variable permettant de parcourir les colonnes
for(i=0;i<na;i++)
{
for(j=0;j<nb;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]){
float detA;
detA=1/((A[0][0]*A[1][1])-(A[1][0]*A[0][1]));
B[0][0]=A[1][1]*detA;
B[0][1]=-A[0][1]*detA;
B[1][0]=-A[1][0]*detA;
B[1][1]=A[0][0]*detA;
}
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;//i=variable permettant de parcourir les lignes et j=variable permettant de parcourir les colonnes
for(i=0;i<na;i++)
{
for(j=0;j<mb;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;//i=variable permettant de parcourir les lignes et j=variable permettant de parcourir les colonnes
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]=R[i][j]+ A[i][k]*B[k][j];
}
}
}
}
......
{0, 1, 0, dt},
{0, 0, 1, 0},
{0, 0, 0, 1}};
double FT[4][4];
double FT[4][4];
double X1[4][1];
double X2[4][1];
double X3[4][1];
double A1[4][4];
double A2[4][4];
double P1[4][4];
double P2[4][4];
double G1[2][4];
double G2[2][2];
double G3[2][2];
double G4[2][2];// inversion de G3
double G5[4][2];
double DELTA1[2][1];
double DELTA[2][1];
double M1[2][1];
double M2[4][1];
double obs[2][1]={{xobs}, {yobs}};
double M3[4][4];
double M4[4][4];
Transpose_Mat(4,4,F,FT);
while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
......
{
t -= t0;xobs -= x0;yobs -= y0;
debug=0; ///Mettre à 1 pour afficher les matrices.
debug=1; ///Mettre à 1 pour afficher les matrices.
///Ajouter votre code ci-dessous///
// Kalman
// Kalman
Plot_Mat(X," X(k|k) = ");
// X = F*X
Plot_Mat(X," X(k+1|k) = ");
//PREDICTION
// X = F*X
Mul_Mat_Mat(4,4,F,4,1,X,X1);// X1=F*X
Plot_Mat(X1," X(k+1|k) = ");
Plot_Mat(P," P(k|k) = ");
//P = F*P*F'+Q;
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
// K = P*H' / ( H*P*H' + R);
//P = F*P*F'+Q;
Mul_Mat_Mat(4,4,F,4,4,P,A1);// A1=F*P
Mul_Mat_Mat(4,4,A1,4,4,FT,A2);// A2=F*P*FT
Add_Mat_Mat(4,4,A2,4,4,Q,P1);// P1=F*P*FT+Q
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
//GAIN
// K = P*H' / ( H*P*H' + R);
Mul_Mat_Mat(4,4,H,4,4,P1,G1);//G1=H*P1
Mul_Mat_Mat(4,4,G1,4,4,HT,G2);//G2=H*P1*HT
Add_Mat_Mat(4,4,G2,4,4,R,G3);//G2=H*P1*HT
Plot_Mat(G3," H.P(k+1|k).HT+R = ");
Inverse_Mat_22(2,2,G3,G4);//G3=(H*P1*HT+R)
Mul_Mat_Mat(4,4,P1,4,2,HT,G5);//G5=P1*TH
Mul_Mat_Mat(4,2,G5,2,2,G3,K);//K=G5*G3
Plot_Mat(G4," INV(H.P(k+1|k).HT+R) = ");
Plot_Mat(K,"K = ");
//X = X + K*([xobs(i);yobs(i)]-H*X);
//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
//MISE A JOUR
//X = X + K*([xobs(i);yobs(i)]-H*X);
//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
Mul_Mat_Mat(2,4,H,4,1,X1,M1);
Sub_Mat_Mat(2,1,obs,2,1,M1,DELTA1);
Mul_Mat_Mat(4,2,K,2,1,DELTA1,M2);
Add_Mat_Mat(4,1,X,4,1,M2,X3);
Sub_Mat_Mat(2,1,obs,2,1,M1,DELTA);
Plot_Mat(obs," obs = ");
Plot_Mat(DELTA,"DELTA =obs -H.X(k+1|k) ");
Plot_Mat(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
// P = P - K*H*P;
// P = P - K*H*P;
Mul_Mat_Mat(4,2,K,2,4,H,M3);
Mul_Mat_Mat(4,4,M3,4,4,P,M4);
Sub_Mat_Mat(4,4,P1,4,4,M4,P2);
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 ///

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