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Révision 575

Ajouté par Erwan DESFRICHES DORIA il y a presque 3 ans

Développement du filtre terminé.
Filtre opérationnel et prêt à être installé dans votre GPS, bonne route!

Voir les différences:

sp4a3_kalman.c
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;
int j;
for(i=0; i<na; i++) //on parcourt les lignes
{
for(j=0; j<ma; j++) // on parcourt les colonnes
{
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]){
float det;
det = (A[0][0]*A[1][1]-A[1][0]*A[0][1]);
if(det !=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]){
......
}
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;
int j;
for(i=0; i<na; i++) //on parcourt les lignes
{
for(j=0; j<ma; j++) // on parcourt les colonnes
{
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]){
int i;
int j;
int 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];
}
}
}
void tests_unitaires(void){
//Matrices d'entrée
double T21a[2][1]={{7},{-5}};
......
{0, 1, 0, dt},
{0, 0, 1, 0},
{0, 0, 0, 1}};
double FT[4][4];
double FT[4][4];
double XA[4][1];
double FxP[4][4];
double FxPxFT[4][4];
double PA[4][4];
double PAxHT[4][2];
double HxPA[2][4];
double HxPAxHT[2][2];
double HxPAxHTplusR[2][2];
double invHxPAxHTplusR[2][2];
double HxXA[2][1];
double DELTA[2][1];
double KxDELTA[4][1];
double XB[4][1];
double KxH[4][4];
double KxHxPA[4][4];
double PB[4][4];
Transpose_Mat(4,4,F,FT);
while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
printf("-------------%04d--------------\n",cpt);
double Obs[2][1] ={{xobs}, {yobs}};
if (cpt ==0)
{
t0=t;x0=xobs;y0=yobs;
......
debug=0; ///Mettre à 1 pour afficher les matrices.
///Ajouter votre code ci-dessous///
// Kalman
double Obs[2][1] ={{xobs}, {yobs}};
Mul_Mat_Mat(4, 4, F, 4, 1, X, XA);// X = F*X
Plot_Mat(XA," X(k+1|k) = ");
// X = F*X
Plot_Mat(X," X(k+1|k) = ");
Mul_Mat_Mat(4, 4, F, 4, 4, P, FxP);
Mul_Mat_Mat(4, 4, FxP, 4, 4, FT, FxPxFT);
Add_Mat_Mat(4, 4, FxPxFT, 4, 4, Q, PA);//P = F*P*F'+Q;
Plot_Mat(PA,"P(k+1|k) = F.P(k|k).FT + Q = ");
//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);
Mul_Mat_Mat(4, 4, PA, 4, 2, HT, PAxHT);
Mul_Mat_Mat(2, 4, H, 4, 4, PA, HxPA);
Mul_Mat_Mat(2, 4, HxPA, 4, 2, HT, HxPAxHT);
Add_Mat_Mat(2, 2, HxPAxHT, 2, 2, R, HxPAxHTplusR);
Inverse_Mat_22(2, 2, HxPAxHTplusR, invHxPAxHTplusR);
Mul_Mat_Mat(4, 2, PAxHT, 2, 2, invHxPAxHTplusR, K);// K = P*H' / ( H*P*H' + R);
Plot_Mat(K,"K = ");
//X = X + K*([xobs(i);yobs(i)]-H*X);
Mul_Mat_Mat(2, 4, H, 4, 1, XA, HxXA);
Sub_Mat_Mat(2, 1, Obs, 2, 1, HxXA, DELTA);
Mul_Mat_Mat(4, 2, K, 2, 1, DELTA, KxDELTA);
Add_Mat_Mat(4, 1, XA, 4, 1, KxDELTA, XB);//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 = ");
Plot_Mat(XB," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
// P = P - K*H*P;
Plot_Mat(P," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
Mul_Mat_Mat(4, 2, K, 2, 4, H, KxH);
Mul_Mat_Mat(4, 4, KxH, 4, 4, PA, KxHxPA);
Sub_Mat_Mat(4, 4, PA, 4, 4, KxHxPA, PB);// P = P - K*H*P;
Plot_Mat(PB," 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 ///
int i;
int j;
for(i=0; i<4; i++)
{
X[i][0] = XB[i][0];
for(j=0; j<4; j++)
{
P[i][j]=PB[i][j];
}
}
}
t = cpt * dt;
dx = (xobs - oldx)/dt;

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