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Révision 278

Ajouté par albest il y a presque 4 ans

TP3 : implémentation du filtre de Kalman

Voir les différences:

branch/best/sp4a3/sp4a3_kalman.c
void Add_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double out[na][ma]){
if ((na == nb) && (ma == mb)){
for (int i=0;i<na;i++){
for (int j=0;j<ma;i++){
for (int 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]){
if (n == m && n == 2){
if (n == m && n == 2 && A[0][0]*A[1][1]-A[1][0]*A[0][1] != 0){
B[0][0] = (1/(A[0][0]*A[1][1]-A[0][1]*A[1][0]))*A[1][1];
B[0][1] = (1/(A[0][0]*A[1][1]-A[0][1]*A[1][0]))*(-A[0][1]);
B[1][0] = (1/(A[0][0]*A[1][1]-A[0][1]*A[1][0]))*(-A[1][0]);
......
void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double out[na][ma]){
if (na == nb && ma == mb){
for (int i=0;i<na;i++){
for (int j=0;j<ma;i++){
for (int 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]){
if (ma == nb){
for (int i=0;i<na;i++){
for (int j = 0;j<mb;i++){
for (int j=0;j<mb;j++){
out[i][j] = 0; //On initialise un coef de la matrice à 0
for (int k=0;k<ma;k++){
out[i][j] += A[i][k]*B[k][j];
out[i][j] += (A[i][k])*(B[k][j]);
}
}
}
}
}
void Cop_Mat(int n,int m, double A[n][m], double out[n][m]){
for (int i =0;i<n;i++){
for (int j=0;j<m;j++){
out[i][j] = A[i][j];
}
}
}
void tests_unitaires(void){
//Matrices d'entrée
double T21a[2][1]={{7},{-5}};
......
Transpose_Mat(4,4,T44a,R44); if (!Equal_Mat_Mat(RTT44,R44)) error("Erreur calcul Transposition 4x4");
Inverse_Mat_22(2,2,T22a,R22); if (!Equal_Mat_Mat(RInvT22,R22)) error("Erreur calcul Inversion 2x2");
Add_Mat_Mat(2,2,T22a,2,2,T22b,R22); if (!Equal_Mat_Mat(RAT22,R22)) error("Erreur calcul Addition 2x2");
//Add_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RAT44,R44)) error("Erreur calcul Addition 4x4");
//Add_Mat_Mat(4,1,T41a,4,1,T41b,R41); if (!Equal_Mat_Mat(RAT41,R41)) error("Erreur calcul Addition 4x1");
//Sub_Mat_Mat(2,1,T21a,2,1,T21b,R21); if (!Equal_Mat_Mat(RST21,R21)) error("Erreur calcul Soustraction 2x1");
//Sub_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RST44,R44)) error("Erreur calcul Soustraction 4x4");
//Mul_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RMT44T44,R44)) error("Erreur calcul Multiplication 4x4 4x4");
//Mul_Mat_Mat(4,4,T44a,4,1,T41a,R41); if (!Equal_Mat_Mat(RMT44T41,R41)) error("Erreur calcul Multiplication 4x4 4x1");
//Mul_Mat_Mat(4,4,T44a,4,2,T42a,R42); if (!Equal_Mat_Mat(RMT44T42,R42)) error("Erreur calcul Multiplication 4x4 4x2");
//Mul_Mat_Mat(4,2,T42a,2,1,T21a,R41); if (!Equal_Mat_Mat(RMT42T21,R41)) error("Erreur calcul Multiplication 4x2 2x1");
//Mul_Mat_Mat(4,2,T42a,2,2,T22a,R42); if (!Equal_Mat_Mat(RMT42T22,R42)) error("Erreur calcul Multiplication 4x2 2x2");
//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");
Add_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RAT44,R44)) error("Erreur calcul Addition 4x4");
Add_Mat_Mat(4,1,T41a,4,1,T41b,R41); if (!Equal_Mat_Mat(RAT41,R41)) error("Erreur calcul Addition 4x1");
Sub_Mat_Mat(2,1,T21a,2,1,T21b,R21); if (!Equal_Mat_Mat(RST21,R21)) error("Erreur calcul Soustraction 2x1");
Sub_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RST44,R44)) error("Erreur calcul Soustraction 4x4");
Mul_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RMT44T44,R44)) error("Erreur calcul Multiplication 4x4 4x4");
Mul_Mat_Mat(4,4,T44a,4,1,T41a,R41); if (!Equal_Mat_Mat(RMT44T41,R41)) error("Erreur calcul Multiplication 4x4 4x1");
Mul_Mat_Mat(4,4,T44a,4,2,T42a,R42); if (!Equal_Mat_Mat(RMT44T42,R42)) error("Erreur calcul Multiplication 4x4 4x2");
Mul_Mat_Mat(4,2,T42a,2,1,T21a,R41); if (!Equal_Mat_Mat(RMT42T21,R41)) error("Erreur calcul Multiplication 4x2 2x1");
Mul_Mat_Mat(4,2,T42a,2,2,T22a,R42); if (!Equal_Mat_Mat(RMT42T22,R42)) error("Erreur calcul Multiplication 4x2 2x2");
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");
printf("Test unitaires OK.\n");
}
......
{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 tampon22[2][2] = {{0, 0},
{0, 0}};
double tampon22bis[2][2] = {{0, 0},
{0, 0}};
double tampon22bisbis[2][2] = {{0, 0},
{0, 0}};
double tampon24[2][4] = {{0, 0, 0, 0},
{0, 0, 0, 0}};
double tampon42[4][2] = {{0, 0},
{0, 0},
{0, 0},
{0, 0}};
double tampon44[4][4] = {{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}};
double tampon44bis[4][4] = {{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}};
double tampon44bisbis[4][4] = {{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}};
double tampon44bisbisbis[4][4] = {{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}};
double tampon44bisbisbisbis[4][4] = {{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}};
double tampon21[2][1] = {{0},
{0}};
double tampon41[4][1] = {{0},
{0},
{0},
{0}};
double tampon41bis[4][1] = {{0},
{0},
{0},
{0}};
double obs[2][1];
double Delta[2][1];
while(fscanf(fichier, "%lf %lf %lf", &t, &x, &y)>0){
printf("-------------%04d--------------\n",cpt);
......
debug=0; ///Mettre à 1 pour afficher les matrices.
///Ajouter votre code ci-dessous///
// Kalman
// X = F*X
Plot_Mat(X," X(k+1|k) = ");
//P = F*P*F'+Q;
// X = F*X
Mul_Mat_Mat(4,4,F,4,1,X,tampon41);//tampon41 vaut X(k+1/k)
Plot_Mat(tampon41," X(k+1|k) = ");
//P = F*P*F'+Q;
Mul_Mat_Mat(4,4,F,4,4,P,tampon44);//P=F*P
Mul_Mat_Mat(4,4,tampon44,4,4,FT,tampon44bis);//*F'
Add_Mat_Mat(4,4,tampon44bis,4,4,Q,P);//+Q
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
// K = P*H' / ( H*P*H' + R);
Plot_Mat(K,"K = ");
//X = X + K*([xb(i);yb(i)]-H*X);
//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
Mul_Mat_Mat(2,4,H,4,4,P,tampon24);//H*P
Mul_Mat_Mat(2,4,tampon24,4,2,HT,tampon22);//*H'
Add_Mat_Mat(2,2,tampon22,2,2,R,tampon22bis);//+R
Inverse_Mat_22(2,2,tampon22bis,tampon22bisbis);//Inverse
Mul_Mat_Mat(4,2,HT,2,2,tampon22bisbis,tampon42);//H'*
Mul_Mat_Mat(4,4,P,4,2,tampon42,K);//P*
Plot_Mat(K,"K = ");
//X = X + K*([xb(i);yb(i)]-H*X);
obs[0][0] = x;
obs[1][0] = y;
Plot_Mat(obs," Obs = ");
Mul_Mat_Mat(2,4,H,4,1,tampon41,tampon21);
Sub_Mat_Mat(2,1,obs,2,1,tampon21,Delta);
Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
// X = X + K.Delta
Mul_Mat_Mat(4,2,K,2,1,Delta,tampon41bis);
Add_Mat_Mat(4,1,tampon41,4,1,tampon41bis,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;
Mul_Mat_Mat(4,2,K,2,4,H,tampon44bisbis);
Mul_Mat_Mat(4,4,tampon44bisbis,4,4,P,tampon44bisbisbis);
Sub_Mat_Mat(4,4,P,4,4,tampon44bisbisbis,tampon44bisbisbisbis);
Cop_Mat(4,4,tampon44bisbisbisbis,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 ///

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