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Révision 548

Ajouté par Papa Abdoulaye NDIAYE il y a presque 3 ans

Fin tp3

Voir les différences:

branch/papa_ndiaye/sp4a3/sp4a3_kalman.c
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "sp4a3_kalman_extra.h"
void Transpose_Mat(int n,int m,double A[n][m],double R[m][n])
{
for (int i=0;i<n;i++)
for (int j=0;j<m;j++)
{
R[j][i]=A[i][j];
}
}
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])
{
for(int i=0;i<na;i++)
for(int j=0;j<ma;j++)
{
R[i][j]=0;
R[i][j]=A[i][j]+B[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])
{
for(int i=0;i<na;i++)
for(int j=0;j<ma;j++)
{
R[i][j]=0;
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 invdet,det;
det=((A[0][0])*(A[1][1])) - (A[1][0])*(A[0][1]);
invdet=1/det;
B[0][0]=invdet*A[1][1];
B[1][1]=invdet*A[0][0];
B[0][1]=-(invdet*A[0][1]);
B[1][0]=-(invdet*A[1][0]);
}
void Transpose_Mat(int n,int m,double A[n][m],double R[m][n]){
int i,j;
for (i=0;i<n;i++)
for (j=0;j<m;j++)
R[j][i]=A[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])
{
for(int i=0;i<na;i++)
for(int j=0;j<mb;j++)
{
R[i][j]=0;
for(int k=0;k<ma;k++)
R[i][j]=R[i][j]+(A[i][k])*(B[k][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 Mul_Mat_Mat(int na,int ma,double A[na][ma], int nb,int mb,double B[nb][mb], double R[na][mb]){
}
void tests_unitaires(void){
void tests_unitaires(void)
{
//Matrices d'entrée
double T21a[2][1]={{7},{-5}};
double T21b[2][1]={{-3},{46}};
......
double RST21[2][1]={{10},{-51}};
double RInvT22[2][2]={{0.02380952380952381,-0.1428571428571428},{0.009157509157509158,0.02197802197802198}};
double RAT22[2][2]={{-13,114},{2,55}};
double RTT24[4][2]={{7,41},{-71,123},{-12,-5},{3,10}};
double RMT24T41[2][1]={{8754},{-16994}};
double RMT24T42[2][2]={{-705,-186},{-1478,3266}};
double RMT24T44[2][4]={{-512,-425,-523,-606},{784,697,1143,1138}};
......
double RMT44T44[4][4]={{816,412,192,304},{1155,583,379,687},{1146,668,466,758},{486,308,222,338}};
printf("Execution des tests unitaires.\n");
Transpose_Mat(2,4,T24,R42); if (!Equal_Mat_Mat(RTT24,R42)) error("Erreur calcul Transposition 2x4");
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");
......
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");
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");
}
int main(int argc,char **argv){
int main(int argc,char **argv)
{
tests_unitaires();
......
int cpt = 0;
// kalman param
double sigma_etat = 10.0;
double sigma_observation = 2.0;
double X[4][1] = {{0},{0},{0},{0}};
double sigma_etat = 10.0;
double sigma_observation = 2.0;
double X[4][1] = {{0},{0},{0},{0}};
double Xa[4][1] = {{0},{0},{0},{0}};
double P1[4][4];
double Pa[4][4];
double P[4][4] = {{sigma_etat*sigma_etat, 0, 0, 0},
{0, sigma_etat*sigma_etat, 0, 0},
{0, 0, 0, 0},
......
{0, 0, 0, 0.1}};
double R[2][2] = {{sigma_observation*sigma_observation, 0},
{0 , sigma_observation*sigma_observation}};
{0 , sigma_observation*sigma_observation}};
double R1[2][2];
double K[4][2];
double K[4][2];
double zero[4][4];
double K1[4][2];
double H[2][4] = {{1, 0, 0, 0},
{0, 1, 0, 0}};
{0, 1, 0, 0}};
double H1[2][4];
double HT[4][2];
Transpose_Mat(2,4,H,HT);
double F[4][4] = {{1, 0, dt, 0},
{0, 1, 0, dt},
{0, 0, 1, 0},
{0, 0, 0, 1}};
double FT[4][4];
Transpose_Mat(4,4,F,FT);
double PH[4][4];
double PHt[4][4];
double RPHt[4][4];
double PF[4][4];
double PFt[4][4];
double Delta[2][1];
double KDelta[4][1];
while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0)
{
printf("-------------%04d--------------\n",cpt);
if (cpt ==0)
......
}
else
{
t -= t0;xobs -= x0;yobs -= y0;
t -= t0;xobs -= x0;yobs -= y0;
double obs[2][1]={{xobs},{yobs}};
Transpose_Mat(2,4,H,HT);
Transpose_Mat(4,4,F,FT);
debug=0; ///Mettre à 1 pour afficher les matrices.
///Ajouter votre code ci-dessous///
// Kalman
// Kalman
// X = F*X
Plot_Mat(X," X(k+1|k) = ");
Mul_Mat_Mat(4,4,F,4,1,X,Xa);// Xa = F*X
//P = F*P*F'+Q;
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
Plot_Mat(Xa," X(k+1|k) = ");
Mul_Mat_Mat(4,4,P,4,4,FT,PFt);//PFt= P*F'
Mul_Mat_Mat(4,4,F,4,4,PFt,PF);//PF= F*P*F'
Add_Mat_Mat(4,4,Q,4,4,PF,P);//Pa = F*P*F'+Q;
// K = P*H' / ( H*P*H' + R);
Plot_Mat(K,"K = ");
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
Mul_Mat_Mat(4,4,P,4,2,HT,PHt);//PHt= P*H'
Mul_Mat_Mat(2,4,H,4,2,PHt,PH);//PH= H*P*H'
Add_Mat_Mat(2,2,R,2,2,PH,R1);//R1= H*P*H' + R
Inverse_Mat_22(2,2,R1,RPHt);//RPHt= 1/ ( H*P*H' + R)
Mul_Mat_Mat(4,2,PHt,2,2,RPHt,K);// K = P*H' / ( H*P*H' + R);
//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 = ");
for(int i=0;i<4;i++)
for(int j=0;j<4;j++)
zero[i][j]=0;
Plot_Mat(K,"K = ");
Mul_Mat_Mat(2,4,H,4,1,Xa,H1);//H1=H*X
Sub_Mat_Mat(2,1,obs,2,1,H1,Delta);// Delta=[xobs(i);yobs(i)]-H*X
Mul_Mat_Mat(4,2,K,2,1,Delta,KDelta);//KDelta=K*(obs -H*X)
Add_Mat_Mat(4,1,Xa,4,1,KDelta,X);//X = X + K*([xobs(i);yobs(i)]-H*X);
// P = P - K*H*P;
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 = ");
Mul_Mat_Mat(4,2,K,2,4,H,K1);//K1=K*H
Mul_Mat_Mat(4,4,K1,4,4,P,P1);// P1= K1*P
Sub_Mat_Mat(4,4,P,4,4,P1,Pa);// Pa = P - K*H*P;
Add_Mat_Mat(4,4,Pa,4,4,zero,P);// 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 ///
}
t = cpt * dt;
dx = (xobs - oldx)/dt;
dy = (yobs - oldy)/dt;
fprintf(Fout,"%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\n",t,xobs,yobs,sqrt(dx*dx+dy*dy)*dt,X[0][0],X[1][0],X[2][0],X[3][0],sqrt(X[2][0]*X[2][0]+X[3][0]*X[3][0])*dt);
oldx = xobs;
oldy = yobs;
cpt ++;
}
t = cpt * dt;
dx = (xobs - oldx)/dt;
dy = (yobs - oldy)/dt;
fprintf(Fout,"%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\n",t,xobs,yobs,sqrt(dx*dx+dy*dy)*dt,X[0][0],X[1][0],X[2][0],X[3][0],sqrt(X[2][0]*X[2][0]+X[3][0]*X[3][0])*dt);
oldx = xobs;
oldy = yobs;
cpt ++;
}
fclose(Fout);
fclose(fichier);
system ("gnuplot -p -e \"plot 'output.dat' u 5:6 w l, '' u 2:3 w l\";");
system ("gnuplot -p -e \"plot 'output.dat' u 1:9 w l, '' u 1:4 w l\";");
system ("gnuplot -p -e \"plot 'output.dat' u 9 w l , 'vitesse_reelle.dat' u 2 w l\";");
system ("gnuplot -p -e \"plot 'output.dat' u 5:6 w l, '' u 2:3 w l\";");
system ("gnuplot -p -e \"plot 'output.dat' u 1:9 w l, '' u 1:4 w l\";");
system ("gnuplot -p -e \"plot 'output.dat' u 9 w l , 'vitesse_reelle.dat' u 2 w l\";");
return 0;
}

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