|
// Pour compiler : gcc sp4a3_kalman.c -lm
|
|
|
|
#include <stdlib.h>
|
|
#include <stdio.h>
|
|
#include <math.h>
|
|
|
|
#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])
|
|
{
|
|
int i,j;
|
|
for (i=0;i<na;i++)
|
|
{
|
|
for (j=0;j<ma;j++)
|
|
{
|
|
R[i][j]=A[i][j]+B[i][j]; //sommes les valeurs de A avec B
|
|
}
|
|
}
|
|
return R[na][ma];
|
|
}
|
|
|
|
void Inverse_Mat_22(int n,int m,double A[n][m],double B[n][m])
|
|
{
|
|
double k;
|
|
k=1/((A[0][0]*A[1][1])-(A[0][1]*A[1][0]));
|
|
//Force les coefs de B aux bonnes valeurs
|
|
B[0][0]=A[1][1]*k;
|
|
B[1][1]=A[0][0]*k;
|
|
B[0][1]=-A[0][1]*k;
|
|
B[1][0]=-A[1][0]*k;
|
|
|
|
//printf("\n %f %f\n %f %f/n", B[0][0] ,B[0][1] ,B[1][0] ,B[1][1]);
|
|
return B[n][m];
|
|
}
|
|
|
|
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]; //échanges les valeurs des lignes avec les colonnes
|
|
}
|
|
}
|
|
return 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,j;
|
|
for (i=0;i<na;i++)
|
|
{
|
|
for (j=0;j<ma;j++)
|
|
{
|
|
R[i][j]=A[i][j]-B[i][j]; //soustrait les valeur de A avec B
|
|
}
|
|
}
|
|
return 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])
|
|
{
|
|
int i,j,k;
|
|
for (i=0; i<na; i++)
|
|
{
|
|
for (j=0; j<mb; j++)
|
|
{
|
|
R[i][j]=0; //s'assure que R est à 0 avant son calcul
|
|
//se met sur le point de R
|
|
for (k = 0; k < ma; k++)
|
|
{
|
|
//fait la somme des multiplication des valeurs de la ligne de A avec les valeurs des colonnes de B
|
|
R[i][j]+=A[i][k]*B[k][j];
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
|
|
void tests_unitaires(void){
|
|
//Matrices d'entrée
|
|
double T21a[2][1]={{7},{-5}};
|
|
double T21b[2][1]={{-3},{46}};
|
|
double T22a[2][2]={{12,78},{-5,13}};
|
|
double T22b[2][2]={{-25,36},{7,42}};
|
|
double T24[2][4]={{7,-71,-12,3},{41,123,-5,10}};
|
|
double T41a[4][1]={{45},{-123},{-78},{-410}};
|
|
double T41b[4][1]={{-10},{45},{27},{-9}};
|
|
double T42a[4][2]={{-73,45},{10,12},{-41,-35},{8,-23}};
|
|
double T44a[4][4]={{1,2,7,4},{6,5,7,8},{9,8,7,6},{5,4,3,2}};
|
|
double T44b[4][4]={{12,13,14,15},{21,22,23,40},{78,45,12,3},{54,10,12,47}};
|
|
|
|
//Matrices résultat
|
|
double R21[2][1],R22[2][2],R24[2][4],R41[4][1],R42[4][2],R44[4][4];
|
|
|
|
//Matrices de validation
|
|
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 RAT41[4][1]={{35},{-78},{-51},{-419}};
|
|
double RMT42T21[4][1]={{-736},{10},{-112},{171}};
|
|
double RMT42T22[4][2]={{-1101,-5109},{60,936},{-317,-3653},{211,325}};
|
|
double RMT42T24[4][4]={{1334,10718,651,231},{562,766,-180,150},{-1722,-1394,667,-473},{-887,-3397,19,-206}};
|
|
double RTT44[4][4]={{1,6,9,5},{2,5,8,4},{7,7,7,3},{4,8,6,2}};
|
|
double RMT44T41[4][1]={{-2387},{-4171},{-3585},{-1321}};
|
|
double RMT44T42[4][2]={{-308,-268},{-611,-99},{-816,118},{-432,122}};
|
|
double RAT44[4][4]={{13,15,21,19},{27,27,30,48},{87,53,19,9},{59,14,15,49}};
|
|
double RST44[4][4]={{-11,-11,-7,-11},{-15,-17,-16,-32},{-69,-37,-5,3},{-49,-6,-9,-45}};
|
|
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");
|
|
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");
|
|
}
|
|
|
|
|
|
int main(int argc,char **argv){
|
|
int i,n,j,m;
|
|
|
|
tests_unitaires();
|
|
|
|
FILE* fichier = fopen("pos_t_x_y.dat","r");
|
|
if (fichier == NULL)
|
|
error("Impossible d'ouvrir le fichier GPGGA_data.dat");
|
|
|
|
FILE * Fout = Fout = fopen("output.dat","w");
|
|
if (fichier == NULL)
|
|
error("Impossible d'ouvrir le fichier output.dat");
|
|
|
|
printf("Kalman\n");
|
|
double t = 0;
|
|
double t0,x0,y0;
|
|
double xobs,yobs;
|
|
double oldx,oldy;
|
|
double dx=0,dy=0,dt=0.1;
|
|
int cpt = 0;
|
|
|
|
// kalman param
|
|
double sigma_etat = 10.0;
|
|
double sigma_observation = 2.0;
|
|
double X[4][1] = {{0},{0},{0},{0}};
|
|
|
|
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}};
|
|
|
|
double Q[4][4] = {{0, 0, 0, 0},
|
|
{0, 0, 0, 0},
|
|
{0, 0, 0.1, 0},
|
|
{0, 0, 0, 0.1}};
|
|
|
|
double R[2][2] = {{sigma_observation*sigma_observation, 0},
|
|
{0 , sigma_observation*sigma_observation}};
|
|
|
|
double K[4][2];
|
|
double H[2][4] = {{1, 0, 0, 0},
|
|
{0, 1, 0, 0}};
|
|
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);
|
|
|
|
while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
|
|
printf("-------------%04d--------------\n",cpt);
|
|
|
|
if (cpt ==0)
|
|
{
|
|
t0=t;x0=xobs;y0=yobs;
|
|
xobs=xobs-x0;yobs=yobs-y0;
|
|
Plot_Mat(F,"F = ");
|
|
Plot_Mat(H,"H = ");
|
|
Plot_Mat(R,"R = ");
|
|
}
|
|
else
|
|
{
|
|
t -= t0;xobs -= x0;yobs -= y0;
|
|
|
|
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;
|
|
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*([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 = ");
|
|
|
|
// P = P - K*H*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 ++;
|
|
}
|
|
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\";");
|
|
return 0;
|
|
}
|