Projet

Général

Profil

Télécharger (9,91 ko) Statistiques
| Révision:

root/branch/DEMAGALHAES/sp4a3/sp4a3_kalman.c @ 457

1 jalaffon
// Pour compiler : gcc sp4a3_kalman.c -lm

#include <stdlib.h>
#include <stdio.h>
#include <math.h>

#include "sp4a3_kalman_extra.h"

428 rademagalh
void Add_Mat_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],int Ligne_MatB, int Colonne_MatB, double B[Ligne_MatB][Colonne_MatB], double Res[Ligne_MatA][Colonne_MatA])
{
for (int i = 0; i < Ligne_MatA; i++)
{
for (int j = 0; j < Colonne_MatA; j++)
{
Res[i][j] = A[i][j]+B[i][j];
}
}
}

void Sub_Mat_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],int Ligne_MatB, int Colonne_MatB, double B[Ligne_MatB][Colonne_MatB], double Res[Ligne_MatA][Colonne_MatA])
{
for (int i = 0; i < Ligne_MatA; i++)
{
for (int j = 0; j < Colonne_MatA; j++)
{
Res[i][j] = A[i][j]-B[i][j];
}
}
}

void Mul_Mat_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],int Ligne_MatB, int Colonne_MatB, double B[Ligne_MatB][Colonne_MatB], double Res[Ligne_MatA][Colonne_MatB])
{
for (int i = 0; i < Ligne_MatA; i++)
{
for (int j = 0; j < Colonne_MatB; j++)
{
Res[i][j]=0;
for(int k=0; k < Ligne_MatB; k++)
{
Res[i][j] += A[i][k]*B[k][j];
}
}
}
}

void Inverse_Mat_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],double Res[Ligne_MatA][Colonne_MatA])
//OBLIGATOIREMENT POUR DES MATRICES DE TAILLES 2x2
{
double unSurDet;
unSurDet = 1/(A[0][0]*A[1][1]-A[0][1]*A[1][0]);
Res[0][0] = A[1][1]*unSurDet;
Res[0][1] = -unSurDet*A[0][1];
Res[1][0] = -unSurDet*A[1][0];
Res[1][1] = A[0][0]*unSurDet;
}

void Transpose_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],double Res[Colonne_MatA][Ligne_MatA])
{
int i,j;
for (i=0;i<Colonne_MatA;i++)
{
for (j=0;j<Ligne_MatA;j++)
{
Res[i][j]=A[j][i];
}
}
}
1 jalaffon
428 rademagalh
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_Mat(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");
1 jalaffon
}

428 rademagalh
int main(int argc,char **argv){
1 jalaffon
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 x,y;
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 F[4][4] = {{1, 0, dt, 0},
{0, 1, 0, dt},
{0, 0, 1, 0},
{0, 0, 0, 1}};

while(fscanf(fichier, "%lf %lf %lf", &t, &x, &y)>0){
printf("-------------%04d--------------\n",cpt);

if (cpt ==0)
{
t0=t;x0=x;y0=y;
x=x-x0;y=y-y0;
Plot_Mat(F,"F = ");
Plot_Mat(H,"H = ");
Plot_Mat(R,"R = ");
}
else
{
t -= t0;x -= x0;y -= y0;

428 rademagalh
debug=1; ///Mettre à 1 pour afficher les matrices.
1 jalaffon
///Ajouter votre code ci-dessous///
455 rademagalh
// Kalmans

Plot_Mat(X,"X(k|k) = ");
428 rademagalh
// X = F*X
457 rademagalh
Mul_Mat_Mat(4,4,F,4,1,X,X);
Plot_Mat(X," X(k+1|k) = ");
428 rademagalh
457 rademagalh
/*-------------------------------*/
455 rademagalh
Plot_Mat(P,"P(k|k) = ");
428 rademagalh
//P = F*P*F'+Q;
457 rademagalh
// Pk = A*F' + Q = B+Q
428 rademagalh
double A[4][4];
double B[4][4];
Mul_Mat_Mat(4,4,F,4,4,P,A);
457 rademagalh
double FT[4][4];
Transpose_Mat(4,4,F,FT);
Mul_Mat_Mat(4,4,A,4,4,FT,B);
Add_Mat_Mat(4,4,B,4,4,Q,P);
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
455 rademagalh
457 rademagalh
/*-------------------------------*/
428 rademagalh
// K = P*H' / ( H*P*H' + R);
457 rademagalh
// P*H' = C
double HT[4][2];
Transpose_Mat(2,4,H,HT);
double C[4][2];
Mul_Mat_Mat(4,4,P,4,2,HT,C);
455 rademagalh
Plot_Mat(C,"P(k+1|k).HT = ");
428 rademagalh
457 rademagalh
// H*P*H' + R
// H*C + R = E + R = E_add
428 rademagalh
double E[2][2];
457 rademagalh
Mul_Mat_Mat(2,4,H,4,2,C,E);
double E_add[2][2];
Add_Mat_Mat(2,2,E,2,2,R,E_add);
Plot_Mat(E_add,"H.P(k+1|k).HT + R = ");
455 rademagalh
457 rademagalh
// INV(H*P*H' + R)
428 rademagalh
double E_inv[2][2];
457 rademagalh
Inverse_Mat_Mat(2,2,E_add,E_inv);
455 rademagalh
Plot_Mat(E_inv,"INV(H.P(k+1|k).HT + R) = ");
428 rademagalh
457 rademagalh
Mul_Mat_Mat(4,2,C,2,2,E_inv,K);
428 rademagalh
Plot_Mat(K,"K = ");

457 rademagalh
/*-------------------------------*/
double OBS[2][1]={{x},{y}};
Plot_Mat(OBS,"Obs = ");
428 rademagalh
// DELTA = obs - H*X
457 rademagalh
// H*X = G;
double G[2][1];
Mul_Mat_Mat(2,4,H,4,1,X,G);
428 rademagalh
double DELTA[2][1];
457 rademagalh
Sub_Mat_Mat(2,1,OBS,2,1,G,DELTA);
428 rademagalh
Plot_Mat(DELTA,"DELTA = Obs - H.X(k+1|k)");

457 rademagalh
/*-------------------------------*/
// X = X + K*DELTA
// X = X + Z
455 rademagalh
457 rademagalh
double Z[4][1];
Mul_Mat_Mat(4,2,K,2,1,DELTA,Z);
Add_Mat_Mat(4,1,X,4,1,Z,X);
Plot_Mat(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");

/*-------------------------------*/
428 rademagalh
// P = P - K*H*P;
457 rademagalh
// P = P - W*P = P - V
455 rademagalh
double W[4][4];
Mul_Mat_Mat(4,2,K,2,4,H,W);
457 rademagalh
double V[4][4];
Mul_Mat_Mat(4,4,W,4,4,P,V);
455 rademagalh
double Pkk[4][4];
457 rademagalh
Sub_Mat_Mat(4,4,P,4,4,V,P);
Plot_Mat(P," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
1 jalaffon
/// La matrice X doit contenir la position filtrée ///
}
t = cpt * dt;
dx = (x - oldx)/dt;
dy = (y - oldy)/dt;
fprintf(Fout,"%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\n",t,x,y,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 = x;
oldy = y;
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 'vitesse_reelle.dat' u 2 w l, 'output.dat' u 9 w l\";");
return 0;
}