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root/branch/CLAUD/sp4a3/sp4a3_kalman.c @ 683

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// Pour compiler : gcc sp4a3_kalman.c -lm

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

#include "sp4a3_kalman_extra.h"

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// Fonction qui effectue l'operation out = A + B (matrice)
void Add_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double out[na][ma])
{
int i, j;
for (i=0;i<na;i++)
{
for (j=0;j<ma;j++)
{
out[i][j] = A[i][j] + B[i][j];
}
}

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}
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// Fonction qui effectue l'operation B = A^-1
void Inverse_Mat_22(int n,int m,double A[n][m],double B[n][m])
{
double determinant = A[0][0]*A[1][1]-A[0][1]*A[1][0];
B[0][0]=A[1][1]/determinant;
B[0][1]=-A[0][1]/determinant;
B[1][0]=-A[1][0]/determinant;
B[1][1]=A[0][0]/determinant;
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}
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// Fonction qui effectue l'operation R = A^T
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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];
}
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// Fonction qui effectue l'operation out = A - B (matrice)
void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double out[na][ma])
{
int i, j;
for (i=0;i<na;i++)
{
for (j=0;j<ma;j++)
{
out[i][j] = A[i][j] - B[i][j];
}
}
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}
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// Fonction qui effectue l'operation out = A * B (matrice)
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void Mul_Mat_Mat(int na,int ma,double A[na][ma], int nb,int mb,double B[nb][mb], double out[na][mb])
{
int i, j, k;
for (i=0;i<na;i++)
{
for (j=0;j<mb;j++)
{
out[i][j] = 0;
for(k=0;k<ma;k++) // ou for(k=0;k<nb;k++)
{
out[i][j] = out[i][j] + A[i][k]*B[k][j];
}
}
}
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}
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void Copie_Mat(int na,int ma,double A[na][ma], double out[na][ma]){
int i=0, j=0;
for (i=0; i<na; i++)
for (j=0; j<ma; j++){
out[i][j]=A[i][j];
}
}
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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){

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 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 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, &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;

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debug=1; ///Mettre à 1 pour afficher les matrices.
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///Ajouter votre code ci-dessous///
// Kalman

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// X = F*X
double mat_copie[4][1];
Copie_Mat(4,1,X,mat_copie);
Mul_Mat_Mat(4,4,F,4,1,mat_copie,X);
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Plot_Mat(X," X(k+1|k) = ");

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//P = F*P*F'+Q;
double mat_inter[4][4], mat_inter_bis[4][4];
Mul_Mat_Mat(4,4,F,4,4,P,mat_inter);
Mul_Mat_Mat(4,4,mat_inter,4,4,FT,mat_inter_bis);
Add_Mat_Mat(4,4,mat_inter_bis,4,4,Q,P);
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Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");

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// K = P*H' / ( H*P*H' + R);
double mat_inter1[4][2];
Mul_Mat_Mat(4, 4, P, 4, 2, HT, mat_inter1); // P*H'
Plot_Mat(mat_inter1,"P(k+1|k).HT = ");

double mat_inter2[2][2], mat_inter3[2][2];
Mul_Mat_Mat(2, 4, H, 4, 2, mat_inter1, mat_inter2); // H*P*H'
Add_Mat_Mat(2, 2, mat_inter2, 2, 2, R, mat_inter3); // H*P*H' + R
Plot_Mat(mat_inter3, "H.P(k+1|k).HT + R = ");

double mat_inter4[2][2];
Inverse_Mat_22(2, 2, mat_inter3, mat_inter4); // inv(H*P*H' + R)
Plot_Mat(mat_inter4, "INV(H.P(k+1|k).HT + R) = ");

Mul_Mat_Mat(4, 2, mat_inter1, 2, 2, mat_inter4, K); // K = P*H' / ( H*P*H' + R)
Plot_Mat(K, "K = ");
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//X = X + K*([xb(i);yb(i)]-H*X);

double Obs[2][1]= {{x},
{y}};
double Delta[2][1], mat_inter5[2][1];
Mul_Mat_Mat(2,4,H,4,1,X,mat_inter5); // H*X
Sub_Mat_Mat(2,1,Obs,2,1,mat_inter5,Delta); // Delta = Obs - H*X
Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");

double mat_inter6[2][1];
Mul_Mat_Mat(4,2,K,2,1,Delta,mat_inter6); // K*Delta
Add_Mat_Mat(4,1,X,4,1,mat_inter6,X); // X = X + K*Delta
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Plot_Mat(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");

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// P = P - K*H*P;
double mat_inter7[4][4], mat_inter8[4][4];
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Mul_Mat_Mat(4,2,K,2,4,H,mat_inter7); // K*H
Mul_Mat_Mat(4,4,mat_inter7,4,4,P,mat_inter8); // K*H*P
Sub_Mat_Mat(4,4,P,4,4,mat_inter8,P); // P = P - K*H*P
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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 = (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;
}