Travaux Pratiques » Polytech Ge SP4abc 2021

static int count=0;

count++;

void test_decode_int()

// Fonction de tests unitaire

if (decode_nombre("135654321",5) != 13564)

{

printf ("Erreur Test unitaire decode_nombre.\n");

exit(-1);

}

if (decode_nombre("93241",3) != 932)

{

printf ("Erreur Test unitaire decode_nombre.\n");

exit(-1);

}

}

typedef struct

{

float latitude;

float longitude;

} Position ;

int decode_trame(char *trame, Position *p)

{

if(trame_cmp(trame, "GPGGA"))

const char *delim = ",";

int i, nb_virgule;

/*On compte deux virgule*/

for(nb_virgule= 0, i=0; nb_virgule <3; i++)

{

if(trame[i]==*delim)

++nb_virgule;

}

/*On lit la latitude*/

i=16;

p->latitude = decode_int(trame[i])*10

+decode_int(trame[i+1])

+decode_int(trame[i+2]/6)

+decode_int(trame[i+3]/60)

+decode_int(trame[i+5]/600)

+decode_int(trame[i+6]/6000)

+decode_int(trame[i+7]/60000)

+decode_int(trame[i+8]/600000);

i=26;

if(trame[26]=='S')

p->latitude = -p->latitude;

/*On lit la longitude*/

i=28;

p->longitude = decode_int(trame[i])*100+decode_int(trame[i+1])*10

+decode_int(trame[i+2])+decode_int(trame[i+3]/6)

+decode_int(trame[i+4]/60)+decode_int(trame[i+6]/600)

+decode_int(trame[i+7]/6000)+decode_int(trame[i+8]/60000)

+decode_int(trame[i+9]/600000);

if(trame[39]=='W')

p->longitude = -p->longitude;

return 1;

else

return 0;

// Appel de la fonction de tests pour decode_int()

test_decode_int();

// Appel de la fonction de tests pour decode_nombre()

test_decode_nombre();

// 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 out[na][ma])

{

if(na==nb && ma==mb)

{

int i,j;

for(i=0; i<na; i++)

for(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])

{

double det=0;

det=A[0][0]*A[1][1]-A[0][1]*A[1][0];

if(det!=0)

{

int i,j;

for(i=0; i<n; i++)

{

for(j=0; j<m; j++)

{

if(i==j)

B[i][j]=1/det*A[(i+1)%2][(j+1)%2];

else

B[i][j]=-1/det*A[i][j];

}

}

}

}

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 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)

{

int i,j;

for(i=0; i<na; i++)

for(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)

{

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++)

out[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)

{

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;

debug=1; ///Mettre à 1 pour afficher les matrices.

///Ajouter votre code ci-dessous///

// Kalman

// X = F*X

Mul_Mat_Mat(4, 4, F, 4, 1, X, X);

Plot_Mat(X," X(k+1|k) = ");

//P = F*P*F'+Q;

double FP[4][4];

double FPFT[4][4];

Mul_Mat_Mat(4, 4, F, 4, 4, P, FP);

Mul_Mat_Mat(4, 4, FP, 4, 4, FT, FPFT);

Add_Mat_Mat(4, 4, FPFT, 4, 4, Q, P);

Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");

// K = P*H' / ( H*P*H' + R);

double PHT[4][2];

double HP[2][4];

double HPHT[2][2];

double denom[2][2];

double inv_denom[2][2];

Mul_Mat_Mat(4, 4, P, 4, 2, HT, PHT);

Mul_Mat_Mat(2, 4, H, 4, 4, P, HP);

Mul_Mat_Mat(2, 4, HP, 4, 2, HT, HPHT);

Add_Mat_Mat(2, 2, HPHT, 2, 2, R, denom);

Inverse_Mat_22(2, 2, denom, inv_denom);

Mul_Mat_Mat(4, 2, PHT, 2, 2, inv_denom, K);

Plot_Mat(K,"K = ");

//X = X + K*([xb(i);yb(i)]-H*X);

double HX[2][1];

double obs[2][1];

double temp[2][1];

double Ktemp[4][1];

obs[0][0]=x;

obs[1][0]=y;

Mul_Mat_Mat(2, 4, H, 4, 1, X, HX);

Sub_Mat_Mat(2, 1, obs, 2, 1, HX, temp);

Mul_Mat_Mat(4, 2, K, 2, 1, temp, Ktemp);

Add_Mat_Mat(4, 1, X, 4, 1, Ktemp, 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;

double KH[4][4];

double KHP[4][4];

Mul_Mat_Mat(4, 2, K, 2, 4, H, KH);

Mul_Mat_Mat(4, 4, KH, 4, 4, P, KHP);

Sub_Mat_Mat(4, 4, P, 4, 4, KHP, 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 = (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;

}