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// Pour compiler : gcc sp4a3_kalman.c -lm
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#include <stdlib.h>
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#include <stdio.h>
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#include <math.h>
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#include "sp4a3_kalman_extra.h"
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void Add_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double R[na][ma]){
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int i,j;
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double l;
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if(na==nb && ma==mb){
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for (int i = 0; i < na; i++){
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for (int j = 0; j < mb; j++){
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l=A[i][j] + B[i][j];
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R[i][j] = l;
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}
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}
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}
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else{
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printf("Dimensions trop grandes\n");
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}
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}
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void Inverse_Mat_22(int n,int m,double A[n][m],double R[n][m]){
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double det=1/((A[0][0]*A[1][1])-(A[0][1]*A[1][0]));
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R[0][0]=A[1][1]*det;
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R[1][1]=A[0][0]*det;
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R[0][1]=-A[0][1]*det;
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R[1][0]=-A[1][0]*det;
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}
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void Transpose_Mat(int n,int m,double A[n][m],double R[m][n]){
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int i,j; // faire la soustraction membre a membre de
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for (i=0;i<n;i++){
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for (j=0;j<m;j++){
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R[j][i]=A[i][j];
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}
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}
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}
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void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double R[na][ma]){
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int i,j;
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if(na==nb && ma==mb){
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for (int i = 0; i < na; i++){
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for (int j = 0; j < mb; j++){
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R[i][j] = A[i][j] - B[i][j]; // faire la soustraction membre a membre de
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}
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}
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}
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else{
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printf("Dimensions trop grandes\n");
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}
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}
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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 R[na][mb]){
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int i,j,l;
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if(ma==nb){
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for (int i = 0; i < na; i++){
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for (int j = 0; j < mb; j++){
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R[i][j] = 0;
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for (int l = 0; l < ma; l++){
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R[i][j] += A[i][l] * B[l][j];
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}
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}
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}
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}
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else{
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printf("Dimensions trop grandes\n");
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}
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}
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void tests_unitaires(void){
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//Matrices d'entrée
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double T21a[2][1]={{7},{-5}};
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double T21b[2][1]={{-3},{46}};
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double T22a[2][2]={{12,78},{-5,13}};
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double T22b[2][2]={{-25,36},{7,42}};
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double T24[2][4]={{7,-71,-12,3},{41,123,-5,10}};
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double T41a[4][1]={{45},{-123},{-78},{-410}};
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double T41b[4][1]={{-10},{45},{27},{-9}};
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double T42a[4][2]={{-73,45},{10,12},{-41,-35},{8,-23}};
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double T44a[4][4]={{1,2,7,4},{6,5,7,8},{9,8,7,6},{5,4,3,2}};
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double T44b[4][4]={{12,13,14,15},{21,22,23,40},{78,45,12,3},{54,10,12,47}};
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//Matrices résultat
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double R21[2][1],R22[2][2],R24[2][4],R41[4][1],R42[4][2],R44[4][4];
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//Matrices de validation
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double RST21[2][1]={{10},{-51}};
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double RInvT22[2][2]={{0.02380952380952381,-0.1428571428571428},{0.009157509157509158,0.02197802197802198}};
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double RAT22[2][2]={{-13,114},{2,55}};
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double RTT24[4][2]={{7,41},{-71,123},{-12,-5},{3,10}};
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double RMT24T41[2][1]={{8754},{-16994}};
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double RMT24T42[2][2]={{-705,-186},{-1478,3266}};
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double RMT24T44[2][4]={{-512,-425,-523,-606},{784,697,1143,1138}};
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double RAT41[4][1]={{35},{-78},{-51},{-419}};
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double RMT42T21[4][1]={{-736},{10},{-112},{171}};
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double RMT42T22[4][2]={{-1101,-5109},{60,936},{-317,-3653},{211,325}};
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double RMT42T24[4][4]={{1334,10718,651,231},{562,766,-180,150},{-1722,-1394,667,-473},{-887,-3397,19,-206}};
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double RTT44[4][4]={{1,6,9,5},{2,5,8,4},{7,7,7,3},{4,8,6,2}};
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double RMT44T41[4][1]={{-2387},{-4171},{-3585},{-1321}};
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double RMT44T42[4][2]={{-308,-268},{-611,-99},{-816,118},{-432,122}};
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double RAT44[4][4]={{13,15,21,19},{27,27,30,48},{87,53,19,9},{59,14,15,49}};
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double RST44[4][4]={{-11,-11,-7,-11},{-15,-17,-16,-32},{-69,-37,-5,3},{-49,-6,-9,-45}};
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double RMT44T44[4][4]={{816,412,192,304},{1155,583,379,687},{1146,668,466,758},{486,308,222,338}};
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printf("Execution des tests unitaires.\n");
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Transpose_Mat(2,4,T24,R42); if (!Equal_Mat_Mat(RTT24,R42)) error("Erreur calcul Transposition2x4");
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Transpose_Mat(4,4,T44a,R44); if (!Equal_Mat_Mat(RTT44,R44)) error("Erreur calcul Transposition4x4");
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Inverse_Mat_22(2,2,T22a,R22); if (!Equal_Mat_Mat(RInvT22,R22)) error("Erreur calcul Inversion 2x2");
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Add_Mat_Mat(2,2,T22a,2,2,T22b,R22); if (!Equal_Mat_Mat(RAT22,R22)) error("Erreur calcul Addition2x2");
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Add_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RAT44,R44)) error("Erreur calcul Addition4x4");
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Add_Mat_Mat(4,1,T41a,4,1,T41b,R41); if (!Equal_Mat_Mat(RAT41,R41)) error("Erreur calcul Addition4x1");
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Sub_Mat_Mat(2,1,T21a,2,1,T21b,R21); if (!Equal_Mat_Mat(RST21,R21)) error("Erreur calculSoustraction 2x1");
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Sub_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RST44,R44)) error("Erreur calculSoustraction 4x4");
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Mul_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RMT44T44,R44)) error("Erreur calculMultiplication 4x4 4x4");
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Mul_Mat_Mat(4,4,T44a,4,1,T41a,R41); if (!Equal_Mat_Mat(RMT44T41,R41)) error("Erreur calculMultiplication 4x4 4x1");
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Mul_Mat_Mat(4,4,T44a,4,2,T42a,R42); if (!Equal_Mat_Mat(RMT44T42,R42)) error("Erreur calculMultiplication 4x4 4x2");
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Mul_Mat_Mat(4,2,T42a,2,1,T21a,R41); if (!Equal_Mat_Mat(RMT42T21,R41)) error("Erreur calculMultiplication 4x2 2x1");
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Mul_Mat_Mat(4,2,T42a,2,2,T22a,R42); if (!Equal_Mat_Mat(RMT42T22,R42)) error("Erreur calculMultiplication 4x2 2x2");
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Mul_Mat_Mat(4,2,T42a,2,4,T24,R44); if (!Equal_Mat_Mat(RMT42T24,R44)) error("Erreur calculMultiplication 4x2 2x4");
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Mul_Mat_Mat(2,4,T24,4,1,T41a,R21); if (!Equal_Mat_Mat(RMT24T41,R21)) error("Erreur calculMultiplication 2x4 4x1");
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Mul_Mat_Mat(2,4,T24,4,2,T42a,R22); if (!Equal_Mat_Mat(RMT24T42,R22)) error("Erreur calculMultiplication 2x4 4x2");
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Mul_Mat_Mat(2,4,T24,4,4,T44a,R24); if (!Equal_Mat_Mat(RMT24T44,R24)) error("Erreur calculMultiplication 2x4 4x4");
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printf("Test unitaires OK.\n");
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}
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int main(int argc,char **argv){
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tests_unitaires();
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FILE* fichier = fopen("pos_t_x_y.dat","r");
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if (fichier == NULL)
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error("Impossible d'ouvrir le fichier GPGGA_data.dat");
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FILE * Fout = Fout = fopen("output.dat","w");
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if (fichier == NULL)
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error("Impossible d'ouvrir le fichier output.dat");
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printf("Kalman\n");
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double t = 0;
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double t0,x0,y0;
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double xobs,yobs;
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double oldx,oldy;
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double dx=0,dy=0,dt=0.1;
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int cpt = 0;
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// kalman param
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double sigma_etat = 10.0;
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double sigma_observation = 2.0;
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double X[4][1] = {{0},{0},{0},{0}};
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double P[4][4] = {{sigma_etat*sigma_etat, 0, 0, 0},
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{0, sigma_etat*sigma_etat, 0, 0},
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{0, 0, 0, 0},
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{0, 0, 0, 0}};
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double Q[4][4] = {{0, 0, 0, 0},
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{0, 0, 0, 0},
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{0, 0, 0.1, 0},
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{0, 0, 0, 0.1}};
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double R[2][2] = {{sigma_observation*sigma_observation, 0},
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{0 , sigma_observation*sigma_observation}};
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double K[4][2];
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double H[2][4] = {{1, 0, 0, 0},
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{0, 1, 0, 0}};
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double HT[4][2];
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Transpose_Mat(2,4,H,HT);
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double F[4][4] = {{1, 0, dt, 0},
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{0, 1, 0, dt},
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{0, 0, 1, 0},
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{0, 0, 0, 1}};
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double FT[4][4];
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Transpose_Mat(4,4,F,FT);
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double X1[4][1];
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double P1[4][4];
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double P2[4][4];
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double P3[4][4];
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double K1[4][2];
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double K2[2][2];
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double K3[2][2];
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double K4[2][2];
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double K5[4][2];
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double K6[4][2];
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double X2[2][1];
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double X3[2][1];
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double X4[4][1];
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double X5[4][1];
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double P4[4][4];
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double P5[4][4];
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double P6[4][4];
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while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
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printf("-------------%04d--------------\n",cpt);
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if (cpt ==0){
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t0=t;x0=xobs;y0=yobs;
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xobs=xobs-x0;yobs=yobs-y0;
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Plot_Mat(F,"F = ");
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Plot_Mat(H,"H = ");
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Plot_Mat(R,"R = ");
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}
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else{
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int i,j=0;
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t -= t0;xobs -= x0;yobs -= y0;
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debug=0; ///Mettre à 1 pour afficher les matrices.
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///Ajouter votre code ci-dessous///
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// Kalman
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double Mobs[2][1] ={{xobs},{yobs}}; //{{xobs},{yobs}}
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// X = F*X
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Mul_Mat_Mat(4,4,F, 4,1,X, X1);
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Plot_Mat(X1," X(k+1|k) = ");
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//P = F*P*F'+Q;
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Mul_Mat_Mat(4,4,F, 4,4, P,P1); //P = F*P
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Mul_Mat_Mat(4,4,P1, 4,4, FT,P2); //P = F*P*F'
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Add_Mat_Mat(4,4,P2,4,4,Q, P3); //P = F*P*F'+Q;
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Plot_Mat(P3,"P(k+1|k) = F.P(k|k).FT + Q = ");
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// K = P*H' / ( H*P*H' + R);
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Mul_Mat_Mat(2,4,H, 4,4, P3,K1); // H*P
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Mul_Mat_Mat(2,4,K1, 4,2, HT,K2); // H*P*H'
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Add_Mat_Mat(2,2,K2,2,2,R, K3);
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Inverse_Mat_22(2,2,K3,K4);
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Mul_Mat_Mat(4,4,P3, 4,2, HT,K5); //P*H'
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Mul_Mat_Mat(4,2,K5, 2,2, K4,K6); // K = P*H' / ( H*P*H' + R);
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Plot_Mat(K6,"K = ");
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//X = X + K*([xobs(i);yobs(i)]-H*X);
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Mul_Mat_Mat(2,4,H, 4,1, X1,X2); //H*X
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Sub_Mat_Mat(2,1,Mobs,2,1,X2,X3) ; //[xobs(i);yobs(i)]-H*X
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Plot_Mat(X3,"DELTA = Obs - H.X(k+1|k)");
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Mul_Mat_Mat(4,2,K6, 2,1,X3,X4); //K*([xobs(i);yobs(i)]-H*X);
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Add_Mat_Mat(4,1,X1,4,1,X4,X5); //X = X + K*([xobs(i);yobs(i)]-H*X);
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Plot_Mat(X5," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
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// P = P - K*H*P;
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Mul_Mat_Mat(4,2,K6, 2,4, H,P4); //K*H
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Mul_Mat_Mat(4,4,P4, 4,4, P3,P5); //K*H*P
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Sub_Mat_Mat(4,4,P3,4,4,P5, P6); // P = P - K*H*P;
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Plot_Mat(P6," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
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/// La matrice X doit contenir la position filtrée ///
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for (int i = 0; i <4 ; i++){
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for (int j = 0; j <1 ; j++){
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X[i][j] = X5[i][j];
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}
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}
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for (int i = 0; i <4 ; i++){
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for (int j = 0; j <4 ; j++){
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P[i][j] = P6[i][j];
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}
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}
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}
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t = cpt * dt;
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dx = (xobs - oldx)/dt;
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dy = (yobs - oldy)/dt;
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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);
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oldx = xobs;
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oldy = yobs;
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cpt ++;
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}
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fclose(Fout);
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fclose(fichier);
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system ("gnuplot -p -e \"plot 'output.dat' u 5:6 w l, '' u 2:3 w l\";");
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system ("gnuplot -p -e \"plot 'output.dat' u 1:9 w l, '' u 1:4 w l\";");
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system ("gnuplot -p -e \"plot 'output.dat' u 9 w l , 'vitesse_reelle.dat' u 2 w l\";");
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return 0;
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}
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