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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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{
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int i,j;
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double AddM;
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if(na==nb && ma==mb) //Si le nombre de lignes de A=B et si les colonnes de A=B
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{
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for(i=0;i<na;i++)
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{
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for(j=0;j<mb;j++)
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{
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AddM=A[i][j] + B[i][j]; //On somme les élements qui se trouvent dans les mêmes positions
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R[i][j]=AddM;
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}
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}
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}
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else
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{
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printf("Les deux matrices nont pas la meme taille\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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{
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double Det;
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Det=(A[0][0]*A[1][1])-(A[0][1]*A[1][0]);//Calcul du déterminant: Det(A={(a,b);(c,d)}=(ad-cb)
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//(A)^(-1)=(1/det(A))*{(d,-b),(-c,a)}
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R[0][0]=(1/Det)*A[1][1];//La matrice résultat a le même nombre de ligne que la matrice A
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R[0][1]=-(1/Det)*A[0][1];
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R[1][0]=-(1/Det)*A[1][0];
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R[1][1]=(1/Det)*A[0][0];
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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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{
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int i,j;
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for (i=0;i<n;i++)
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{
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for (j=0;j<m;j++)
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{
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R[j][i]=A[i][j];//Les lignes deviennent les colonnes et les colonnes devinnent les lignes
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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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{
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int i,j;
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double SubM;
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if(na==nb && ma==mb)// Même condition que l'adiction
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{
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for(i=0;i<na;i++)
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{
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for(j=0;j<mb;j++)
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{
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SubM=A[i][j] - B[i][j];//On soustrait les élements qui se trouvent dans les mêmes positions
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R[i][j]=SubM;
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}
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}
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}
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else
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{
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printf("Les deux matrices nont pas la meme taille\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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{
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int i,j,k;
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if(ma==nb)//Si le nombre de colonnes de la matrice A égale au nombre de ligne de la matrice B
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{
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for (i = 0; i < na; i++)//La matrice résultat a le même nombre de ligne que la matrice A
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{
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for (j = 0; j < mb; j++)//La matrice résultat a le même nombre de colonne que la matrice B
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{
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R[i][j] = 0;
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for (k = 0; k < ma; k++)
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{
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R[i][j] += A[i][k] * B[k][j];//On somme les résultats de la multiplication des élements de chaque ligne de A par celles de chaque colonne de B
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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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{
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printf("Les colonnes de A et les lignes de B ne sont pas les memes\n");
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}
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}
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void tests_unitaires(void)
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{
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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 Transposition 2x4");
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Transpose_Mat(4,4,T44a,R44); if (!Equal_Mat_Mat(RTT44,R44)) error("Erreur calcul Transposition 4x4");
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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 Addition 2x2");
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Add_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RAT44,R44)) error("Erreur calcul Addition 4x4");
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Add_Mat_Mat(4,1,T41a,4,1,T41b,R41); if (!Equal_Mat_Mat(RAT41,R41)) error("Erreur calcul Addition 4x1");
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Sub_Mat_Mat(2,1,T21a,2,1,T21b,R21); if (!Equal_Mat_Mat(RST21,R21)) error("Erreur calcul Soustraction 2x1");
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Sub_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RST44,R44)) error("Erreur calcul Soustraction 4x4");
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Mul_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RMT44T44,R44)) error("Erreur calcul Multiplication 4x4 4x4");
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Mul_Mat_Mat(4,4,T44a,4,1,T41a,R41); if (!Equal_Mat_Mat(RMT44T41,R41)) error("Erreur calcul Multiplication 4x4 4x1");
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Mul_Mat_Mat(4,4,T44a,4,2,T42a,R42); if (!Equal_Mat_Mat(RMT44T42,R42)) error("Erreur calcul Multiplication 4x4 4x2");
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Mul_Mat_Mat(4,2,T42a,2,1,T21a,R41); if (!Equal_Mat_Mat(RMT42T21,R41)) error("Erreur calcul Multiplication 4x2 2x1");
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Mul_Mat_Mat(4,2,T42a,2,2,T22a,R42); if (!Equal_Mat_Mat(RMT42T22,R42)) error("Erreur calcul Multiplication 4x2 2x2");
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Mul_Mat_Mat(4,2,T42a,2,4,T24,R44); if (!Equal_Mat_Mat(RMT42T24,R44)) error("Erreur calcul Multiplication 4x2 2x4");
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Mul_Mat_Mat(2,4,T24,4,1,T41a,R21); if (!Equal_Mat_Mat(RMT24T41,R21)) error("Erreur calcul Multiplication 2x4 4x1");
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Mul_Mat_Mat(2,4,T24,4,2,T42a,R22); if (!Equal_Mat_Mat(RMT24T42,R22)) error("Erreur calcul Multiplication 2x4 4x2");
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Mul_Mat_Mat(2,4,T24,4,4,T44a,R24); if (!Equal_Mat_Mat(RMT24T44,R24)) error("Erreur calcul Multiplication 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 X_1[4][1],X_2[2][1],X_3[2][1],X_4[4][1],X_5[4][1];
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double P_1[4][4],P_2[4][4],P_3[4][4],P_4[4][4],P_5[4][4],P_6[4][4];
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double K_1[4][2],K_2[2][2],K_3[2][2],K_4[2][2],K_5[4][2],K_6[4][2];
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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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{
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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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{
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t -= t0;xobs -= x0;yobs -= y0;
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debug=1; ///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 Mobservation[2][1] ={{xobs},{yobs}};
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// X = F*X
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Mul_Mat_Mat(4,4,F, 4,1,X, X_1); //Multiplication de F et X, résultat stocké dans X_1
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Plot_Mat(X_1," 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,P_1);//P_1=F*P
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Mul_Mat_Mat(4,4,P_1, 4,4, FT,P_2);//P_2=P_1*FT=
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Add_Mat_Mat(4,4,P_2,4,4,Q, P_3);//P_3=P_2+Q
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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);
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Mul_Mat_Mat(2,4,H, 4,4, P_3,K_1);//K_1=H*P_3
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Mul_Mat_Mat(2,4,K_1, 4,2, HT,K_2);//K_2=K1*HT
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Add_Mat_Mat(2,2,K_2,2,2,R, K_3);//K_3=K_2+R
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Inverse_Mat_22(2,2,K_3,K_4);//K_4=(K_3)^(-1)
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Mul_Mat_Mat(4,4,P_3, 4,2, HT,K_5);//K_5=P_3*HT
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Mul_Mat_Mat(4,2,K_5, 2,2, K_4,K_6);//K_6=K_5*K_4
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Plot_Mat(K,"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, X_1,X_2);//X_2=H*X_1
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Sub_Mat_Mat(2,1,Mobservation,2,1,X_2,X_3);//X_3=Mobservation-X_2
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//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
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Plot_Mat(X_3,"DELTA = Obs - H.X(k+1|k)");
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Mul_Mat_Mat(4,2,K_6, 2,1,X_3,X_4);//X_4=K_6*X_3
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Add_Mat_Mat(4,1,X_1,4,1,X_4,X_5);//X_5=X_1+X_4
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Plot_Mat(X_5," 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,K_6, 2,4, H,P_4);//P_4=K_6*H
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Mul_Mat_Mat(4,4,P_4, 4,4, P_3,P_5);//P_5=P_4*P_3
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Sub_Mat_Mat(4,4,P_3,4,4,P_5, P_6);//P_6=P_3-P_5
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Plot_Mat(P_6," 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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int i, j;
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for ( i = 0; i <4 ; i++)
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{
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for ( j = 0; j <1 ; j++)
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{
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X[i][j] = X_5[i][j];
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}
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}
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for ( i = 0; i <4 ; i++)
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{
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for ( j = 0; j <4 ; j++)
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{
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P[i][j] = P_6[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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