Index: branch/PUECH_Alexis/sp4a3/sp4a3_kalman.c
===================================================================
--- branch/PUECH_Alexis/sp4a3/sp4a3_kalman.c	(revision 458)
+++ branch/PUECH_Alexis/sp4a3/sp4a3_kalman.c	(revision 459)
@@ -2,36 +2,80 @@
 
 #include <stdlib.h>
 #include <stdio.h>
-#include <math.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 R[na][ma]){
-
+    int i,j;
+	for (i=0;i<na;i++)
+    {
+        for (j=0;j<ma;j++)
+        {
+            R[i][j]=A[i][j]+B[i][j];
+            //printf("%d  ",R[i][j]);
+        }
+        //printf("\n");
+    }
 }
 
-void Inverse_Mat_22(int n,int m,double A[n][m],double B[n][m]){
+void Inverse_Mat_22(int n,int m,double A[n][m],double R[n][m]){
 
+    double coef,det;
+    det=(A[0][0]*A[1][1])-(A[1][0]*A[0][1]);
+    coef=1/det;
+
+    R[0][0]=A[1][1]*coef;
+    R[1][0]=-A[1][0]*coef;
+    R[1][1]=A[0][0]*coef;
+    R[0][1]=-A[0][1]*coef;
+
 }
 
 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];
+	for (i=0;i<n;i++)
+    {
+        for (j=0;j<m;j++)
+        {
+            R[j][i]=A[i][j];
+            //printf("%d  ",R[j][i]);
+        }
+        //printf("\n");
+    }
 }
 
 void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double R[na][ma]){
-
+    int i,j;
+	for (i=0;i<na;i++)
+    {
+        for (j=0;j<ma;j++)
+        {
+            R[i][j]=A[i][j]-B[i][j];
+            //printf("%d  ",R[i][j]);
+        }
+        //printf("\n");
+    }
 }
 
 void Mul_Mat_Mat(int na,int ma,double A[na][ma], int nb,int mb,double B[nb][mb], double R[na][mb]){
-
+    int i,j,k;
+	for (i=0;i<na;i++)
+    {
+        for (j=0;j<mb;j++)
+        {
+            R[i][j]=0;
+            for (k=0;k<ma;k++)
+            {
+                R[i][j]+=A[i][k]*B[k][j];
+            }
+            printf("%d  ",R[i][j]);
+        }
+        printf("\n");
+    }
 }
 
-
-
 void tests_unitaires(void){
 	//Matrices d'entrée
 	double T21a[2][1]={{7},{-5}};
@@ -86,109 +130,158 @@
 	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){
+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 xobs,yobs;
+    double oldx,oldy;
+    double dx=0,dy=0,dt=0.1;
+    int cpt = 0,i,j;
+    // 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);
+
+	//variables intermediaires
+
+    double FX[4][1];
+    double FP[4][4];
+    double Ftrans[4][4];
+    double FPFtrans[4][4];
+    double FPFtransPlusQ[4][4];
+    double Htrans[4][2];
+    double PHtrans[4][2];
+    double HP[2][4];
+    double HPHtrans[2][2];
+    double HPHtransPlusR[2][2];
+    double InvHPHtransPlusR[2][2];
+    double PHtransInvHPHtransPlusR[4][2];
+    double HFX[2][1];
+    double ObsMoinsHFX[2][1];
+    double KObsMoinsHFX[4][1];
+    double FXPlusKObsMoinsHFX[4][1];
+    double KH[4][4];
+    double KHP[4][4];
+    double PMoinsKHP[4][4];
 
-	tests_unitaires();
+    while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
+        printf("-------------%04d--------------\n",cpt);
+        if (cpt ==0)
+        {
+            t0=t;x0=xobs;y0=yobs;
+            xobs=xobs-x0;yobs=yobs-y0;
+            Plot_Mat(F,"F = ");
+            Plot_Mat(H,"H = ");
+            Plot_Mat(R,"R = ");
+        }
+        else
+        {
+            int i,j;
+
+            t -= t0;xobs -= x0;yobs -= y0;
+            debug=1; ///Mettre à 1 pour afficher les matrices.
+                     ///Ajouter votre code ci-dessous///
+                    // Kalman
 
-	FILE* fichier = fopen("pos_t_x_y.dat","r");
-	if (fichier == NULL)
-        error("Impossible d'ouvrir le fichier GPGGA_data.dat");
+            double Obs[2][1]={{xobs},{yobs}};
 
-    FILE * Fout = Fout = fopen("output.dat","w");
-	if (fichier == NULL)
-        error("Impossible d'ouvrir le fichier output.dat");
+			// X = F*X
+			Mul_Mat_Mat(4,4,F,4,1,X,FX);
+			Plot_Mat(FX," X(k+1|k) = ");
 
-	printf("Kalman\n");
-	double t = 0;
-	double t0,x0,y0;
-	double xobs,yobs;
-	double oldx,oldy;
-	double dx=0,dy=0,dt=0.1;
-	int cpt = 0;
+			//P = F*P*F'+Q;
+			Mul_Mat_Mat(4,4,F,4,4,P,FP);
+			Transpose_Mat(4,4,F,Ftrans);
+			Mul_Mat_Mat(4,4,FP,4,4,Ftrans,FPFtrans);
+			Add_Mat_Mat(4,4,FPFtrans,4,4,Q,FPFtransPlusQ);
+			Plot_Mat(FPFtransPlusQ,"P(k+1|k) = F.P(k|k).FT + Q = ");
 
-	// kalman param
-	double sigma_etat = 10.0;
-	double sigma_observation = 2.0;
-	double X[4][1] = {{0},{0},{0},{0}};
+			// K = P*H' / ( H*P*H' + R);
+			Transpose_Mat(2,4,H,Htrans);
+			Mul_Mat_Mat(4,4,FPFtransPlusQ,4,2,Htrans,PHtrans);
+            Mul_Mat_Mat(2,4,H,4,4,FPFtransPlusQ,HP);
+            Mul_Mat_Mat(2,4,HP,4,2,Htrans,HPHtrans);
+            Add_Mat_Mat(2,2,HPHtrans,2,2,R,HPHtransPlusR);
+            Inverse_Mat_22(2,2,HPHtransPlusR,InvHPHtransPlusR);
+            Mul_Mat_Mat(4,2,PHtrans,2,2,InvHPHtransPlusR,PHtransInvHPHtransPlusR);
+			Plot_Mat(PHtransInvHPHtransPlusR,"K = ");
 
-	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, &xobs, &yobs)>0){
-		printf("-------------%04d--------------\n",cpt);
-
-		if (cpt ==0)
-		{
-			t0=t;x0=xobs;y0=yobs;
-			xobs=xobs-x0;yobs=yobs-y0;
-			Plot_Mat(F,"F = ");
-			Plot_Mat(H,"H = ");
-			Plot_Mat(R,"R = ");
-		}
-		else
-		{
-			t -= t0;xobs -= x0;yobs -= y0;
-
-			debug=0; ///Mettre à 1 pour afficher les matrices.
-			///Ajouter votre code ci-dessous///
-			// Kalman
-
-			// X = F*X
-			Plot_Mat(X," X(k+1|k) = ");
-
-			//P = F*P*F'+Q;
-			Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
-
-			// K = P*H' / ( H*P*H' + R);
-			Plot_Mat(K,"K = ");
-
 			//X = X + K*([xobs(i);yobs(i)]-H*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 = ");
+			//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
+			Mul_Mat_Mat(2,4,H,4,1,FX,HFX);
+			Sub_Mat_Mat(2,1,Obs,2,1,HFX,ObsMoinsHFX);
+			Mul_Mat_Mat(4,2,PHtransInvHPHtransPlusR,2,1,ObsMoinsHFX,KObsMoinsHFX);
+			Add_Mat_Mat(4,1,FX,4,1,KObsMoinsHFX,FXPlusKObsMoinsHFX);
+            Plot_Mat(FXPlusKObsMoinsHFX," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
 
-			// P = P - K*H*P;
-            Plot_Mat(P," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
+			// P = P - K*H*P;
+			Mul_Mat_Mat(4,2,PHtransInvHPHtransPlusR,2,4,H,KH);
+			Mul_Mat_Mat(4,4,KH,4,4,FPFtransPlusQ,KHP);
+			Sub_Mat_Mat(4,4,FPFtransPlusQ,4,4,KHP,PMoinsKHP);
+            Plot_Mat(PMoinsKHP," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
+
+                    /// La matrice X doit contenir la position filtrée ///
+            for(i=0;i<4;i++)
+            {
+                for(j=0;j<1;j++)
+                {
+                    X[i][j]=FXPlusKObsMoinsHFX[i][j];
+                }
+            }
+
+
+            for(i=0;i<4;i++)
+            {
+                for(j=0;j<4;j++)
+                {
+                    P[i][j]=PMoinsKHP[i][j];
+                }
+            }
 
-			/// La matrice X doit contenir la position filtrée ///
-		}
-		t = cpt * dt;
-		dx = (xobs - oldx)/dt;
-		dy = (yobs - oldy)/dt;
-		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);
-		oldx = xobs;
-		oldy = yobs;
-		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 'output.dat' u 9 w l  , 'vitesse_reelle.dat' u 2 w l\";");
-	return 0;
-}
+		 }
+         t = cpt * dt;
+         dx = (xobs - oldx)/dt;
+         dy = (yobs - oldy)/dt;
+         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);
+         oldx = xobs;
+         oldy = yobs;
+         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 'output.dat' u 9 w l  , 'vitesse_reelle.dat' u 2 w l\";");
+    return 0;
+}
