Index: branch/aseck/sp4a3/sp4a3_kalman.c
===================================================================
--- branch/aseck/sp4a3/sp4a3_kalman.c	(revision 279)
+++ branch/aseck/sp4a3/sp4a3_kalman.c	(revision 280)
@@ -7,12 +7,22 @@
 #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]){
-
+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=0;
+    if(na==nb && ma==mb)
+       for(i=0;i<=na-1;i++)
+        for(j=0;j<=ma-1;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]){
-
+void Inverse_Mat_22(int n,int m,double A[n][m],double B[n][m]){
+     float Idet;
+    Idet=1/((A[0][0]*A[1][1])-(A[0][1]*A[1][0]));
+
+            B[0][0]=Idet*A[1][1];
+            B[1][1]=Idet*A[0][0];
+            B[0][1]=-Idet*(A[0][1]);
+            B[1][0]=-Idet*(A[1][0]);
 }
 
 void Transpose_Mat(int n,int m,double A[n][m],double R[m][n]){
@@ -22,16 +32,33 @@
 			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]){
-
+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=0;
+    if(na==nb && ma==mb)
+    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]){
+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=0;
+    int j=0;
+    int k=0;
+    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}};
@@ -66,7 +93,7 @@
 	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}};
-
+Plot_Mat(DELTA,"DELTA = Obs - H.X(k+1|k) ");
 	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");
@@ -159,17 +186,59 @@
 			// Kalman
 
 			// X = F*X
-			Plot_Mat(X," X(k+1|k) = ");
+			Plot_Mat(X," X(k+1|k) = ");
+                Mul_Mat_Mat(4,4,F,4,1,Xp,X);  // Xp=F*X
+                Plot_Mat(X," X(k+1|k) = ");
+                Plot_Mat(P,"P(k|k) = ");
+
+                double A[4][4];
+                double A1[4][4];
+                Mul_Mat_Mat(4,4,F,4,4,P,A);    // F*P = A
+                Mul_Mat_Mat(4,4,A,4,4,FT,A1);  // F*P*FT=A1
+                Add_Mat_Mat(4,4,A1,4,4,Q,P);   //P = F*P*FT+Q;
 
 			//P = F*P*F'+Q;
-			Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
+			Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
+                double B[2][4];
+                double INVERS[2][2];
+                double B1[2][2];
+                double B2[2][2];
+                Mul_Mat_Mat(2,4,H,4,4,P,B);  // HP=B
+                Mul_Mat_Mat(2,4,B,4,2,HT,B1);  // H*P*HT = B1
+                Add_Mat_Mat(2,2,B1,2,2,R,B2);  // H*P*HT + R = B2
+                Plot_Mat(B2,"H.P(k+1|k).HT+R  = ");
+                Inverse_Mat_22(2,2,B2,INVERS);  // 1/(H*P*HT + R) = B2
+                Plot_Mat(INVERS,"INV(H.P(k+1|k).HT+R)  = ");
+
+                double D[4][2];
+                Mul_Mat_Mat(4,4,P,4,2,HT,D);
+                Mul_Mat_Mat(4,2,D,2,2,INVERS,K);  // P*HT/(H*P*HT + R) = K
 
+
 			// K = P*H' / ( H*P*H' + R);
-			Plot_Mat(K,"K = ");
+			Plot_Mat(K,"K = ");
+                double DELTA1[2][1];
+                double DELTA[2][1];
+                double W[2][1];
+                double F[4][1];
+
+                Mul_Mat_Mat(2,4,H,4,1,X,W);
+                Sub_Mat_Mat(2,1,obs,2,1,W,DELTA1);
+                Mul_Mat_Mat(4,2,K,2,1,DELTA1,F);
+
+                X=X + K*([xobs(i);yobs(i)]-H*X);
+                X=X + K*DELTA
+
+                Sub_Mat_Mat(2,1,obs,2,1,W,DELTA);
+                Plot Mat(obs,"obs=")
+                Plot_Mat(DELTA,"DELTA = Obs - H.X(k+1|k) ");
 
 			//X = X + K*([xb(i);yb(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(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
+
+                double G1[4][4];
+                double G[4][4];
 
 			// P = P - K*H*P;
             Plot_Mat(P," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
