Révision 579
Ajouté par Romain CHAMBELLON il y a presque 3 ans
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/// On definit des matrices intermediaires pour les calculs pour eviter l'utilisation
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/// d'une meme variable matricielle en entree et en sortie de fonction d'opérations
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double Xk[4][1];
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double Xk1_k[4][1];
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double P1[4][4];
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double P2[4][4];
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double Pk[4][4];
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double Pk1_k[4][4];
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double NK1[4][2];
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double DK3[2][2];
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double DK4[2][2];
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double X1[2][1];
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double X2[4][1];
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double P3[4][4];
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double P4[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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///Ajouter votre code ci-dessous
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/// Kalman
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// X = F*X
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// Xk1_k = F*X
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Mul_Mat_Mat(4, 4, F, 4, 1, X, Xk);
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Plot_Mat(Xk," X(k+1|k) = ");
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Mul_Mat_Mat(4, 4, F, 4, 1, X, Xk1_k); // Xk1_k = F*X
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Plot_Mat(Xk1_k," X(k+1|k) = ");
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//P = F*P*F'+Q;
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//Pk1_k = F*P*F'+Q;
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Mul_Mat_Mat(4,4,F,4,4,P,P1);
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Mul_Mat_Mat(4,4,P1,4,4,FT,P2);
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Add_Mat_Mat(4,4,P2,4,4,Q,Pk);
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Plot_Mat(Pk,"P(k+1|k) = F.P(k|k).FT + Q = ");
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Mul_Mat_Mat(4,4,F,4,4,P,P1); // P1 = F*P
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Mul_Mat_Mat(4,4,P1,4,4,FT,P2); // P2 = F*P*F'
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Add_Mat_Mat(4,4,P2,4,4,Q,Pk1_k); // Pk1_k = F*P*F'+Q;
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Plot_Mat(Pk1_k,"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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// K = Pk1_k*H' / ( H*Pk1_k*H' + R);
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Mul_Mat_Mat(4,4,Pk,4,2,HT,NK1); // Calcul du numerateur de K
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Mul_Mat_Mat(4,4,Pk1_k,4,2,HT,NK1); // NK1 = Pk1_k*H'
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Mul_Mat_Mat(2,4,H,4,4,Pk,DK1); // Calcul du dénominateur de K
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Mul_Mat_Mat(2,4,DK1,4,2,HT,DK2);
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Add_Mat_Mat(2,2,DK2,2,2,R,DK3);
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Inverse_Mat_22(2,2,DK3,DK4); // Calcul de l'inverse pour faire la division
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Mul_Mat_Mat(2,4,H,4,4,Pk1_k,DK1); // DK1 = H*Pk1_k
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Mul_Mat_Mat(2,4,DK1,4,2,HT,DK2); // DK2 = H*Pk1_k*H'
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Add_Mat_Mat(2,2,DK2,2,2,R,DK3); // DK3 = H*Pk1_k*H' + R
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Inverse_Mat_22(2,2,DK3,DK4); // DK4 = 1 /(H*Pk1_k*H' + R)
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Mul_Mat_Mat(4,2,NK1,2,2,DK4,K);
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Mul_Mat_Mat(4,2,NK1,2,2,DK4,K);// K = Pk1_k*H' / ( H*Pk1_k*H' + R);
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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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//X = Xk1_k + K*([xobs(i);yobs(i)]-H*Xk1_k);
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double obs[2][1]={{xobs},{yobs}};
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double delta[2][1];
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Mul_Mat_Mat(2,4,H,4,1,Xk1_k,X1); // X1 = H*Xk1_k
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Sub_Mat_Mat(2,1,obs,2,1,X1,delta); // Delta = Obs - H*Xk1_k
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Plot_Mat(delta,"DELTA = Obs - H.X(k+1|k)");
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Mul_Mat_Mat(4,2,K,2,1,delta,X2); // X2 = K*Delta
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Add_Mat_Mat(4,1,Xk1_k,4,1,X2,X); // X = Xk1_k + K*Delta
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Plot_Mat(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
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//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
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Plot_Mat(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
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// P = P - K*H*P;
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// P = Pk1_k - K*H*Pk1_k;
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Mul_Mat_Mat(4,2,K,2,4,H,P3); // P3 = K*H
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Mul_Mat_Mat(4,4,P3,4,4,Pk1_k,P4); // P4 = K*H*Pk1_k
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Sub_Mat_Mat(4,4,Pk1_k,4,4,P4,P); // P = Pk1_k - K*H*Pk1_k
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Plot_Mat(P," 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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Formats disponibles : Unified diff
Programme final : Filtre de Kalman fonctionnel, les courbes sont bonnes
Commentaires + indentations réalisés