Discussion :

[Lamnor]

Bonjour bonjour,

je tiens à solliciter votre aide encore fois ! voilà, je voudrais filtrer des données afin d'obtenir des résultats qu'on pourrait utiliser parce qu'avec ce que je travail y a trop de bruits et ce n'est pas l'idéale si on veut les interpréter

donc je vous montre vite fais. ça c'est les positions en x y z , vous voyez que le Z n'arrête pas de faire des pics en bas.

ce qui nous donne un résultat un peu médiocre :


ce que j'ai essayé de faire est simple : comparer les valeur Z(i+1) et Z(i) si Z(i+1) est grand 2 fois Z(i) alors on affecte Z(i) à Z(i+1) sinon rien et on réitère jusqu'à length(z)-1 comme ça ça sera plus linéaire, m'enfin je crois que c'est l'idée ... ^^ je vous montre le code :

Code :

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function [ DP ] = Func_delta_Pos(value_marker)
 
%Crée des variables dynamiques pour les X,Y,Z =>Position & calcul distance
for i = 1:1:10   %Avec 10 marqueurs_
    X(:,(i) )= value_marker.(['Marker' num2str(i, '%02d')]).value(:,1);
    Y(:,(i)) = value_marker.(['Marker' num2str(i, '%02d')]).value(:,2);
    Z(:,(i)) = value_marker.(['Marker' num2str(i, '%02d')]).value(:,3);
end
 
 
%%reconstruire les données (++100 --100)
limit = 100;
X=X(limit:1:length(X)-limit,:);
Y=Y(limit:1:length(Y)-limit,:);
Z=Z(limit:1:length(Z)-limit,:);    
 
 
for k=1:1:10
    for i = 2:(length(X)-1)
        delta_z(i,k)=Z(i,k)-Z(i-1,k);
        if i > 1
            if  delta_z(i,k) > 2*(delta_z(i-1,k))
                Z(i,k)=Z(i-1,k);
                Y(i,k)=Y(i-1,k);
                X(i,k)=X(i-1,k);
            end          
        end   
    end
end
 
DP.delta_z=delta_z;
DP.X=X;
DP.Y=Y;
DP.Z=Z;
end

voilà c'est ça en gros, mais en fait j'ai pas eu ce que je voulais, c'est devenu juste un peu carré ... :/ si quelqu'un me propose une amélioration ou si y a une meilleur idée ça serait magique

[phryte]

Bonjour,
Peux-tu nous donner un échantillon de z ?
Merci

[Lamnor]

Bonjour,

comment je fais pour vous envoyer l'échantillon ? apparemment je peux pas joindre des fichiers .mat et si je copie ici ça va être très très long :p (24000 donnée). Entre temps j'ai vu que les pics correspondait plus à des valeurs nuls, je les ai enlever (NaN) , ça donnait des trous ce qui est normal mais pas interprétable, donc bon je cherche encore ^^

[phryte]

Bonjour,
Tu peux n'envoyer que le début du signal.
Voilà un exemple pour éliminer les zéros et faire une prédiction avec le filtre de Kalman stationnaire d'ordre 3 simplifié :

Code :

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clear
Te = 0.01;% Période d'échantillonnage du signal
f=0.5;% Fréquence du signal
N=200;
i=1:N;
z=sin(2*pi*f*i*Te);% Signal
z(10:11)=0;z(20:25)=0;z(27:30)=0;% Mise à zéro de la mesure
K1 = 0.6; K2 = 5; K3 = 5;% Gains stationnaires de kalman
for i = 1:N
    if i==1 %Initialisation
        Z(i)=z(i);VZ=0;AZ=0;
    else
        %Prédiction
        Z(i)=Z(i-1)+VZ*Te+0.5*AZ*Te*Te;
        VZ=VZ+AZ*Te;
        AZ=0.5*AZ;
        %Innovation
        if z(i)==0 % Test mesure = 0 force la prédiction
            Er=0;
        else
            Er=z(i)-Z(i);
        end
        %Estimation 6 Filtrage
        Z(i)=Z(i)+K1*Er;
        VZ=VZ+K2*Er;
        AZ=AZ+K3*Er;
    end
end
%Tracé
figure
plot(Z,'r')
hold
plot(z,'b')
grid

[Lamnor]

Voilà un petit échantillon de Z;

[1601,03820800781 1602,15576171875 1603,76831054688 1605,50781250000 1607,07861328125 1608,92004394531 1610,43688964844 1612,08911132813 1614,66699218750 1616,42932128906 1618,32910156250 1620,24877929688 1621,31164550781 1623,26232910156 1627,03442382813 1628,49047851563 1628,70471191406 1633,47644042969 1634,01684570313 1637,86267089844 1638,27770996094 1642,30969238281 1644,58630371094 1646,64526367188 1648,91394042969 1651,32055664063 1653,86657714844 1656,21594238281 1657,16564941406 1661,17492675781 1663,71679687500 1665,90722656250 1668,06347656250 1671,95727539063 1673,96984863281 1673,24353027344 1676,62500000000 1678,66723632813 1682,12402343750 1683,99877929688 1682,95678710938 1687,71472167969 1689,53149414063 1691,10412597656 0 1693,87048339844 0 0 0 0 1699,97119140625 1701,28027343750 0 1702,95361328125 0 1705,04174804688 1705,89270019531 0 0 0 0 0 0 0 0 0 0 0 0 1716,97570800781 0 0 0 0 0 0 0 1721,04467773438 0
0 0 0 0 0 0 1729,49621582031 0 1730,65991210938 0 0 0 1735,77783203125 1736,49011230469 1738,10156250000 0 1740,01245117188 1740,66027832031 0 1742,59997558594 1743,63867187500 1744,63024902344 1745,18518066406 1746,22619628906 1747,18762207031 1748,34619140625 1749,02770996094 1749,76794433594 1750,90673828125 0 0 1753,85742187500 0 1755,72180175781 0 1757,82702636719 1758,72290039063 0 1760,78210449219 1760,85668945313 1762,58276367188 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1782,05615234375 0 0 0 0 0 0 0 0 0 0 1787,37744140625 0 0 0 ]

sinon j'ai pas bien compris comment utiliser le filtre de Kalman, j'avoue que le traitement de signal n'est pas vraiment mon domaine ..^^

[phryte]

Bonjour,
Quelle est la période d'échantillonnage ?

[Lamnor]

j'ai la fréquence d'échantillonnage qui est de 100 hertz

[phryte]

Bonjour,
Un exemple.
Si le nombre de zéros est trop important il faut réinitialiser le filtre.

Code :

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clear
z=[1601.03820800781
    1602.15576171875
    1603.76831054688
    1605.50781250000
    1607.07861328125
    1608.92004394531
    1610.43688964844
    1612.08911132813
    1614.66699218750
    1616.42932128906
    1618.32910156250
    1620.24877929688
    1621.31164550781
    1623.26232910156
    1627.03442382813
    1628.49047851563
    1628.70471191406
    1633.47644042969
    1634.01684570313
    1637.86267089844
    1638.27770996094
    1642.30969238281
    1644.58630371094
    1646.64526367188
    1648.91394042969
    1651.32055664063
    1653.86657714844
    1656.21594238281
    1657.16564941406
    1661.17492675781
    1663.71679687500
    1665.90722656250
    1668.06347656250
    1671.95727539063
    1673.96984863281
    1673.24353027344
    1676.62500000000
    1678.66723632813
    1682.12402343750
    1683.99877929688
    1682.95678710938
    1687.71472167969
    1689.53149414063
    1691.10412597656
    0
    1693.87048339844
    0
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    1699.97119140625
    1701.28027343750
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    0
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    1716.97570800781
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    1721.04467773438
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    1729.49621582031
    0
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    1747.18762207031
    1748.34619140625
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    1750.90673828125
    0
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    0
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    0
    1757.82702636719
    1758.72290039063
    0
    1760.78210449219
    1760.85668945313
    1762.58276367188
    0
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    1782.05615234375
    0
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    0
    1787.37744140625
    0
    0
    0];
 
N=length(z);
Fe=100;
Te=1/Fe;
K1 = 0.6;% Gain position < 1
K2 = 5; % Gain vitesse
K3 = 5;% Gains accélération
 
for i = 1:N
    if i==1 %Initialisation
        Z(i)=z(i);VZ=0;AZ=0;
    else
        %Prédiction
        Z(i)=Z(i-1)+VZ*Te+0.5*AZ*Te*Te;
        VZ=VZ+AZ*Te;
        AZ=0.5*AZ;
        %Innovation
        if z(i)==0 % Test mesure = 0 force la prédiction
            Er=0;
        else
            Er=z(i)-Z(i);% Mesure - Prédiction
        end
        %Estimation 6 Filtrage
        Z(i)=Z(i)+K1*Er;
        VZ=VZ+K2*Er;
        AZ=AZ+K3*Er;
    end
end
 
%Tracé
figure
plot(Z,'r') % Signal filtré
hold
plot(z,'b')
grid

[Lamnor]

j'ai utilisé le filtre de kalman pour la prédiction, ça m'a donné ça :



je vais juste l'ajouter dans une fonction et travailler avec, c'est vraiment puissant , mais y a des paramètre que je n'ai pas compris, le gain de postion, vitesse et accélération .. ça correspond à quoi exactement ?

[phryte]

Bonjour,
Le script utilisé ici est un exemple très simplifié du filtre de Kalman.
Il y a une infinité de documents ou tutos sur ce thème.
Pour avoir une idée il faut 4 paramètres :
- La période d'échantillonnage
- la constante de temps d'évolution
- la matrice de covariance du bruit de mesure R
- la matrice de covariance du bruit de process (ou de la dynamique)

Les gains K1,k2,K3 sont proportionnels à Q/R

---> Plus il y a de bruit plus ils sont faibles
---> plus il y a d'évolution plus ils sont forts (avec K1 < 1)

[Lamnor]

Merci pour ton aide, j'essaye d'y comprendre un petit peu

j'ai utilisé le filtre sur la totalité du signal et à un certain moment y a des pics, c'est dû au grand nombre de perte, je pense .. quel paramètre je dois rajuster ? j'ai essayé de faire des trucs mais ça n'a pas vraiment marché

[phryte]

Bonjour,


K1 est la confiance à la mesure (K1=1 le filtre suit le signal donc pas de filtrage. K1=0 le filtre ignore la mesure et tourne en prédiction)
K2 est le gain vitesse (dans ton cas tu peux le baisser)
K3 est le gain accélération ( tu peux le baisser, même le mettre à zéro)

Sinon mets-nous l'échantillon de ton signal.

[Lamnor]

c'est ce que j'ai essayé de faire mais sans un résultat satisfaisant,



ça génère encore des bruits dans le signal ...

voilà mon échantillon :

Code :

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Edit : en fait, après avoir mis K2 et K3 à 0, j'ai eu un bon résultat avec beaucoup moins de perte

[phryte]

Bonjour,

Ton exemple est très difficile à résoudre parfaitement.
Il faut faire du spécifique :
Normalement le filtre de Kalman est utilisé pour le temps réel car il est prédictif.
Si le signal à traiter est connu (traitement différé) il vaut mieux utiliser le lissage (moindres carrés par exemple).

Code :

Sélectionner tout - Visualiser dans une fenêtre à part

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clear
 
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N=length(z);
Fe=100;
Te=1/Fe;
K1 = 0.8;% Gain position < 1
K2 = 1; % Gain vitesse
K3 = 1;% Gains accélération
kv=1;
for i = 1:N
    if i==1 %Initialisation
        Z(i)=z(i);VZ=0;AZ=0;
    else
        %Prédiction
        Z(i)=Z(i-1)+VZ*Te+0.5*AZ*Te*Te;
        VZ=kv*VZ+AZ*Te;
        AZ=0.9*AZ;
        %Innovation
        if z(i)==0 % Test mesure = 0 force la prédiction
            Er=0;
            kv=0.98;
        else
            Er=z(i)-Z(i);% Mesure - Prédiction
            kv=1;
        end
        %Estimation 6 Filtrage
        Z(i)=Z(i)+K1*Er;
        VZ=VZ+K2*Er;
        AZ=AZ+K3*Er;
    end
end
 
%Tracé
figure
plot(Z,'r') % Signal filtré
hold
plot(z,'.b')
grid
axis([0 600 1680 1860])