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Kalman Filter Tunning

I am trying to figure out a problem with Kalman Filter in Matlab. I have two time series as input y(t) and x(t). I want to regress these data and get B (beta) with Kalman Filter in the following form:

y(t) = B*x(t) + e

- y(t) is my observable vector

- B is my hidden variable that the variable that I want to obtain

I have been applying Kalman Filter in Matlab to solver my problem and I stuck because I do not which value of the covariance matrix I should use. I got a book with a recommendations values but the problems has not been solver yet.

The book suggests Montana formula to initialize the covariance matrix but I do not really like the results. Surfing on the internet, I found a good Matlab toolbox that helps to solve my problem and I do not how to use it. The web site is:

[url removed, login to view]

If anyone wants to give me a hand is my project, please contact me.

The code I wrote in Matlab is:

x=[x ones(size(x))];

delta=0.0001; % delta=1 gives fastest change in beta, delta=0.000....1 allows no change (like traditional linear regression).

yhat=NaN(size(y)); % measurement prediction

e=NaN(size(y)); % measurement prediction error

Q=NaN(size(y)); % measurement prediction error variance

% initialize R, P and beta.

R=zeros(2);

P=zeros(2);

beta=NaN(2, size(x, 1));

Vw=delta/(1-delta)*eye(2);

Ve=0.001;

% Initialize beta(:, 1) to zero

beta(:, 1)=0;

% Given initial beta and R (and P)

for t=1:length(y)

if (t > 1)

beta(:, t)=beta(:, t-1); % state prediction.

R=P+Vw; % state covariance prediction.

end

yhat(t)=x(t, :)*beta(:, t); % measurement prediction.

Q(t)=x(t, :)*R*x(t, :)'+Ve; % measurement variance prediction.

% Observe y(t)

e(t)=y(t)-yhat(t); % measurement prediction error

K=R*x(t, :)'/Q(t); % Kalman gain

beta(:, t)=beta(:, t)+K*e(t); % State update.

P=R-K*x(t, :)*R; % State covariance update.

end

After that I'd like to graph e (error) and see a stationary series with too much volatility. Now, I graph e and get a stationary low volatile series. I think the results depend of the value of delta and Ve.

If you want more references, please go to the following websites:

[url removed, login to view]

[url removed, login to view]

Compétences : Algorithme, Electronique, Mathématiques, Matlab and Mathematica, Statistiques

Voir plus : which graph to use for data, vector of ones, solve graph problems, problem graph, how to graph data, how do you graph data, graph problem, delta com, filter kalman excel, bierman filter kalman, filter kalman, filter kalman tracking, filter kalman object tracking, filter design matlabdesign linear phase fir lpf, matlab linear filter, matlab linear phase filter, linear phase filter matlab

Concernant l'employeur :
( 3 commentaires ) Quito, Ecuador

N° du projet : #8473051

Décerné à :

JinDongZhe

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