function [scorrected spredict K minPredictMSE minMSE] = KalmanFilter (s, x, a, varu, varn, ms, vars)

N = length(x);
spredictInit = ms;
minMSEInit = vars;
for k=1:N
    % PREDICTION
    if k>1
        spredict(k) = a*scorrected(k-1);
    else
        spredict(k) = a*spredictInit;
    end;
    
    % Min Prediction MSE
    if k>1
        minPredictMSE(k) = (a^2)*minMSE(k-1) + varu;
    else
        minPredictMSE(k) = (a^2)*minMSEInit + varu;
    end;
    
    % Kalman Gain
    K(k) = minPredictMSE(k)/(minPredictMSE(k)+varn(k));
    
    % Correction
    scorrected(k) = spredict(k) + K(k)*(x(k)-spredict(k));
    
    % Min MSE
    minMSE(k) = (1-K(k))*minPredictMSE(k);
    
    clf;
    subplot(3,1,1); 
    plot(s(1:k),'.-');hold on;
    plot(x(1:k),'c.-');
    plot(spredict(1:k),'k.-');plot(scorrected(1:k),'ro-');
    legend('true signal','observed','predicted','corrected');
    subplot(3,1,2); plot(K(1:k),'.-');legend('K[n]');
    subplot(3,1,3); plot(minPredictMSE,'.-');hold on;
    plot(minMSE,'r.-');legend('Prediction MSE','MSE');
    pause(0.2);
end;