Kalman Filter to track sine wave

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Hi everyone,

currently I'm measuring the skin temperature to track it over time and get more information about the circadian rhythm, which follows a sine function and can be seen in the following plot for a 48h-period:

To get more reliable data I applied an Extended Kalman Filter (EKF) with following parameters:

    % Dynamic state transition matrix in continous-time domain.
    F = [0 1 0 0;
         0 0 0 0;
         0 0 0 0;
         0 0 0 0];

    % Noise effect matrix in continous-time domain.
    L = [0 0 0;
         1 0 0;
         0 1 0;
         0 0 1];

    % Spectral power density of the white noise.
    q1 = 0.2;
    q2 = 0.1;
    q3 = 0.2;
    Qc = diag([q1 q2 q3]);

where my state vector contains the sine curve's argument, it's angular velocity, amplitude and I also tried to tie in it's offset. In this case, the measurement model is

    Y = a.*sin(f) + m;
    % The Jacobian of the measure model
    dY = [(a.*cos(f))' 0 (sin(f))' 1];

and here's a plot of the estimated parameters:

I am using the Matlab toolbox EKF/UKF (see <http://becs.aalto.fi>) to process the model.

For me, only the offset (m; like Mesor) looks correctly estimated. Does anybody can say whether my model is wrong or whats my mistake? Thanks in advance!

Filip

In addition to this: without the fourth state the offset would be modeled as Gaussian white noise with zero mean. Therefore, to model the offset I added it as the fourth state variable. Is this approach right?