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The example that I've seen on state estimation involves deriving the ABCD matrix of a physical system (i.e. falling object) and tracking that object.

I would like to use Kalman Filter for signal denoising applications (specifically EEG signal). How could I apply KF in this situation since ABCD matrix cannot be derived for a signal.

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You'd probably be better off with a an adaptive filter like LMS (Least Mean Squares) or RLS (Recursive Least Squares) than Kalman for something like an EEG signal. As you've pointed out, it can be difficult or even impossible to develop the state model for Kalman for that type of signal. LMS and RLS are "learning" algorithms and better suited.

The Wikipedia article on adaptive filters

mentions the case of an ECG signal as an example application, although it doesn't go into detail.

Simon Haykin's "Adaptive Filter Theory" is a good reference on these types of filters.

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The power of the Kalman filter lies in the effect that it predicts the next "state" of the signal/object by using an internal model of the process. That why it is very effective for physical processes, because they can (often) be modelled with quite large precision.

The fact that you point out that it is impossible to derive a model for your signal renders the effect of using (and even the possibility of using) Kalman filter usesless/impossible.

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There are research papers which mentioned the used of Kalman filter in EEG signals. One of the major challenges is deriving or implementation of a model. It may be difficult but not impossible.

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    $\begingroup$ Looks like this question has been answered one year ago :D $\endgroup$ – Antoine Bassoul Jun 4 '15 at 7:01
  • $\begingroup$ Welcome to DSP.SE @dvd! Please try to answer more current questions, especially where there is NOT currently an answer with the green tick. $\endgroup$ – Peter K. Jun 5 '15 at 12:59

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