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I have experience with the design of FIR, IIR digital filters. I also know about the Kalman filter, but I am not skilled at using them. Consider the case of a low frequency signal from discrete samples and the signal is corrupted by high frequency noise. It seems a digital low pass filter and a Kalman filter are two ways of removing the high frequency noise. When is it best to use a digital low pass filter, and when is it best to use a Kalman filter?

* EDIT * More specifically, it seems a FIR filter with linear phase or an IIR filter with nearly linear phase might be a better estimator than a Kalman filter in some cases. This might be true when the desired signal is low frequency and the noise is limited to the upper frequencies. A Kalman filter is designed for Gaussian noise, and I described a case where a linear phase digital low pass filter would work very well.

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    $\begingroup$ In short: a Kalman filter is suitable when you have a dynamic model that you can use to predict the value of a signal in the future (e.g. the next time step). A Kalman filter fuses its stream of noisy observations with the assumed model to optimally estimate the true signal value. As an example: if you assume your measurements are of the position of a target that has constant velocity, you can watch your measurements over time to estimate what that constant velocity is. You then use that value to predict where it "should" be on each sample; this can help provide better estimates. $\endgroup$ – Jason R Aug 30 '15 at 12:59
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    $\begingroup$ 1) The Kalman filter is the optimal filter under various assumptions. You need to check whether those assumptions hold in your case. Without further detail I can't say whether your statement it seems a FIR filter with linear phase or an IIR filter with nearly linear phase might be a better estimator than a Kalman filter is true or not. 2) The generally presented version of the Kalman filter is done for Gaussian noise, but the formalism works for any noise distribution (with some caveats). 3) Use Occam's Razor: the simplest approach that works is the best. :-) $\endgroup$ – Peter K. Aug 31 '15 at 15:00

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