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A Kalman-Filter could be applied to sensor-readings in order to smooth them. The Kalman-Filter, however, assumes Gaussian distributed sensor-noise with zero-mean.

Now, I found that my sensor-noise is non-Gaussian distributed. Is is still valid to apply the Kalman-Filter? I was considering to fit a Gaussian to my sensor-noise and assume this fit as the sensor-noise the Kalman filter assumes.

Does anyone know a good reference about this problem?

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  • $\begingroup$ How much different is the distribution, namely a Kalman filter is optimal for a given zero mean Gaussian white noise? For other distributions it might still give a good estimate, but it might just be not the best estimate given the knowledge about the distribution. $\endgroup$
    – fibonatic
    May 7, 2019 at 1:40
  • $\begingroup$ hmm... the PDF doesn't look too different from a Gaussian. But it clearly is not Gaussian. The biggest problem that I see is, that even when I fit a Gaussian to this data, its mean is not zero. The mean is 0.2 ... how is this influencing my Kalman Filter equations? $\endgroup$
    – user503842
    May 7, 2019 at 9:06
  • $\begingroup$ if it is not zero mean you can model this with an exogenous system, maybe other parts of its distribution can be captured this way as well. What does the autocorrelation of the noise look like? It should be close to zero everywhere except at zero, otherwise you can still model it. $\endgroup$
    – fibonatic
    May 7, 2019 at 9:15
  • $\begingroup$ @fibonatic: I just figured out my data follows a bimodal distribution with mean1=0.037 and mean2=1.25 . I don't know about the autocorrelation. $\endgroup$
    – user503842
    May 13, 2019 at 11:11

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