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I'm new to Kalman filters so this might be a stupid question.

I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a random walk.

However, I also want to be able to estimate the standard deviation of my observations, similar to how I'm using it to estimate the mean of a time series. I know I have to provide the filter with a constant observation covariance matrix, but I don't know if there's a way I can get an estimate of the observation's variance (so I can compute the standard deviation).

Is there a way I can extract this information from my Kalman filter? Is there a better way to estimate the standard deviation of a time series using a Kalman filter?

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  • $\begingroup$ To get a better response, you'll need to show us what your signal model looks like. Have a look at this paper, particularly equations (17) and (18) which deal with the scalar case of what you're looking for, I believe. $\endgroup$ – Peter K. Feb 5 '18 at 15:14
  • $\begingroup$ Nice paper. Definitely helpful. $\endgroup$ – Grant Bartel Feb 8 '18 at 15:41

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