How to determine covariance matrices $\mathbf P$, $\mathbf Q$, and $\mathbf R$ in Extended Kalman Filter

Question

I am implementing an Extended Kalman-Filter and an Unscented Kalman-Filter for state and parameter estimation of a conveyer belt system. The problem is that I don't really know how to determine the process-covariance $\mathbf Q$, the measurement-covariance $\mathbf R$ and the error-covariance $\mathbf P$. I would like to determine them before the simulation started just with two measurements given.

Do you know how I can do it or do you know of a paper or book which could explain how to do it to me ?

Answer 1

For a Kalman filter -- either extended or plain old, you compute the state covariance ($\mathbf P$) at each iteration of the filter.

Nearly always, the measurement and process noise need to be known beforehand, or -- in the case of the Extended Kalman -- computable from the state from known information about the problem.

Your task is to take the problem, turn it into a problem statement in math that includes the $\mathbf Q$ and $\mathbf R$ matrices (either as constants, or as functions of time and/or the state), and the starting value of $\mathbf P$.

Do this correctly, and subsequent values of $\mathbf P$ will be taken care of by the filter.

"Optimal State Estimation" by Dan Simon is good -- if you were in an old-time physical university library, I'd tell you to find that one in the card catalog and then browse amongst its neighbors to find the one you like best. The book title isn't a bad search term to find other books, though.