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I'm interested in computing of cross-covariance between state vectors at two different times; Cov{xk,xk-m}. For example considering xk & Pk, the state vector and covariance matrix at time step of k, and xk-m & Pk-m the state vector at time step of k-m, I want to express Cov{xk,xk-m} w.r.t Pk. I appreciate any help.

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I think this question would be better on math.stackexchange.com or dsp.stackexchange.com (where I found help with a Kalman filter question).

I don't have the time to do this calculation, but in principal I think it should be possible. However, the answer will depend on more than just the xi and the Pi, because there will be dependencies on all the other Kalman inputs (in particular the measurements and their covariances etc). If I was going to do the calculation, I would start with the simplest m=1 case, and generalise from there.

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