[Gretl-users] Re: Kalman Filter together with maximum likelihood - clarification about the Variance-Covariance things

I realized that I am a bit confused as to what happens with the various VCV matrices when Kalman Filter is used together with maximum likelihood. Assume a time-invariant state space model. What I understand is the following: The Kalman Filter will run as usual and will provide the various VCV estimates as described in Ch. 36 of the user's guide, based, in the end, on the final ML estimates to obtain the residual series (the etas and the epsilons). But at the same time, we may have asked the mle to estimate also the elements of the VCV matrices, (see eg. the ARMA estimation example Listing 36.1). This will give us another, different estimate of the VCV matrices... or will this agree with the KF estimates above, due perhaps to the fact that this is Normal mle that we necessarily assume?