Re: About orthogonal projection theorem for Kalman filtering

From: James (wireless_at_tampabay.rr.com)
Date: 07/27/04 

Date: Tue, 27 Jul 2004 15:40:25 GMT

Beihai wrote:
> In Kalman filtering, the minimum variance estimator can be found by
> orthogonal projection of X(k) on the space spanned by linear
> combinations of observations Y(0), Y(1),...Y(k).
>
> Is this estimator unbiased? How to show, if it is?
>
> Because if I were to look at the best estimator from another way, e.g.
> a conditional expectation approach i.e. minimum variance estimator =
> E{X(k)|Y(0), Y(1),...Y(k)}, then taking expectation on both sides, I
> can show that the estimator is unbiased. What about in the orthogonal
> projection case?
>
> Please advise. Thanks!
>
> Regards

Kalman filters are usually only described in detail, in DSP
algorithms, in my experience. If you find a good, detailed reference
on Kalman filters, that is not deeply embedded in DSP mathematics and
techniques, please let me know.

I prefer Kalman Filters (implemented with algebra) but, I'm still
looking for that detailed, simplistic reference.

James

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