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