ON THE OPTIMALITY OF 2-STAGE STATE ESTIMATION IN THE PRESENCE OF RANDOM BIAS

This note provides sufficient conditions for the optimality of a two-s tage estimator for state estimation in the presence of random bias. Un der an algebraic constraint on the correlation between the state and b ias process noises, the optimal estimate of the system state can be ob tained as a linear combination of the output of the first stage (a ''b ias-free'' filter) and the second stage (a bias filter). Because the a lgebraic constraint is restrictive in practice, the results of this no te indirectly indicate that for most practical systems the proposed so lution to the two-stage estimation problem will be suboptimal.