On the optimality of two-stage state estimation in the presence of random bias

Sufficient conditions for the optimality of a two-stage state estimator in the presence of random bias are derived. Under an algebraic constraint on the correlation between the state and bias process noises, the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage (a bias-free filter) and the second stage (a bias filter). Because the algebraic constraint is restrictive in practice, the results indirectly indicate that for most practical systems the proposed solution to the two-stage estimation problem will be suboptimal