A Two-Stage Filter for State Estimation in the Presence of Dynamical Stochastic Bias

This paper provides the optimal solution of a two-stage estimation problem of state estimation in the presence of a dynamical stochastic bias driven by a white or colored process noise. It is shown that under an algebraic constraint on the statistics of the bias process, the optimal estimate of the system state can be obtained as a linear combination of the outputs of the "bias-free" and bias filters. Because the algebraic constraint can be too restrictive in practice, the results of this paper indirectly prove that all practical two-stage filters are suboptimal.