Observability Informed Partial-Update Schmidt Kalman Filter

Abstract

The partial-update filter concept is a recent development that generalizes the Schmidt Kalman filter and extends the range of nonlinearities and uncertainties that a Kalman filter can tolerate. Similar to the Schmidt filter, the intention of the partial-update filter is to ameliorate the negative impact that certain states have within the filter, often due to their poor observability. In contrast with the Schmidt filter, the partial-update filter can update the problematic states at any time step. In practice, the partial-update technique can apply a full (nominal), partial, or no update (Schmidt) to states, depending on user-selected percentages (or weights) that indicate how much of the nominal Kalman update is applied. To date, the update percentages are selected via trial and error, and any change in the system configuration requires re-tuning. Furthermore, because the update percentages are fixed, the partial-update is agnostic to situations where a full update, or even a Schmidt-like filter can be more suitable. To address these drawbacks, this paper proposes two observability informed approaches for online weight selection that do not require manual tuning. The proposed techniques are targeted for systems where the states to be partially updated are only the problematic states. Numerical simulation results demonstrate that the proposed approaches produce estimates comparable to those of a manually fine-tuned fixed partial-update, and that they leverage occasions where local observability increases to produce more accurate estimates.