CS06: Control and Estimation in Stochastic Systems

Organizer: Alessandro Arlotto (Duke University)

Goggin’s corrected Kalman Filter: Guarantees and Filtering Regimes

Itai Gurvich

In this paper we revisit a non-linear filter for non-Gaussian noises that was introduced by Goggin in 1992. Goggin proved that transforming the observations by the score function and then applying the Kalman Filter (KF) to the transformed observations results in an asymptotically optimal filter. In the current paper, we study the convergence rate of Goggin’s filter in a pre-limit setting that allows us to study a range of signal-to-noise regimes which includes, as a special case, Goggin’s setting. Our guarantees are explicit in the level of observation noise, and importantly, we do not assume Gaussianity of the noises.

Our proofs build on combining simple tools from two separate literature streams. One is a general posterior Cramér-Rao lower bound for filtering. The other is convergence-rate bounds in the Fisher information central limit theorem.

Along the way, we also study filtering regimes for linear state-space models, characterizing clearly degenerate regimes—where trivial filters are nearly optimal—and a balanced regime, which is where Goggin’s filter has the most value.