2025/02/19 by Itai Gurvich, Banerjee, Imon, Gurvich, Itai · 1 citation
Computer Science · Engineering · #FOS: Computer and information sciences #Inertial Sensor and Navigation #Information Theory (cs.IT) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.2502.14053
openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we revisit a non-linear filter for \em non-Gaussian noises that was introduced in [1]. 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 unlike most other works in filtering, 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 \em balanced regime, which is where Goggin's filter has the most value. \footnoteThis work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.