Bayesian Knowledge Transfer for a Kalman Fixed-Lag Interval Smoother

TL;DR

This paper introduces a Bayesian transfer learning method for Kalman fixed-lag smoothers that effectively incorporates external information, even when the external observation model is not fully known, improving state estimation accuracy.

Contribution

It proposes a fully probabilistic Bayesian knowledge transfer mechanism with a latent variable to handle inaccurate external data in FLIS, enhancing its robustness and performance.

Findings

Better exploitation of precise external knowledge compared to similar methods.

Achieves comparable results with imprecise external information.

Reduces estimation error accumulation through retrospective refinement.

Abstract

A Bayesian knowledge transfer mechanism that leverages external information to improve the performance of the Kalman fixed-lag interval smoother (FLIS) is proposed. Exact knowledge of the external observation model is assumed to be missing, which hinders the direct application of Bayes' rule in traditional transfer learning approaches. This limitation is overcome by the fully probabilistic design, conditioning the targeted task of state estimation on external information. To mitigate the negative impact of inaccurate external data while leveraging precise information, a latent variable is introduced. Favorably, in contrast to a filter, FLIS retrospectively refines past decisions up to a fixed time horizon, reducing the accumulation of estimation error and consequently improving the performance of state inference. Simulations indicate that the proposed algorithm better exploits precise external knowledge compared to a similar technique and achieves comparable results when the information is imprecise.