Minimal regret state estimation of time-varying systems

TL;DR

This paper introduces a convex optimization-based minimal regret observer for time-varying systems, outperforming traditional Kalman and H-infinity filters by adapting to noise patterns.

Contribution

It reformulates the regret minimization problem into a convex semi-definite program using a novel system level synthesis approach for time-varying systems.

Findings

Observer significantly outperforms H-2 and H-infinity filters in experiments.

Convex formulation makes minimal regret observer practically implementable.

New parametrization handles both disturbance and measurement noise effectively.

Abstract

Kalman and H-infinity filters, the most popular paradigms for linear state estimation, are designed for very specific specific noise and disturbance patterns, which may not appear in practice. State observers based on the minimization of regret measures are a promising alternative, as they aim to adapt to recognizable patterns in the estimation error. In this paper, we show that the regret minimization problem for finite horizon estimation can be cast into a simple convex optimization problem. For this purpose, we first rewrite linear time-varying system dynamics using a novel system level synthesis parametrization for state estimation, capable of handling both disturbance and measurement noise. We then provide a tractable formulation for the minimization of regret based on semi-definite programming. Both contributions make the minimal regret observer design easily implementable in practice. Finally, numerical experiments show that the computed observer can significantly outperform both H-2 and H-infinity filters.