Equalized Recovery State Estimators for Linear Systems with Delayed and Missing Observations

TL;DR

This paper introduces a novel dynamic state observer for linear systems with delayed or missing data, optimizing recovery levels for improved estimation accuracy across all data loss patterns.

Contribution

It proposes a new observer design that models data loss patterns with a reduced language and optimizes recovery levels as decision variables for better performance.

Findings

Outperforms existing estimators in illustrative examples

Achieves equalized recovery for all data loss patterns

Optimizes recovery level as a decision variable

Abstract

This paper presents a dynamic state observer design for discrete-time linear time-varying systems that robustly achieves equalized recovery despite delayed or missing observations, where the set of all temporal patterns for the missing or delayed data is modeled by a finite-length language. By introducing a mapping of the language onto a reduced event-based language, we design a state estimator that adapts based on the history of available data at each step, and satisfies equalized recovery for all patterns in the reduced language. In contrast to existing equalized recovery estimators, the proposed design considers the equalized recovery level as a decision variable, which enables us to directly obtain the global minimum for the intermediate recovery level, resulting in improved estimation performance. Finally, we demonstrate the effectiveness of the proposed observer when compared to existing approaches using several illustrative examples.