A Robust Continuous Time Fixed Lag Smoother for Nonlinear Uncertain Systems

TL;DR

This paper introduces a robust fixed lag smoother for nonlinear uncertain systems that improves estimation accuracy by combining nonlinear robust estimation with a stable smoothing approach, demonstrated on quantum optical phase estimation.

Contribution

It proposes a unified scheme integrating nonlinear robust estimation with fixed lag smoothing using Integral Quadratic Constraints and minimax LQG control, enhancing estimation error covariance.

Findings

Significant reduction in estimation error covariance.

Effective handling of nonlinear uncertainties.

Validated on quantum optical phase estimation.

Abstract

This paper presents a robust fixed lag smoother for a class of nonlinear uncertain systems. A unified scheme, which combines a nonlinear robust estimator with a stable fixed lag smoother, is presented to improve the error covariance of the estimation. The robust fixed lag smoother is based on the use of Integral Quadratic Constraints and minimax LQG control. The state estimator uses a copy of the system nonlinearity in the estimator and combines an approximate model of the delayed states to produce a smoothed signal. In order to see the effectiveness of the method, it is applied to a quantum optical phase estimation problem. Results show significant improvement in the error covariance of the estimator using fixed lag smoother in the presence of nonlinear uncertainty.