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This paper presents a robust fixed lag smoother for a class of nonlinearuncertain systems. A unified scheme, which combines a nonlinear robustestimator with a stable fixed lag smoother, is presented to improve the errorcovariance of the estimation. The robust fixed lag smoother is based on the useof Integral Quadratic Constraints and minimax LQG control. The state estimatoruses a copy of the system nonlinearity in the estimator and combines anapproximate model of the delayed states to produce a smoothed signal. In orderto see the effectiveness of the method, it is applied to a quantum opticalphase estimation problem. Results show significant improvement in the errorcovariance of the estimator using fixed lag smoother in the presence ofnonlinear uncertainty.

A Robust Continuous Time Fixed Lag Smoother for Nonlinear Uncertain Systems