{'fraction_non_alphanumeric': 0.01818181818181818, 'fraction_numerical': 0.003463203463203463, 'mean_word_length': 5.21505376344086, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A robust continuous‐time fixed‐lag smoother for nonlinear uncertain systems

This paper presents a scheme for the design of a robust fixed‐lag smoother for a class of nonlinear uncertain systems. The proposed approach combines a nonlinear robust estimator with a stable fixed‐lag smoother, to improve the estimation error covariance. The robust fixed‐lag smoother is based on the use of integral quadratic constraints and minimax linear quadratic regulator estimation and control theory. 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 smoother signal. Also in this work, a characterization of the delay approximation error is presented, and the corresponding integral quadratic constraint is included in the design, which gives a guaranteed bound on the performance cost function. In order to see the effectiveness of the method, it is applied to a quantum optical phase estimation problem. Results show a significant improvement in the error covariance of the estimator when compared with a robust nonlinear filter. Copyright © 2015 John Wiley & Sons, Ltd.