A robust fixed-interval smoothing framework for nonlinear systems based on similarity measures

Yue Hu and Weidong Zhou

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: This study presents a novel robust fixed-interval smoothing framework for nonlinear systems affected by outliers and unknown noise covariance matrices (NCMs). To enhance robustness, two distinct similarity measures are developed—one for vectors and one for covariance matrices—which enable the joint estimation of system states and NCMs. A unified cost function based on these measures is formulated and optimized to derive the proposed smoother, while nonlinearities are addressed through first-order Taylor approximations. Simulation results verify that the proposed method effectively suppresses the influence of outliers, improves estimation accuracy, and maintains stability under uncertain noise statistics, providing a practical and general solution for nonlinear state estimation problems.

Keywords: Noise covariance matrices; Nonlinear systems; Outliers; Similarity measure; Fixed-interval smoother (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925015000

DOI: 10.1016/j.chaos.2025.117487

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