A new smoothing algorithm for jump Markov linear systems. (June 2022)

• Record Type: Journal Article
• Authors: Balenzuela, Mark Peter; Wills, Adrian G.; Renton, Christopher; Ninness, Brett
• Is Part Of: Automatica. Volume 140(2022)
• Publication Date: 2022-06
• Subjects: Bayesian estimation -- Smoothing -- Jump Markov linear systems (JMLS) -- Switched linear dynamical systems (SLDS) -- Interacting multiple models (IMM); Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110218
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper presents a method for calculating the smoothed state distribution for Jump Markov Linear Systems. More specifically, the paper details a novel two-filter smoother that provides closed-form expressions for the smoothed hybrid state distribution. This distribution can be expressed as a Gaussian mixture with a known, but exponentially increasing, number of Gaussian components as the time index increases. This is accompanied by exponential growth in memory and computational requirements, which rapidly becomes intractable. To ameliorate this, we limit the number of allowed mixture terms by employing a Gaussian likelihood mixture reduction strategy, which results in a computationally tractable, but approximate smoothed distribution. The approximation error can be balanced against computational complexity in order to provide an accurate and practical smoothing algorithm that compares favourably to existing state-of-the-art approaches.