Analysis of reduced-search BCJR algorithms for input estimation in a jump linear system

Linear systems with unknown finite-valued inputs are of interest in all those hybrid frameworks where switches or jumps may change the continuous dynamics of a linear system. Many models have been proposed in this sense; in most cases, a probabilistic distribution on the input is assumed to be known and used as prior information for estimation. In this paper, we propose a simple model of jump linear system and develop low complexity algorithms, based on BCJR, to retrieve the input. We consider systems over a possibly infinite time horizon, which motivates the study of on-line, causal algorithms. Our main purpose is to provide a rigorous theoretical analysis of the performance of the proposed techniques: an error function is defined and its distribution is proved to converge, exploiting mathematical tools from Markov Processes theory and ergodic theorems. HighlightsStudy of input estimation of jump linear systems.Our work combines elements arising from different fields: signal processing, information theory, probability and Markov processes theory.Our mathematical analysis, which theoretically describes the performance of the proposed algorithms, is based on non-standard mathematical tools of Markov processes theory.

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