A Note on the Relation Between Balenzela's Algorithm for Two-Filter Formula for Smoothing and Information Filter

2023/06/21 by G. Kitagawa, Kitagawa, G.
Computer Science · Engineering · #62M10(Primary) #65D25(Secondary) #Blind Source Separation Techniques #Computation (stat.CO) #FOS: Computer and information sciences #Fault Detection and Control Systems #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.2306.12184

openalex publication_date 2023/06/21 · openalex created_date 2023/06/24 · openalex updated_date 2026/07/28

Abstract

Recent paper by Balenzuela et al. presented an exact algorithm for computing the posterior distribution of current and future observations given the current state, p(x_n|y_n,… ,y_N), which is required when computing fixed-interval smoother of the state by a two-filter formula. In this note, it will be shown that their algorithm is equivalent to the backward filter obtained by applying an information filter to the reverse state-space model. Although their algorithm is proposed for complex Gaussian mixture distribution models, in this note, we consider the case of simple state-space models with respect to filter computation.

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