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Title: Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond
Authors: Li, Tiancheng
Su, Jinya
Liu, Wei
Corchado, Juan M.
Keywords: Kalman filter
Gaussian filter
Time series estimation
Bayesian filtering
Nonlinear filtering
Constrained filtering
Gaussian mixture
Unknown inputs
Issue Date: 2017
Publisher: © Springer & Zhejiang University Press
Citation: LI, T. ... et al, 2017. Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond. Frontiers of Information Technology & Electronic Engineering, 18 (12), pp.1913–1939.
Abstract: Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity.
Description: This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379
Sponsor: This work is in part supported by the Marie Sklodowska-Curie Individual Fellowship (H2020-MSCA-IF-2015) under Grant no. 709267 and the Open Project Program of Ministry of Education Key Laboratory of Measurement and Control of CSE under Grant MCCSE2017A01.
Version: Accepted version
DOI: 10.1631/FITEE.1700379
URI: https://dspace.lboro.ac.uk/2134/25484
Publisher Link: https://doi.org/10.1631/FITEE.1700379
ISSN: 2095-9184
Appears in Collections:Published Articles (Aeronautical and Automotive Engineering)

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