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Title: Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodal, 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, multimodal, uncertainty, and constraint, and beyond. Frontiers of Information Technology & Electronic Engineering, In Press.
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 exact analytical estimates based on 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 general time series filter design. Due to challenges arising from nonlinearity, multimode (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), and so on, new theories, algorithms and technologies are continuously being developed in order to maintain, or approximate to be more precise, such a conjugacy. They have in a large part contributed to the prospective developments of time series parametric filters in the last six decades. This paper reviews the stateof-the-art in distinctive categories and highlights some insights which may otherwise be overlooked. In particular, specific attention is paid to nonlinear systems with very informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, intractable unknown inputs and constraints, to fill the voids in existing reviews/surveys. To go beyond a pure review, we also provide some new thoughts on Markov-free state process modeling and filter evaluation regarding computing speed.
Description: This paper is closed access until 12 months after publication.
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
URI: https://dspace.lboro.ac.uk/2134/25484
Publisher Link: http://www.springer.com/computer/journal/11714
ISSN: 2095-9184
Appears in Collections:Closed Access (Aeronautical and Automotive Engineering)

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