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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
Parametric filtering
Time series estimation
Bayesian filtering
Nonlinear filtering
Constrained filtering
Gaussian mixture
Maneuvering target
Unknown inputs
Uncertainty
Issue Date: 2017
Publisher: © Springer
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 benchmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for dynamic estimation widespread in a large variety of applications. In particular, parametric filters that seek exact analytical estimates based on closed-form MarkovBayes recursion, e.g., recursion from a Gaussian prior to a Gaussian posterior (termed Gaussian conjugacy in this paper), form the backbone for general time series filter design and have attracted considerable attention. Due to the challenges arising from nonlinearity, multimodal (including general Gaussian mixture posterior and maneuvering target dynamics), intractable uncertainties (including unknown or non-Gaussian inputs and noises) and constraints on state or measurement (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 state-of-the-art in distinctive categories and highlights some insights which may otherwise be overlooked. In particular, specific attention is paid to very informative nonlinear systems, Gaussian mixture reduction, unknown inputs and constraints, to fill the voids in existing reviews/surveys. To go beyond a pure review, we also provide some thoughts about hidden Markov modeling and filter evaluation.
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: Submitted for publication
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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