Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Tian cheng Li*, Jin ya Su, Wei Liu, Juan M. Corchado

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1913-1939
Number of pages27
JournalFrontiers of Information Technology and Electronic Engineering
Volume18
Issue number12
DOIs
Publication statusPublished - 2017

Keywords

  • Bayesian filtering
  • Constrained filtering
  • Gaussian filter
  • Gaussian mixture
  • Kalman filter
  • Maneuver
  • Nonlinear filtering
  • Time series estimation
  • Unknown inputs

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