近似高斯共轭：非线性、多模态、不确定以及约束下的参数递归滤波等

李天成; 苏金亚; 刘伟; Juan M Corchado

doi:10.1631/FITEE.1700379

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近似高斯共轭：非线性、多模态、不确定以及约束下的参数递归滤波等

特邀文章 | Updated：2022-06-06

- 近似高斯共轭：非线性、多模态、不确定以及约束下的参数递归滤波等
  Enhanced Publication
- Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond
- 信息与电子工程前沿（英文） 2017年18卷第12期页码：1913-1939
- Affiliations：
  
  School of Sciences, University of Salamanca, Salamanca 37007, Spain
  Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough LE11 3TU, UK
  Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 4ET, UK
- Author bio：
  
  [ "", "Dr. Tian-cheng LI, first author of this invited review, received his Bachelor’s degree in Mechanical and Electrical Engineering, with a minor degree in Business Administration, from Harbin Engineering University (China), in 2008, his first PhD in Electrical and Electronic Engineering from London South Bank University (United Kingdom), in 2013, and his second doctoral degree in Mechatronics Engineering from Northwestern Polytechnical University (China), in 2015. He has been a Research Associate with the BISITE Group, University of Salamanca (Spain) since June 2014 and presently, he holds a Marie Skłodowska-Curie Individual Fellowship (H2020-MSCA-IF-2015) with the same Host and the Partner Vienna University of Technology (Austria).He has been on the Editorial Board of peer-reviewed journals: Advances in Distributed Computing and Artificial Intelligence Journal (2016–) and Frontiers of Information Technology & Electronic Engineering (2017–), and on the organizing and/or technical program committee of several international symposiums and conferences, including FUSION 2014–2017, DCAI 2015–2017, and ACM-SAC 2015–2017.His research interests lie in the general area of statistical signal processing and distributed information fusion, with particular interest in novel sensor data clustering, fitting and mining algorithms for advanced multi-sensor multi-object detection, tracking, and forecasting." ]
  [ "Jin-ya SU, E-mail: J.Su2@lboro.ac.uk" ]
  [ "Wei LIU, E-mail: w.liu@sheffield.ac.uk" ]
  [ "Juan M. CORCHADO, E-mail: corchado@usal.es" ]
- Funds：
  
  Project supported by the Marie Skłodowska-Curie Individual Fellowship (H2020-MSCA-IF-2015) (No. 709267) and the Open Project Program of Ministry of Education Key Laboratory of Measurement and Control of Complex Systems of Engineering, Southeast University, China (No. MCCSE2017A01)
- DOI：10.1631/FITEE.1700379
  中图分类号： TP391
- 纸质出版日期：2017-12，
  
  收稿日期：2017-06-11，
  
  修回日期：2017-11-22，
- Accepted：
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李天成, 苏金亚, 刘伟, 等. 近似高斯共轭：非线性、多模态、不确定以及约束下的参数递归滤波等[J]. 信息与电子工程前沿（英文）, 2017,18(12):1913-1939.

LI TIAN-CHENG, SU JIN-YA, LIU WEI, et al. Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond. [J]. Frontiers of information technology & electronic engineering, 2017, 18(12): 1913-1939.
李天成, 苏金亚, 刘伟, 等. 近似高斯共轭：非线性、多模态、不确定以及约束下的参数递归滤波等[J]. 信息与电子工程前沿（英文）, 2017,18(12):1913-1939. DOI： 10.1631/FITEE.1700379.

LI TIAN-CHENG, SU JIN-YA, LIU WEI, et al. Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond. [J]. Frontiers of information technology & electronic engineering, 2017, 18(12): 1913-1939. DOI： 10.1631/FITEE.1700379.

摘要

自上世纪60年代作为现代估计开山之作的卡尔曼滤波器（Kalman filter）的诞生，时间序列状态空间模型应用于各类动态估计问题吸引了大量的研究关注。特别是，寻求实现闭环马尔科夫?贝叶斯递归（比如，从一个高斯先验到一个高斯后验，本文称之为高斯共轭）的解析解成为一般时间序列滤波器设计的主流思路。其面临的主要挑战包括：系统的非线性、多模态（包括机动模型）、复杂不确定性（比如未知的系统输入，非高斯噪声等）和系统约束（包括循环随机变量）等。这些挑战不断触生新的理论、算法与滤波技术，以实现所期望的参数共轭递归。本文对最新研究进行分类、系统回顾，强调了一些容易被忽略的要点。着重介绍了高精观测非线性系统、高斯后验和机动多模态、以及复杂未知系统输入与约束，以弥补当前文献介绍的不足。同时，本文提出一些新的思考：一是一阶马尔科夫转移模型的替代模型，二是有关计算复杂度的滤波器评价。

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.

关键词

卡尔曼滤波高斯滤波时间序列估计贝叶斯滤波非线性滤波约束滤波高斯混合机动未知输入

Keywords

Kalman filterGaussian filterTime series estimationBayesian filteringNonlinear filteringConstrained filteringGaussian mixtureManeuverUnknown inputs

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