基于多变量Laplace分布的非线性系统分布式鲁棒状态估计

doi:10.12263/DZXB.20220141

电子学报 ›› 2022, Vol. 50 ›› Issue (11): 2610-2618.DOI: 10.12263/DZXB.20220141

基于多变量Laplace分布的非线性系统分布式鲁棒状态估计

王国庆¹^,², 杨春雨¹^,²(), 马磊¹^,²

^1.中国矿业大学信息与控制工程学院，江苏徐州 221116
^2.地下空间智能控制教育部工程研究中心，江苏徐州 221116

收稿日期:2022-01-29 修回日期:2022-04-25 出版日期:2022-11-25
- 通讯作者:
- 杨春雨
- 作者简介:
- 王国庆男，1990年6月出生于山东省滕州市.现为中国矿业大学信息与控制工程学院副教授、硕士生导师.从事状态估计、信息融合和机器人导航方面的研究.E-mail: wangguoqing0632@163.com
  杨春雨（通讯作者）　男，1979年9月出生于辽宁省朝阳市.现为中国矿业大学信息与控制工程学院教授、博士生导师.从事智能系统控制技术、奇异摄动系统优化控制等方面的研究.
  马磊男，1989年6月出生于江苏省徐州市.现为中国矿业大学信息与控制工程学院助理研究员.从事奇异摄动系统的分析与设计、网络化控制系统的控制与滤波、信息物理系统的安全估计与控制的研究.E-mail: malei@cumt.edu.cn
- 基金资助:
- 国家自然科学基金 (62003348); 江苏省自然科学基金 (BK20200633)

Distributed Robust State Estimation for Nonlinear Systems Based on Multivariate Laplace Distribution

WANG Guo-qing¹^,², YANG Chun-yu¹^,²(), MA Lei¹^,²

^1.School of Information and Control Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China
^2.Engineering Research Center of Intelligent Control for Underground Space, Ministry of Education, Xuzhou, Jiangsu 221116, China

Received:2022-01-29 Revised:2022-04-25 Online:2022-11-25 Published:2022-11-19
- Corresponding author:
- YANG Chun-yu

摘要/Abstract

摘要：

本文考虑非高斯噪声下传感器网络的状态估计问题.在机动目标跟踪、室内定位、水声导航等应用中，传感器的非高斯噪声会造成针对高斯噪声设计的常规状态估计算法精度下降.在现有针对单传感器系统的基于多变量Laplace（Multivariate Laplace，ML）鲁棒状态估计（Robust State Estimation based on ML，RSE-ML）算法基础上，本文借助信息滤波的特点，推导了针对多传感器系统的集中式RSE-ML（Centralized RSE-ML，CRSE-ML）算法，进一步利用一致性平均得到分布式RSE-ML（Distributed RSE-ML，DRSE-ML）算法.本文提出的DRSE-ML算法中利用ML建模非高斯噪声，借助变分贝叶斯方法估计噪声和状态参数，采用一致性算法进行分布式信息交互，克服了集中式算法通信和计算负担重的缺点，且具有自由参数少、估计精度高的特点.仿真结果表明，所提出的DRSE-ML算法估计精度优于现有相关算法，且能逼近集中式CRSE-ML算法的估计精度.

关键词: 非高斯噪声, 鲁棒状态估计, 分布式状态估计, 多变量Laplace分布, 卡尔曼滤波, 变分贝叶斯

Abstract:

This paper considers the state estimation problem of sensor networks with non-Gaussian noise. In many applications, such as maneuvering target tracking, indoor positioning and underwater acoustic navigation, the non-Gaussian noise of the sensors may reduce the accuracy of the estimation algorithm designed for Gaussian noise. The centralized robust state estimation based on multivariate Laplace(CRSE-ML) algorithm is derived according to the characteristics of information filtering on the basis of existing RSE-ML, which is designed for single-sensor systems. Following that, the distributed RSE-ML(DRSE-ML) algorithm is then obtained with the introduction of consensus average. Within the DRSE-ML algorithm, the ML distribution is used to model non-Gaussian noise, the variational Bayesian method is applied to estimate noise and state parameters, and the consensus algorithm is adopted for distributed information exchange. The distributed algorithm overcomes the shortcomings of the centralized one, which has heavy communication and computational burden, and has few free parameters and high estimation accuracy. Simulation results show that the estimation accuracy of the proposed DRSE-ML is better than the existing related algorithms, and can approach the estimation accuracy of the centralized CRSE-ML algorithm.

Key words: non-Gaussian noise, robust state estimation, distributed state estimation, multivariate Laplace distribution, Kalman filter, variational Bayesian

中图分类号:

TP24

王国庆, 杨春雨, 马磊. 基于多变量Laplace分布的非线性系统分布式鲁棒状态估计[J]. 电子学报, 2022, 50(11): 2610-2618.

WANG Guo-qing, YANG Chun-yu, MA Lei. Distributed Robust State Estimation for Nonlinear Systems Based on Multivariate Laplace Distribution[J]. Acta Electronica Sinica, 2022, 50(11): 2610-2618.

图/表 7

图1 基于传感器网络的机器人目标跟踪示意图

图2 一维变量服从高斯分布、高斯混合分布和高斯分布+脉冲噪声时的概率密度函数

图3 情况1下不同算法的位置ARMSEs

图4 情况1下不同算法的速度ARMSEs

图5 情况2下不同算法的位置ARMSEs

图6 情况2下不同算法的速度ARMSEs

表1 不同情况下各算法运行时间 (s)

算法名称	情况1	情况2
CRSE-ML	25.4230	24.3340
DRSE-ML(M=3)	24.9070	24.4400
DRSE-ML(M=5)	25.2910	26.3010
DMCUKF	6.4230	5.3240
CUKF	1.7460	1.7030
CMCUKF	2.0310	2.0150
HCMCI-UKF	5.0360	5.4110

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基于多变量Laplace分布的非线性系统分布式鲁棒状态估计

Distributed Robust State Estimation for Nonlinear Systems Based on Multivariate Laplace Distribution

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