贝叶斯序贯重要性积分滤波器

doi:10.12263/DZXB.20210716

电子学报 ›› 2022, Vol. 50 ›› Issue (4): 823-831.DOI: 10.12263/DZXB.20210716

所属专题：智能时空信息服务技术

• 智能时空信息服务技术 • 上一篇下一篇

贝叶斯序贯重要性积分滤波器

张宏伟¹^,², 张小虎¹, 曹勇³

^1.中山大学航空航天学院，广东广州 510725
^2.中国科学院空间精密测量技术重点实验室，陕西西安 710119
^3.北京东方计量测试研究所，北京 100029

收稿日期:2021-06-06 修回日期:2022-01-06 出版日期:2022-04-25
- 作者简介:
- 张宏伟女，1982年出生，河南南阳人.博士，中山大学航天航空学院副研究员.主要研究方向为智能信息处理、信息融合、目标跟踪. E-mail: zhanghw69@sysu.edu.cn
  张小虎男，1973年出生，陕西凤翔人.博士，中山大学航天航空学院教授，图像感知与信息处理学科学术带头人.主要研究方向为精密测量、图像信息处理.
- 基金资助:
- 广东省基础与应用基础研究基金 (2019A1515111099); 中山大学青年培育项目 (20lgpy72); 中国科学院空间精密测量重点实验室开放基金 (SPMT2021002)

Bayesian Sequential Importance Quadrature Filter

ZHANG Hong-wei¹^,², ZHANG Xiao-hu¹, CAO Yong³

^1.School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou, Guangdong 510725, China
^2.CAS Key Laboratory of Space Precision Measurement Technology, Xi’an, Shaanxi 710119, China
^3.BeiJing Orient Institute of Measurement and Test, Beijing 100029, China

Received:2021-06-06 Revised:2022-01-06 Online:2022-04-25 Published:2022-04-25
- Supported by:
- Basic and Applied Basic Research Foundation of Guangdong Province (2019A1515111099); Youth Talent Training Program of Sun Yat-sen University (20lgpy72); Open fund of Key Laboratory of Space Precision Measurement Technology, CAS (SPMT2021002)

摘要/Abstract

摘要：

为解决非线性滤波中存在模型歧义和预测偏差情况下似然函数、目标重要性密度函数和实际目标分布不匹配的问题，提出了贝叶斯序贯重要性积分滤波器（Bayesian Sequential Importance Quadrature Filter，SIQF）.为了消减贝叶斯推理中似然函数和目标分布之间的偏差，通过空时软约束定义最新观测的有界似然，截断观测噪声概率密度函数以近似可行域的修正先验.为了调制重要性函数和目标分布的匹配程度，并行对修正和原始先验下的状态进行Gauss-Hermite积分，引入最大相关信息熵构建覆盖多模分布的重要性函数，从而提升序贯重要性采样的多样性和预测协方差的容错性.实验结果表明：相比无迹粒子滤波估计一维单变量增长模型，SIQF算法在无需牺牲计算复杂度的情况下平均误差减小了63%；相比多模型Rao-blackwell粒子滤波器跟踪空域机动目标，SIQF算法的均方根误差减小了33%，所需计算量降低了一个数量级.

关键词: 非线性滤波, 贝叶斯序贯重要性积分, 软约束, 有界似然, 相关信息熵测度

Abstract:

To solve the mismatch problems between the measurement likelihood function, importance density function and the target true distribution for the nonlinear filtering in the presence of the model attribute ambiguity and prediction bias, we derive and present a Bayesian sequential importance quadrature filter(SIQF) algorithm. To reduce the deviation between the likelihood function and the target true distribution in the Bayesian reference, the bounded measurement likelihood of the latest measurement is defined via the soft spatiotemporal constraint, the modified prior of the feasible area is approximated by truncating the probability density function of the measurement noise. To modulate the matching degree between the importance function and the target distribution, the state under the modified and original priors is evaluated via Gauss-Hermite Kalman filter in parallel, the maximum correntropy criterion is introduced to construct the mixture importance function, both the diversity of sequential importance sample and the tolerance of prediction covariance can be thereby improved. The simulation results show that, compared with the unscented particle filter for the estimation of one-dimensional univariate nonstationary growth model, the average estimate error of the SIQF algorithm has decreased 63% without sacrificing computational complexity. Compared with the multi-model Rao-blackwell particle filter for the maneuvering target tracking in the airspace, the root mean square error of the SIQF algorithm has decreased 33%, and the computational load is reduced by an order of magnitude.

Key words: nonlinear filtering, Bayesian sequential importance quadrature filter, soft constraint, bounded likelihood, maximum correntropy criterion

中图分类号:

TN953

张宏伟, 张小虎, 曹勇. 贝叶斯序贯重要性积分滤波器[J]. 电子学报, 2022, 50(4): 823-831.

Hong-wei ZHANG, Xiao-hu ZHANG, Yong CAO . Bayesian Sequential Importance Quadrature Filter[J]. Acta Electronica Sinica, 2022, 50(4): 823-831.

图/表 10

图1 算法流程框架

图2 10个样本

图3 200个样本

图4 300个样本

图5 500个样本

图6 目标GPS定位和观测航迹

图7 二维空间的均方根误差

图8 X轴方向的均方根误差

图9 Y轴方向的均方根误差

表1 100轮蒙特卡罗轮实验的滤波误差均值平均执行时间

算法	滤波误差均值/km	执行时间/s
IMMEKF	0.16	0.29
IMMUKF	0.17	0.43
MMRBPF	0.15	31.32
SIQF	0.10	2.07

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贝叶斯序贯重要性积分滤波器

Bayesian Sequential Importance Quadrature Filter

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