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基于自然梯度的非线性变分贝叶斯滤波算法

胡玉梅 潘泉 邓豹 郭振 陈立峰

胡玉梅, 潘泉, 邓豹, 郭振, 陈立峰. 基于自然梯度的非线性变分贝叶斯滤波算法. 自动化学报, 2024, 50(4): 1−15 doi: 10.16383/j.aas.c230359
引用本文: 胡玉梅, 潘泉, 邓豹, 郭振, 陈立峰. 基于自然梯度的非线性变分贝叶斯滤波算法. 自动化学报, 2024, 50(4): 1−15 doi: 10.16383/j.aas.c230359
Hu Yu-Mei, Pan Quan, Deng Bao, Guo Zhen, Chen Li-Feng. A novel nonlinear variational bayesian filtering algorithm using natural gradient. Acta Automatica Sinica, 2024, 50(4): 1−15 doi: 10.16383/j.aas.c230359
Citation: Hu Yu-Mei, Pan Quan, Deng Bao, Guo Zhen, Chen Li-Feng. A novel nonlinear variational bayesian filtering algorithm using natural gradient. Acta Automatica Sinica, 2024, 50(4): 1−15 doi: 10.16383/j.aas.c230359

基于自然梯度的非线性变分贝叶斯滤波算法

doi: 10.16383/j.aas.c230359
基金项目: 国家自然科学基金(61790552, 61976080)资助, 西北工业大学博士论文创新基金(CX201915)资助
详细信息
    作者简介:

    胡玉梅:航空工业西安航空计算技术研究所工程师. 主要研究方向为多源信息融合, 航空电子系统. E-mail: hym_henu@163.com

    潘泉:西北工业大学自动化学院教授, 信息融合技术教育部重点实验室主任. 主要研究方向为信息融合理论, 目标跟踪与识别技术, 无人机探测导航与安全控制. 本文通信作者. E-mail: quanpan@nwpu.edu.cn

    邓豹:航空工业西安航空计算技术研究所研究员. 主要研究方向为航空电子系统, 分布式并行处理. E-mail: dengbao15@sina.com

    郭振:湖北航天技术研究院总体设计所工程师. 主要研究方向为多源信息融, 目标跟踪. E-mail: guozhennpu@126.com

    陈立峰:湖北三江航天险峰电子信息有限公司研究员. 主要研究方向为目标探, 雷达信号处理. E-mail: chenlf22@mails.tsinghua.edu.cn

A Novel Nonlinear Variational Bayesian Filtering Algorithm Using Natural Gradient

Funds: Supported by National Natural Science Foundation of China (61790552, 61976080) and Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (CX201915)
More Information
    Author Bio:

    HU Yu-Mei Engineer at Xi'an Aeronautics Computing Technique Research Institute, AVIC. Her research interest covers information fusion and avionics systems

    PAN Quan Professor at the School of Automation, Northwestern Polytechnical University. He is also the Director of the Key Laboratory of Information Fusion Technology, Ministry of Education. His research interest covers information fusion theory, target tracking and recognition technology, and UAV detection navigation and safely control. Corresponding author of this paper

    DENG Bao Professor at Xi'an Aeronautics Computing Technique Research Institute, AVIC. His research interest covers avionics systems and distributed parallel processing

    GUO Zhen Engineer at System Design Institute, Hubei Aerospace Technology Academy. His research interest covers multi-source information fusion, target tracking

    CHEN Li-Feng Professor at Hubei Sanjiang Aerospace Xianfeng Electronic Information Co., Ltd. His research interest covers target detection and radar signal processing

  • 摘要: 在统计流形空间中, 从信息几何角度考虑非线性状态后验分布近似的实质是后验分布与相应参数化变分分布之间的Kullback-Leibler散度最小化问题, 同时也可以转化为变分置信下界的最大化问题. 为了提升非线性系统状态估计的精度, 在高斯系统假设条件下结合变分贝叶斯推断和Fisher信息矩阵推导出置信下界的自然梯度, 并通过分析其信息几何意义, 阐述在统计流形空间中置信下界沿其方向不断迭代增大, 实现变分分布与后验分布的 “紧密” 近似; 在此基础上, 以状态估计及其误差协方差作为变分超参数, 结合最优估计理论给出一种基于自然梯度的非线性变分贝叶斯滤波算法; 最后, 通过天基光学传感器量测条件下近地轨道卫星跟踪定轨仿真实验验证: 与对比算法相比, 所提算法具有更高的精度.
  • 图  1  变量分布近似过程中的KL散度示意图

    Fig.  1  The KL divergence of the distribution approximation of a variable

    图  2  非线性动态系统状态转移和量测的示意图

    Fig.  2  The state transition and measurement in a nonlinear dynamic system

    图  3  单变量高斯分布的欧氏距离示意图

    Fig.  3  The Euclidean distance for univariate Gaussian distributions

    图  4  多变量高斯分布的欧氏距离示意图

    Fig.  4  The Euclidean distance for multivariate Gaussian distributions

    图  5  非线性状态估计在不同空间中的含义示意图

    Fig.  5  The meaning of nonlinear state estimation in different spaces

    图  6  O沿切向量方向向点P处移动的示意图

    Fig.  6  Point O moves in the tangential direction towards P

    图  7  变分迭代过程中置信下界自然梯度的示意图

    Fig.  7  The natural gradient of ELBO in variation1al Bayesian iteration

    图  8  天基量测条件下LEO跟踪定轨仿真场景

    Fig.  8  Scenario of LEO orbit determination and tracking with space-based measurement

    图  9  x轴位置估计RMSE的对比

    Fig.  9  RMSE of position estimation in x axis

    图  10  y轴位置估计RMSE的对比

    Fig.  10  RMSE of position estimation in y axis

    图  11  z轴位置估计RMSE的对比

    Fig.  11  RMSE of position estimation in z axis

    图  12  x轴速度估计RMSE的对比

    Fig.  12  RMSE of velocity estimation in x axis

    图  13  y轴速度估计RMSE的对比

    Fig.  13  RMSE of velocity estimation in y axis

    图  14  z轴速度估计RMSE的对比

    Fig.  14  RMSE of velocity estimation in z axis

    表  1  目标的轨道根数

    Table  1  The orbital elements of target

    半长轴 (km) 离心率 倾角 (deg) 近地点角 (deg) 升交点赤经 (deg)
    7500 0.1 15 30 12
    下载: 导出CSV

    表  2  算法平均运行时间$( \times 10^{-4}\;{\rm{s}}) $的对比

    Table  2  The comparison of the average run time $( \times 10^{-4}\;{\rm{s}}) $ of algorithms

    算法 EKF UKF IEKF VBKF-NG
    时间 0.2580 0.9542 1.0989 1.1205
    下载: 导出CSV
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  • 收稿日期:  2023-06-12
  • 录用日期:  2023-11-20
  • 网络出版日期:  2024-02-19

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