基于自然梯度的非线性变分贝叶斯滤波算法  

A Novel Nonlinear Variational Bayesian Filtering Algorithm Using Natural Gradient

作　　者：胡玉梅 潘泉[2,3] 邓豹[1] 郭振 陈立峰 HU Yu-Mei;PAN Quan;DENG Bao;GUO Zhen;CHEN Li-Feng(Xi'an Aeronautics Computing Technique Research Institute,Aviation Industry Corporation of China,Xi'an 710065;School of Automation,Northwestern Polytechnical University,Xi'an 710072;Key Laboratory of Information Fusion Technology,Ministry of Education,Xi'an 710072;System Design Institute of Hubei Aerospace Technology Academy,Wuhan 430040)

机构地区：[1]航空工业西安航空计算技术研究所,西安710065 [2]西北工业大学自动化学院,西安710072 [3]信息融合技术教育部重点实验室,西安710072 [4]湖北航天技术研究院总体设计所,武汉430040

出　　处：《自动化学报》2025年第2期427-444,共18页Acta Automatica Sinica

基　　金：国家自然科学基金(61790552,61976080);西北工业大学博士论文创新基金(CX201915);航空科学基金(2024M066031002)资助。

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(KL)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(Variational Bayes,VB)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和纯角度被动传感器量测条件下运动目标跟踪仿真实验验证,与对比算法相比,所提算法具有更高的精度.In statistical manifold space,the essence of nonlinear state posterior distribution approximation from the perspective of information geometry is minimizing Kullback-Leibler(KL)divergence between posterior distribution and the corresponding approximated distribution;Meanwhile,it is equivalent to maximizing evidence low bound.Aiming at the problem of improving the estimation accuracy of nonlinear system state,the natural gradient of evidence lower bound is derived under Gaussian system assumption by combining with Fisher information matrix and variational Bayesian(VB)inference,which produces a faster movement direction to the posterior distribution,and realizing a close approximation between variational distribution and the posterior.On this basis,a variational Bayesian Kalman filtering algorithm using natural gradient is proposed for updating the variational hyperparameters of state estimation and the associated error covariance.Simulations in low earth orbit target tracking system with space-based optical sensors and bearing-only target tracking system are presented verifying that the proposed algorithm has higher accuracy than the comparison algorithms.

关 键 词：非线性滤波 信息几何 变分贝叶斯推断 自然梯度 Fisher信息矩阵 

分 类 号：TN713[电子电信—电路与系统]