高斯混合扩展目标概率假设密度滤波器的收敛性分析  

Convergence Analysis of the Gaussian Mixture Extended-target Probability Hypothesis Density Filter

作　　者：连峰[1] 韩崇昭[1] 刘伟峰[2] 元向辉[1] 

机构地区：[1]西安交通大学电子与信息工程学院智能网络与网络安全教育部重点实验室,西安710049 [2]杭州电子科技大学自动化学院,杭州310018

出　　处：《自动化学报》2012年第8期1343-1352,共10页Acta Automatica Sinica

基　　金：国家自然科学基金(61004087;91016020;61005026);中国博士后科学基金(20100481338);中央高校基本科研业务费专项资金资助~~

摘　　要：研究了高斯混合扩展目标概率假设密度(Gaussian mixture extended-target probability hypothesis density,GM-EPHD)滤波器的收敛性问题,证明了在杂波强度先验已知且扩展目标的期望测量个数连续有界的假设条件下,若该GM-EPHD滤波器的GM项趋于无穷多,那么它一致收敛于真实的EPHD滤波器.并且,本文还证明了该算法在弱非线性条件下的扩展卡尔曼(Extended Kalman,EK)滤波近似实现—EK-GM-EPHD滤波器,在每个GM项的协方差趋于0时,也一致收敛于真实的EPHD滤波器.本文的研究目的在于从理论上给出GM-EPHD和EK-GM-EPHD滤波器的收敛性结果以及它们满足一致收敛性的条件.The convergence of the Gaussian mixture extended-target probability hypothesis density （GM-EPHD） filter is studied. Under the assumptions that the clutter intensity is known a priori and the expected number of measurements arising from an extended target is continuous and bounded, this paper proves that the GM-EPHD filter converges uniformly to the true EPHD filter as the number of GM terms tends to infinity. In addition, this paper also proves that the extended Kalman （EK） filter approximation of the algorithm in weak nonlinear condition, which is called EK-GM-EPHD filter, converges uniformly to the true EPHD filter as the covariance of each GM term tends to zero. The purpose of this paper is to theoretically present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which they satisfy uniform convergence.

关 键 词：扩展目标跟踪 概率假设密度滤波器 高斯混合方法 收敛性分析 

分 类 号：TN713[电子电信—电路与系统]