Abstract: Aiming at the tracking problem of multiple extended targets under the circumstances with unknown measurement noise covariance, an extension of standard Extended Target Probability Hypothesis Density (ET-PHD) filter and the way to realize its analysis were proposed by using ET-PHD filter and Variational Bayesian (VB) approximation theory. Firstly, on the basis of the target state equations and measurement equations of the standard ET-PHD filter, the augmented state variables of target state and measurement noise covariance as well as the joint transition function of the above variables were defined. Then, the prediction and update equations of the extended ET-PHD filter were established based on the standard ET-PHD filter. And finally, under the condition of linear Gaussian assumptions, the joint posterior intensity function was expressed as the Gaussian and Inverse-Gamma (IG) mixture distribution, and the analysis of the extended ET-PHD filter was realized. Simulation results demonstrate that the proposed algorithm can obtain reliable tracking results, and can effectively track multiple extended targets in the circumstances with unknown measurement noise covariance.

Key words: extended target tracking, Probability Hypothesis Density (PHD), Random Finite Set (RFS), Variational Bayesian (VB), noise covariance

摘要： 针对未知测量噪声协方差情况下的多扩展目标跟踪问题，利用扩展目标概率假设密度（ET-PHD）滤波器和变分贝叶斯（VB）近似理论，提出了一种标准ET-PHD滤波器的扩展方法及其解析的实现方法。首先，根据标准ET-PHD滤波器的目标状态方程和测量方程，定义了目标状态和测量噪声协方差的增广状态变量及二者的联合转移函数；然后，根据标准ET-PHD滤波器，构建了扩展的ET-PHD滤波器的预测和更新公式；最后，在线性高斯假设的条件下，利用高斯和逆伽马（IG）混合分布表示目标的联合后验强度函数，从而给出了扩展ET-PHD滤波器的解析实现。仿真结果表明：所提算法能提供可靠的跟踪结果，可有效地处理未知测量噪声协方差环境中的多扩展目标跟踪问题。

关键词: 扩展目标跟踪, 概率假设密度, 随机有限集, 变分贝叶斯, 噪声协方差