Under the Gaussian noise assumption, the probability hypothesis density (PHD) filter represents a promising tool for tracking a group of moving targets with a time-varying number. However, inaccurate prior statistics of the random noise will degrade the performance of the PHD filter in many practical applications. This paper presents an adaptive Gaussian mixture PHD (AGM-PHD) filter for the multi-target tracking (MTT) problem in the scenario where both the mean and covariance of measurement noise sequences are unknown. The conventional PHD filters are extended to jointly estimate both the multi-target state and the aforementioned measurement noise statistics. In particular, the Normal-inverse-Wishart and Gaussian distributions are first integrated to represent the joint posterior intensity by transforming the measurement model into a new formulation. Then, the updating rule for the hyperparameters of the model is derived in closed form based on variational Bayesian (VB) approximation and Bayesian conjugate prior heuristics. Finally, the dynamic system state and the noise statistics are updated sequentially in an iterative manner. Simulations results with both constant velocity and constant turn model demonstrate that the AGM-PHD filter achieves comparable performance as the ideal PHD filter with true measurement noise statistics.

在高斯噪声假设下，概率假设密度（PHD）滤波器代表了一种跟踪具有时变数的运动目标的有前途的工具。但是，在许多实际应用中，随机噪声的先验统计不准确会降低PHD滤波器的性能。本文提出了一种在测量噪声序列的均值和协方差均未知的情况下针对多目标跟踪（MTT）问题的自适应高斯混合PHD（AGM-PHD）滤波器。常规的PHD滤波器被扩展以共同估计多目标状态和上述测量噪声统计量。特别是，首先，通过将测量模型转换为新公式，将正态-反维沙特和高斯分布进行积分，以表示关节后强度。然后，基于变分贝叶斯（VB）近似和贝叶斯共轭先验启发法，以封闭形式导出模型超参数的更新规则。最后，动态系统状态和噪声统计信息以迭代方式顺序更新。恒定速度和恒定转弯模型的仿真结果表明，AGM-PHD滤波器具有与理想PHD滤波器相当的性能，具有真实的测量噪声统计数据。动态系统状态和噪声统计信息以迭代方式顺序更新。恒定速度和恒定转弯模型的仿真结果表明，AGM-PHD滤波器具有与理想PHD滤波器相当的性能，具有真实的测量噪声统计数据。动态系统状态和噪声统计信息以迭代方式顺序更新。恒定速度和恒定转弯模型的仿真结果表明，AGM-PHD滤波器具有与理想PHD滤波器相当的性能，具有真实的测量噪声统计数据。