基于高斯混合PHD滤波的多目标跟踪

多目标的跟踪的主要目的是通过一个存在关联不确定性、检测不确定性以及噪声和虚警的观测序列集，联合估计目标数目和目标状态.传统的多目标跟踪算法中的数据关联算法计算量大不易实现，而基于随机集的PHD滤波算法可避免数据数据关联问题，直接估计目标状态.本文针对目前PHD递推算法难以获得闭和解的问题，阐明了在目标运动模型和新生强度都是线性高斯模型的情况下，每一时刻的后验强度都是高斯混合的.进而推导出表示后验强度的高斯成分的均值，方差和权值的递推方程.由仿真结果可以看出在非线性高斯情况下，本算法对多目标有良好的跟踪性能.

Gaussian Mixture Probability Hypothesis Density Filter for Multi-Target Tracking

The main purpose of the multiple target tracking is jointly estimating the number of targets and their states from a sequence of observation sets, which has the feature of association uncertainty, detection uncertainty, noise and false alarms. In the view of the data association of traditional multiple target tracking algorithm, the large amount of calculation is hard to achieve, while the PHD filter algorithm based on random sets can avoid the problems mentioned above and can estimate the status directly. At present, there is no closed form of solution for the PHD recursion algorithm. This work shows that when both the target dynamics and birth process are linear Gaussian models, the posterior intensity at any time step is a Gaussian mixture. Therefore, the recursive equation can be derived, which can represent the mean of the posterior intensity in terms of Gaussian components, variances and weights. It is demonstrated by simulation that this algorithm can track multiple targets well under non linear, Gaussian assumption.