Abstract: When the number of targets is unknown or varied with time，the target state and measurements can be represented as random sets.The Gaussian mixture Probability Hypothesis Density（PHD） filter is implemented to track the multi-targets.The analytical analysis of the method show that the posterior intensity at any subsequent time step remains a Gaussian mixture under the assumption that the state noise，the measurement noise，target spawn intensity，new birth intensity，target survival probability，and detection probability are all Gaussian mixture.The Kalman filter is embedded in the Gaussian mixture PHD filter.This method uses Gaussian components to predict and update the PHD of random sets，and estimates targets states.Experiments show that the Gaussian mixture PHD filter can be used to track multi-target in clutter effectively.

Key words: multi-target tracking, random set, Gaussian mixture, probability hypothesis density

摘要： 为解决目标数未知或随时间变化时的多目标跟踪问题，将多目标状态和观测信息表示为随机集的形式，建立了多目标跟踪的混合高斯概率假设密度（PHD）滤波方法。当目标初始的先验概率密度满足高斯分布的形式时，通过将状态噪声、观测噪声、目标的繁衍、新目标的产生、目标的存活概率和检测概率表示成混合高斯的形式，之后每个时刻的后验概率密度均能表示成混合高斯的形式。线性混合高斯PHD滤波方法将Kalman滤波引入到PHD滤波中，利用混合高斯成分预测和更新随机集的PHD，并估计出目标的状态。实验结果表明，在杂波环境下混合高斯PHD滤波方法可以有效地跟踪目标状态。

关键词: 多目标跟踪, 随机集, 混合高斯, 概率假设密度