概率假设密度高斯混合实现的分量删减

针对概率假设密度(Probability hypothesis density, PHD)高斯混合实现算法中的分量删减问题, 提出了基于Dirichlet分布的分量删减算法以改进概率假设密度高斯混合实现算法的性能. 算法采用极大后验准则估计混合参数, 采用仅依赖于混合权重的负指数Dirichlet分布作为混合参数的先验分布, 利用拉格朗日乘子推导了混合权重的更新公式. 算法利用负指数Dirichlet分布的不稳定性,在极大后验迭代过程中驱使与目标强度不相关的分量消亡. 该不稳定性还能够解决多个相近分量共同描述一个强度峰值的问题, 有利于后续多目标状态的提取. 仿真结果表明, 基于Dirichlet分布的分量删减算法优于典型高斯混合实现中的删减算法.

Component Pruning in Gaussian Mixture Implementation of Probability Hypothesis Density

As far as component pruning in Gaussian mixture (GM) implementation of probability hypothesis density (PHD) is concerned, a component pruning algorithm based on Dirichlet distribution is proposed to improve the performance of Gaussian mixture implementation of probability hypothesis density. The maximum a posterior criterion is adopted for estimation of mixing parameters. Dirichlet distribution with negative exponent parameters, which only depends on mixing weights, is adopted as the prior distribution of mixing parameters. The update formulation of mixing weight is derived by Lagrange multiplier. The instability of Dirichlet distribution with negative exponent parameters is applied to driving the components irrelevant with target intensity to extinction during the maximum a posterior iteration. Besides, the problem that one peak of intensity is presented by several proximate mixing component, can be solved by this instability. It is useful for the following state extraction. Simulation results show that the component pruning algorithm based on Dirichlet distribution is superior to that of typical Gaussian mixture implementation.