基于增量式有限混合模型的多目标状态极大似然估计

提出了增量式有限混合模型来提取概率假设密度滤波器序贯蒙特卡罗实现方式中的多目标状态. 该模型以增量方式构建, 其混合分量采用逐个方式插入其中. 采用极大似然准则来估计多目标状态. 对于给定分量数目的混合模型, 应用期望极大化算法来获得参数的极大似然解. 在新分量插入混合模型时, 保持已有混合模型的参数不变, 仍旧采用极大似然准则从候选新分量集合中选择新插入分量. 新分量插入混合步和期望极大化算法拟合混合参数步交替应用直到混合分量数目达到概率假设密度滤波器的目标数目估计值. 利用k-d树生成插入到混合模型的新分量候选集合. 增量式有限混合模型统一了分量数目变化趋势和粒子集合似然函数的变化趋势, 有助于一步一步地搜寻混合模型的极大似然解. 仿真结果表明, 基于增量式有限混合模型的概率假设密度滤波器状态提取算法在多目标跟踪的应用中优于已有的状态提取算法.

Maximum Likelihood Estimation of Multiple Target States Based on Incremental Finite Mixture Model

The incremental finite mixture model (IFMM) is proposed to extract target states in the sequential Monte Carlo implementation of probability hypothesis density (PHD) filter. The proposed model is constructed in an incremental way. The mixture components are inserted into mixture model one after another. Maximum likelihood (ML) criterion is adopted in the model for multiple target state estimation. For the mixture model with given component number, expectation maximum (EM) algorithm is applied in obtaining the maximum likelihood solution of model parameters. When the new component is inserted into the mixture model, maximum likelihood criterion is yet adopted for the selection of new component from the candidate set of new components, while the parameters of existing components in mixture model remain invariable. The step of inserting new component into mixture model and the step of maximum likelihood parameter fitting of mixture model by expectation maximum algorithm are alternately applied until the number of mixture components is equal to the estimate of target number produced by the probability hypothesis density filter. The candidate set of new components for inserting into mixture model is generated by k-dimensional tree. The incremental finite mixture model unifies the tendency of component number and that of likelihood of particle set so that it contributes to searching maximum likelihood solution of mixture model step by step. Simulation results show that the state extraction algorithm based on incremental finite mixture model is superior to the existing algorithms for the probability hypothesis density filter in multiple target tracking.