基于均方根容积粒子的SMC-PHD算法

传统的序贯蒙特卡罗概率假设密度(SMC-PHD)算法采用状态转移密度作为重要性采样函数.当目标非线性运动时,少数粒子将具有较大的权值,导致估计精度低、结果发散.针对上述问题,提出了一种基于均方根容积卡尔曼滤波(SCKF)和统计门限技术的重要性采样函数设计方法.在重要性采样函数估计时,首先利用SCKF对重要性采样函数的均值和协方差阵进行预测,而后利用统计门限技术提取与重要性采样粒子相关联的量测.通过相应的权值对所提取的量测进行合并,更新重要性采样函数的均值和协方差阵.在此基础上将设计的重要性采样函数应用于SMC-PHD的强度预测和更新,最终实现多目标状态和数目的估计.实验表明,本算法在非线性多目标跟踪中具有精度高、估计结果稳定的优点. 

SMC-PHD algorithm based on squared cubature particles

Most of the conventional sequential Monte Carlo probability hypothesis density (SMC-PHD) approaches adopt the state transition density as importance sampling function. When targets are with nonlinear motions, such a selection makes few particles with large weights, leading to inaccurate estimation and particle divergence. To avoid such problems, a novel importance sampling function approximation approach with the squared cubature Kalman filter (SCKF) and statistical gating method was proposed. To design such an importance sampling function, the mean and covariance of importance sampling function were predicted at first. Then, the statistical gating method were utilized to extract observations associated with the importance sampling particle from the current observation set. Merging the extracted observations with corresponding weights, the mean and covariance of importance sampling function were updated. Using the designed importance sampling function, the intensity of particles can be predicted and updated, according to the conventional SMC-PHD method. At last, the states and number of multi-target can be approximated by the intensity of particles. The simulation results demonstrate that the proposed approach has the advantages of high accuracy and stable estimation in nonlinear target tracking.