核函数K-粒子滤波算法研究

摘要

In order to solve the problem of particle degradation caused by particle filtering,through the introduction of the kernel function K,a new kernel function K-particle filtering algorithm is presented,which absorbs the merits of the kernel function and the particle filter.According to the probability characteristics of the particle aggregation in the particle filter,the kernel density K(·) and kernel bandwidth are designed to make the mean square error between the real posterior probability density and the corresponding K estimation minimum.The discrete distribution is simulated by the kernel function to reconstruct its continuous distribution,and then the re-sampling particles are re-obtained from the continuous approximation of the posterior distribution.Further,the diversity of the particle is guaranteed,and the particle degradation is suppressed.The proposed KPF and PF algorithm are applied to the single variable non-static growth model and SINS/SAR integrated navigation system.Simulation results and their analysis demonstrate preliminarily that the proposed KPF algorithm can improve the filter performance and calculation precision than the PF algorithm.%针对粒子滤波易出现粒子退化这一问题,引入核函数K,提出一种核函数K粒子滤波算法.根据粒子滤波中重采样得到的粒子集合的概率特征,设计合适的核密度K(·)和核带宽h,使得真实的后验概率密度与对应的K估计之间的均方误差均值最小.通过设计的核函数模拟离散分布重建它的连续分布,然后从后验分布的连续近似中重新获得重采样粒子,从而保证粒子的多样性,抑制粒子退化.将提出的KPF算法与PF算法应用到单变量非静态增长模型和SINS/SAR组合导航系统中,通过仿真验证结果表明,提出的KPF算法能改善滤波性能,进一步提高解算精度.