针对传统重采样算法易引起粒子贫化的问题,提出了自适应不完全重采样粒子滤波(A particle filter based on adaptive part resampling,APRPF)算法.APRPF以分步的方式仅对部分粒子进行重采样,以递推的方式计算表征粒子退化程度的度量函数(Measurement of particle degeneracy,MPD),直到满足给定条件.重采样后的粒子由新生粒子和未参与重采样的粒子组成,前者的存在有助于缓解退化问题,后者可使粒子集保持一定多样性.实验结果表明,与标准粒子滤波(Sampling importance resampling,SIR)、辅助变量粒子滤波(Auxiliary particle filter,APF)、正则化粒子滤波(Regularized particle filter,RPF)三种滤波器相比,APRPF的估计精度高;由于平均重采样次数少,计算量也小.
A new approach of smoothing the white noise for nonlinear stochastic system was proposed. Through presenting the Gaussian approximation about the white noise posterior smoothing probability density fimction, an optimal and unifying white noise smoothing framework was firstly derived on the basis of the existing state smoother. The proposed framework was only formal in the sense that it rarely could be directly used in practice since the model nonlinearity resulted in the intractability and infeasibility of analytically computing the smoothing gain. For this reason, a suboptimal and practical white noise smoother, which is called the unscented white noise smoother （UWNS）, was further developed by applying unscented transformation to numerically approximate the smoothing gain. Simulation results show the superior performance of the proposed UWNS approach as compared to the existing extended white noise smoother （EWNS） based on the first-order linearization.
