基于最优采样函数的粒子滤波算法与贝叶斯估计

传统粒子滤波器(PF)直接根据状态演化方程产生新的粒子,由于没有考虑新近观测对状态估计的影响,这种滤波器性能较差,即便在粒子数目很大的情况也是如此。为此,本文提出一种基于序贯重要采样(SIS)的改进粒子滤波算法,该算法采用集成了新近观测量的最优采样(或重要密度)函数指导粒子的生成,使粒子权值的方差最小化,能有效减轻粒子退化问题;同时。在粒子重采样之后增加了马尔科夫链蒙特卡洛(MCMC)过程,消除了重采样引起的粒子贫化的负面影响,从而使粒子的多样性得以保持。对非线性系统的状态估计和只测角跟踪的仿真实例均表明,本文所提出的算法比传统估计算法如EKF,UKF具有更高的精度和更强的鲁棒性;与标准PF相比,其性能也有较大的提高,并可以在相同的估计精度下大大减少所需的粒子数目,是一种有效的非线性滤波算法。

Optimal Sampling Function-Based Particle Filter and Bayesian Estimation

In conventional particle filter,the required particles are generated according to the transition function of the system dy- namics,and the performance of the filter is far from the optimal fashion even a large number of particles are used because the latest measurement is not incorporated for generating the desired particles.In this paper,an improved particle filter is proposed using the tech- nique of sequential importance resampling.The particles are sampled from the optimal importance density function in term of minimizing the variance of the weights,which mitigates the effects of particle degeneracy problem.Additionally,the Markov chain Monte Carlo step is adopted to counteract the problem of particle impoverishment caused by resampling step and thus the diversity of the particles is main- tained.Simulations are performed using the classical nonlinear state estimation and the bearing only tracking examples.The results show that the proposed algorithm is not only more accurate and robust than the traditional filters(such as EKF and UKF)but also significant- ly superior to the general particle filter,and the new approach can greatly reduce the particle number under the same performance re- quirement,indicating that the improved method is very effective for nonlinear filtering.