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针对粒子滤波存在的退化问题,提出一种基于最优重要性密度对应的分布函数的逆映射采样的粒子滤波方法.该方法首先在[0,1]区间均匀采样一组随机样本,然后根据分布函数的单值逆映射关系,将这些随机样本映射成对应于最优重要性密度的粒子,其中分布函数通过数值积分计算.这些粒子的分布非常逼近所求状态的后验概率密度函数,有效解决了粒子退化问题.理论分析和仿真结果表明:与现有粒子滤波方法相比,所提方法明显改善了滤波性能.
Aiming at the problem of degradation of particle filter, a particle filter based on inverse mapping sampling of distribution function with optimal importance density is proposed. This method first samples a group of random samples evenly in [0,1] Function, and map these random samples into particles corresponding to the optimal importance density, where the distribution function is calculated by numerical integration.The distribution of these particles is very close to the posterior probability density function of the state sought, which is effectively solved The problem of particle degeneration is solved.The theoretical analysis and simulation results show that compared with the existing particle filtering methods, the proposed method obviously improves the filtering performance.