基于似然分布的样本数自适应UPF算法

Adaptive sample-size unscented particle filter based on likelihood distribution

针对粒子滤波算法的实时性较差,计算量随着粒子数的增加成级数增加,提出一种基于似然分布的样本数自适应UPF算法。该算法以UPF为基础,吸收了似然分布自适应和样本数自适应的优点,在每一步状态方差估计中规定样本数的下限,同时考虑状态方差过大和过小的情况,在重采样阶段嵌入似然采样,根据反映量测噪声实时统计性能的精度因子?自适应地调整似然分布状态,使之尾部更为平坦,增加先验和似然的重叠区,减少粒子退化。利用UT变换获得各个粒子的重要性密度函数,并将最新的量测信息引入到重要性密度函数设计以及重采样过程中,从而达到提高算法估计性能的目的。将提出的算法应用到SINS/SAR组合导航系统中进行仿真验证,结果表明,与PF和UPF算法相比,提出的基于似然分布的粒子数自适应UPF算法能有效改善滤波性能,提高解算精度。

Aiming at the poor real-time performance of particle filtering and the computation amount＇s exponentially increasing with particle numbers, this paper presents an adaptive sample size UPF（unscented particle filtering） algorithm, which takes the advantages of the adaptivities of likelihood distribution and sample number. In the state variance estimation, the lower limit of sample is set at each step, and the cases when state variance is too large or too small are taken into account. In the resampling phase, the likelihood samples are embedded, and the likelihood distribution state is adaptively adjusted based on the precision factor α which can reflect the real-time statistical performance of observational noises to increase the overlapping area of the prior and the likelihood and reduce particle degeneration. In addition, the method uses the unscented transformation to obtain the importance density function of each particle, and introduces the latest observational information to the importance density function and resample, thus effectively improves the estimation performance. By applying the proposed algorithm to the SINS/SAR integrated navigation system, the simulation results and their analysis demonstrate that, compared with the PF and UPF algorithms, the proposed algorithm can effectively improve filter performance and calculation precision.