改进的无迹粒子滤波算法

Improved unscented particle filter

本文提出了一种改进的无迹粒子滤波算法(IUPF).与传统的粒子滤波算法不同,IUPF中每个粒子并不代表状态序列的一个可能实现,而是代表由初始状态以及过程噪声序列所构成的扩展过程噪声序列的一个可能实现.根据状态空间方程所属的类型,IUPF可以采用不同的无迹变换方法来设计建议分布.并借鉴了基于无迹变换的辅助粒子滤波器(UTAPF)的思想来改进重采样过程.与UPF和UTAPF相比,新算法有3处改进.第一,IUPF无需假定状态转移核函数已知,因而应用范围较UPF和UTAPF广泛.第二,IUPF的计算开销较少.第三,UPF和UTAPF中每个粒子均被假设拥有一个从其父母粒子中继承下来的状态分布,然而这种假设是否合理目前尚难定论,IUPF避免了该假设.在两组仿真实验下将新算法与其它4种算法进行比较,新算法体现了较好的估计能力.并且结果显示与UPF以及UTAPF相比,IUPF所节省的计算时间与状态向量和噪声向量的维数有关.

Being different to the unscented particle filter（UPF） in which each particle represents a sample of the statesequence, the improved unscented particle filter（IUPF） has its particle representing a sample of the extended processnoise-sequence which is the combination of the initial states and the process-noise-sequence. For the different form of the state-space, a correspondent unscented transformation（UT） method is adopted to construct the proposal distribution. This method draws ideas from the unscented-transformation-based-auxiliary-particle-filter（UTAPF） to improve the re-sampling process. The IUPF has three advantages over the UPF and the UTAPF. Firstly, the IUPF requires no knowledge of the state transition kernel; thus, it has a wider application scope. Secondly, the IUPF has a lower computational cost. Thirdly, each particle in the UPF or the UTAPF is generally assumed to have a state distribution inherited from its parent particles, but the reason is questionable. However, this assumption can be avoided in the IUPF. In two simulation experiments of ours, the IUPF shows better estimation performance than the other four algorithms. Compared with the UPF and the UTAPF, the IUPF reduces the computation time by an amount depending on the dimension of the state vector and the dimension of the noise vector.