Abstract:

To deal with the weight degeneration and particle impoverishment of the particle filter, firstly, the diversity index of particle distribution is defined, and the reason why standard fireworks algorithm (FWA) can??t be directly used to optimize particle filter is analyzed, then hybrid Gaussian distribution is used to improve the Gauss function of standard FWA to the hybrid Gauss mutation operator, which is used to increase the probability of generating better particles. To optimize particle filter with improved FWA, fireworks selection strategy is improved, which makes time complexity of fireworks selection strategy reduce from [O(N2)] to [O(N)]. To ensure optimized particle filter doesn??t lose the basis of bias filter theory, the calculation method of particle weight is redefined. And then, the      convergence of FWA-PF (fireworks algorithm particle filter) is discussed, and the operation mechanism of FWA-PF is expounded. Finally, through the experiment simulation, the BenchMark test of imp-FWA is carried out, the performance of FWA-PF is analyzed synthetically, and the setting method of the explosion radius and the number of spark explosions which affect the performance of the algorithm is described in detail. The experimental results show that the improved FWA optimize standard particle filter can effectively solve the problem of degeneration and impoverishment of the particle filter.

Key words: fireworks algorithm, Gauss distribution, particle filter, particle diversity

摘要：

为了解决粒子滤波中粒子权值退化和粒子贫化问题，定义了粒子分布多样性的指标，并分析了标准烟花算法（standard fireworks algorithm，FWA）不能直接用于优化粒子滤波的原因，再利用混合高斯分布将FWA的高斯函数改进为混合高斯变异算子，进而提高生成更优良粒子的概率。为了利用改进的FWA优化粒子滤波，改进了FWA烟花选择策略，使得烟花选择策略的时间复杂度由[O(N2)]降为[O(N)]。为了确保优化的粒子滤波不丧失贝叶斯滤波理论基础，重新定义粒子权值的计算方法。然后，重点分析了FWA-PF（fireworks algorithm particle filter）的收敛性，阐述了FWA-PF的运行机制。最后，通过实验仿真，对imp-FWA进行了BenchMark测试，综合分析了FWA-PF的性能，并详细表述了影响算法性能的烟花爆炸半径和火花爆炸数的设定方法。实验结果表明，改进的FWA优化标准粒子滤波的方法能够有效地解决粒子权值退化和粒子贫化问题。

关键词: 烟花算法, 高斯分布, 粒子滤波, 粒子多样性