带不确定量测和未知虚警概率的粒子滤波器

Particle filter with uncertain measurement and unknown false alarm probability

中文关键词  不确定量测  虚警概率  粒子滤波器  非线性滤波  极大似然估计

英文关键词  uncertain measurements  false alarm probability  particle filter  nonlinear filtering  maximum likelihood estimation

中文摘要

      为了解决带不确定量测和未知虚警概率的非线性非高斯系统状态估计问题, 本文提出了一种新的粒子滤 波方法, 利用随机不确定量测模型来更新粒子和权值, 并基于极大似然准则来辨识未知的虚警概率. 本文所提出的 带不确定量测和已知虚警概率的粒子滤波方法与现有标准的粒子滤波方法具有几乎一致的计算复杂度，但是更适 合用于处理带不确定量测的非线性非高斯系统状态估计问题. 此外, 在状态转移密度函数被选择为建议密度函数 时, 本文证明了基于所提出的虚警概率辨识方法的极大似然估计唯一, 从而为精确辨识虚警概率提供了理论保证. 单变量非平稳增长模型和纯方位跟踪的数值仿真验证了所提出粒子滤波方法的有效性和与现有方法相比的优越性.

英文摘要

      A new particle filtering method is proposed to solve the state estimation problem for nonlinear and non- Gaussian systems with uncertain measurement and unknown false alarm probability. Particles and their weights are updated in Bayesian estimation framework by utilizing randomly uncertain measurement model, and unknown false alarm probability is identified by maximum likelihood rule. The proposed particle filtering method with uncertain measurement and known false alarm probability has almost the same computation complexity as existing standard particle filtering methods, but it is more suitable for addressing the state estimation problem of nonlinear and non-Gaussian systems with uncertain measurement. Besides, the maximum likelihood estimation based on the proposed identification method of false alarm probability is unique when state transition density function is chosen as proposal density function, which provides accurate theoretical support for identifying false alarm probability. The effectiveness and superiority of the proposed particle filtering method as compared with existing methods are illustrated in numerical examples concerning univariate non-stationary growth model and bearing only tracking.