摘要
卡尔曼滤波理论是适应实时控制的需要,对于系统的状态参数进行线性估计的一种递推算法。在卡尔曼滤波理论中,需要假设系统的状态噪声{w_k}和量测噪声{v_k}及系统的初始状态x_0均服从于高斯分布且相互独立;然而,在工程应用中上述假设条件并非都能满足,观测数据中常常含有异常值(outliers),而且量测噪声也往往是含有异常值的“长尾分布”,而从本质上讲是递推最小二乘估计的卡尔曼滤波对异常值的“长尾分布”非常敏感,甚至一个异常值会严重破坏对状态参数的估计。针对上述问题,本文应用贝叶斯定理,给出了状态噪声和量测噪声均为含有异常值的“长尾分布”的条件下一类动态模型状态的稳健贝叶斯估计;给出状态噪声为含有异常值的“长尾分布”条件下的状态参数的稳健贝叶斯估计。
The Kalman filter is an optional recursive data processing method widely used in engneering applications. However, the performance of the linear will degarde when dynamic noise is not Gaussian.In this paper the authors propose robust-Byaesian estimation for the state parameters of one kind of synamic models to deal with the problem. Two situations are considerated:a. The observation noise is Gaussian but the state noise is not Gaussian (scale-contaminated normal distribution).b. Both state noise and observation noise are not Gaussian (scale-contaminated normal distribution).The paper shows how a Bayesian approach allows the development of a simple recursive estimation algorithm that has the desired property of 'filtering' bad(i.s. estreme) obserbatioxns.
基金
国家航空科学基金
