具有双重不确定性系统的联合滤波算法

卡尔曼滤波在高斯白噪声的假设下是一种最优滤波, 基于区间数学理论的集员滤波 (Set-membership filter, SMF)能够有效处理有界噪声假设下的滤波问题. 然而, 随机噪声和有界噪声在许多情况下会同时干扰控制系统. 由于两种滤波算法都受到各自适用范围的限制, 使用单一滤波算法难以得到理想的估计结果. 本文通过建立具有双重不确定性系统的模型, 提出了一种基于贝叶斯估计联合滤波算法. 该算法用卡尔曼滤波处理系统的随机不确定性, 用集员滤波处理系统的有界不确定性, 得出一个易于实现的滤波器. 最后通过对雷达跟踪系统的仿真, 结果表明, 较单一滤波算法, 联合滤波具有更强的噪声适应性和有效性.

A New Combined Filtering Algorithm for Systems with Dual Uncertainties

Kalman filter is optimal under the assumption of Gaussian white noise, while the set-membership filter (SMF), which is based on interval mathematics, can deal with bounded noise efficiently. However, in many situations, the actual control system is usually interrupted by both random noises and bounded noises simultaneously. It is not easy to obtain expected results by using only one single filter, due to the limited application fields of the two filtering algorithms. In this paper, according to the established system model with dual uncertainties, a new kind of filter named combined filter is proposed, which is based on Bayesian estimation. This algorithm can deal with random uncertainties by applying Kalman filter, and can deal with bounded uncertainties by applying set-membership filter. Accordingly, a new kind of easy filter is produced. The effectiveness of the new filtering algorithm is verified in a radar tracking simulation system. From the simulation results, the combined filter algorithm can produce better adaptability and effectiveness than any one single filter.