一种基于广义延拓逼近的动态滤波方法初步研究

A Dynamic Filtering Method Based on GeneralizedExtension Approximation Theory

从广义延拓逼近原理出发,提出了一种动态滤波方法,构造了滤波器模型与算法框架,并推导给出了相应的求解方法和流程。通过在一段移动平滑窗口内构造和求解广义延拓插值多项式,实现对系统状态量的时间转移,具有更好的平滑效果。数据窗口内插值点的位置及数量均可灵活选取,从而通过锁定最新观测点或最准确的先验观测点,实现更高的精度和抗差能力。在此基础上,对方法可行性与性能进行了仿真计算和验证,结果表明,在高斯噪声和非高斯噪声状态下均获得了优于卡尔曼滤波器(Kalmen Filtering,KF)的性能,具有较大的发展潜力和应用价值。

Based on a generalized extension approximation principle,a dynamic filtering method is proposed.The model and algorithm framework of the method are constructed,and the corresponding solution method and process are derived.By constructing and solving the generalized extension interpolation polynomial in a moving smoothing window,the time transition of system state is realized,which has better smoothing effect.The position and number of interpolation points in the smoothing window can be flexibly selected,thereby achieving higher accuracy and robustness by locking the latest observation point or the most accurate prior to observation point.The feasibility and performance of the method are simulated and verified.The results show that the method has better performance than the Kalman filter in terms of both Gaussian and non-Gaussian noise,and has development potential and application value.