A Dynamic Filtering Method Based on Generalized Extension Approximation Theory

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.