The Parallel Recursive Sub-optimal Sage Filter Based on SPRT

Sage filter can simultaneously estimate the expectation values and the corresponding variance matrices of the unknown system and measurement noises.But in practice,we find that there are often constant biases in the results of the classic sub-optimal Sage filter,caused by the inaccurate estimation of the noise expectations.So a novel structure of two parallel filters that proceed simultaneously is presented in this paper.This new structure can not only eliminate the result biases of the classic sub-optimal Sage filter but also provide a more improved accuracy.In addition,SPRT method is used to control the adjustment of the noise statistics,so as to ameliorate the tracking performance of time-variant noises,however,the classic Sage filter does not suit the dynamic system of time-variant noises.Furthermore,the calculation burden is released and the numerical stability is improved by applying SPRT.Then a completely new parallel sub-optimal Sage adaptive filter is provided in this paper.The specific characters of the new filter can be summarized as follows:1) There are always constant biases in the results of classic sub-optimal Sage adaptive filter,so a parallel filter structure of adding a concomitant filter is designed to eliminate these constant biases;2) SPRT testing method is applied to the above parallel structure to test whether the statistical properties of the model noises are disturbed or not,so as to control the adjustment of the statistics.Then the filter's performance of tracking time-variant noises is significantly improved and the calculation burden is also released.In a word,the new adaptive Sage filter attempts to innovate the standard sub-optimal Sage filter,and make it practical.