有色噪声情况下逐次静态滤波公式的简化推导方法

A SIMPLIFIED DERIVATION OF THE FORMULAS OF STATIC FILTERING WITH COLOURED NOISES

白噪声情况下的静态逐次滤波可用极大验后或最小二乘虚拟观测值的方法简要表达其递推公式。但在有色噪声的情况下,一般仍用递推方法证明,过程繁琐。本文将有色噪声情况下的观测方程加以改化,变为等价的白噪声观测方程,可直接利用白噪声情况下的静态逐次滤波公式写出其逐次滤波式。不仅推导大大简化,且便于学习和理解。

In generalized adjustment when the observation noises are white we can derive the recursion formulas of static succesive filtering based on the criterion of maximum posteriori or the method of least squares with fictious observation values.When the observation noises are coloured is correlated, the recursion formulas usually are derived by steps in accordance to the practical corretation, thus the approaches are very complicated.In this paper the observation equations with coloured noises have been transformed into a set of equivalent equations with white noises and the recursion formulas can be obtained directly according to the recursion formulas in the case of white noises, therefore the derived procedure has not only been simplified but also compehended.