非线性函数协方差传播公式的两种方法及其等价性

本文将非线性观测值函数泰勒级数展开，并取至二次项，得到线性一二次项形式。一方面在线性空间L，M]］n中推导出含有二次项的非线性函数的广义协方差传播公式，该公式在形式上类似于经典欧氏空间中的协方差传播公式；另一方面又利用矩阵理论等推导出含有二次项的非线性函数的协方差传播公式的矩阵形式。分析并证明了二者的等价性及与经典传播公式间的关系。

TWO METHODS OF THE COVARIANCE PROPAGATION FORMULAE OF THE NON-LINEAR FUNCTION AND THEIR EQUIVALENCE

This paper expands the non-linear observation function in Taylor's series, takes to the quadratic term and obtains the form of the linear-quadratic term. On the one hand, it derives the generalized covariance propagation formula containing quadratic tertns in the linear space L,M]., which is in the form similar to the covariance propagation formula in the classical Euclidian space. On the other hand, it also derives the covariance propagation formula of non-linear function containing quadratic term in matrix form using the matrix theory etc. It analyzes and proves the equivalence of these two methods and the rel8tion with the classical propagation formulae.