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Linear Space [L, M]N and the Law of Generalized Variance-covariance Propagation

Liu Guolin, Zhang Lianpeng, Jiang Tao

Nonlinear functions are expanded into Taylor series up to the first two terms in true value L~. Coefficient vector f of the first-order terms and coefficient matrix F of the quadratic terms constitute [f, F], a vector in the linear space [L, M]N. And the generalized covariance operator D is defined in this space. The formulas of the law of generalized variance-covariance propagation for nonlinear function containing linear-quadratic terms are derived in this linear space. These formulas are unified in the form with that of linear function in the Euclidian space. On the other hand, making use of the theory of matrix also derives the matrix formulas of variance-covariance propagation for nonlinear function containing quadratic terms. It can be analyzed and proved the equivalence of these two methods and the relations with the linear propagation formulas.

 

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