Rotation method for reconstructing process and field from imperfect data

Abstract

Reconstruction of a process and fields from noisy data is to solve a set of linear algebraic equations. Three factors affect the accuracy of reconstruction: (a) a large condition number of the coefficient matrix, (b) high noise-to-signal ratio in the sorce term, and (c) no a priori knowledge of noise statistics. To improve reconstruction accuracy, the set of linear algebraic equations is transformed into a net set with minimum condition number and noise-to-signal ratio using the rotation matrix. The procedure does not require any knowledge of low-order statistics of noises. Several examples including highly distorted Lorenz attractor illustrate the benefit of using this procedure.