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Solution for Coordinates Collocation Based on Covariance Function

The traditional algorithm for coordinates system conversion applies a mathematical model for computation of control points’ coordinates in the target coordinate system. However, it needs to be pointed out that the traditional algorithm is irrational because the control points’ coordinates are made up of systematic and stochastic parts, and the traditional algorithm applies a conversion model to fit the systematic part of coordinates, ignoring the stochastic part of coordinates. In this paper, a new solution that establishes the covariance function based on Reilly function to fit the stochastic part of coordinates is presented. Furthermore, the detailed steps for establishment of the covariance function, which takes the residual error of known control points’ coordinates in the target coordinates system as its basis, are proposed. To prove the solution presented in this paper is feasible, an instance is cited, and the numerical results clearly demonstrate that computation control points’ coordinates based on an algorithm that applies covariance function to fit the value of the coordinates is more accurate.