Collocation Based on Different Variance Component Estimators with Application in GIS Error Fitting

摘要

Collocation needs to know the covariance matrix of the signal vector,which is usually evaluated by a chosen covariance function and corresponding coefficient fitting. The covariance matrices of the observational noises and the stochastic signals should be harmonic,the corresponding weight matrices of the observations and the signals should correspond to the same variance scale. Otherwise,the collocation results will be twisted. This paper introduces the variance component estimation to balance the stochastic models of the observations and signals in a collocation model. The maximum likelihood estimator,MINQUE estimator and Helmert estimator of variance components are applied and compared in the collocation. A practical example of error fitting and correcting for a scanning map is given. It is shown that the collocation supported by variance component estimation improves the accuracy of scanning maps,and three kinds of variance component estimations and the approximate Helmert type estimation are nearly equivalent.