Adaptive collocation with application in height system transformation |
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| Authors: | Y Yang A Zeng J Zhang |
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| Institution: | (1) Xi’an Research Institute of Surveying and Mapping, No. 1 Middle Yanta Road, Xian, 710054, China;(2) Xi’an Information Division of Surveying and Mapping, 36 Xiying Road, Xian, 710054, China;(3) School of Geological and Surveying Engineering, Chang’an University, 126 Yanta Road, Xian, 710054, China |
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| Abstract: | In collocation applications, the prior covariance matrices or weight matrices between the signals and the observations should
be consistent to their uncertainties; otherwise, the solution of collocation will be distorted. To balance the covariance
matrices of the signals and the observations, a new adaptive collocation estimator is thus derived in which the corresponding
adaptive factor is constructed by the ratio of the variance components of the signals and the observations. A maximum likelihood
estimator of the variance components is thus derived based on the collocation functional model and stochastic model. A simplified
Helmert type estimator of the variance components for the collocation is also introduced and compared to the derived maximum
likelihood type estimator. Reasonable and consistent covariance matrices of the signals and the observations are arrived through
the adjustment of the adaptive factor. The new adaptive collocation with related adaptive factor constructed by the derived
variance components is applied in a transformation between the geodetic height derived by GPS and orthometric height. It is
shown that the adaptive collocation is not only simple in calculation but also effective in balancing the contribution of
observations and the signals in the collocation model. |
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| Keywords: | Collocation Adaptive estimation Variance component estimation geodetic height orthometric height |
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