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Adaptive collocation with application in height system transformation.pdf

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Adaptive collocation with application in height system transformation

J Geod (2009) 83:403–410 DOI 10.1007/s00190-008-0226-9 ORIGINAL ARTICLE Adaptive collocation with application in height system transformation Y. Yang · A. Zeng · J. Zhang Received: 10 October 2007 / Accepted: 31 March 2008 / Published online: 15 May 2008 ? Springer-Verlag 2008 Abstract In collocation applications, the prior covariance matrices or weight matrices between the signals and the observations shouldbe consistent to their uncertainties; other- wise, 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 obser- vations. A maximum likelihood estimator of the variance components is thus derived based on the collocation func- tional model and stochastic model. A simplified Helmert type estimator of the variance components for the colloca- tion is also introduced and compared to the derivedmaximum likelihood type estimator. Reasonable and consistent cova- riance matrices of the signals and the observations are arri- ved 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 trans- formation 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 balan- cing the contribution of observations and the signals in the collocation model. Y. Yang (B) Xi’an Research Institute of Surveying and Mapping, No. 1 Middle Yanta Road, Xian 710054, China e-mail: yuanxi@; yuanxi_yang@163.com A. Zeng Xi’an Information Division of Surveying and Mapping, 36 Xiying Road, Xian 710054, China A. Zeng · J. Zhang School of Geological and Surveying Engineering, Chang’an University, 126 Yanta Road, Xian 710054, China Keywords Collocation · A