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Parameter estimation of least squares collocation

PAN Xiong1,2, SUN Hai-yan1(1. School of Geodesy and Geomatics ,Wuhan University ,Wuhan 430079, China;2. Dept. of mathematical and physical,Wuhan Polytechnic University ,Wuhan 430023, China)  
In this paper, based on penalized least squares, the penalized weighted sum of squares is set up, the calculation method of a positive definite regularized matrix is deduced and the corresponding results in least squares collocation model are obtained. According to the foundational properties of the random errors, how to choice a reasonable smoothing parameter and regularized matrix is studied. Concepts of confidence region in probability and method of region estimation are used. The adaptability of this technique is more flexible than the traditional model.
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