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## Direct Solution to Generalized Ridge Estimate

YOU Yangsheng 1 WANG Xinzhou 2 LIU Xing 3 (1 School of Geodesy and Geomatics,Wuhan University,129 Luoyu Road,Wuhan,China,430079) (2 Projects and Consulting Office,Wuhan University,Luojia Hill,Wuhan,China,430072) (3 School of Civil Engineering,C
Generally,under the Gauss_Markov model L=BX+Δ,the least square estimators of the parameters X=N -1 B TL possess some nice characters.In surveying,especially in dynamic GPS surveying,ill_conditioned problems may be encountered.When the surveying system is morbid and then the characters of the least square estimators become bad.Adding a diagonally matrix K to N will improve the state of N and then decrease the total variance of the estimates.Recent investigations of ill_conditioned problems have demonstrated that ridge_type estimation methods provide increased solution accuracy over conventional estimation techniques. That the generalized ridge estimate has less mean square error than the least square estimation.Naturally,the gotten estimators is expected to reach the minimum of mean square error.Because the mean square error of estimators is the function of K,we should fix K depending on the minimum of the mean square error.On the basis of this idea,this paper brings about a method to solve the above problem,which is called direct solution to generalized ridge estimate (DSGRE).With DSGRE,we can obtain the optimal solution (that possesses the minimum of MSE) to the generalized ridge estimate directly and the ridge parameters K needn't to be calculated.
【Fund】： 国家自然科学基金资助项目 ( 4 98740 0 2 ) ;; 国家测绘局测绘科技发展基金资助项目 ( 990 10 )
【CateGory Index】： P207
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