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A virtual observational approach to ill-conditioned problem

FENG Guang-cai,DAI Wu-jiao,ZHU Jian-jun,CHEN Zhen-yang(School of Info-Physics and Geomantic Engineering,Central South University,Changsha 410083,China)  
To resolve the ill conditioned problem exists in geodesy data processing,there are many methods such as ridge estimation,singular value decomposition,Tihonov regularization.Most of these methods pay attention to the mathematic theory while lack the true physical meaning.These lead to difficulties in understanding and study of the ill-conditioned problem.In order to set real meaning to the method for ill-conditioned problem,a new method of ridge estimation based on virtual observation is developed in this paper.The apriori information was taken as one class of virtual independent observations,and then the ill-conditioned problem was translated to a problem of adjustment.So the ridge parameter can be resolved using Helmert variance components estimation which is a very common method in adjustment.And the weight matrix between the parameters can be derived from this method.The new method also can be used in general ridge estimation when the weight matrix of the virtual observations was replaced by the weight matrix between the parameters.The result of the examples show the new method is much simpler and more effective than the traditional methods.
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