Study on the Singular Value Decomposition Method of Weighted Rank-deficient Free Network Adjustment
To solve the problem that the traditional weighted rank-deficient free network adjustment methods need to obtain the gener-alized inverse of the coefficient matrix of the normal equation or to obtain the constraint conditions or pseudo-observation equations in advance,this paper proposes a weighted rank-deficient free network adjustment method based on singular value decomposition system.This method not only avoids the above steps of the traditional methods,but also could be applied to the case where the observation val-ue weight matrix and the parameter priori weight matrix are of arbitrary forms,which realizes the simplification of the calculation process and the expansion of the application range.The weighted rank-deficient free network adjustment is widely used in leveling net-work and GPS network,and the corresponding examples are verified in this paper.The results show that the adjustment accuracy and calculation efficiency of the proposed method are completely consistent with the traditional approaches.Thus,it provides an alternative method for the weighted rank-deficient free network adjustment and can play a role in the fields of data quality inspection and deforma-tion analysis within the control network.
weighted rank-deficient free network adjustmentsingular value decompositionweighted least-norm least squares solu-tion
NETL
NSTL
万方数据
