The Uniform Tykhonov-Phillips Regularization (α-weighted S-homBLE) and its Application in GPS Rapid Static Positioning

In high accuracy GPS positioning the conventional least-squares method is widely applied in processing of carrier phase observation. But it will not be always succeed in estimating of unknown parameters, in particular when the problem is ill-posed, for example, there is the weak multicollinear problem in the normal matrix with shorter period GPS phase observation. Here the newly developed method of determining the optimal regularization parameter α in uniform Tykhonov-Phillips regularization (α-weighted S-homBLE) by A-optimal design (minimizing the trace of the Mean Square Error matrix MSE) is reviewed. This new algorithm with A-optimal Regularization can be applied to overcome this kind problem in both GPS rapid static and real time kinematic positioning with single or dual frequency measurements, especially for the shorter period observation. In the case study, both the estimate methods are applied to process the two-epoch L1 data in single frequency GPS rapid static positioning. A detailed discuss about effects of the initial coordinate accuracy will also be presented. The results show that newly algorithm with optimal regularization can significantly improve the reliability the GPS ambiguity resolution in shorter observation period.