The Optimal Regularization Method and its Appli- cation in GNSS Rapid Static Positioning

In rapid static or kinematic positioning, especially with single frequency and shorter period GPS phase observations, the normal matrix may be weak multicollinear since the GPS satellite’s positions and geometries are changing slightly. Therefore the conventional least squares float solution may cause large biases due to the weak multicollinearity and thus make the ambiguity search techniques fail to work. Here the newly developed method of determining the optimal regularization parameter α in uniform Tykhonov-Phillips regularization (α-weighted ShomBLE) 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 of problem in both GPS rapid static and real time kinematic positioning with single or dual frequency measurements, especially for the shorter observation period. In the case study, the estimate method is applied to process the two-epoch L1 data in single frequency GPS rapid static positioning. A detailed discussion about effects of the initial coordinate accuracy to the determination of the A-optimal regularization parameter will also be presented. The results show that a new algorithm with optimal regularization can significantly improve the reliability of the GPS ambiguity resolution in shorter observation periods.