Single Epoch Algorithm Based on Tikhonov Regularization for Deformation Monitoring Using Single Frequency GPS Receivers

A new single epoch algorithm for deformation monitoring using single frequency GPS receivers, based on Tikhonov Regularization, is proposed in this paper. At first, the characteristic of the normal matrix for carrier phase measurements is analyzed. Since the normal matrix is rank-deficient, Tikhonov regularization theorem is applied to the least squares problem, and a regulariser is chosen to transform the matrix from the rank-deficient to the full rank. Then, the float ambiguity solutions and their Mean Squared Error Matrix (MSEM) are obtained. MSEM can be used to determine the search space for the integer ambiguities, combined with other integer ambiguity fixers such as LAMBDA. The proposed single epoch algorithm is tested using carrier phase measurements of two single frequency GPS receivers with a baseline over 3km and the results show that the success rate of the integer ambiguity fix is greater than 90%.