Regularization approach for dynamic resolution of phase integer ambiguity in GPS rapid positioning

In view of the ill-condition of normal matrix which is formed by few epoch observations in GPS rapid positioning, a new ambiguity resolution method was proposed, in which the modified singular value decomposition (SVD) is designed to acquire the accurate singular values of coefficient matrix, which avoids the influence of small singular value disturbance. Then an improved Tikhonov regularization method is proposed, and a regularizer matrix is constructed based on the characteristics of ill-condition matrix and modified SVD. Experimental example shows that, compared with least squares estimation and Tikhonov regularization combining with LAMBDA algorithm, the improved method has reduced the condition number of normal matrix by about 3 orders of magnitude, and has reduced the variance of float ambiguity deviated from true value to 1.04 from the original 41.89. As a result, a more accurate and stable float solution can be quickly obtained only by the L1-frequency data of four epochs, while the success rate is improved to 100%. © 2015, Editorial Department of Journal of Chinese Inertial Technology. All right reserved.