Optimal Tikhonov Regularization Matrix and Its Application in GNSS Ambiguity Resolution

This contribution can be mainly divided into 3 aspects:(1) Based on Bayesian theory, unknown parameters are treated as random varies and their non-informative prior distribution function is introduced. Mathematical analysis is carried out to drive the optimal Tikhonov regularization matrix in the sense of minimizing the mean square error (MSE) of the solutions. (2) Combining the efficient truncated singular value decomposition (eTSVD), a new regularization method is proposed. (3) Global Navigation Satellite System(GNSS) ambiguity resolution application of the new method is discussed. Least squares (LS) estimation, ridge estimation of L curve and the new algorithm are compared by a group of GNSS ambiguity resolution experiments. The results show that the MSE of the new algorithm is slightly smaller than ridge estimation of L curve and much smaller than LS, however, the computational cost of the new algorithm is slightly more than LS but much less than ridge estimation of L curve.