Solving ill-posed problem of whole-cycle ambiguities estimation using damped singular value decomposition

In this paper we deal with the ill-posed problems of whole-cycle ambiguities estimation by damped singular value decomposition (DSVD). First, we presented a singular normal equation matrix of whole-cycle ambiguities estimation, and then added synthetic noises to the right hand side to create two “noisy problems”. Second, we performed DSVD in conjunction with some parameter-choice approaches (e.g., the L-curve, generalized cross-validation (GCV) function, and normalized cumulative periodogram (NCP)), to solve ill-posed problems under different noise conditions. Finally, we also discussed the performance of these parameter-choice approaches. The results indicate that DSVD is promising in solving ill-posed problems, and the selection of regularization parameter has significant effect on the ambiguities estimation.