IGS station coordinates time series analysis requires precise and reliable noise model. A white noise plus power law noise with unknown spectral index model is considered in this study. The noise characterization resorts to a discrete wavelet based fractal analysis. However, the accuracy of the algorithm can be greatly influenced by the singular points consisting of step function and slope change in time series. To address the problem, we apply a compounded automatic detection method, including edge-preserved wavelet de-noise (EPWDN), total variation regularization estimation (TVR), pruned exact linear time (PELT) searching and synchrosqueezed wavelet transform (WSST) approaches. The proposed method sharpens the time-frequency representation of the IGS station coordinates time series with respect to singular point candidates, extracts seasonal signals without the artificial signal driven by power law noise, and overcomes the noise variance heterogeneity due to the evolution of the measuring techniques. The significances of all the candidates are checked by two-sample Kolmogorov-Smirnov test. Such nonparametric statistical test prevents the over-segmentation owing to the presence of temporal correlated power law noise which violates the basic assumption of Bayesian theory. The method is validated by 1000 Monte-Carlo simulated time series and applied to real IGS station coordinates time series in north, east and up directions for more than 200 IGS stations. The elicited segmentation results agree with manual analysis. Finally, with the singular points free IGS station coordinates time series, the noise characters including the estimated spectral indices and the variance constants of the power law noise can be provided.