Deformation Information Extraction from Multi-GNSS Coordinate Series Based on EWT-ICA-R

Global navigation satellite system (GNSS) has been widely used in many deformation monitoring fields in recent years and can achieve centimeter-level or even sub-centimeter-level real-time monitoring accuracy through the carrier phase double-differenced technique. However, this technique cannot eliminate or weaken multipath errors, which become the main error source for GNSS deformation monitoring. Therefore, extracting deformation information from coordinate series mixed with multipath errors has become a key issue for further improving the accuracy of GNSS deformation monitoring. In this paper, we propose an approach to overcome this issue called empirical wavelet transform-independent component analysis with reference (EWT-ICA-R). The specific process is as follows. First, EWT is employed to model the multipath errors from a priori GNSS coordinate series, and the model is input to ICA-R as a reference signal. Then, the GNSS deformation monitoring series mixed with multipath errors and deformation information is decomposed into sub-series of different scales using EWT, and these sub-series are input to ICA-R as multi-channel signals. Finally, ICA-R is used to calculate the input signals together to obtain the multipath errors in the GNSS deformation monitoring series and then subtract the multipath errors from the GNSS deformation monitoring series to obtain accurate deformation information. Experiments show the following: (1) For the vibration deformation experiments, the correlation coefficients between the deformation information extracted by the proposed method and the real values reached 0.981, 0.981, and 0.885 in the E, N, and U directions, respectively, and the corresponding root mean square errors decrease to 0.694 mm, 0.694 mm, 1.852 mm, respectively. (2) For the slow-deformation experiment, the correlation coefficients in the three directions were all higher than 0.98, and the corresponding root mean square errors decrease to 1.345 mm, 1.546 mm, and 3.866 mm, respectively. The experiments verified the feasibility of the proposed method to accurately extract deformation information, which makes it possible to obtain sub-millimeter GNSS deformation information and provide effective technical support for deformation monitoring in related fields.