## 4 Conclusions  
With the increasing interest in the use of low-frequency SAR systems, such as L- and P-bands, the influence on SAR interferometry due to the ionosphere continues to become significant and therefore limits further development of the InSAR technique. In this situation, this paper presents an efficient FR-based method to mitigate the ionospheric phase errors on polarimetric SAR interferograms. Compared with the existing methods, the proposed method uses an integrated phase model, which can correct the ionospheric errors as well as residual ionospheric phase errors caused by inaccurate parameters on SAR interferometry, and thus improve the correction precision. For the performance test, L-band ALOS/PALSAR full-polarimetric SAR images over high-latitude and low-latitude regions are processed. Based on this study, the following conclusions are summarized:  
(1) Ionospheric phase error on full-polarimetric SAR interferometry is effectively mitigated by the proposed FR-based method. Using inversed VTEC distribution from FR angles, an integrated phase model is used to jointly mitigate the ionospheric phase errors. The experimental results show that most ionospheric phase errors are removed from the original phase. These results validate that the FR-based method can effectively mitigate the ionospheric phase errors. (2) The VTEC distribution with high spatial resolution is successfully mapped from the full-polarimetric SAR data. In this study, the high-spatial-resolution VTEC distribution is inversed from FR angles. When comparing with the GPS-measured ionospheric variations, we found that they are basically consistent. These results prove that it is possible to map the high-spatial-resolution VTEC distribution from the full-polarimetric SAR data. Although the reliability of the FR-based method has been proven by two experiments, there are still some limitations. The first is the FR estimation error due to the inaccurate calibration parameters, such as channel imbalance\(f1\) and \(f2\), crosstalk terms \(\delta 1\), \(\delta 2\), \(\delta 3\) and \(\delta 4\), additional noise N, as well as backscatter characteristics of the imaged surface. Since the ionosphere-induced phase shift in (10) is derived from the estimated FR, this error will inevitably introduce bias in the ionospheric correction when using (11). Another limitation is the imprecise geomagnetic field parameters, such as the intensity of earth's magnetic field. In this study, the geomagnetic field parameters are derived from the IGRF, which is a standard mathematical description of the Earth's main magnetic field. In other words, it is difficult to obtain the actual local geomagnetic activity, resulting in the imprecise estimation of VTEC. Figure 12: Comparison among the interferometric phase in the profile B-B’ in Figure 11a,c,d. Although the proposed method can correct part of residual ionospheric phase error caused by the inaccurate calibration parameters and imprecise geomagnetic field parameters, it is difficult to remove them completely, particularly for the small-scale residual ionospheric phase. The final limitation is that some useful phase signals with long-wavelength characteristics may be removed when using our proposed method, such as interseismic deformation. Therefore, multi methods, such as range split-spectrum based method, range/azimuth offset based methods, as well as the FR based method, will be fused in the future to improve the precision of the ionospheric correction on SAR interferometry. Validation, J.-Y.C. ; Writing--original draft, W.Z. ; Writing--review & editing, H.-S.J. This research was funded by Chang'an university (Xi'an, China) through National Key R&D Program of China (2018 YFC1505101), Natural Science Foundation of China projects (NSFC) (No: 41790445, 41731066, 41504005, 41674001, 41604001), Natural Science Basic Research Plan in Shaanxi Province of China (2018)Q4031), and the Fundamental Research Funds for the Central Universities, CHD (No: 300102269207, 300102269303).