IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 56, NO. 1, JANUARY 2018 49 A Wavelet Decomposition and Polynomial Fitting-Based Method for the Estimation of Time-Varying Residual Motion Error in Airborne Interferometric SAR Hai Qiang Fu, Jian Jun Zhu, Chang Cheng Wang, Member, IEEE, Hui Qiang Wang, and Rong Zhao Abstract— Compensating the residual motion error (RME) is very important in airborne interferometric synthetic aper- ture radar (InSAR). In this paper, the wavelet decomposition and polynomial fitting-based (WDPF) method is proposed for detecting and correcting the RME. Wavelet decomposition with root-mean-square error (RMSE) change ratio-based decompo- sition scale identification is used to detect the RME from the differential interferogram. Polynomial fitting in combination with robust estimation-based least squares is used to absorb the incidence-angle-dependent and topography-dependent com- ponents of the RME. A simulated experiment was conducted to test the proposed WDPF method. High-precision RME (with an RMSE of 0.0375 rad) was obtained, which can meet the require- ments of InSAR. Real-data L- and P-band InSAR experiments were also performed to test the WDPF method. The results confirmed that the WDPF method can effectively correct the RME for the interferogram. The RMSE of the estimated digital elevation model (DEM) was reduced from 8.03 to 3.46 m and 8.18 to 3.10 m for the L- and P-band interferograms, respectively. Finally, the effects of the external DEM error and polarization on the RME calibration were investigated. The results indicated that the global InSAR DEM products can fulfill the requirement of differential interferogram generation for the WDPF method, and the multipolarization interferograms can help to reduce the effect of the topographic error phase on RME estimation. Index Terms— Interferometric synthetic aperture radar (InSAR), motion compensation (MoCo), repeat pass, residual motion error (RME). I. I NTRODUCTION A IRBORNE interferometric synthetic aperture radar (InSAR) systems have been shown to be a powerful tool for the monitoring of forests [1], [2], agriculture [3], [4], and geological hazards [5], [6]. In order to build a rigorous Manuscript received March 14, 2017; revised June 15, 2017; accepted July 9, 2017. Date of publication November 8, 2017; date of current version December 27, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 41531068, Grant 41671356, and Grant 41371335, in part by the Hunan Provincial Innovation Foundation for Postgraduate under Grant 150140004, and in part by the PA-SB ESA EO Project Campaign. (Corresponding author: Jian Jun Zhu.) The authors are with the School of Geosciences and Info-Physics, Central South University, Changsha 410083, China (e-mail: haiqiangfu@csu.edu.cn; zjj@csu.edu.cn; wangchangcheng@csu.edu.cn; wanghuiqiang@csu.edu.cn; zhaorong1018@126.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2017.2727076 geometrical relationship between the interferometric phase and ground target position, it is important to exactly record platform motion by the SAR sensor’s navigation system so that motion compensation (MoCo) [7]–[9] can later be per- formed during the SAR imaging process. However, any MoCo approach is restricted by the positioning quality of the SAR sensor’s navigation system. As a result, the residual motion error (RME) induces misregistration and undesirable phase artifacts in the interferogram. For a single-pass interferometry, most of the RME can be canceled out since the two interfer- ometric images will have similar RMEs. However, the MoCo cannot meet the requirement of the positioning quality in repeat-pass interferometry. The reason for this is that it is difficult for the navigation system to exactly capture atmospheric turbulence motion, and the RMEs of each flight track are independent. Even when a high-precision navigation system is employed, the RME can still cause significant interferometric phase errors. As a result, the RME prohibits the extraction of accurate interferometric information from InSAR or differential InSAR (D-InSAR) data. In order to reduce the effect of the RMEs on the interfer- ograms, some efforts have been made to detect the RME and remove them from SAR and InSAR data by postprocessing steps, which differ from each other based on how the RMEs are estimated and modeled. The first kind of method is based on the multisquint processing technique [10]–[12], whose main principle is that the RMEs differ in different subapertures. This kind of method has widely been adopted in airborne D-InSAR applications [13], but its capacity is limited by low coherence, terrain displacement, and different phase centers of the sublook interferograms [14], [15]. The second kind of method, such as the weighted phase curvature autofo- cus (WPCA) method [16], is free from the limitation of any interferometric process or assumption on the interferometric phase, but it needs targets with high signal-to-noise ratio. The last kind of method based on detecting stable point-like targets is suitable for multibaseline InSAR data stacks [17]–[20]. However, sufficient SAR or polarimetric SAR data are needed to secure satisfactory results. As an alternative, in this paper, we propose a simpler way to correct the RMEs for the coregistered SAR images by the wavelet decomposition and polynomial fitting-based (WDPF) method. The main principle of this method is that along the range direction, the errors of the baseline parameters are scaled by incidence angles and ground elevations, which present definite trend and allow to be parameterized. This approach 0196-2892 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.