Phase-linking (PL) plays a crucial role in distributed scatterer (DS) InSAR, but conventional approaches often rely on strong prior assumptions about the underlying data distribution and involve solving highly nonlinear optimization problems. In this study, we propose a novel PL framework based on the central limit theorem for circular data (CLTC), which models interferometric phases through trigonometric moments and avoids any prior assumptions about the data distribution. The CLTC-PL formulation transforms the originally nonlinear PL problem into an inherently well-posed and locally linear weighted least-squares estimation, enabling efficient optimization with minimal iterations and error propagation analysis. The proposed method offers clear structural transparency and statistical interpretability, while having strong estimation performance. This work not only improves robust phase estimation, but also introduces a model-free framework where a multivariate normal distribution of trigonometric moments arises naturally via CLTC, allowing statistically grounded inference. Both simulated and real-data experiments validate the effectiveness of the proposed PL mathematical framework.

In this paper, we present a new method for weighting the wrapped phases of each interferogram to obtain a set of single reference phases, i.e. phase-linking. Unlike existing works that exploit the coupling between interferometric amplitudes and phases, the new method utilizes the principle of circular statistics and focuses only on the interferometric phases. In our method, the only assumption is that the averaged phases are von-Mises distributed. The simplicity of this model allows not to rely on the fully developed speckle assumption and to avoid optimizing additional parameters caused by more generalized speckle models. Simulation experiments show that, compared to conventional PL methods that assume a multivariate complex circular Gaussian model, our method is less accurate when the fully developed speckle assumption is perfectly valid, but more accurate when small deviations from this assumption occur.

Circular statistics is the mathematical theory for dealing with variables distributed on a circle. The interferometric phase of distributed targets can be modeled with circular statistics due to its wrapped and pseudorandom nature. In this study, we introduce a novel adaptive neighborhood selection (ANS) method and a novel phase-linking (PL) method for distributed scatterer (DS) interferometry, both based on circular statistics principles. The proposed ANS method enables the direct selection of pixels with similar SAR interferometry (InSAR) decorrelation behaviors, called similarly decorrelated pixels (SDP), from the interferometric phases. The proposed PL method: 1) shows significant resistance to the potential departure from the fully developed speckle assumption in the SAR observations (also known as non-Gaussianity) compared to methods that rely on this assumption; 2) does not introduce substantial implementation complexity, computational cost, or numerical solution challenges compared to methods that elaborately model the non-Gaussianity, e.g., through a product model; and 3) can achieve higher consistent wrapped phase estimation precision compared to other methods solely based on interferometric phases. In addition to validating the proposed methods through simulation experiments, we also found that a combination of the two proposed methods can produce interferograms with minimal noise in a real data experiment.

In distributed scatterer (DS) interferometry, fringes within a multi-looking window can cause bias on coherence estimation and degrade phase-linking precision. Furthermore, fringes might also bias the estimated consistent phases. The problem can be solved by estimating and removing these fringes, i.e., defringing; however, imprecise estimation can significantly affect the results. Thus, a new defringing method for DS time series analysis is proposed. Different from the previous defringing methods, the new method makes use of the information from redundant interferometric combinations under the assumption of Gaussian speckle, and a series of consistent fringes with single reference can be obtained. The basic idea is to establish a framework of weighted least square adjustments with gross error elimination, exploiting the triangular consistency of fringe frequencies as a constraint to estimate fringes. The statistical properties of fringe frequency estimation were exploited to determine the optimum choice for the weight matrix. The quality of the estimated fringes can be improved significantly using the proposed method and therefore the quality of consistent phases in non-stationary areas can be increased. Simulated and real data experiments demonstrate the effectiveness of this new defringing method.

It is necessary to timely and accurately estimate the surface deformations in mining areas, especially the three-dimensional (3D) deformations during surface movement. At present, nearly all mining-induced 3D deformations retrieved by interferometric synthetic aperture radar (InSAR) pertain to the SAR imaging interval. Research on progressive 3D deformations during surface movement is limited, and the existing approaches are unsatisfactory in practical engineering. Aiming at these challenges, we proposed a novel method for deriving mining-induced 3D surface deformations at any moment by integrating single InSAR interferogram (SII), the Gompertz time function, and the probability integral model (PIM), named the SII-GPIM method. We established an inversion approach for GPIM parameters and derived the mining-induced 3D surface deformations at any moment. Subsequently, we conducted experiments considering two ALOS PALSAR images in the Huaibei mining area. The accuracy of the proposed method was evaluated in subsidence, tilt, curvature, horizontal displacement, and horizontal strain. Compared with existing methods, the SII-GPIM method is state of the art. Additionally, we assessed the building damage, performance of parameter inversion, and method generality. The results demonstrated that the proposed method can accurately determine the mining-induced 3D surface deformations and deformation level at any moment under different geological mining conditions. Moreover, accurate GPIM parameters can be acquired with only two SAR images and traditional measurement is nearly not required. Consequently, the SII-GPIM method owns great value for improving economic efficiency, assessing building damage, and restoring the ecological environment in the mining area.