CLTC-PL: A Robust Mathematical Framework and Algorithm for InSAR Phase-Linking Using the Central Limit Theorem of Circular Statistics

Phase-linking (PL) plays a crucial role in distributed scatterer (DS) synthetic aperture radar interferometry (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 statistics (CLTC) data, 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 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.