Fringe-Enhanced Phase Unwrapping Method Based on an Iterative Bayes–Sard Quadrature Kalman Filter

Phase unwrapping plays a vital role in interferometric synthetic aperture radar (InSAR) processing. However, the presence of noise can introduce inconsistencies in phase discontinuities, giving rise to residue points that may cause unwrapping errors. To address this challenge, this paper for the first time applies the Bayes–Sard quadrature transform to the phase unwrapping problem and proposes an iterative Bayes–Sard quadrature Kalman filter phase unwrapping method (IBSQKF). In contrast to the conventional unscented Kalman filter algorithm, the Bayes–Sard moment transform can quantify the additional uncertainty introduced by quadrature errors. Through integration with the proposed iterative strategy, it enables more accurate calibration of state estimation and effectively reduces the root mean square error. To further enhance unwrapping accuracy, a multi-level and multi-scale feature fusion neural network (PFTNet) is developed as a pre-filtering module to independently process the real and imaginary components of the complex interferometric phase representation, which can effectively enhance the clarity of the interferometric fringes. By integrating PFTNet with IBSQKF, a complete phase unwrapping framework (PFT-IBSQKF) is constructed to further improve unwrapping accuracy. Experiments on both simulated and real data demonstrate that IBSQKF can reliably restore phase continuity, while PFT-IBSQKF can further reduce unwrapping errors, especially in low signal-to-noise-ratio or fringe-blurred scenarios. Despite the introduction of the iterative strategy, the proposed framework still maintains an acceptable computational cost while achieving high unwrapping accuracy.