Mitigating Ill-Posedness in SAR Ionospheric Tomography Toward Multisatellite Collaboration

Abstract

In recent years, spaceborne low-frequency fully polarimetric synthetic aperture radar (PolSAR) ionospheric tomography has been an emerging technology for 3-D ionospheric computerized tomography (CIT). However, conventional single-satellite SAR (e.g., PALSAR) tomography suffers from pronounced ill-posedness due to restricted observation geometry, resulting in low reconstruction accuracy. Motivated by this issue and the future trend of multisatellite collaborative observation, where each satellite operates in a similar low-frequency fully polarimetric mode (e.g., PALSAR-2/3, BIOMASS SAR, and NISAR), this article proposes a novel joint 3-D reconstruction framework for low-frequency PolSAR CIT. A semi-physical simulation framework is established based on historical PALSAR-1 data to construct a robust ray observation geometry. Mathematical evaluations demonstrate that the multisatellite configuration significantly reduces the condition number of the geometric matrix, mitigating the ill-posedness of the tomographic equations. Furthermore, by constructing an augmented state vector, the proposed method adaptively isolates and calibrates heterogeneous platform-specific polarimetric system errors, enabling reliable absolute total electron content (TEC) estimation without relying on external Global Navigation Satellite System (GNSS) references. The 3-D reconstruction results reveal that, compared to the conventional single-satellite model, the root-mean-square error (RMSE) is reduced by 12.2%, and the condition number of the normal matrix (associated with the tomographic inversion) is reduced by a factor of 1.63, demonstrating a measurable enhancement in the numerical stability of the multisatellite configuration. This study can provide vital theoretical support and an algorithmic reference for 3-D ionospheric sensing in future L-band multisatellite SAR constellations.