The current and planned synthetic aperture radar (SAR) sensors mounted on satellite platforms will continue to operate over the coming years, providing unprecedented SAR data for monitoring wide-range surface deformations. The near real-time processing of SAR interferometry (InSAR) data for the retrieval of ground-deformation time series is urgently required in the current era of big data. The state-of-the-art Kalman filter (KF) and sequential least squares (SLS) algorithms have been proposed to update an InSAR-driven ground-deformation time series. As a contribution of this study, we customize the conventional KF and SLS for big InSAR data for near real-time processing. The development of an accurate prediction model for KF-based InSAR processing is a challenge owing to the large scale of the targets for surface monitoring. We developed a modified KF algorithm, abbreviated as npKF, that does not require any prediction information, abbreviated as npKF. In this context, to avoid occupying a large storage space in SLS-based InSAR processing, we developed a modified SLS algorithm with a truncated cofactor matrix, abbreviated as TSLS. Using both simulated and actual SAR data, we evaluated the performance of these methods under three different aspects: accuracy, computation, and storage performance. With big data, the proposed method can estimate the deformation time series in near real time. It will be a reliable and effective tool for producing near real-time InSAR deformation products in the coming era of processing big SAR data and will play a part in the geologic hazard routine monitoring and early warning system.