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A space-time adaptive processing (STAP) algorithm for delay tracking and acquisition of the GPS signature sequence with interference rejection capability is developed. The interference can consist of both broadband and narrowband jammers. The narrowband jammers are modeled as vector autoregressive (VAR) processes and rejected by temporal whitening. The spatial nulling is implicitly achieved by estimating a sample covariance matrix and feeding its inverse into the extended Kalman filter (EKF). Computer simulations demonstrate robust performance of the algorithm in severe jamming, and also show that the algorithm outperforms the conventional delay-locked loop (DLL).