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Global Navigation Satellite System (GNSS) receivers are vulnerable to intentional spoofing attacks which can manipulate position, velocity, and time (PVT) measurements. Previous work has demonstrated that Time Synchronization Attacks (TSAs) can be detected and mitigated using sparse optimization techniques which reveal spoofers’ presence in inflicted signals’ derivative domains. Aiming to provide an efficient protection algorithm against spoofing, this paper expands the scope of the sparse signal processing framework to address more complicated attacks for stationary and low-dynamic receivers. In particular, TSAs against stationary receivers should be addressed differently if the position and velocity are manipulated by the spoofer at the same time. A new sparse processing method is presented employing a novel linearization of the measurement equation that includes attacks against time, position, and velocity. The method is assessed against both authentically and synthetically spoofed signals to verify its robustness in two test beds: 1) a lab-based software defined GPS receiver; and 2) a commercial hand-held device.