This paper evaluates the implementation of a low-complexity adaptive full DS-KF for robust tracking of GNSS signals. The full DS-KF includes FLL, DLL, and PLL tracking schemes. The DS-KF implementation in real-time applications requires a high computational cost. Additionally, the DS-KF performance decays in time-varying scenarios where the statistical distribution of the measurements changes due to noise, signal dynamics, multi-path, and non-line-of-sight effects. This study derives the full LUT-DS-KF: a simplified full DS-KF considering the steady-state convergence of the Kalman gain. Moreover, an extended version of the LBCA is presented to adapt the response time of the full LUT-DS-KF. This adaptive tracking technique aims to increase the synchronization robustness in time-varying scenarios. The proposed tracking architecture is implemented in an GNSS hardware receiver with an open software interface. Different configurations of the adaptive full LUT-DS-KF are evaluated in simulated scenarios with different dynamics and noise cases for each implementation. The results confirm that the LBCA used in the FAP is essential to maintain a PVT fix in high dynamics.