In this research, we focused on producing a tightly-coupled (TC) integrated navigation system using consumer-grade GNSS and INS. Measurements of two GNSS constellations, the global positioning system (GPS) and the BeiDou navigation satellite system (BDS), were adopted in order to increase and strengthen satellite availability and geometric distribution. The extended Kalman filter (EKF) was then introduced to play a data fusing role through blending the GNSS and INS measurements, which comprised the core of the entire integrated navigation system. In an urban environment scenario, however, the GNSS signal suffers from various errors, which may not only give rise to poor navigation performance but also lead to EKF divergence. Hence, to enhance and improve both the robustness of the EKF and navigation accuracy, the receiver autonomous integrity monitoring (RAIM) fault detection and an exclusion (FDE) algorithm are also adopted in this research for the purpose of removing abnormal GNSS measurements and maintaining the quality of the EKF state estimation. Finally, a series of experiments were conducted in various environments to verify the proposed TC integration system.