With the increase in the number of Global Navigation Satellite System (GNSS) satellites and their operating frequencies, richer observation data are provided for the tightly coupled Global Navigation Satellite System/Inertial Navigation System (GNSS/INS). In this paper, we propose an efficient and robust combined navigation scheme to address the key issues of system accuracy, robustness, and computational efficiency. The tightly combined system fuses multi-source data such as the pseudo-range, the pseudo-range rate, and dual-antenna observations from the GNSS and the horizontal attitude angle from the vertical gyro (VG) in order to realize robust navigation in a sparse satellite observation environment. In addition, to cope with the high computational load faced by the system when the satellite observation conditions are good, we propose a weighted quasi-optimal satellite selection algorithm that reduces the computational burden of the navigation system by screening the observable satellites while ensuring the accuracy of the observation data. Finally, we comprehensively evaluate the proposed system through simulation experiments. The results show that, compared with the loosely coupled navigation system, our system has a significant improvement in state estimation accuracy and still provides reliable attitude estimation in regions with poor satellite observation conditions. In addition, in comparison experiments with the optimal satellite selection algorithm, our proposed satellite selection algorithm demonstrates greater advantages in terms of computational efficiency and engineering practicability.