In challenging environments such as forests, valleys and higher latitude areas, there are usually fewer than four visible satellites. For cases with only two visible satellites, we propose a dual-satellite alternate switching ranging integrated navigation algorithm based on the broadband low earth orbit (LEO) constellation, which integrates communication and navigation (ICN) technology. It is different from the traditional dual-satellite integrated navigation algorithm: the difference is that it can complete precise real-time navigation and positioning without an altimeter and continuous observation. First, we give the principle of our algorithm. Second, with the help of an unscented Kalman filter (UKF), we give the observation equation and state equation of our algorithm, and establish the mathematical model of multipath/non-line of sight (NLOS) and noise interference. Finally, based on the SpaceX constellation, for various scenarios, we analyze the performance of our algorithm through simulation. The results show that: our algorithm can effectively suppress the divergence of the inertial navigation system (INS), in the face of different multipath/NLOS interference and various noise environments it still keeps good robustness, and also has great advantages in various indicators compared with the traditional dual-satellite positioning algorithms and some existing 3-satellite advanced positioning algorithms. These results show that our algorithm can meet the real-time location service requirements in harsh and challenging environments, and provides a new navigation and positioning method when there are only two visible satellites.