Challenging environments such as cities, canyons, and forests have become key factors affecting navigation stability. When users pass through intricate overpasses and winding road sections, due to the fluctuation of the geoid, there will be a large fluctuation problem in the elevation measurement error of the user’s receiver. In addition, even if the low Earth orbit (LEO) constellation has thousands of satellites, there will be no technical problems in regard to destroying LEO satellites with existing technology in extreme situations such as warfare and in challenging environments such as dense forests, canyons, and ravines, where three or fewer visible satellites is a foreseeable scenario. To solve the problem of providing location services in such challenging environments, first, we analyze the relationship between temperature and atmospheric pressure and altitude; and then, based on this, we propose an initialization correction method for elevation measurements. Next, based on the broadband LEO constellation, we give an integrated navigation and positioning scheme with the assistance of both a clock bias elimination system and an altimeter. Finally, the proposed scheme is simulated and verified. The experimental results show that the dynamic switching of LEO satellites, combined with the assistance of the altimeter, can effectively improve the stability and positioning accuracy of navigation and positioning and can suppress the large navigation errors caused by the long switching time without the assistance of the altimeter. This allows the switching time to be extended; thus, it can be used as a technical reference solution for integrated communication and navigation (ICN) in the future.