Satellite positioning systems are essential for outdoor navigation applications and location-based services. Global navigation satellite systems (GNSS) have proven to be reliable, abundant, and efficient in providing location information for movable resources on Earth. Additionally, similar navigation systems can be adapted for extraterrestrial environments to support human and vehicular activities on celestial bodies. However, GNSS location services can be disrupted in harsh environments or under signal denial conditions. The increasing density of low Earth orbit (LEO) satellite constellations offers a new opportunity to provide positioning, navigation, and timing (LEO-PNT) services from satellites in closer proximity to Earth’s surface. Similarly, this new concept of LEO-PNT can be extended to suit other solar system entities such as the Moon and Mars. This article proposes a resilient satellite-based positioning methodology to obtain location information from LEO satellites in GNSS-denied scenarios. By combining positioning information from numerous LEO satellite beams incident on Earth’s surface, the new LEO-based positioning scheme can serve as a backup navigation system when primary GNSS services are disrupted. This method is entirely passive that exploits signals of opportunity, with minimal power consumption on the receiver’s side, and does not require: time synchronization, perfect geometric dilution of precision, or clear lines of sight. Simulation results indicate superior performance of the proposed LEO-based method compared to GNSS in vehicular positioning. The improvements in positioning accuracy ranged between (70%–95%) and (191%–205%) based on the analysis of two distinct vehicular datasets originating from the Google decimeter challenge.