On the Impact of the Number of the Constellation Shells on Standalone LEO-PNT Positioning Metrics

Low Earth Orbit Positioning, Navigation and Timing (LEO-PNT) is an emerging paradigm in wireless navigation community, aiming at systems that both complement the existing Global Navigation Satellite Systems (GNSS) and can act as alternative global positioning methods in the events of outages or discontinuous availability of GNSS. Such limited availability can of GNSS can occur, for example, in indoor scenarios or deep outdoor canyons, or in the presence of strong jammers in GNSS bands. LEO-PNT solutions have been studied so far either in the context of signals of opportunity, where existing LEO mega-constellation signals can be re-used and repurposed, in an opportunistic way, also for positioning purposes, or in terms of standalone LEO-PNT solutions, where novel single-shell and multi-shell constellations are designed for the sole purpose of positioning, navigation, and tracking applications. In both approaches, the constellation geometry, as measured by the Geometric Dilution of Precision (GDOP) metric, the 4-fold coverage, meaning the percentage of Earth points having at least four satellites in view, and the carrier-to-noise ratio at the receiver are important positioning metrics. The focus of this paper is on analyzing the impact of increasing the number of constellation shells on the positioning metrics when the overall number of satellites in the orbits is fixed. The analysis is done with an advanced constellation simulator, under indoor and outdoor scenarios. Five heuristic constellations are introduced and compared with three benchmarks from the literature: two benchmark constellations based on Pareto optimization approaches and one commercial constellation. The focus is on small-sized constellations with less than 300 satellites. We find out that two-shell and three-shell heuristic approaches can reach satisfactory performance metrics under a wide range of orbital altitudes, and that more than three shells in the constellations are not necessarily bringing in additional improvements.