Multi-Layer LEO Constellation Optimization for GLONASS Augmentation: Geometric Complementarity and Rapid PPP Convergence

The GLONASS constellation suffers from inherent geometric weaknesses in mid–low latitude regions, where uneven satellite elevation distribution leads to degraded PDOP and limits high-precision positioning performance. To address this gap, this paper proposes a three-layer heterogeneous LEO augmentation architecture, jointly optimized using an adaptive gradient-based framework and a CVaR-augmented objective to enhance geometric robustness under both average and worst-case conditions. The optimized design demonstrates significant performance improvements. For a 180-satellite configuration, the global mean PDOP is reduced from 2.31 to 1.39 (40.0% improvement), while polar-region PDOP improves by over 50%. More importantly, the proposed multi-layer LEO architecture substantially enhances Precise Point Positioning (PPP) convergence, reducing the convergence time from 27.6 min to 2.8 min, achieving a 9.8× acceleration. This improvement can be primarily attributed to the complementary multi-altitude and multi-inclination geometry, which significantly increases satellite visibility and strengthens observation diversity. These results highlight the effectiveness of heterogeneous multi-layer LEO constellations in overcoming the intrinsic limitations of legacy GNSSs. The proposed framework provides a scalable and robust design paradigm for future LEO-PNT systems, with direct implications for next-generation high-precision navigation services in challenging environments.