Optimized Deployment of HAPS Systems for GNSS Localization Enhancement in Urban Environments

TL;DR

The paper addresses the nonconvex, discrete problem of deploying a minimal number of HAPS to enhance GNSS localization in dense urban environments. It introduces a tailored ASDNSGA-II algorithm with decision-space ANND-based diversity, adaptive crossovers, and a conical feasibility projection to jointly optimize HAPS count and placement under a CRLB QoS constraint derived from ray-traced urban models. By evaluating LOS/NLOS via a Gaussian mixture model and using a 3D city model for visibility, the approach identifies near-optimal configurations that minimize infrastructure while achieving target localization accuracy; simulations indicate four HAPS can provide a strong accuracy-cost balance. The work offers a scalable, realistic framework for deploying HAPS-aided positioning systems with practical constraints and robust performance guarantees.

Abstract

While high altitude platform stations (HAPS) have been primarily explored as network infrastructure for communication services, their advantageous characteristics also make them promising candidates for augmenting GNSS localization. This paper proposes a metaheuristic framework to jointly optimize the number and placement of HAPS for GNSS enhancement in dense urban environments, considering practical constraints such as elevation masks, altitude limits, and ray-traced visibility from 3D city models. The problem is highly nonconvex due to the discrete HAPS count and the environment-dependent 3D Cramer-Rao lower bound (CRLB). To address this, we develop a tailored version of the adaptive special-crowding distance non-dominated sorting genetic algorithm II (ASDNSGA-II). Simulations show the method successfully identifies the minimum number of HAPS needed to satisfy a CRLB threshold and selects the configuration with the lowest CRLB within that minimum, offering a cost-effective and scalable solution for future HAPS-aided positioning systems.

Figures (5)

• Figure 1: System model for HAPS-augmented GNSS localization in dense urban environments (HAPS are placed within a conical volume between 18km and 22km altitude while maintaining a minimum elevation angle $\theta_{\text{min}}$ relative to the region center).
• Figure 2: Randomly placed receiver locations around the Wall Street.
• Figure 3: Number of HAPS in best solution over generations.
• Figure 4: Lowest average 3D CRLB vs HAPS count per generation.
• Figure 5: Lowest average 3D CRLB vs HAPS count in the final generation (blue dots: lowest average 3D CRLB; red line: average 3D CRLB).