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

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.

💡 Research Summary

The paper investigates the use of high‑altitude platform stations (HAPS) as a supplemental source for GNSS positioning in dense urban environments where signal blockage and multipath severely degrade accuracy. Recognizing that HAPS can provide line‑of‑sight (LOS) geometry from the stratosphere (18–22 km altitude) and that their deployment cost must be kept low, the authors formulate a joint optimization problem that simultaneously decides (i) how many HAPS to launch and (ii) where to position them within a conical sky region defined by a minimum elevation angle of 10° relative to the region’s centroid.

The objective is two‑fold: minimize the number of HAPS while ensuring that the average three‑dimensional Cramér‑Rao lower bound (CRLB) over a set of representative receiver locations stays below a predefined threshold τ. The CRLB is derived from the Fisher Information Matrix (FIM), which aggregates information contributions from all ranging links (satellites and HAPS). LOS links are modeled with zero‑mean Gaussian errors of known variance; NLOS links are modeled with Gaussian‑mixture models (GMMs) whose parameters are taken from empirical studies in Berlin. The building geometry B, extracted from a high‑resolution 3‑D city model, is used in ray‑tracing to label each link as LOS or NLOS, and the resulting information weights ψk are computed either analytically (LOS) or via numerical quadrature (NLOS).

Because the decision variables include a discrete cardinality term (the number of HAPS) and continuous spatial coordinates, the problem is highly non‑convex, non‑differentiable, and infeasible for exact convex reformulations. The authors therefore adopt a meta‑heuristic approach based on the Adaptive Special‑Crowding Distance Non‑Dominated Sorting Genetic Algorithm II (ASDNSGA‑II), a recent enhancement of NSGA‑II. Several key modifications are introduced: (1) Decision‑space crowding distance is replaced by an Aggregated Nearest‑Neighbor Distance (ANND) to fairly compare individuals with different HAPS counts; (2) A special crowding distance (SCD) that accounts for both decision and objective spaces is used to preserve diversity; (3) Crossover dynamically switches between Simulated Binary Crossover (SBX) and Blend Crossover (BLX‑α) based on an individual’s rank and its crowding distances, using a heuristic threshold; (4) After crossover or mutation, the integer nature of the HAPS count is enforced by rounding. The algorithm proceeds through standard GA steps—initial population generation, fitness evaluation (average CRLB and HAPS count), fast non‑dominated sorting, elite preservation, crowding‑distance computation, improved binary tournament selection, adaptive crossover, polynomial mutation, offspring evaluation, and environmental selection—repeated for a fixed number of generations.

Simulation experiments are conducted on a realistic 3‑D model of New York’s Wall Street area. A set of ~100 randomly placed receivers represents the region of interest, while satellite positions are taken from real ephemerides. Parameters include HAPS altitude limits (18–22 km), minimum elevation angle (10°), CRLB threshold τ = 5 m², population size 200, and 500 generations. Results show that the algorithm converges to a configuration with only two HAPS, achieving an average 3‑D CRLB of 4.3 m², compared to 12 m² when using satellites alone—a reduction of more than 60 %. Random HAPS placements with the same count yield CRLB values roughly 30 % higher, confirming the benefit of the optimization. The Pareto front clearly illustrates the trade‑off between deployment cost (number of HAPS) and positioning quality (CRLB), allowing system designers to select a solution that matches budgetary constraints.

The paper’s contributions are threefold: (i) integration of high‑fidelity ray‑tracing with GMM‑based error modeling to compute environment‑aware CRLB; (ii) formulation of a mixed integer‑continuous multi‑objective optimization for HAPS count and placement; (iii) development of a tailored ASDNSGA‑II algorithm that incorporates ANND and adaptive crossover to handle the peculiarities of the problem. Limitations include the computational burden of ray‑tracing (mitigated by using representative points), reliance on GMM parameters derived from a different city (requiring re‑calibration for other locales), and the offline nature of the optimization, which precludes real‑time reconfiguration. Future work is suggested in the direction of online adaptive placement under dynamic weather or traffic conditions, experimental validation with actual HAPS platforms, and extension of the objective function to include operational costs, power consumption, and communication bandwidth constraints.