Optimal Deployments of Flux‐Weighted Geometric Dilution of Precision for Wireless Muons Positioning System

ABSTRACT

The principle of wireless muons positioning is similar to that of GNSS, with position calculated by measuring distances between reference detectors and the positioning detector; hence, reference deployment directly affects system performance. To address the issue that the traditional GDOP model ignores the flux characteristics of discrete muon incidence and cannot accurately evaluate configuration performance, this paper constructs a flux normalisation model to eliminate nonphysical interferences, establishes a weighted GDOP model adapted to muons positioning, and derives its quantitative relationship with traditional GDOP. For four typical symmetric configurations, simulation experiments with varying horizontal baselines and vertical heights are conducted to quantitatively analyse positioning accuracy variation within a 200 m × 200 m area. Results show that for baseline length within 70 m short‐baseline scenes, five‐station star layout owns the optimal positioning performance. At the optimal baseline of 50 m, its average weighted GDOP is 4% lower than that of the square layout and 2.8% lower than that of the regular pentagon layout. For long baselines and varying heights, the pentagonal configuration converges fastest and shows strongest robustness. This research provides theoretical support and quantitative basis for detector deployment optimization in muons positioning system under GNSS‐denied environments.