Near-Space Geolocation Using Sequential Stellar Refraction Angle Observations With an Explicit Measurement Model

Abstract

Autonomous geolocation is required for near-space aircraft when the Global Navigation Satellite System (GNSS) is unavailable. Stellar refraction navigation, which exploits the bending of starlight through the atmosphere, can serve as an independent aiding source. Conventional stellar-refraction models, however, assume spacecraft outside the atmosphere where ray-path symmetry holds, and are therefore not directly applicable to in-atmosphere aircraft; moreover, a fixed single-direction star sensor provides limited position observability. To address these two limitations, this article develops an explicit stellar refraction angle measurement model for near-space positioning and a single-sensor sequential observation method. The measurement model combines atmospheric refraction physics with the in-atmosphere ray-path geometry to form an implicit system relating the refraction angle to the aircraft position. The implicit system is solved offline, and its solutions are approximated using a 2-D log-domain Chebyshev polynomial. The resulting explicit model achieves an rms residual of $0.124^{\prime \prime }$ , corresponding to a relative rms error of 0.046%, on a held-out test set. The resulting explicit function is analytically differentiable for direct use in an extended Kalman filter (EKF). The sequential observation method employs a rotating star sensor that alternates between two viewing directions, with a delayed measurement fusion scheme to combine the nonsimultaneous observations; a trace-normalized D-efficiency metric further indicates that orthogonal directions provide the most balanced position information. Monte Carlo simulations (100 runs) show that the proposed sequential two-direction scheme achieves a mean 3-D RMSE of 295.88 m, a 61.3% reduction relative to the fixed single-direction configuration (764.43 m), with a mean RMSE only 52.07 m higher than that obtained using two continuously available directions (243.81 m). Among the tested rotation angles, the minimum mean error is obtained at 90°. These results demonstrate that single-sensor sequential stellar refraction observation provides a feasible, hardware-efficient solution for autonomous near-space geolocation in GNSS-denied environments.