Physically Constrained Bayesian Optimization for Quantum Ranging under Complex Environments

Entangled photon ranging has the potential to surpass the classical precision limit, providing a key way for next-generation high-precision positioning and navigation systems. However, free-space photon transmission suffers from atmospheric turbulence and background noise, yielding a multimodal and nonconvex coincidence curve. Traditional methods relying on local peaks and fixed-shape assumptions easily fall into false peaks, leading to unstable time-delay estimations. Conventional global optimization algorithms ignore the physical traits of the coincidence peaks. They still suffer from slow convergence or misjudgments in noisy environments. To address this, we propose a robust quantum ranging method based on physically constrained Bayesian optimization (PCBO). By building a scoring function embedded with physical priors, this method effectively suppresses false peaks and optimizes global search efficiency, approaching the true delay within limited evaluations. In a 10-m free-space simulation, PCBO achieved a 96.0 % convergence rate under severe interference. For the successfully converged trials, the mean-absolute error (MAE) was as low as 3.34 mm, with the 90 % confidence interval bounded within 8.52 mm. Under identical conditions, PCBO outperforms traditional Bayesian optimization (BO) and particle swarm optimization (PSO) in both convergence speed and robustness. Ultimately, it provides an effective solution for high-precision quantum ranging in complex environments.