Modeling and Correction Methods for Stellar Tracking Measurement Errors in Marine Celestial Navigation Equipment

To address the compensation and correction of stellar tracking measurement errors in marine celestial navigation equipment with a small field of view, this study investigates error modeling and correction methods. A rectangular coordinate system for stellar tracking is established, and the sources of measurement errors along with their propagation processes are analyzed. A classical stellar tracking error model is constructed under small-angle error constraints. However, the classical model's reliance on small-angle approximations imposes stringent requirements on machining, alignment precision of the tracking axis, and optical system imaging accuracy, making it unsuitable for cases involving nonlinear installation errors or optical distortion. To overcome this limitation, a neural network-based approach for stellar tracking error modeling and correction is further explored, including input-output design, network architecture, model training, and error compensation implementation. Experimental validation using real-world stellar tracking data demonstrates that the classical method achieves a compensation accuracy of 0.034′ (RMS) for azimuth error and 0.041′ (RMS) for elevation error in stellar tracking measurements, while the neural network method achieved accuracies of 0.018′(RMS) for azimuth error and 0.035′(RMS) for elevation error. The results confirm the effectiveness of both approaches, with the neural network method outperforming the classical one in compensation precision.