Iterative Parameter Fitting for Nonlinear Functions (Ionospheric Delay Model)

This study addresses the iterative parameter fitting problem for nonlinear functions, specifically focusing on ionospheric delay models. The ionospheric delay model incorporates ionospheric delay effects into GNSS (Global Navigation Satellite System) measurement error modeling. Parameter fitting for ionospheric delay models represents a significant research focus in ionospheric studies, as it enhances positioning accuracy in GNSS measurements. Our research implements an iterative approach for parameter fitting of nonlinear ionospheric delay functions, enabling better alignment with actual observational data and consequently improving GNSS measurement precision. The implementation employs gradient-based optimization algorithms that iteratively adjust model parameters to minimize the residual between predicted and observed delays. During this process, we conducted comprehensive experiments to validate the effectiveness of our proposed method. Specifically, we utilized multiple sets of real GNSS observation data and compared our approach against existing methods. The comparative analysis demonstrates that our method achieves significant improvements in parameter fitting accuracy, with implementation featuring convergence checks and adaptive step-size control to ensure stable optimization. The code structure includes key functions for residual calculation, Jacobian matrix computation, and parameter update routines that handle the nonlinear characteristics of ionospheric delay functions.