Regional Geomagnetic Field Modeling Based on Associated Legendre Polynomials

Global geomagnetic field models typically have low spatial resolution, whereas regional models are constrained by boundary effects and limited truncation levels. To address these limitations, this study introduces a novel regional geomagnetic anomaly field model called the regional associated Legendre polynomials magnetic model (R−ALPOLM). This model employs the associated Legendre polynomials method, which combines the QR decomposition approach and a comprehensive evaluation index formula to enhance the computational efficiency of parameter estimation. In addition, it allows for scientific and intuitive determination of the optimal truncation level of the model. The overall prediction accuracy of the model is significantly enhanced by identifying and re-predicting outliers using the exponential moving average approach. The results indicate that the degree 83 R−ALPOLM achieves a root mean square error (RMSE) of 3.21 nT. Compared to traditional models, the proposed model exhibits lower error rates, highlighting its superior efficiency and predictive accuracy. This underscores the potential value of the proposed model in both scientific research and practical applications.