A neural network-based automatic semi-variogram modeling approach for geomagnetic map construction in multi-source indoor and outdoor navigation.

High-precision geomagnetic maps are essential for geomagnetic-assisted navigation, yet their construction is constrained by kriging interpolation's reliance on accurately modeled semi-variogram. Conventional approaches depend heavily on geological expertise, introducing subjectivity and limiting both mapping accuracy and navigation performance. Here, we present geomagnetic map via auto-semi-variogram kriging(GMAS-K), a framework that integrates geomagnetic map via auto-semi-variogram convolutional neural network(GMAS-CNN) to automatically infer semi-variogram parameters. GMAS-CNN adopts an encoder-decoder architecture: the encoder compresses and fuses multi-scale features of geomagnetic samples to enrich semi-variance representations, while the decoder reconstructs latent feature spaces to estimate semi-variogram parameters. To further enhance cross-scale consistency, we introduce a multiple convolutional block attention module (M-CBAM). Experiments show that GMAS-K surpasses ordinary kriging, producing smoother and more accurate geomagnetic maps while streamlining the mapping workflow. These results highlight the promise of coupling deep learning with geostatistical interpolation to advance geomagnetic mapping and improve navigation accuracy.