Research on the refined construction method of Kriging marine gravity field based on Matérn model optimization

Abstract To address the issue that the traditional Kriging algorithm has poor interpolation effect of the existing variogram when the data set is complete, and the pattern search method is heavily influenced by the initial value, it is easy to fall into the optimal value, making it difficult to obtain the optimal parameters. In this paper, an improved Kriging method based on Matérn model optimization is proposed. The Matérn model in the Gaussian regression process is introduced, and the model parameters are optimized by the sequential quadratic programming algorithm to achieve accurate interpolation of gravity reference map data. The results of cross-validation experiments show that the absolute average interpolation error of the improved algorithm is better than 0.02 mGal in the process of interpolating the gravity reference map with grid accuracy of 2’ × 2’ to 1’ × 1’, which is 45% better than that of the traditional interpolation algorithm. The improved algorithm effectively improves the precision of gravity field refinement. Through the simulation platform, the matching navigation experiments are carried out on the gravity reference map with grid accuracy of 2’ × 2’ and the gravity reference map refined to 1’ × 1’ by the improved algorithm. The results show that the average positioning accuracy of the refined gravity reference map is improved by 17.9%.