关键词: 最小二乘配置, 重力场建模, 贪婪算法, 稀疏表示, 大地水准面, 计算瓶颈

Abstract:

Least squares collocation (LSC) is a key theory for processing geophysical and geodetic data. However, its application to large-scale observations is constrained by the substantial computational and storage costs required to construct and invert a dense covariance matrix whose size scales with the number of observations. To overcome this bottleneck, we propose a greedy-algorithm-based sparse approximation method for LSC. Specifically, LSC is reformulated within a sparse-representation framework as a sparse coefficient recovery problem, which is then solved iteratively using matching pursuit (MP) and orthogonal matching pursuit (OMP), thereby avoiding explicit factorization and inversion of the full dense covariance matrix. A case study on geoid modelling using multi-source gravity data in Colorado, USA, shows that the proposed method achieves an external validation accuracy (2.24 cm) comparable to that of LSC (2.27 cm). Moreover, the resulting sparse model stores only 3.9% of the coefficients, leading to more than a 25-fold improvement in gridded prediction efficiency and enabling model lightweighting. Further semi-simulation statistical experiments indicate that, when covariance parameters estimated from noisy data aggravate model mismatch, the greedy collocation scheme exhibits more robust statistical behavior. Overall, the proposed method enhances scalability while maintaining modelling accuracy, providing a computationally feasible solution for high-precision gravity field modelling under large-scale observations.

Key words: least squares collocation, gravity field modeling, greedy algorithms, sparse representation, geoid, computational bottleneck