Gaussian random fields are powerful tools for the modeling of the environmental processes. For high dimensional samples, the classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as evaluation of the Cholesky factorization or solving linear systems with a matrix. Recently, Anitescu et al. proposed a fast and scalable algorithm which does not need such burdensome computations. The main focus of this article is to study the asymptotic behavior of Anitescu's algorithm, which is usually called inversion-free, for perturbed regular grids in the increasing domain setting. Consistency, minimax optimality and asymptotic normality of this algorithm are proved under mild differentiability conditions on the covariance function. However, applying the inversion-free algorithm on the raw data does not lead to consistency in the fixed-domain asymptotic regime. We propose the split preconditioned inversion-free as a consistent alternative and investigate its connection to MLE and quadratic variation based estimate (proposed by E. Anderes, 2010).