We study the distributed estimations of a spatially correlated random field with decentralized wireless sensor networks (WSNs). Nodes in the WSN take spatial samples of the random field, then each node estimates the values of arbitrary points on the random field by iteratively exchanging information with each other, without the need of a central controller. The objective is to minimize the time (or number of iterations) required for all nodes in the network to reach a distributed consensus on the estimation result, with mean squared error (MSE) below a certain threshold. We find the sufficient conditions for this optimization problem, and identify the asymptotically optimum solutions when time is large and the MSE threshold is small. Specifically, we propose a distributed iterative estimation algorithm that defines the procedures for both information propagation and information estimation in each iteration. The key parameters of the algorithm, including an edge weight matrix and a sample weight matrix, are designed by following the asymptotically optimum criteria. It is shown that the asymptotically optimum performance can be achieved by distributively projecting the measurement samples into a subspace related to the covariance matrices of data and noise samples. Simulation results show that all nodes in a large network can obtain accurate estimation results with only a few iterations.