Among many prevalent acoustic location techniques, the location problems can be modelled as solving a linear equation. Although many mature algorithms have been developed to solve the linear equation in acoustic location applications, few of them consider the inevitable noises in a real computing system that might degrade the convergence and accuracy of the algorithms or even lead to failure. Thus, to achieve promising performance when solving a linear equation in a noisy environment, a robust Newton iterative (RNI) algorithm is proposed in this paper based on control theory. Theoretical analyses indicated that the RNI algorithm can not only suppress the constant noise to zero but also maintain convergence against an increasing linear noise and random noise. In addition, extensive simulation results compared with the classic algorithms and their last variants are provided. Among these algorithms, the RNI algorithm achieves the best robustness and accuracy in the presence of noises, while it requires a longer convergence time.