<p>This investigation involves acoustic vector sensor array (AVSA) for estimating direction of arrival (DOA) in the circumstance of impulsive noise. To eliminate the outliers driven by impulsive noise, the bounded nonlinear function (BNF) is usually employed. However, one limitation of BNF is that it can only suppress impulsive noise exceeding the linear threshold. Moreover, there is no guarantee that data below the threshold is not contaminated by impulsive noise, given the random nature of noise. To address this issue, a globally bounded nonlinear function is formulated by utilizing the low-order characteristics of impulsive noise. Moreover, the DOA prediction of AVSA under impulsive noise is solved using a globally bounded nonlinear covariance sparse iterative approach. Moreover, the complexity and convergence of the proposed algorithm are analyzed. The simulation and experimental results demonstrate that the suggested strategies provide substantial improvements in performance compared to existing methods in scenarios with impulsive noise.</p>