Abstract: The Inverse Beamforming（IBF） theory uses the cross-spectral functions at elements to estimate the acoustic field plane-wave density.Compared to the conventional beamforming，IBF provides much better performance in direction-of-arrival estimation and interference suppression. Based on the IBF theory and its Fourier solutions，this paper developed a new solution to the IBF integral equation based on the modified auto-regressive model and formed a corresponding method for DOA estimation. This method makes full use of the receiving information of the array and views the receiving signal of each element as a spatial sequence satisfying a certain parametric model. The forward-backward averaging was employed to overcome the imprecise problem of the covariance matrix which occurred when there were only few snapshots available for a low SNR target signal.Together with theoretical deduction，computer simulation showed the feasibility and effectiveness of this approach in solving the IBF integral equation and DOA estimation.

Key words: inverse beamforming, Fourier integral method, auto-regressive model, forward-backward averaging

摘要： 逆波束形成是利用各阵元接收信号间的互功率谱估计声场平面波强度的理论，较之常规波束形成，它具有更高的方位分辨能力和噪声干扰抑制能力。在分析逆波束形成理论及其傅立叶类求解算法的基础上，提出了基于改进的AR模型的求解方法。该方法将参数模型引入到逆波束形成的求解当中，通过引入前向后向平均，克服了信号协方差矩阵在小信噪比和快拍数较少情况下估计不准的问题，从而减轻了旁瓣的起伏，有助于实现对弱目标信号的检测与估计。通过大量计算机仿真实验，证实了所提算法的可行性和优越性。

关键词: 逆波束形成, 傅立叶积分法, 自回归模型, 前向后向平均