In this letter, the order recursive least squares (ORLS) is applied to the azimuth-only ULA to probe the DoA estimation under the unknown number of external sources. In the ORLS-based method, the iterative measured matrix equations are feasibly constructed by combining the two spatial modified Yule-Walker (MYW) systems of linear equations and are required to remain Hankel-block-matrix structure of augmented matrices after arrangement order of the unknowns and the maximum number of detectable sources are preset. Under the stationary assumption on source signals and noises, the remarkable advantage of the proposed method lies in that it can theoretically provide the zero LS error as iteration times is equal to the number of sources. The zero LS error is an evident mark to judge the number of sources, especially for the scenario of the unknown noise variances. The proposed method is free of uncorrelated and coherent signals and the corresponding various mixtures and remains computationally efficient in estimation owing to no eigenvalue decomposition (EVD) and matrix inversion operation. The effectiveness of the determination of the number and azimuth angles of sources versus the different SNRs and numbers of snapshots is numerically confirmed.

中文翻译：

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未知源数量下不相关和相干信号的未知混合的基于 ORLS 的 DoA 估计


在这封信中，将阶递归最小二乘法 (ORLS) 应用于仅方位角 ULA，以探测未知数量的外部源下的 DoA 估计。在基于ORLS的方法中，迭代测量矩阵方程是通过组合两个空间修正Yule-Walker（MYW）线性方程组来构造的，并且要求在排列顺序后保持增广矩阵的Hankel块矩阵结构未知数和可检测源的最大数量是预设的。在源信号和噪声平稳的假设下，该方法的显着优点在于，当迭代次数等于源数量时，理论上可以提供零LS误差。零LS误差是判断源数量的明显标志，特别是对于未知噪声方差的情况。所提出的方法没有不相关和相干信号以及相应的各种混合，并且由于没有特征值分解（EVD）和矩阵求逆运算，因此在估计中保持计算效率。确定源的数量和方位角与不同的信噪比和快照数量的有效性得到了数值证实。