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Effect of unitary transformation on Bayesian information criterion for source numbering in array processing

机译：单一转型对阵列处理源编号码头信息标准的影响

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摘要

An approach based on unitary transformation for the problem of estimating the number of signals is proposed in this study. Among the information theoretic criteria, the authors focus on the conventional Bayesian information criterion (BIC) in the presence of a uniform linear array. The sample covariance matrix of this array is transformed into the real symmetric one by using a unitary transformation. This real symmetric matrix has real eigenvalues and eigenvectors. Therefore its eigenvalue decomposition needs only real computations. Since the eigenvalues of this real symmetric matrix are equal to the eigenvalues of the sample covariance matrix, by replacing them in BIC formula, the term log-likelihood of BIC does not change but it is obtained by fewer computations. Also by considering the resulting real eigenvectors instead of the complex eigenvectors as a part of free parameters in the parameter vector of the model, they have a reduction in the number of degrees of freedom in the penalty term of BIC. This reduction makes their proposed method outperform BIC. They refer to this approach as unitary BIC. A series of simulations are included to demonstrate the usefulness of this approach.
机译：本研究提出了一种基于估计信号数量的酉变换的方法。在信息理论标准中，作者在存在均匀的线性阵列存在下关注传统的贝叶斯信息标准（BIC）。通过使用酉变换将该阵列的示例协方差矩阵变换为真实对称的矩阵。这个真正的对称矩阵具有真正的特征值和特征向量。因此，其特征值分解仅需要实际计算。由于该实际对称矩阵的特征值等于样本协方差矩阵的特征值，因此通过在BIC公式中替换它们，BIC的术语对数不改变，但是通过较少计算获得。另外，通过考虑所得到的实际特征向量而不是复杂的特征向量作为模型的参数向量中的自由参数的一部分，它们的自由度在BIC中的惩罚项中的自由度减少。这种减少使其提出的方法优于BIC。他们将这种方法称为单一的BIC。包括一系列模拟以证明这种方法的有用性。

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