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Localization of wideband signals using least-squares and total least-squares approaches

机译：使用最小二乘法和总最小二乘法对宽带信号进行定位

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摘要

In this paper, we introduce a new focusing technique for localization of wideband signals. Relaxing the unitary assumption for the focusing matrices, we formulate the least-square (LS) and the total least-square (TLS) coherent signal-subspace methods. The TLS is an alternative to the conventional LS and uses the fact that errors can exist both in the focusing location matrix as well as in the estimated location matrix at a given frequency bin. To prevent the focusing loss, we use a class of focusing matrices that are constant under multiplication by their Hermitian transpose. The class of unitary matrices comports with this property. We then develop a new focusing technique based on a modification to the TLS (MTLS). It is shown that the computational complexity of the new technique is significantly lower than that for the rotational signal subspace method (RSS). The focusing gain of the new technique is also larger than the focusing gain of the RSS algorithm. The simulation study shows that, compared with the RSS, the new algorithm has a smaller resolution signal to-noise ratio (SNR).
机译：在本文中，我们介绍了一种用于宽带信号定位的新聚焦技术。放宽对聚焦矩阵的统一假设，我们制定了最小二乘（LS）和总最小二乘（TLS）相干信号子空间方法。 TLS是常规LS的替代方法，它使用以下事实：在给定频率仓中，聚焦位置矩阵以及估计的位置矩阵中都可能存在错误。为了防止聚焦损失，我们使用一类聚焦矩阵，这些矩阵在通过其Hermitian转置而相乘时是恒定的。 of矩阵的类别与此属性相称。然后，我们基于对TLS（MTLS）的修改，开发了一种新的聚焦技术。结果表明，新技术的计算复杂度明显低于旋转信号子空间方法（RSS）。新技术的聚焦增益也大于RSS算法的聚焦增益。仿真研究表明，与RSS相比，新算法具有较小的分辨率信噪比（SNR）。

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