均匀线阵窄带高斯信号的渐近最优盲校正
Asymptotically Optimal Blind Calibration of Uniform Linear Sensor Arrays for Narrowband Gaussian Signals
摘要：
提出了一种窄带高斯信号下均匀线阵的渐近最优盲校准方案。而不是采取直接的最大似然（ML）的方法联合估计的所有未知的模型参数，这将导致一个多维优化问题，没有封闭的形式的解决方案，我们重温Paulraj和Kailath的（P-K的）经典方法，利用特殊的（Toeplitz）结构的观测值的协方差。然而，我们提供了一个实质性的改进，P-K的普通最小二乘（LS）估计，通过使用渐近近似，以获得简单的，非迭代的，（准）线性最优加权LS（OWLS）估计的传感器增益和相位偏移渐近最优加权，仅基于经验的协方差矩阵的测量。此外，我们证明了我们的估计也是渐近最优的w.r.t.原始数据，因此可以被视为等同于ML估计值（MLE），否则通过所有未知模型参数的联合ML估计获得。在推导出相应的Cramér-Rao下界的计算方便的表达式后，我们还表明，当应用于非高斯信号（和/或噪声）作为类似设置中的准MLE时，我们的估计提供了更好的性能。我们的估计的最佳性能表现在模拟实验中，与相当大的改善（达到一个数量级以上），在所产生的均方误差w.r.t. P-K的LS估计。我们还证明了在多源波达方向估计任务的精度提高。
英文摘要：
An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, which leads to a multi-dimensional optimization problem with no closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical approach in exploiting the special (Toeplitz) structure of the observations' covariance. However, we offer a substantial improvement over P-K's ordinary Least Squares (LS) estimates by using asymptotic approximations in order to obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS) estimates of the sensors gains and phases offsets with asymptotically optimal weighting, based only on the empirical covariance matrix of the measurements. Moreover, we prove that our resulting estimates are also asymptotically optimal w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates (MLE), which are otherwise obtained by joint ML estimation of all the unknown model parameters. After deriving computationally convenient expressions of the respective Cramér-Rao lower bounds, we also show that our estimates offer improved performance when applied to non-Gaussian signals (and/or noise) as quasi-MLE in a similar setting. The optimal performance of our estimates is demonstrated in simulation experiments, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy in a multiple-sources directions-of-arrivals estimation task.
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