论文标题
窄带高斯信号的均匀线性传感器阵列的渐近最佳盲校准
Asymptotically Optimal Blind Calibration of Uniform Linear Sensor Arrays for Narrowband Gaussian Signals
论文作者
论文摘要
提出了针对窄带高斯信号的均匀线性阵列的渐近最佳盲校准方案。我们没有采用直接最大可能性（ML）方法来对所有未知模型参数进行联合估算，这导致了具有无封闭形式解决方案的多维优化问题，而是在利用特殊（TOEPLITZ）结构的covarriance'COVARANCE的结构时，我们重新访问Paulraj和Kailath's（P-K的经典方法）。但是，我们通过使用渐近近似值对P-K的普通最小二乘（LS）估计进行了实质性改进，以获得简单的，非辅助性的（Quasi）线性最佳的LS（OWLS）估计值，对传感器的估计值和相位的估计值，并基于渐近级别的量表，基于渐进式covariaccianciance covariaccianciancianciance covarix covariace covariace covariace covariace covariace covariace covars covars covars covars covariace covarience covarience covrix covarience。此外，我们证明我们所得的估计也是渐近的最佳W.R.T.原始数据，因此可以认为等同于ML估计值（MLE），否则它们是通过对所有未知模型参数的联合ML估计获得的。在得出各个Cramér-Rao下限的计算方便表达式之后，我们还表明，在类似的环境中，当应用于非高斯信号（和/或噪声）时，我们的估计值可提高性能。在仿真实验中证明了我们的估计值的最佳性能，并在所得的平方误差W.R.T.中具有相当大的改进（达到数量级和更多）。 P-K的普通LS估计。我们还证明了在多个源方向估算任务中的精度提高。
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.
