Sensor Calibration for Off-the-Grid Spectral Estimation
Sensor Calibration for Off-the-Grid Spectral Estimation
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DOI：
10.1016/j.acha.2018.08.003
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发表时间：
2017-07
期刊：
影响因子：
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通讯作者：
Yonina C. Eldar;Wenjing Liao;Sui Tang
中科院分区：
文献类型：
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作者：
Yonina C. Eldar;Wenjing Liao;Sui Tang
本文研究了光谱估计中的传感器校准，其中真实频率位于连续域。我们考虑一个均匀的传感器阵列，它收集测量值，其频谱由有限数量的频率组成，其中每个传感器都有一个未知的校准参数。我们的目标是从多个测量快照中同时恢复光谱和校准参数。在具有无限数量快照的无噪声情况下，只要传感器数量多于频率，我们就可以基于代数方法证明这个问题的独特性，直至某些微不足道的、不可避免的模糊性。然后，我们分析了这种代数技术对快照数量和噪声的敏感性。接下来，我们提出了一种优化方法，通过最小化非凸目标来充分利用测量结果，该非凸目标是非负的并且在所有校准参数和托普利茨矩阵上连续可微。我们证明，在无限快照和无噪声测量的情况下，目标仅在真实校准参数和测量协方差矩阵的等效解时消失。使用 Wirtinger 梯度下降来最小化目标，事实证明该梯度下降可以收敛到临界点。我们凭经验证明，这个临界点提供了真实校准参数和基础频率的良好近似。
This paper studies sensor calibration in spectral estimation where the true frequencies are located on a continuous domain. We consider a uniform array of sensors that collects measurements whose spectrum is composed of a finite number of frequencies, where each sensor has an unknown calibration parameter. Our goal is to recover the spectrum and the calibration parameters simultaneously from multiple snapshots of the measurements. In the noiseless case with an infinite number of snapshots, we prove uniqueness of this problem up to certain trivial, inevitable ambiguities based on an algebraic method, as long as there are more sensors than frequencies. We then analyze the sensitivity of this algebraic technique with respect to the number of snapshots and noise.We next propose an optimization approach that makes full use of the measurements by minimizing a non-convex objective which is non-negative and continuously differentiable over all calibration parameters and Toeplitz matrices. We prove that, in the case of infinite snapshots and noiseless measurements, the objective vanishes only at equivalent solutions to the true calibration parameters and the measurement covariance matrix. The objective is minimized using Wirtinger gradient descent which is proven to converge to a critical point. We show empirically that this critical point provides a good approximation of the true calibration parameters and the underlying frequencies.