Sensor calibration for off-the-grid spectral estimation
Autor: | Wenjing Liao, Sui Tang, Yonina C. Eldar |
---|---|
Rok vydání: | 2020 |
Předmět: |
FOS: Computer and information sciences
Calibration (statistics) Covariance matrix Computer Science - Information Theory Information Theory (cs.IT) Applied Mathematics 010102 general mathematics Spectral density estimation 010103 numerical & computational mathematics 01 natural sciences Noise (electronics) Toeplitz matrix Optimization and Control (math.OC) FOS: Mathematics Sensitivity (control systems) 0101 mathematics Algebraic number Gradient descent Mathematics - Optimization and Control Algorithm Mathematics |
Zdroj: | Applied and Computational Harmonic Analysis. 48:570-598 |
ISSN: | 1063-5203 |
DOI: | 10.1016/j.acha.2018.08.003 |
Popis: | 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. |
Databáze: | OpenAIRE |
Externí odkaz: |