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Robust Frequency Estimation of Multi-sinusoidal Signals Using Orthogonal Matching Pursuit with Weak Derivatives Criterion

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Abstract

In this paper, the weak derivatives (WD) criterion is introduced to solve the frequency estimation problem of multi-sinusoidal signals corrupted by noises. The problem is therefore modeled as a new least squares optimization task combined with WD. To overcome the potential basis mismatch effect caused by discretization of the frequency parameters, a modified orthogonal matching pursuit algorithm is proposed to solve the optimization problem by coupling it with a novel multi-grid dictionary training strategy. The proposed algorithm is validated on a set of simulated datasets with white noise and stationary colored noise. The comprehensive simulation studies show that the proposed algorithm can achieve more accurate and robust estimation than state-of-the-art algorithms.

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Acknowledgements

This work is supported by the open research project of The Hubei Key Laboratory of Intelligent Geo-Information Processing with Grants KLIGIP2016A01 and KLIGIP2016A02, the specific funding for education science research by self-determined research funds of CCNU from the colleges’ basic research and operation of MOE with Grants 230-20205160288 and CCNU15A05022.

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Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Lihua Fu, Zhihui Liu & Hongwei Li

  2. School of Computer Science, Central China Normal University, Wuhan, 430079, China

    Meng Zhang

  3. Hubei Subsurface Multi-scale Imaging Key Laboratory, China University of Geosciences, Wuhan, 430074, China

    Hongwei Li

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  1. Lihua Fu
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  2. Meng Zhang
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  4. Hongwei Li
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Correspondence to Hongwei Li.

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Fu, L., Zhang, M., Liu, Z. et al. Robust Frequency Estimation of Multi-sinusoidal Signals Using Orthogonal Matching Pursuit with Weak Derivatives Criterion. Circuits Syst Signal Process 38, 1194–1205 (2019). https://doi.org/10.1007/s00034-018-0906-5

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