Circuits, Systems, and Signal Processing

, Volume 38, Issue 7, pp 3251–3268 | Cite as

Hierarchical Principle-Based Iterative Parameter Estimation Algorithm for Dual-Frequency Signals

  • Siyu Liu
  • Feng DingEmail author
  • Ling Xu
  • Tasawar Hayat


In this paper, we consider the parameter estimation problem of dual-frequency signals disturbed by stochastic noise. The signal model is a highly nonlinear function with respect to the frequencies and phases, and the gradient method cannot obtain the accurate parameter estimates. Based on the Newton search, we derive an iterative algorithm for estimating all parameters, including the unknown amplitudes, frequencies, and phases. Furthermore, by using the parameter decomposition, a hierarchical least squares and gradient-based iterative algorithm is proposed for improving the computational efficiency. A gradient-based iterative algorithm is given for comparisons. The numerical examples are provided to demonstrate the validity of the proposed algorithms.


Iterative algorithm Signal modeling Hierarchical identification Least squares Newton search Gradient search 



This work was supported by the National Natural Science Foundation of China (No. 61873111) and the 111 Project (B12018).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things EngineeringJiangnan UniversityWuxiPeople’s Republic of China
  2. 2.School of Electrical and Electronic EngineeringHubei University of TechnologyWuhanPeople’s Republic of China
  3. 3.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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