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

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.