The Gradient Descent Adaptive Moment Parameter Estimation for Multi‐Frequency Sine Signal Systems

ABSTRACT The objective of this paper is to investigate the joint estimation of unknown frequency, amplitude, and phase parameters in multi‐frequency signal models. In response to the slow convergence and the precision constraints of conventional gradient identification approaches, this study presents an adaptive moment estimation algorithm integrated with gradient information to enhance parameter identification performance in a multi‐frequency signal modeling. The algorithm achieves optimized parameter updates through the integration of first‐order moment estimation (momentum term) and second‐order moment estimation (adaptive step‐size scaling). Concretely, the first‐order moment estimation employs a momentum term to stabilize parameter update directions, while the second‐order moment estimation adaptively adjusts step sizes in response to gradient changes, ensuring flexible adaptation to the unique traits of individual parameters. Numerical simulations and experimental tests verify that the proposed algorithm maintains superior stability over the Newton gradient recursive parameter estimation algorithm and the least squares parameter algorithm in harsh, strong‐noise environments.