A computationally efficient non‐iterative four‐parameter sine fitting method

Abstract

Abstract A computationally efficient four‐parameter least squares (LS) sine fitting method in the time domain is presented here. Unlike the most widespread procedure defined in the relevant IEEE standard, the proposed fitting is non‐iterative. This is achieved by the second‐order approximation of the cost function (CF) around the actual frequency of the sinusoidal excitation. The approximation reduces the four‐parameter non‐linear fitting problem to a defined set of three‐parameter linear fitting problems. Therefore, the computational demand can be predicted precisely, which is an essential aspect of real‐life applications. Furthermore, the proposed method is shown to have increased numerical stability. Finally, measurements and computer simulations are carried out to demonstrate the reduced computational demand, while preserving the accuracy compared with the algorithm proposed in the IEEE standard.

Keywords

• curve fitting
• IEEE standards
• iterative methods
• least squares approximations
• numerical stability