Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree

The estimation of complex natural frequencies in linear systems through its transient response analysis is a common practice in engineering and applied physics. In this context, the conventional Generalized Pencil of Function (GPOF) method that employs a matrix pencil of degree one, utilizing Singular Value Decomposition (SVD) filtering, has emerged as a prominent strategy to carry out a complex natural frequencies estimation. However, some modern engineering applications increasingly demand higher accuracy estimation. In this context, some intrinsic properties of Hankel matrices and exponential functions are utilized in this paper in order to develop a modified GPOF method which employs a matrix pencil of degree greater than one. Under conditions of low noise in the transient response, our method significantly enhances accuracy compared to the conventional GPOF approach. This improvement is especially valuable for applications involving closely spaced complex natural frequencies, where a precise estimation is crucial.