Forward and backward extended Prony method for complex exponential signals with/without additive noise

摘要

We introduce a new strategy for finding the pole locations of signals composed of complex exponentials, and incorporate this strategy into the "Forward and Backward Extended Prony" (FBEP) method. The performance of the proposed method is investigated using statistical analysis and simulation experiments. Initial validation is accomplished using time-series data without additive noise, and the advantages of this method in accurately identifying both growing and decaying modes in moderate noise is then demonstrated by adding noise to the time-series data with different signal-to-noise ratios (SNRs). The FBEP method is compared with the TLS-Prony method and subspace-based methods by determining the mean squared errors (MSEs) of the frequency and damping factor estimates given by each method with comparing these to the corresponding Cramer-Rao (CR) bounds for white Gaussian noise cases. The FBEP method is also compared with a recent optimization-based iterative algorithm. The performance of the FBEP method using the pseudoinverse and Total Least Squares (TLS) approaches for different SNR is also studied. Previous polynomial methods are considered to be inferior to subspace-based methods (e.g., MODE, ESPRIT and Matrix Pencil) due to poor estimation accuracy under noise. As a polynomial method the FBEP method provides better performance than the MODE algorithm and comparable performance to the subspace-based methods that are well known for their accuracy and efficiency. (C) 2019 Elsevier Inc. All rights reserved.