An Accurate Estimation of a Modal System with Initial Conditions (ICCAS 2004)

In this paper, we propose the AWLS/MFT (Adaptive Weighed Least Squares/ Modulation Function Technique) devised by A. E. Pearson et al. for the transfer function estimation of a modal system and investigate the performance of several algorithms, the Gram matrix method, a Luenberger Observer (LO), Least Squares (LS), and Recursive Least Squares (RLS), for the estimation of initial conditions. With the benefit of the Modulation Function Technique (MFT), we can separate the estimation problem into two phases: the transfer function parameters are estimated in the first phase, and the initial conditions are estimated in the second phase. The LO method produces excellent IC estimates in the noise free case, but the other three methods show better performance in the noisy case. Finally, we compared our result with the Prony based method. In the noisy case, the AWLS and one of the three methods - Gram matrix, LS, and RLS- show better performance in the output Signal to Error Ratio (SER) aspect than the Prony based method under the same simulation conditions.