Parameter Estimation of Multiple Poles by Subspace-Based Method

This work deals with the problem of estimating the parameters (i.e., pole multiplicity structure, pole locations, and complex amplitudes) of exponential polynomials for a given model order. We start from an exponential polynomial signal model and algebraically demonstrate the reasoning behind and the manner in which this model generalizes to the broader class of signals containing multiple poles. The poles and complex amplitudes are estimated by a subspace-based method. With the given model order as prior, a heuristic algorithm is developed to estimate the multiplicity structure of poles. Numerical simulations are conducted to study the performance of the subspace-based method and the sensitivity of poles and multiplicity estimation. Our simulations show that our pole estimation method is accurate for signals with poles of multiplicity greater than one, particularly for signals with lower orders. This allows for successful signal regeneration, producing estimates that closely match the original data. The estimation is sensitive, particularly in the presence of noise, and when the poles are complex and have a higher order of multiplicity.