Perturbation Analysis of Subspace-Based Methods in Estimating a Damped Complex Exponential

We present a study of mode variance statistics for three SVD-based estimation methods in the case of a single-mode damped exponential. The methods considered are namely Kumaresan-Tufts, matrix pencil and Kung´s direct data approximation. Through first-order perturbation analysis, we derive closed-form expressions of the variance of the complex mode, frequency and damping factor estimates. These expressions are used to compare the different methods and to determine the optimal prediction order for matrix pencil and direct data approximation methods. Application to the undamped case shows the coherence of the results with those already stated in the literature. It is also found that the variances converge linearly towards the Cramer-Rao bound. Finally, the theoretical results are verified using Monte Carlo simulations.