Statistical analysis of the Kumaresan-Tufts and Matrix Pencil methods in estimating a damped sinusoid

Several methods have been developed for estimating the parameters of damped and undamped exponentials in noise, but the performances of such techniques are generally known only in the undamped case. In this paper, we consider two estimation methods: the Kumaresan-Tufts method and the Matrix Pencil approach, and we obtain their estimation performances in the case of a single exponentially damped sinusoid. Assuming a high signal-to-noise ratio, closed form expressions for the bias and the variance of the damping factor are derived. The analytical results are confirmed using Monte Carlo simulations. The analysis indicates that the Matrix Pencil method exhibits a lower variance but has a greater bias than the Kumaresan-Tufts approach.