Methods to estimate the parameters of a noisy signal are discussed. The signal typically consists of a large number of signal components. The signal components are assumed to be decaying exponentials. It is found that the standard iterative methods which attempt to fit a signal model are unsatisfactory. An iterative pole-by-pole method is proposed in which one signal component is updated in each iteration. This method is a promising method for system identification. It allows the incorporation of prior information which is useful in accelerating convergence, and produces reasonable results when the model order is high.