Maximum likelihood estimation of exponential signals in noise using a Newton algorithm

The authors present a Newton algorithm for exact maximum likelihood estimation of the parameters of multiple exponential signals in additive white Gaussian noise. Closed-form expressions are derived for the gradient and Hessian of the criterion function. These are used in the algorithm to locate the optimum polynomial whose roots represent the parameters of the signals. It is concluded that the algorithm is useful for direction-of-arrival estimation using uniform linear sensor arrays, and for estimating parameters of exponentially damped sine waves in noise.