Newton Algorithms for Conditional and Unconditional Maximum Likelihood Estimation of the Parameters of Exponential Signals in Noise

This paper presents polynomial-based Newton algorithms for maximum likelihood estimation (MLE) of the parameters of multiple exponential signals in noise. This formulation can be used in the estimation, for example, of the directions of arrival (DOA‘s) of multiple noise-corrupted narrowband plane waves using uniform linear arrays and the frequencies of multiple noise-corrupted complex sine waves. The algorithms offer rapid convergence, and exhibit the computational efficiency associated with the polynomial approach. Compact, closed-form expressions are presented for the gradients and Hessians. Various model assumptions concerning the statistics of the underlying signals are considered. Numerical simulations are presented to demonstrate the algorithms’ performance.