On Model Order Determination For Complex Exponential Signals: Performance Of An FFT-initialized ML Algorithm

We present an algorithm for model order determination and simultaneous maximum likelihood parameter estimation for complex exponential signal modeling. The algorithm exploits initial nonparametric (i.e., FFT) frequency location estimates and Cram&-Rru, Bound (CRB) resolution limits to significantly reduce the search space for the correct model order and parameter estimates. The algorithm initially overestimates the model order. After iterative minimization to obtain maximum likelihood (ML) parameter estimates for that order, a post-processing step eliminates the extraneous sinusoidal modes using CFU3 resolution limits and statistical detection tests. Because the algorithm searches on only a limited set of model orders and parameter regions, it is computationally tractable even for large data lengths and model orders. In this paper we analyze the performance of the algorithm and compare with other existing approaches.