Efficient Maximum Likelihood Estimation for Multiple and Coupled Harmonics

Report No. ARL-TR-2014
Authors: Lake, Douglas
Date/Pages: December 1999; 41 pages
Abstract: The maximum likelihood estimates (MLEs) and Cramer-Rao bounds (CRBs) for parameters of harmonics in Gaussian noise have been well studied. If the phase of the signal is defined in the middle of the time interval rather than at the beginning (as is more common), the information matrix is approximately diagonal, and the formulation and analysis of the MLEs and CRBs are simplified. More significantly, this simple modification decouples the estimation of phase and frequency and leads to efficient MLE gradient descent algorithms. In this report, these MLE procedures and CRB analysis are presented for the multiple and coupled harmonic case, as well as for colored noise. A new criterion on the required sample size is presented to give uniform bounds on the accuracy of diagonal information matrix approximation; uniform bounds are needed to ensure the effectiveness of the gradient descent methods. These methods are demonstrated on real data from battlefield acoustic sensors, where they can be used to help identify targets of interest, such as tanks or trucks.
Distribution: Approved for public release
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Last Update / Reviewed: December 1, 1999