LIKELIHOOD AND LEAST-SQUARES APPROACHES TO THE M-CORNERED HAT

Charles A. Greenhall

Abstract:	A simple model of the m-cornered hat estimation problem is set up and solved by the method of maximum likelihood. The method is compared by simulation to a least-squares method of Barnes and is shown to be inferior to it on the basis of mean square error. A bootstrap method of computing estimator performance is presented. INTRODUCTION Because fluctuations of frequency sources can be measured only by pairwise comparisons, the estimation of the noise level of each individual source is not straightforward. In the m-cornered hat problem there are m sources (m > 3); let the phase of the it source as function of time t be e(t. The observations consist of the m-1 pair-differences i(t) - $1(e) over some stretch of time, and it is required to estimate the Allan variances, o (), i=1 to m, of all the sources, for some fixed r. We shall set up an oversimplified model of the situation, and show (without proof) how the unknown corner Allan variances can be estimated by the method of maximum likelihood. Using simulation, we shall compare the performance of these estimators to those generated by a weighted least squares approach of Barnes. Finally, a method for estimating the variances of the estimators themselves will be given.
Published in:	Proceedings of the 19th Annual Precise Time and Time Interval Systems and Applications Meeting December 1 - 3, 1989 Sheraton Hotel Redondo Beach, California
Pages:	219 - 226
Cite this article:	Greenhall, Charles A., "LIKELIHOOD AND LEAST-SQUARES APPROACHES TO THE M-CORNERED HAT," Proceedings of the 19th Annual Precise Time and Time Interval Systems and Applications Meeting, Redondo Beach, California, December 1987, pp. 219-226.
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