Exponential Fourier Densities on S2 and Optimal Estimation and Detection for Directional Processes.
MARYLAND UNIV BALTIMORE COUNTY BALTIMORE DIV OF MATHEMATICS AND PHYSICS
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Two classes of probability densities, the exponential Fourier densities and the exponential trigonometric densities, are introduced on S2 as well as four kinds of displacements. In general, neither class is closed under the operation of taking conditional distributions with respect to any of the displacements. A combined usage of both classes is required to study the estimation and detection models obtained from various combinations of the displacements. The merits and disadvantages of each model are discussed. Recursive formulas for the conditional densities and the likelihood ratios are derived for many of the models. The additive measurement noise case is also considered in detail. An error criterion for direction estimation is presented with respect to which the optimal estimates can be easily computed from the probability distribution. A deficiency of the models and techniques developed in this paper is that random driving terms are disallowed in the signal processes. How to remove this deficiency remains an open problem. Author
- Statistics and Probability