Exponential Fourier Densities on S2 and Optimal Estimation and Detection for Directional Processes.
Abstract
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1976
- Accession Number
- ADA029556
Entities
People
- James Ting-ho Lo
- Linda R. Eshleman
Organizations
- University of Maryland, Baltimore County