Exponential Fourier Densities on SO(3) and Optimal Estimation and Detection for Rotational Processes.
Abstract
This paper presents a new representation of a probability density function on the three dimensional rotation group, SO(3), which generalizes the exponential Fourier densities on the circle. As in the circle case, this class of densities on SO(3) is also closed under the operation of taking conditional distributions. Several simple multistage estimation and detection models will be considered in this paper. The closure property will determine the sequential conditional densities by recursively updating a finite and fixed number of coefficients. An error criterion, which is compatible with a Riemannian metric, will be introduced and discussed. The optimal orientation estimates with respect to this error criterion will be derived for a given probability distribution, illustrating how the updated conditional densities can be used to sequentially determine the optimal estimates on SO(3).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1976
- Accession Number
- ADA032852
Entities
People
- James Ting-ho Lo
- Linda R. Eshleman
Organizations
- University of Maryland, Baltimore County