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).

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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

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Space

DTIC Thesaurus Topics

  • Coefficients
  • Data Science
  • Detection
  • Equations
  • Euler Angles
  • Information Science
  • Mathematics
  • New York
  • Numbers
  • Orientation (Direction)
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Rotation
  • Sequences
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.