Exponential Fourier Densities on SO(3) and Optimal Estimation and Detection for Rotational Processes

A new representation of a probability density function on the three dimensional rotation group, SO(3) is presented, which generalizes the exponential Fourier densities on the circle. As in the circle case, this class of densities on SO(3) is closed under the operation of taking conditional distribut...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on applied mathematics 1979-02, Vol.36 (1), p.73-82
Main Authors: Lo, James Ting-Ho, Eshleman, Linda R.
Format: Article
Language:English
Subjects:
Approximation
Density
Estimates
Mathematical functions
Noise measurement
Probability distributions
Quaternions
Rotation
Signal noise
Sine function
White noise
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A new representation of a probability density function on the three dimensional rotation group, SO(3) is presented, which generalizes the exponential Fourier densities on the circle. As in the circle case, this class of densities on SO(3) is closed under the operation of taking conditional distributions. Several simple multistage estimation and detection models are considered. The closure property enables us to determine the sequential conditional densities by recursively updating a finite and fixed number of coefficients. It also enables us to express the likelihood ratio for signal detection explicitly in terms of the conditional densities. An error criterion, which is compatible with a Riemannian metric, is introduced and discussed. The optimal orientation estimates with respect to this error criterion are derived for a given probability distribution, illustrating how the updated conditional densities can be used to recursively determine the optimal estimates on SO(3).
ISSN:0036-1399
1095-712X
DOI:10.1137/0136007