Direction estimation by minimum squared arc length

McKilliam, Robby G., Quinn, Barry G. and Clarkson, I. Vaughan L. (2012) Direction estimation by minimum squared arc length. Ieee Transactions On Signal Processing, 60 5: 2115-2124. doi:10.1109/TSP.2012.2186444

Author McKilliam, Robby G.
Quinn, Barry G.
Clarkson, I. Vaughan L.
Title Direction estimation by minimum squared arc length
Journal name Ieee Transactions On Signal Processing   Check publisher's open access policy
ISSN 1053-587X
Publication date 2012-05
Sub-type Article (original research)
DOI 10.1109/TSP.2012.2186444
Volume 60
Issue 5
Start page 2115
End page 2124
Total pages 10
Place of publication Piscataway NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Collection year 2013
Language eng
Formatted abstract
Circular statistics has found substantial application in science and engineering. One of the fundamental problems in circular statistics is that of estimating the mean direction of a circular random variable from a number of observations. The standard approach in the literature is called the sample circular mean and its asymptotic properties are well known. It can also be computed efficiently in a number of arithmetic operations that is linear in the number of observations. In this paper we consider an alternative estimator called the sample intrinsic mean that is based on minimizing squared arc length. We show how this estimator can be computed efficiently in a linear number of operations using an algorithm from algebraic number theory and we derive its asymptotic properties. In some scenarios the sample circular mean and the sample intrinsic mean are estimators of the same quantity and can therefore be compared. We show both theoretically and by simulation that in some of these scenarios the sample intrinsic mean is statistically more accurate than the sample circular mean. As such the results in this paper potentially have implications for the wide variety of fields in science, engineering and statistics that currently use the sample circular mean.
Keyword Circular statistics
Intrinsic mean
Lattice theory
Mean direction estimation
Nearest lattice point problem
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Date of publication February 06, 2012; date of current version April 13, 2012.

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2013 Collection
School of Information Technology and Electrical Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 15 times in Thomson Reuters Web of Science Article | Citations
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