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Selecting wavelengths for least squares range estimation
- Publication Year :
- 2016
-
Abstract
- We consider the problem of estimating the distance, or range, between two locations by measuring the phase of multiple sinusoidal signals transmitted between the locations. Traditional estimators developed for optical interferometry include the beat wavelength and excess fractions methods. More recently, estimators based on the Chinese remainder theorem (CRT) and least squares have appeared. Recent research suggests the least squares estimator to be the most accurate in many cases. The accuracy of all of these range estimators depends upon the wavelengths chosen. This leads to the problem of selecting wavelengths that maximize accuracy. Procedures for selecting wavelengths for the beat wavelength and excess fractions methods have previously been described, but procedures for the CRT and least squares estimators are yet to be developed. In this paper, we develop an algorithm to automatically select wavelengths for use with the least square range estimator. The algorithm minimizes an optimization criterion connected with the mean square error. Interesting properties of a particular class of lattices simplify the criterion allowing minimization by depth first search. Monte-Carlo simulations indicate that wavelengths that minimize the criterion can result in considerably more accurate range estimates than wavelengths selected by ad hoc means. Refereed/Peer-reviewed
- Subjects :
- FOS: Computer and information sciences
lattice theory
Mathematical optimization
Mean squared error
Information Theory (cs.IT)
Computer Science - Information Theory
Breadth-first search
Estimator
020206 networking & telecommunications
02 engineering and technology
01 natural sciences
Least squares
range estimation
010309 optics
Wavelength
Interferometry
0103 physical sciences
Signal Processing
0202 electrical engineering, electronic engineering, information engineering
Minification
Electrical and Electronic Engineering
phase ambiguity
Chinese remainder theorem
Algorithm
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9cce2b54184cda26fa069f3039968b07