Editorial Type:
Article
Article Type:
Research Article

Asymptotic Properties of an Autocorrelation Coefficient for Coherent Doppler Sonar

Jeremy Dillon Memorial University of Newfoundland, St. John’s, Newfoundland, Canada

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Len Zedel Memorial University of Newfoundland, St. John’s, Newfoundland, Canada

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Alex E. Hay Dalhousie University, Halifax, Nova Scotia, Canada

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Print Publication:
01 Jul 2011
DOI:
https://doi.org/10.1175/JTECH-D-10-05002.1
Page(s):
966–973
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Abstract

A new formula is derived for the asymptotic form of the magnitude of an autocorrelation coefficient for coherent Doppler sonar. The autocorrelation magnitude is shown to be a biased estimator in the limit of infinite ensemble length. Numerical simulation of a Gaussian random process is used to verify the asymptotic formula and to show that a bias persists for finite pulse-pair averages. Validity of the asymptotic formula is also confirmed using a high-fidelity coherent Doppler sonar simulation, and from sonar measurements in a towing tank. It is shown that the distribution of observed autocorrelation coefficients is well predicted by a Gaussian random process once the autocorrelation bias has been removed.

Corresponding author address: Jeremy Dillon, Memorial University of Newfoundland, St. John’s NL A1C 5S7, Canada. E-mail: jeremy.dillon@mun.ca

Abstract

A new formula is derived for the asymptotic form of the magnitude of an autocorrelation coefficient for coherent Doppler sonar. The autocorrelation magnitude is shown to be a biased estimator in the limit of infinite ensemble length. Numerical simulation of a Gaussian random process is used to verify the asymptotic formula and to show that a bias persists for finite pulse-pair averages. Validity of the asymptotic formula is also confirmed using a high-fidelity coherent Doppler sonar simulation, and from sonar measurements in a towing tank. It is shown that the distribution of observed autocorrelation coefficients is well predicted by a Gaussian random process once the autocorrelation bias has been removed.

Corresponding author address: Jeremy Dillon, Memorial University of Newfoundland, St. John’s NL A1C 5S7, Canada. E-mail: jeremy.dillon@mun.ca
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Cover Journal of Atmospheric and Oceanic Technology
Journal of Atmospheric and Oceanic Technology

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