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Published in:
Introduction to Underwater Acoustic Signal Processing Read chapter Read first chapter

2019 | OriginalPaper | Chapter

9. Detecting Signals with Unknown Form: Energy Detectors

Author : Douglas A. Abraham

Published in: Underwater Acoustic Signal Processing

Publisher: Springer International Publishing

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Abstract

In many applications of underwater acoustic signal processing, very little is known about the structure of signals of interest either because they are inherently random (e.g., radiated ship noise) or because of insufficient a priori knowledge about the sound source (e.g., marine mammal acoustic emissions). Energy detectors are derived and analyzed for such signals under varying levels of knowledge about the power spectral density (PSD) shape, strength, and frequency band. The derivation shows how the Eckart filter, which was derived to optimize detection index when the signal PSD shape is known, is also a locally optimal energy detector. Additional energy detectors are derived or presented to handle cases where less information is available about the signal PSD, including the noise-normalized, generalized-likelihood-ratio (GLR), modified GLR, and power-law energy detectors. Time- and frequency-domain implementations of energy detectors are presented, along with how to choose the size and spacing of coherent processing intervals. Various approximations to the detection threshold term in the sonar equation are presented for the noise-normalized energy detector operating on Gaussian random signals and noise. Fixed-window and exponential averagers are presented and analyzed for estimating the noise power and normalization in frequency-domain energy detectors. The important topic of time-delay estimation is covered with both estimator derivation and Cramér-Rao-lower-bound analysis for inter-sensor delay estimation via cross-correlation processing and multipath-delay estimation via auto-correlation processing. Parameter estimation for narrowband signals includes the frequency, phase, and amplitude of sinusoidal signals and the bandwidth and center frequency of Gaussian random signals.

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previous chapter Detecting Signals with Known Form: Matched Filters
next chapter Detecting Signals with Unknown Duration and/or Starting Time: Sequential Detectors
Appendix
Available only for authorised users
Footnotes
1
Acknowledgment with gratitude to Prof. S. Parks, Biology Dept., Syracuse University, who acquired the data under funding from the National Oceanic and Atmospheric Administration (NOAA) and a Department of Fisheries and Oceans (DFO) Canada permit.
 
2
In mathematical statistics, this condition arises from the sufficiency [11, Sect. 6.2] of the squared moduli for the model parameters.
 
3
A somewhat arcane difference between the development of the LO detector here and in Sect. 9.2.5.2 is that here there are M partial derivatives with respect to the DFT-bin SNRs that are then evaluated at zero whereas in Sect. 9.2.5.2 there is only one partial derivative with respect to A. In both cases, application to the joint PDF of the independent DFT-bin data results in a decision statistic comprising a sum over the detector non-linearities formed for the individual DFT bins.
 
4
Note that Fig. 8.​30 is shown as radial velocity, which is related to the measured frequency through an affine transformation.
 
5
This assumption is pertinent only in the CRLB analysis and not in deriving the delay estimator itself.
 
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Metadata
Title
Detecting Signals with Unknown Form: Energy Detectors
Author
Douglas A. Abraham
Copyright Year
2019
Book
Underwater Acoustic Signal Processing

Print ISBN: 978-3-319-92981-1

Electronic ISBN: 978-3-319-92983-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-92983-5_9