Detecting Signals with Unknown Form: Energy Detectors

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 Cramer-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.