Detection of random transient signals via hyperparameter estimation

Abstract

Difficulties arise with the generalized likelihood ratio test (GLRT) in situations where one or more of the unknown signal parameters requires an enumeration that is computationally intractable. In the transient signal detection problem, the frequency characteristics of the signal are typically unknown; therefore, even if an aggregate signal bandwidth is assumed, the estimation problem intrinsic to the GLRT requires an enumeration of all possible sets of signal locations within the monitored band. In this paper, a prior distribution is imposed over those portions of the signal parameter space that traditionally require enumeration. By replacing intractable enumeration over possible signal characteristics with an a priori signal distribution and by estimating the "hyperparameters" (of the prior distribution) jointly with other signal parameters, it is possible to obtain a new formulation of the GLRT that avoids enumeration and is computationally feasible. The GLRT philosophy is not changed by this approach-what is different from the original GLRT is the underlying signal model. The performance of this new approach appears to be competitive with that of a scheme of emerging acceptance: the "power-law" detector.

All-purpose and plug-in power-law detectors for transient signals

“…Recall (20) which converges in law to a normal distribution by CLT, provided has finite second moment. As shown before, follows an iid distribution under , and thus, we can compute the mean and variance of as Var (21) Having obtained this mean and variance, we have the following result for : Under the assumption that s are iid for converges in law for large to Var .…”

“…To exploit only the latter, there are detectors that begin their work on frequency domain data (usually DFT bins). Via (maximum likelihood) estimation of unknown signal parameters via the estimation-maximization (EM) algorithm, a GLRT approach is presented [21]. Of greatest interest here is Nuttall's frequency domain "power-law" detector [12], which will be introduced shortly.…”

A performance study of some transient detectors

“…In our simulation, we use M = 128, which, admittedly, is well matched to the signals of interest. EM: EM Detector: In [10] it is proposed to model DFT data as either a single population of independent exponential random vaxiables (the transient-free situation) or as two populations. Under the additional assumption that the membership of the DFT data in these two populations is i.i.d.…”

“…1-7, the upper left and right plots show, respectively, the transient signal (without added noise) itself and its spectrum. The middle plot in each figure is a receiver operating characteristic (ROC) based on 10 5 simulation runs. Here each transient signal has total energy 81, whereas the additive noise is white and Gaussian with zero mean and unity variance.…”

Adaptive window-length detection of underwater transients using wavelets

“…Signals may also have local oscillatory behavior, thereby yielding high spectral peaks. Many current transient detectors apply an appropriate linear transform, such as wavelet transform ͑Del Marco and Weiss, 1997;Liu and Fraser-Smith, 2000͒, Gabor transform ͑Fried-lander and Porat, 1989, 1993͒, or Fourier transform ͑Nuttall, 1996, 1997Streit and Willett, 1999͒, to the received signal.…”