Detection of oscillatory and impulsive transients using higher-order correlations and spectra

Abstract

Higher-order cross and ordinary correlation detectors are applied to four deterministic transients contaminated by uncorrelated Gaussian noise only. Histograms and moments are used to examine the properties of the signals and their effect on detector performance. Receiver operating characteristic (ROC) curve analysis and limiting signal-to-noise ratios for ‘‘good’’ detection provide comparative measures for different detectors. Probability density functions of detection ordinate values of signal-present and noise-only correlations are used to explain ROC curve behavior. Using a known source, the cross-correlation detector performs better than the higher-order correlation detectors for each transient studied. However, for an unknown narrow pulse source signal, the bicorrelation and tricorrelation detectors outperform the cross-correlation detector. In contrast, the bicorrelation detector performs very poorly for low-frequency narrow-band signals with a small third moment embedded in uncorrelated Gaussian noise. Rectification as part of the detection process improves the performance of the bicorrelation detector and also places the peak of maximum magnitude at the origin. This eliminates the problem in detection or time delay estimation that the existence of multiple peaks due to symmetries in the auto-bicorrelation or the bicorrelation of repeated signals may cause. The tricorrelation detector also performs better with rectification than without. For an unknown source, the bicorrelation and tricorrelation detectors with rectification perform on a level comparable to the cross-correlation detector for certain signals. Comparisons are made between repeating a known source and repeating noisy received signals in the bicorrelation.

Prediction of signal-to-noise ratio gain for passive higher-order correlation detection of energy transients

“…The bicorrelation and tricorrelation can also be formed using output from only two sensors and repeating signals in various ways (Pflug et al, 1992b(Pflug et al, , 1994.…”

“…Previous studies by the authors have shown that the normalized third-and fourth-order signal moments are reliable indicators of higher-order correlation detector performance [Pflug et al (1992b)]. For a deterministic energy transient of known moments through fourth order, it is possible to predict theoretically the amount of gain over an ordinary cross-correlation detector for a bicorrelation or tricorrelation detector applied in a noise environment of known variance.…”

Detection and Tracking of Underwater Targets Using Directional Sensors

“…In order not to miss a possibly valid TDOA measurement, the threshold of the transient detector [7] can be lowered, and, consequently, the probability of false alarm is increased. In this way, all sensor pairs that contain sensors with invalid data may not be eliminated, and, as a result, some TDOAs in the measurements batch Z may be erroneous (clutter).…”

“…, R, and use them to compute TDOAs for the detected transients as follows. First, we attempt to identify the sensor pairs that have received replicas of the emitted transient and for this purpose we use the cross-correlationbased transient detectors described in [7]. These detectors apply ordinary and higher-order cross-correlations computed using the signals received by two or more different sensors.…”

“…These detectors apply ordinary and higher-order cross-correlations computed using the signals received by two or more different sensors. Denote by J i the set that contains the indexes of all sensor pairs that have received valid signal from the source at time t i as determined by using a transient detector proposed in [7]. The TDOAs related to the ith transient {Z i,j } j∈Ji are then computed by utilising the sensor pairs indicated in J i .…”