Known source detection predictions for higher order correlators

The problem addressed in this paper is whether higher order correlation detectors can perform better in white noise than the cross correlation detector for the detection of a known transient source signal, if additional receiver information is included in the higher order correlations. While the cross correlation is the optimal linear detector for white noise, additional receiver information in the higher order correlations makes them nonlinear. In this paper, formulas that predict the performance of higher order correlation detectors of energy signals are derived for a known source signal. Given the first through fourth order signal moments and the noise variance, the formulas predict the SNR for which the detectors achieve a probability of detection of 0.5 for any level of false alarm, when noise at each receiver is independent and identically distributed. Results show that the performance of the cross correlation, bicorrelation, and tricorrelation detectors are proportional to the second, fourth, and sixth roots of the sampling interval, respectively, but do not depend on the observation time. Also, the SNR gains of the higher order correlation detectors relative to the cross correlation detector improve with decreasing probability of false alarm. The source signal may be repeated in higher order correlations, and gain formulas are derived for these cases as well. Computer simulations with several test signals are compared to the performance predictions of the formulas. The breakdown of the assumptions for signals with too few sample points is discussed, as are limitations on the design of signals for improved higher order gain. Results indicate that in white noise it is difficult for the higher order correlation detectors in a straightforward application to achieve better performance than the cross correlation. © 1998 Acoustical Society of America

Known source detection predictions for higher order correlators

The problem addressed in this paper is whether higher order correlation detectors can perform better in white noise than the cross correlation detector for the detection of a known transient source signal, if additional receiver information is included in the higher order correlations. While the cross correlation is the optimal linear detector for white noise, additional receiver information in the higher order correlations makes them nonlinear. In this paper, formulas that predict the performance of higher order correlation detectors of energy signals are derived for a known source signal. Given the first through fourth order signal moments and the noise variance, the formulas predict the SNR for which the detectors achieve a probability of detection of 0.5 for any level of false alarm, when noise at each receiver is independent and identically distributed. Results show that the performance of the cross correlation, bicorrelation, and tricorrelation detectors are proportional to the second, fourth, and sixth roots of the sampling interval, respectively, but do not depend on the observation time. Also, the SNR gains of the higher order correlation detectors relative to the cross correlation detector improve with decreasing probability of false alarm. The source signal may be repeated in higher order correlations, and gain formulas are derived for these cases as well. Computer simulations with several test signals are compared to the performance predictions of the formulas. The breakdown of the assumptions for signals with too few sample points is discussed, as are limitations on the design of signals for improved higher order gain. Results indicate that in white noise it is difficult for the higher order correlation detectors in a straightforward application to achieve better performance than the cross correlation. © 1998 Acoustical Society of America

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

In general, higher‐order correlation detectors perform well in passive detection for signals of high third‐ and fourth‐order moments. 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. In this paper, formulas that predict detector performance for passive detection at the minimum detectable level are derived. The noise is assumed to be stationary and zero mean with Gaussian correlation central ordinate probability density functions. To test the formulas, SNR detection and gain curves are generated using hypothesis testing and Monte Carlo simulations on a set of test signals. The test signals are created by varying the time width of a pulse‐like signal in a sampling window of fixed time duration, resulting in a set of test signals with varying signal moments. Good agreement is found between the simulated and theoretical results. The effects of observation time (length of detection window) and sampling interval on detector performance are also discussed and illustrated with computer simulations. The prediction formulas indicate that decreasing the observation time or the sampling interval (assuming the signal is sufficiently sampled and the detection window contains the entire signal) improves detection performance. However, the rate of improvement is different for the three detectors. The SNR required to achieve the minimum detectable level of detection performance at a given probability of false alarm (Pfa) decreases with the fourth root of the observation time and sampling interval for the cross‐correlation detector, the sixth root for the bicorrelation detector, and the eighth root for the tricorrelation detector. Relative detector performance also varies with Pfa. The probability of detection (Pd) for higher‐order detectors degrades less rapidly with decreasing Pfa than the Pd for ordinary correlations. Thus higher‐order correlators can be especially appropriate when a very low Pfa is required

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

In general, higher‐order correlation detectors perform well in passive detection for signals of high third‐ and fourth‐order moments. 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. In this paper, formulas that predict detector performance for passive detection at the minimum detectable level are derived. The noise is assumed to be stationary and zero mean with Gaussian correlation central ordinate probability density functions. To test the formulas, SNR detection and gain curves are generated using hypothesis testing and Monte Carlo simulations on a set of test signals. The test signals are created by varying the time width of a pulse‐like signal in a sampling window of fixed time duration, resulting in a set of test signals with varying signal moments. Good agreement is found between the simulated and theoretical results. The effects of observation time (length of detection window) and sampling interval on detector performance are also discussed and illustrated with computer simulations. The prediction formulas indicate that decreasing the observation time or the sampling interval (assuming the signal is sufficiently sampled and the detection window contains the entire signal) improves detection performance. However, the rate of improvement is different for the three detectors. The SNR required to achieve the minimum detectable level of detection performance at a given probability of false alarm (Pfa) decreases with the fourth root of the observation time and sampling interval for the cross‐correlation detector, the sixth root for the bicorrelation detector, and the eighth root for the tricorrelation detector. Relative detector performance also varies with Pfa. The probability of detection (Pd) for higher‐order detectors degrades less rapidly with decreasing Pfa than the Pd for ordinary correlations. Thus higher‐order correlators can be especially appropriate when a very low Pfa is required

Detection of Oscillatory and Impulsive Transients Using Higher Order Correlations and Spectra

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

EARS Buoy Applications By LADC: I. Marine Animal Acoustics

Littoral Acoustic Demonstration Center (LADC) scientists have investigated sperm and beaked whale clicks as recorded on Environmental Acoustic Recording System (EARS) buoys to analyze whale behavior and the possibility of identifying individual whales acoustically. The research began in 2001 and continues through the present. LADC has conducted three experiments in the northern Gulf of Mexico and participated with the Naval Undersea Research Centre with three experiments in the Ligurian Sea. Initially the research centered on sperm whale coda clicks and echolocation clicks. In 2007 it was extended to the study of beaked whale echolocation clicks. The measured data suggest that click properties can be used to identify individual whales. Initially the identifications were done by grouping clicks using self-organizing maps and other means of cluster analysis. Each cluster or class represents an individual whale. These methods have been refined and have become reasonably robust. Verification of the identification has been a problem since using visual observations has not been satisfactory. Presently localization of the clicking animals is being coupled with cluster analysis to verify the identifications. A new finding that rhythms of echolocation clicks can be used to identify sperm whale individuals is now a part of the research, and cluster analysis, rhythm analysis, and localization are mutually reinforcing the identifications. Other results using EARS buoys for marine animal acoustics are listed among the key findings of LADC acoustic research