Transient Signal Detection and Time Delay Estimation Using Higher Order Correlations and Spectra

Abstract : This memorandum report contains a current summary of the authors' research on detection and time delay estimation for acoustic or other transients for which only one short-time realization exists. Thus, an energy signal model is used, rather than a power signal model. The energy signal model is more realistic for a brief transient, such as might be generated by a tool dropping on a metal floor or the return of an active sonar ping. Performance analysis is done for detection and time delay estimation of these transients embedded in Gaussian noise over a domain of signal-to-noise ratios. Monte Carlo simulations and hypothesis testing are used to generate receiver operating characteristic (ROC) curves to compare higher order and ordinary correlation detector and time delay estimator performance. Results indicate that for signals of high skewness and kurtosis, the higher order methods significantly outperform the cross correlation detector and time delay estimator. For signals of low skewness and kurtosis, rectification before detection often improves higher order detection to levels comparable to or even surpassing that of the cross correlator. For both signal classes, if the signal passband is approximately known, prefiltering prior to detection significantly improves higher order correlator performance. In the active sonar case, the higher order correlators with prefiltering can outperform the matched filter by more than 4 dB. Even larger improvements are observed in the passive case.... Altimetry, Mesoscale oceanography, Ocean forecasting.