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

Utilisation de tests basés sur des statistiques d'ordre supérieur dans l'analyse de séries temporelles mesurées dans l'espace

Tests of hypotheses based on Higher Order Statistics (HOS) are reviewed in the particular context of the identification of nonlinear processes in space plasma. The time series under study are associated with the measurements of electric or/and magnetic field components, or/and counting rates of particles. The basic principles of HOS techniques are reviewed. A general and unified procedure is suggested in order to construct statistical tests: (1) for detecting a non-gaussian or transient signal in a gaussian (or non-gaussian) noise, (2) testing a stochastic time series for non-gaussianity (including non-linearity), (3) studying non-linear wave interactions by using the kth-order coherency function. Asymptotic theory of estimates of the kthorder spectra is implemented in a digital signal processing framework. The effectiveness of the signal detection algorithms is demonstrated through computer simulations. Examples of application on the analysis of satellite data are given.Des tests d'hypothèses basés sur des statistiques d'ordre supérieur sont revus dans le contexte particulier de l'identification de processus non-linéaires dans les plasmas spatiaux. Les séries temporelles étudiées sont associées à la mesure de composantes du champ électrique et/ou magnétique d'ondes ou de turbulences, et/ou de données particules. Les principes de base des statistiques d'ordre supérieur sont brièvement rappelés. Une procédure générale et unifiée est suggérée afin de construire des tests statistiques permettant: (1) de détecter des signaux non-gaussiens ou transitoires au sein d'un bruit gaussien (ou non-gaussien), (2) de tester si une série temporelle est associée ou non à un processus stochastique issu d'un processus non-linéaire, (3) d'étudier des interactions non-linéaires à plusieurs ondes par l'utilisation de la fonction de cohérence d'ordre k. La théorie asymptotique des estimés des spectres d'ordre k est mise en oeuvre dans le cas discret. L'efficacité des algorithmes de détection est démontrée par le biais de simulations numériques. Des exemples d'applications à des données satellites sont présentés