Detection of Randomly Occuring Signals Using Spectra and Frequency Domain Kurtosis Estimates

摘要

Several detection statistics are compared in the frequency domain based on the asymptotic probability of detection criterion. These include, second-order, fourth-order, and two forms of kurtosis estimates. The results show that for randomly occurring signals or non-Gaussian signals, the fourth-order and kurtosis estimates can have higher asymptotic probability of detection levels compared with second-order estimates. But, only for the kurtosis estimates do the results seem significant. Moreover, if a second-order estimate of the noise is available to normalize a fourth-order estimate of signal and noise, the resultant modified kurtosis estimate has higher asymptotic probability of detection levels even for Gaussian signals. This result only holds when there is a significant positive covariance between the numerator and the normalizing noise sample in the denominator. On the other hand, if an independent noise sample is used to normalize a second-order or fourth-order estimate the overall performance based on the asymptotic probability of detection will be degraded compared with the unnormalized second-order or fourth-order estimates, respectively. This result could impact current sonar processing methods. (Author)