Detection of Randomly Occuring Signals Using Spectra and Frequency Domain Kurtosis Estimates.
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB
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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
- Statistics and Probability