A new technique for detecting Gaussian signals in non-Gaussian noise

The signal and noise processes arising in passive underwater acoustic detection are usually modeled as being random processes, with the dominant noise often being best modeled as a non-Gaussian process [H. V. Poor and J. B. Thomas, J. Acoust. Soc. Am. 63, 75–80 (1978] due to the effects of noise phenomena resulting from sources such as cracking ice, marine animals, or surface shipping. A new technique for the detection of Gaussian signals that can be modeled as being produced by linear stochastic systems, in the presence of such non-Gaussian noise, has been developed. This technique is based on an approximation to the likelihood-ratio statistic [H. V. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1988)] for such situations. This likelihood-ratio approximation is in turn based on the Masreliez approximation of nonlinear filtering [R. Vijayan and H. V. Poor, IEEE Trans. Commun. 38, 1060–1065 (1990)], in which the predicted state probability density (i.e., the time update) of the underlying stochastic system is approximated with a multivariate Gaussian distribution. This approximation allows calculation of the likelihood-ratio statistic using a pair of sufficient statistics satisfying a simple nonlinear recursion. An approximation to the locally optimum detection statistic [Poor, op. cit.] for this situation has also been derived, by considering the limiting behavior of the approximate likelihood-ratio statistic as the signal-to-noise ratio vanishes. [Work supported by the U.S. Office of Naval Research under Grant N00014-89-J-1321.]