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

Abstract

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.]