In a variety of DoD applications, sensor data routinely consist of (linear) mixtures of signals generated from different sources (acoustic objects). The problems of source separation/identification and source localization are central to the use of auditory pre-processing on such sensor data [.Comon 1991.]. It is a good idea to attack the identification problem separately from the localization problem. Since typically the specific mixture is unknown, this is also referred to as the blind separation/identification problem. Independent Component Analysis (ICA) is a class of nonlinear techniques, applicable here under suitable hypotheses, that is properly viewed as extending the ``diagonalization'' approach of PCA from second order statistics to higher order statistics.
Briefly, ICA attempts to estimate the coefficients of an unknown mixture of n signal sources under the hypotheses that the sources are statistically independent, the medium of transmission is deterministic, and crucially, the mixture coefficients are constant with respect to time. One then solves for the sources from the observations by ``inverting'' the mixture matrix. ICA solves this problem by invoking cumulant equations, setting all cross-cumulants of the sources to be zero (because of independence). The well-known Herrault-Jutten algorithm applicable to this setting [.Jutten 1986, Jutten Comon 1991.] is interpretable as a stochastic approximation technique [.Comon 1991.]. It is also neuro-mimetic in character, suggesting biological plausibility. A further advance along these lines is due to Bell and Sejnowski [.Bell 1995.] who show that there is an information-maximization approach to ICA with concomitant modifications to the Herrault-Jutten class of algorithms. There is also striking experimental support for the Bell-Sejnowski approach which solves a challenging ``cocktail-party problem'' (incorporating ten sources) that proves to be beyond the capabilities of the Herrault-Jutten algorithm [.Bell 1995.].
We propose to focus on a fundamental weakness of existing ICA algorithms, namely that the mixture matrix is assumed to be essentially constant. This is unsatisfactory when moving sources are involved. We propose to attack this problem by using time-frequency characteristics of the mixture matrix in the source identification problem. We also plan to make use of the ICA algorithm in conjunction with multiscale representation (analogous to the three above applications).