UNSUPERVISED ESTIMATION AND PROCESSING OF UNKNOWN SIGNALS.
Technical rept. Feb 68-Jun 69,
PURDUE UNIV LAFAYETTE IND SCHOOL OF ELECTRICAL ENGINEERING
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Many communications systems, sonar and radar systems, control systems and pattern recognition systems such as biomedical signal processing systems must partition a multidimensional sample space so that decisions can be made on the underlying active source events. Unfortunately, the a priori information necessary to construct an acceptable partition is not always available. For many problems estimation using samples of unknown classification is the only source of additional knowledge on the sample space statistical structure. Since the sample classifications are unknown, these estimators are called unsupervised estimation algorithms. This research is concerned with investigating practical approaches to the unsupervised estimation problem which are in some sense optimum. The emphasis is on recursive estimation algorithms having fixed storage requirements and on sequential sample processing. A Bayesian framework is utilized as a guide towards optimality, and to provide a unifying relationship for the approaches of the report. The relationship between Bayes a posteriori, stochastic approximation, and decision directed approaches is determined. It is shown, for example, that an optimization criterion derived from the Bayes approach can be used to relate maximum likelihood-related stochastic approximation algorithms with decision directed estimators. The application of unsupervised estimation algorithms to a practical problem is illustrated using the problem of intersymbol interference. Author