An conditionally optimal a posteriori algorithm for detection: the change of properties of a class of multidimensional signal

The problem of a posteriori detection of abrupt changes in the parameters of multidimensional autoregressive (AR) processes on the condition of full a priori uncertainty is considered. The main difference in the approach from the widely used ones is the pattern recognition statement of the problem. The detection rule is derived as the discrimination function of the corresponding pattern recognition system whose classes are defined so that the decision about the most probable class uniquely determines the most probable instant of change in the signal parameters. The class conditional probability density functions are estimated from the given training samples according to the Bayesian estimation principle. In this respect, the proposed decision procedure guarantees the exact minimum of the misclassification and, hence, minimum error of the determination of the instants of change in the signal properties. Finally, the asymptotic property of the detection rule and the experimental results both for synthesized and real speech signals are discussed.