Optimal simultaneous detection and estimation of filtered discrete semi-Markov chains

An optimal algorithm for the detection of noisy filtered discrete semi-Markov chains is presented. Estimation of the underlying model parameters is also considered. For a given path of the discrete semi-Markov chain the optimum estimates of the model parameters obtained by the maximum likelihood method are expressed as functions of the path. These functions are then used to derive a single maximum a posteriori criterion for the optimal detection of the unknown single path. The final optimization is carried out numerically by a combination of gradient, divide-and-conquer, and search techniques. This set of techniques is referred to as the integer most likely search detector. Experimental results, using synthetic data, demonstrate the potential of the algorithm