Implementation of a continuous-state Viterbi algorithm for MAP state estimation

The authors address the formation of a Viterbi algorithm for maximum a posteriori (MAP) state sequence estimation of a discrete-time continuous-valued Markov process observed in memoryless noise. The usual approach to this problem is to quantize the state space of the Markov process to obtain a standard discrete-state Viterbi algorithm. They introduce an alternate approach based on piecewise linear approximation that allows a continuous-state formulation of the Viterbi algorithm. The metric and survivor calculation is illustrated by using the piecewise linear approximations, and an example of the algorithm´s use is presented