A MEASURE CHANGE DERIVATION OF CONTINUOUS STATE BAUM-WELCH ESTIMATORS

Vector valued signal and observation processes are considered with additive noise. Using changes of measure they are transformed into sequences of independent random variables. The situation where the noise in the signal is singular is discussed. The measure change enables easy recursions to be obtained for the forward and backward unnormalized conditional densities. These are analogs of the Baum–Welch algorithm.