An instrumental variable approach for identification of hidden Markov models

In this paper we derive recursive filters for both the online and off-line identification of hidden Markov models (HMMs). The identification is achieved by taking conditional mean estimates of certain summation non-linear functions of the states and measurements and using these values to estimate the parameters of the system. This instrumental variable method we propose offers the possibility of improved parameter estimation when the state of the HMM is correlated with the system noise