Fault detection in hidden Markov models : a local asymptotic approach

The problem of detecting a change in the transition probability matrix of a hidden Markov chain is addressed, using the local asymptotic approach. The score function, evaluated at the nominal value, is used as the residual, and is expressed as an additive functional of the extended Markov chain consisting of the hidden state, the observation, the prediction filter and its gradient w.r.t. the parameter. The problem of residual evaluation is solved using available limit theorems on the extended Markov chain, which allow us to replace the original detection problem by the simpler problem of detecting a change in the mean of a Gaussian r.v