This paper deals with a nonlinear filtering approach to the problem of intensity parameter estimation of a doubly stochastic Poisson process, driven by an unob‐ servable Markov process. We present a method for the evaluation of the conditional likelihood ratio, given the observations of one path of the point process. By the methodsof Ibragimov, Khasminskii and Kutoyants we investigate the asymptotic properties of the corresponding maximum likelihood estimator. In the ergodic case consistency, asymptotic normality, convergence of the moments and asymptotic efficiency are established.