In this paper, we develop methods of nonlinear filtering and interpolation of an unobservable Markov chain with a finite set of states. This Markov chain controls coefficients of AR(p) model. Using observations generated by AR(p) model, we have to estimate the state of Markov chain at each time moment in the case of unknown probability transition matrix. To solve this problem we construct a system of equations with respect to the posterior probability of Markov states. According to the idea of the Empirical Bayes approach we represent these equations in the form independent of unknown transition matrix. The resulting equations are solved using nonparametric kernel procedures. Comparison of the proposed non-parametric algorithm with the optimal method in the case of the known transition matrix is carried out by simulation.