Methods of nonlinear filtering and interpolation of an unobservable Markov chain with a finite set of states are developed here. 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 in the case of an 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 empirical Bayes approach we represent these equations in the form independent of the unknown transition matrix. The resulting equations are solved using non-parametric kernel procedures by dependent observations. Comparison of proposed non-parametric algorithms with the optimal methods in the case of the known transition matrix is carried out by simulating.