Abstract: In this paper, the synthesis problem of interpolation algorithms for an unobservable stationary sequence in a partly observable (hidden) Markov process is considered. When the distributions of the compound Markov sequence are completely known, the problem solution can be found by applying the transformation equations for the posterior probability density of the unobservable sequence. This equations were firstly obtained for filtration and interpolation problems by Stratonovich (1966). Khazen (1978) managed to present the interpolation equation in the form of the product of filtration posterior probability densities in forward and backward time. The similar equation is also valid for dynamic observation models, but in this case the main equation is to be supplemented by another recursive equation connected with the dynamic properties of observations. Unfortunately, it is impossible to make use of this equations when the probability family for the unobservable sequence is unknown. However, for some conditional probability family of observations, the equation admits the representation which does not depend on statistical characteristics unknown a priori. The solution is based on the principles of the empirical Bayes approach and the theory of kernel non-parametric functional estimation. The solutions of the equation may be unstable in some points. Therefore the optimal regularization procedure was developed to obtain the stable nonparametric estimator of interpolation. Modeling showed a high quality of the proposed interpolation estimators as compared with the optimal backward interpolation.