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The parameter estimation problem of a partly observed linear stochastic system is considered. The unobserved component of the system is a scalar stable autoregressive process of the p-th order, observed in presence of multiplicative and additive noises. The distributions of all the noises of the system are supposed to be unknown. The problem is to estimate the dynamic parameters of the object and the variances of the additive noises of the system. Strongly consistent estimators are obtained on the basis of the correlation method. Sequential estimation plans with given in advance mean square accuracy of estimation are constructed.