On identification of parameter of scalar autoregressiveprocess with noisy parameter

There is proposed the sequential procedure for estimating of parameter ƒ in the model1 1, n n n x a x + + = + ƒ + ƒ 0 n ≥ .Here a is a noisy parameter. Random variables n ƒ are assumed to be independent with zeromean and unit variance. By appropriate choice of the parameters of procedure one can guaranteethe precise quality of estimators in mean square sense. Some known algorithms can be applied toestimate a and ƒ . The problem is that using of known procedures might demand a great numberof observations to guarantee the quality in the case of nonzero a. In contrast to the knownones the proposed procedure doesnt depend on the value of noisy parameter a. The main idea isto use the current estimator of noisy parameter for excluding it from equation (1). By making useof least squares method with special choice of auxiliary sequence of numbers the estimator withguaranteed quality is constructed. The obtained results are illustrated by numerical modeling.

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