Analysis of convergence of adaptive single­step algorithms for the identification of non­stationary objects

The study deals with the problem of identification of non-stationary parameters of a linear object which can be described by first-order Markovian model, with the help of the simplest in computational terms single-step adaptive identification algorithms – modified algorithms by Kaczmarz and Nagumo-Noda. These algorithms do not require knowledge of information on the degree of non-stationarity of the studied object. When building the model, they use the information only about one step of measurements. Modification involves the use of the regularizing addition in the algorithms to improve their computing properties and avoid division by zero. Using a Markovian model is quite effective because it makes it possible to obtain analytic estimates of the properties of algorithms. It was shown that the use of regularizing additions in identification algorithms, while improving stability of algorithms, leads to some slowdown of the process of model construction. The conditions for convergence of regularizing algorithms by Kaczmarz and Nagumo-Noda at the evaluation of stationary parameters in mean and root-mean-square and existing measurement interference were determined. The obtained estimates differ from the existing ones by higher accuracy. Despite this, they are quite general and depend both on the degree of non-stationarity of an object, and on statistical characteristics of interference. In addition, the expressions for the optimal values of the parameters of algorithms, ensuring their maximum rate of convergence under conditions of non-stationarity and the presence of Gaussian interferences, were determined. The obtained analytical expressions contain a series of unknown parameters (estimation error, degree of non-stationarity of an object, statistical characteristics of interferences). For their practical application, it is necessary to use any recurrent procedure for estimation of these unknown parameters and apply the obtained estimates to refine the parameters that are included in the algorithms

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