Informatica

In the previous papers (Masreliez and Martin, 1977; Novovičova, 1987; Schick and Mitter, 1994) the problem of recursive estimation of linear dynamic systems parameters and of the state of such systems in the presence of outliers in observations have been considered. In this connection various ordinary recursive techniques are worked out, when systems output is corrupted by an additive noise with a time homogeneous contamination of outliers. The aim of the given paper is the development of an approach for robust recursive state estimation of linear dynamic systems in a case of additive noises with time-varying outliers. The recursive technique based on the abovementioned theoretical results is obtained and proved by state estimation of the real chemical process (Box and Jenkins, 1970). The results of numerical simulation by computer (Fig. 1–3) are given.

In the previous papers (Pupeikis, 1990; 1991; 1992) the problems of model oder determination and recursive estimation of dynamic systems parameters in the presence of outliers in observations have been considered. The aim of the given paper is the development, in such a case, of classical off-line algorithms for systems of unknown parameters estimation using batch processing of the stored data. An approach, based on a substitution of the corresponding values of the sample covariance and cross-covariance functions by their robust analogues in respective matrices and on a further application of the least square (LS) parameter estimation algorithm, is worked out. The results of numerical simulation by IBM PC/AT (Table 1, 2) are given.

In the previous paper (Pupeikis, 1990) the problem of model order determination in the presence of outliers in observations has been considered by means of introducing robust analogues of the sample covariance and cross-covariance functions instead of the respective classical function meanings used in the determinant ratio test. The aim of the given paper is the development of statistical hypothesis-testing procedures for determination of the model order of dynamic objects, described by linear difference equations. The results of numerical simulations by computer (Table 1) show the efficiency of the proposed statistical procedures for determining the model order by input-output data in the presence of outliers in observations.

In the previous paper (Pupeikis, 1990) the problem of model order determination in the presence of outliers in observations has been considered. The aim of the given paper is the development of the recursive algorithms of computation of M-estimates ensuring their stability conditions. In this connection the approach, based on adaptive Huber's monotone psi-function, is worked out. It is also used for the detection of the outliers in time series and for the correction both outliers and M-estimates during successive calculations. The results of numerical simulation by computer (Fig. 1 and Table 1) are given.

In the papers (Pupeikis, 1988a, b; 1989a, b, c) the problems of efficiency determination, stopping and increase of the effectiveness of asymptotically optimal recursive algorithms are considered respectively by means of estimating time delay in an object and also introducing their robust analogues, stable to outliers in observations. The aim of the given paper is the development of the robust method for a determination of the model order on the basis of determinant ratio. The three methods forming the initial moment matrices are considered. By the first method the elements of the matrix, being the corresponding values of the sample covariance and cross-covariance functions, are calculated by classical formulas. In the case of the second method the same elements are substituted by their robust analogues. The third method is based on an application of auxiliary variables. The results of numerical simulation on a computer (Table 1) indicate the advisability to apply the robust method for determining the model order in the presence of outliers.