Informatica

The aim of the given paper is a development of the direct approach used for the estimation of parameters of a closed-loop discrete-time dynamic system in the case of additive noise with outliers contaminated uniformly in it (Fig. 1). To calculate M-estimates of unknown parameters of such a system by means of processing input and noisy output observations (Fig. 2), the recursive robust H-technique based on an ordinary recursive least square (RLS) algorithm is applied here. The results of numerical simulation of closed-loop system (Fig. 3) by computer (Figs. 4–7) are given.

In the previous paper (Pupeikis, 1998), the problem of recursive estimation of the state of linear dynamic systems, described by an autoregressive model (AR), in the presence of time-varying outliers in observations to be processed has been considered. An approach to the robust recursive state estimation has been obtained and proved by estimating the real chemical process (Box and Jenkins, 1970). The aim of the given paper is the development of the abovementioned approach for the robust recursive state estimation of an autoregressive-moving average (ARMA) process in a case of additive noises with patchy outliers. The results of numerical simulation and the state estimation of the AR model (Figs. 1–4) and the real chemical process, described by the ARMA model, which is chosen from the same book of Box and Jenkins (Figs. 5–8) are given.

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 papers (Kaminskas, 1973; Kaminskas and Nemura, 1975) the stopping rule of recursive least squares (RLS) is worked out using the length of the confidence interval for the respective current meaning of the true output signal of a linear dynamic system. The aim of the given paper is the development of techniques for calculating threshold intervals of respective criteria, used in such a stopping rule. In this connection adaptive threshold intervals based on the Cramer-Rao lower bound according to Pupeikis (1995) are proposed here, too. The results of numerical simulation by IBM PC/AT are given.

In the papers (Kaminskas, 1972; Kaminskas and Nemura, 1975; Yin, 1989) the stopping rules of recursive least squares (RLS) are worked out using the ellipsoidal confidence region for the respective parameter vector of a linear dynamic system. The aim of the given paper is the development of the technique for calculating threshold intervals of respective criterions, used in a stopping rule, which are presented in Kaminskas (1972). In this connection adaptive threshold intervals based on the Cramer-Rao lower bound are proposed here. The results of numerical simulation by IBM PC/AT are given.

The aim of the given paper is the development of optimal and tuned models and ordinary well-known on-line procedures of unknown parameter estimation for inverse systems (IS) using current observations to be processed. Such models of IS are worked out in the case of correlated additive noise acting on the output of the initial direct system (DS). The results of numerical investigation by means of computer (Table 1) are given.

In the previous papers (Novovičova, 1987; Pupeikis 1991) the problem of recursive least square (RLS) estimation of dynamic systems parameters in the presence of outliers in observations has been considered, when the filter, generating an additive noise, has a transfer function of a particular form, see Fig. 1, 2. The aim of the given paper is the development of well-known classical techniques for robust on-line estimation of unknown parameters of linear dynamic systems in the case of additive noises with different transfer functions. In this connection various ordinary recursive procedures, see Fig. 2–6, are worked out when systems' output is corrupted by the correlated noise containing outliers. The results of numerical simulation by IBM PC/AT (Table 1) are given.

In the previous paper (Pupeikis, 1992) the problem of off-line estimation of dynamic systems parameters in the presence of outliers in observations have been considered, when the filter generating an additive noise has a very special form. The aim of the given paper is the development, in such a case, of classical generalized least squares method (GLSM) algorithms for off-line estimation of unknown parameters of dynamic systems. Two approaches using batch processing of the stored data are worked out. The first approach is based on the application of S-, H-, W- algorithms used for calculation of M-estimates, and the second one rests on the replacement of the corresponding values of the sample covariance and cross-covariance functions by their robust analogues in respective matrices of GLSM and on a further application of the least squares (LS) parameter estimation algorithms. The results of numerical simulation by IBM PC/AT (Table 1) 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.