Recursive optimization of state estimation of dynamic processes in the presence of patchy outliers in observations

Abstract

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.

Straipsnyje nagrinėjamas proceso, aprašomo autoregresijos – slenkančio vidurkio (ARMA) modeliu (1)–(8), būsenų ivertinimo uždavinys, taikant lygiagrečių Kalmano filtrų banką. Irodytos teoremos teigia, kad esant pakankamai bendroms sąlygoms mažėjant filtravimo paklaidų reikšmėms atitinkamai mažėja atkurtų įėjimų dispersijų reikšmės, kurias nesunku suskaičiuoti rekurentiškai.