Matrix estimation using matrix forgetting factor and instrumental variable for nonstationary sequences with time variant matrix gain

Abstract

Consider us the problem of time-varying parameter estimation. The most immediate and simple idea is to include a discounting procedure in an estimation algorithm i.e., a procedure for discarding (forgetting) old information. The most common way to do is to introduce an exponential forgetting factor (FF) into the corresponding estimation procedure (to see: Ljung and Gunnarson (1990)). In this paper, the authors going to describe a good enough estimator considering a system with nonstationary time variant properties with respect to input and output qualities. The techniques used are Instrumental Variable (IV) and Matrix Forgetting Factor (MFF). The results previously obtained by (Poznyak and Medel 1999a, 1999b) were the basis of this paper. The theoretical description illustrates the advantages with respect to others filters below cited.