Optimal tracking of time-varying systems with the overdetermined recursive instrumental variable algorithm

The stability and the performance of the overdetermined recursive instrumental variable (ORIV) algorithm when tracking non-stationary systems have been studied. In particular, the effect on the system estimation via ORIV of the measurement noise and the non-stationarity of the system has been studied. The optimum value of the forgetting factor, giving the minimum mean square error, is then derived. No independence assumptions are used. Furthermore, a new orthogonality condition is obtained that extracts all the important features of ORIV. Finally, simulations corroborate the analysis.