Realizations of BELS as WIV method in both direct and indirect closed-loop system identification
ABSTRACT The bias eliminated least squares (BELS) method, which is known as efficient for unknown parameter estimation of transfer
function in the correlated noise case, has been developed and applied effectively to the closed-loop system identification.
In this paper, under the general settings, the realizations of the BELS method as a weighted instrumental variables (WIV)
method in both direct and indirect closed-loop system identification are established through constructing an appropriate weighting
matrix in the WIV method. The constructed structures are similar in both cases, which reveals that all the proof procedures
of the two realizations are the same. Thus, the unified realizations of the BELS as the WIV method for the closed-loop system
identification can be built. A simulation example is given to validate our theoretical analysis.