Periodic instrumental variable identification

An approach to the selection and use of instruments in which the input signal is restricted to be a periodic pseudorandom binary sequence (PRBS) is proposed. The method exploits the periodicity of the input and the steady-state periodic output by choosing the instruments to be the input and the output delayed by the period of the input. This proposed choice has desirable statistical properties and identifies the unknown parameters in a relatively few number of iterations when compared to other choices of instruments. The proposed instruments produce asymptotically unbiased estimates with a covariance that approaches zero as the number of iterations becomes large.