An instrumental variable procedure for the identification of probabilistic frequency response uncertainty regions

A procedure is developed to identify probabilistic frequeney response system uncertainty regions. The procedure utilizes time-domain measurement data and prior information about the system and the noise. There are no restrictions on the input signal, it may even be generated in closed loop. The system is assumed to be linear, time invariant, and a bound is assumed on the system´s (generalized) pulse response parameters. The noise is assumed to be a realization of a stationary stochastic process, and independent of the input signal (in open loop operation) or an external reference signal (in closed loop operation). Frequency response confidence regions are constructed by explicitly evaluating the bias and variance errors of an instrumental variable estimate