The Cramer-Rao lower bound for noisy input-output systems

The asymptotic Cramer-Rao lower bound (CRLB) describes the best possible ac curacy attainable by an efficient estimator as the number of data samples i ncrease. It is developed here for the case of identifying noisy input-outpu t systems. In this case, the measured variables and their statistical prope rties depend in a complicated way on the unknown parameters. A form of the CRLB is derived, generalizing a classical result by Whittle to include also a deterministic component in the data. The case where the undisturbed inpu t is an ARMA process and the measurement noise on the input and output are white is treated in detail, and an explicit computational algorithm is deve loped. (C) 2000 Elsevier Science B.V. All rights reserved.