Cumulant-based identification of noisy closed loop systems

Abstract

SUMMARY Conventional parameter estimation approaches fail to identify linear systems operating in closed loop when both input and output measurements are contaminated by additive noise of unknown (cross)spectral characteristics. However, even in the absence of measurement noise, parameter estimation is involved owing to the additive system noise entering the loop. The present work introduces a novel criterion which is theoretically insensitive to a class of disturbances and yields the same parameter estimates that one obtains using mean squared error (MSE) minimization in the absence of noise. A strongly convergent sample-based approximation of the proposed criterion is introduced for consistent parameter estimation in practice. It is also shown that in the common case of ARMA modelling the resulting parameter estimates coincide with those obtained from a set of linear equations which can be solved using a time-recursive algorithm. Simulation results are presented to verify the performance of the proposed schemes in low-signal-to-noise-ratio environments.