SYSTEM-IDENTIFICATION FROM NOISY MEASUREMENTS BY USING INSTRUMENTAL VARIABLES AND SUBSPACE FITTING

This paper considers the estimation of the parameters of a linear disc rete-time system from noise-perturbed input and output measurements. T he conditions imposed on the system are fairly general. In particular, the input and output noises are allowed to be auto-correlated and the y may be cross-correlated as well. The proposed method makes use of an instrumental variable (IV)-vector to produce a covariance matrix that is pre- and postmultiplied by some prechosen weights. The singular ve ctors of the so-obtained matrix possess complete information on the sy stem parameters, A weighted subspace fitting (WSF) method is then appl ied to the aforementioned singular vectors to consistently estimate th e parameters of the system. The IV-WSF technique suggested herein is n oniterative and easy to implement, and has a small computational burde n. The asymptotic distribution of its estimation errors is derived and the result is used to motivate the choice of the weighting matrix in the WSF step and also to predict the estimation accuracy. Numerical ex amples are included to illustrate the performance achievable by the me thod.