Algebraic approach to system identification

A variety of identification procedures exists for estimating the parameters of an autoregressive moving-average (ARMA) process from noise-free excitation and noise-contaminated response data. In this paper, an identification procedure is proposed for the more realistic situation in which both the excitation and response are contaminated by white noises. The method is based upon the null space characterization of an associated "data matrix." Some of the more important algebraic properties possessed by this data matrix are first established in the ideal noise-free data case. In particular, it is found that an overordering of the ARMA model will not impair the identification of the Underlying system. In the more realistic noise-contaminated data case, an approximation of the data matrix\´s null space is affected by using an eigenvalue-eigenvector decomposition. By incorporating this null space approximation, the deleterious effects of the noise are significantly reduced thereby giving rise to improved modeling performance. This improvement is demonstrated by means of a standard example in which the proposed identification method is shown to produce a better modeling behavior than does the classical least-squares method, the corresponding iterative generalized least-squares method, and a commonly employed instrumental variable method.