Bias-compensating least squares method for identification of continuous-time systems from sampled data

Abstract

Least squares (LS) techniques are applied to the identification problem of continuous-time systems from sampled data of input-output measurements. The linear integral filter, which solves the intial condition problem, is employed for handling time derivatives. The asymptotic bias in the LS estimator is derived, and is compensated in a modified LS algorithm (called a bias-compensating LS method) to obtain consistent estimates of the unknown parameters. When it is unknown, the variance of the noise can be estimated recursively together with the system parameters. The bias-compensating LS method not only has all merits of the LS method but also possesses good consistency properties. It is applicable to both time-invariant and time-varying continuous-time systems. In the time-varying case, an adaptive LS algorithm with a variable forgetting factor is chosen to make the estimates track the changing parameters quickly, and the bias is compensated as is done in the time-invariant case. Representative numerical results are also included to demonstrate the effectiveness and the feasibility of the present method.