Identification of Continuous Systems from Noisy Sampled Input-Output Data

Abstract

The problem of identification of continuous systems is considered when both the discrete input and output measurements are contaminated by white noises. Using a pre-designed digital filter, a discrete-time estimation model is constructed easily without direct approximations of system signal derivatives. If the pass-band of the filter is designed so that it includes the main frequencies of both the system input and output signals in some range, the noise effects are sufficiently reduced, accurate estimates can be obtained by least squares(LS) algorithm in the presence of low measurement noises. Two classes of filters (infinite impulse response(IIR) filter and finite impulse response(FIR) filter) are employed. The former requires less computational burden and memory than the latter while the latter is suitable for the bias compensated least squares(BCLS) method, which compensates the bias of the LS estimate by the estimates of the input-output noise variances and thus yields unbiased estimates in the presence of high noises.