Analysis of over-sampling based identification

In this work, firstly, an asymptotic variance expression is derived for the transfer function estimates in the over-sampling based identification scheme. Then the result is used to analyze the over-sampling scheme. The asymptotic variance expression says that the joint covariance matrix of the transfer function estimates is proportional to the “generalized” noise-to-signal ratio. It is an application of the result in Ljung (1985); and it covers both open-loop and closed-loop tests. Using the result, one can show that informativity of the closed-loop tests without external excitation can be attained by using the over-sampling scheme, but only when the output disturbance has high frequency content beyond the bandwidth of the plant. Moreover, when the output disturbance has high frequency content and when test signal is used, the result points out that the over-sampling scheme can increase model accuracy, and, it will outperform conventional method with anti-aliasing filtering. Numerical examples are used to illustrate the asymptotic variance expression and the analysis about over-sampling scheme of identification.