Confidence regions and experiment design for non-parametric estimation

When estimating the response of a linear system at a specific frequency under ideal conditions, the presence in the excitation signal of other frequencies has no effect on the bias and variance of the estimate. Nevertheless, such additional excitation may have a detrimental effect on the ability to choose confidence regions. This is discussed for the case of finite data experiments with both white and coloured noise. The choice of confidence regions for plants in closed-loop is also considered. In particular, the legitimate use of a-priori and a-posteriori information is discussed