Why are errors-in-variables problems often tricky?

There are several identification methods designed for the errors-in-variables problem. In this paper we focus on discussing the underlying assumptions for several of these methods. Some assumptions are shown to have far reaching consequences. For example, if the noise-free input happens to be periodic, simple estimators that give consistent parameter estimates of the system parameters can easily be designed. If the variances of the input and output noises are unknown, some structural assumption must be added for the system dynamics to be identifiable. On the other hand, should the ratio between output noise variance and input noise variance be known, it is possible not only to estimate the system parameters consistently, but also to combine this with a reasonable estimate of the unperturbed input.