On the identifiability of errors-in-variables models with white measurement errors

We discuss identifiability of dynamic SISO errors-in-variables (EIV) models with white measurement errors. Although this class of models turns out to be generically identifiable, it has been pointed out that in certain circumstances there may be two EIV models which are indistinguishable from external input–output experiments. This lack of (global) identifiability may be prejudicial to identification and needs better understanding. The identifiability conditions found in the literature guarantee uniqueness under certain coprimality assumptions on the (rational) transfer function of the ideal “true” system and the spectral density of the noiseless “true” input. Unfortunately these conditions are not testable since they concern precisely the unknowns of the problem which are not available to the experimenter. We provide new identifiability conditions which are instead expressible in terms of the external description of the observable signals, namely their joint power spectral densities.