Facing undermodelling in Sign-Perturbed-Sums system identification

Sign-Perturbed Sums (SPS) is a finite sample system identification method that constructs exact, non-asymptotic confidence regions for the unknown parameters of linear systems without using any knowledge about the disturbances except that they are symmetrically distributed. In the available literature, the theoretical properties of SPS have been investigated under the assumption that the order of the system model is known to the user. In this paper, we analyse the behaviour of SPS when the model assumed by the user does not match the data generation mechanism, and we propose a new SPS algorithm able to detect the circumstance that the model order is incorrect.