Set-membership identification of ARX models with quantized measurements

System identification with binary or quantized measurements is a problem relevant to a number of applications in different fields. While identification of FIR models has been studied in depth, more complex model structures still need to be investigated. In this paper, identification of ARX models with quantized measurements is addressed in a set membership setting. In particular, the problem of characterizing and bounding the feasible parameter set (FPS), i.e., the set of model parameters which are compatible with the available data, is tackled. Being the FPS in general nonconvex, an algorithm is proposed for constructing an outer approximation. The proposed technique relies on quasiconvex relaxations of the original problem, based on generalized linear fractional programming. Structural properties of the FPS and convergence issues are analyzed, and numerical examples are presented to validate the proposed procedure.