An algorithm for the identification of ARX systems in the errors-in-variables framework

The paper addresses the problem of identifying a single-input single-output linear discrete-time time-invariant auto-regressive with exogenous input (ARX) system within the errors-in-variables framework. The ARX model is considered in terms of its deterministic and stochastic parts, where the latter part, i.e. the coloured process noise, is characterised by the poles of the deterministic part. Consequently, the overall identified errors-in-variables system is subject to three sources of additive disturbances, i.e. the process noise and the noise on both the input and output. The proposed approach which differs from alternative approaches existing in the literature exploits a novel parametrisation of the locus of admissible solutions upon which an algorithm for solving the identification problem is based. A Monte-Carlo simulation study demonstrates that the proposed algorithm, when compared to an existing technique in the literature, i.e. the radial sheaf approach, yields estimates of similar precision and allows a reduction of the computational burden to be achieved.