Parameter bounds for ARMAX models from records with bounded errors in variables

Abstract

The errors in variables problem is that of parameter estimation where all observed variables are corrupted by noise. So far, the computation of parameter bounds for dynamical models has been performed using equation-error and output-error approaches. In this paper, parameter bounds for autoregres-sive-moving-average-exogenous (ARMAX) models are derived on the assumption that both input and output are affected by bounded noise. Parameter bounding by both the ‘bounded equation error’ and the ‘bounded errors-in-variables’ approach is outlined, together with the approximation of the feasible parameter region by an orthotope outer-bounding set, and is tested on simulated data.