### Approximation of Confidence Sets for Output Error Systems Using Interval Analysis

#### Abstract

Standard identification techniques usually result in a single point estimate of the system parameters. This is justified in cases when the number of observations is large compared to the number of system parameters. However in case of small sample count it is more reasonable to identify a set of possible parameters which contain the nominal parameters with a given probability. These confidence sets cannot be calculated directly. The paper proposes interval analytic techniques to approximate confidence sets of model parameters up to arbitrary precision. The origins of interval analysis lie in the field of reliable computing, giving certified results for every computation. It has been used to solve global optimization problems numerically providing theoretical certificates on the optimality of the results. This method of global optimization is modified in a suitable way to generate the needed confidence sets. Introduction to interval analytic techniques is given and the methodology of global optimization via these is also presented. The modifications of this algorithm needed to construct the confidence sets are discussed and the method is illustrated on a simple example. The presented algorithm is focused on the output error model structure but the methodology can be extended to more general cases as well.