Nonlinear set-membership identification using a Bayesian approach

This paper deals with the problem of set-membership identification of nonlinear-in-the-parameters models. To solve this problem a Bayesian approach is presented. The paper illustrates how the Bayesian approach can be used to approximate the feasible parameter set (FPS) by assuming uniform distributed estimation error and flat model prior probability distributions. The methodology leads to an approximation of the FPS consisting of a set of boxes, where two regions can be identified. The inner region constitutes an inner approximation of the FPS whereas the external region can be viewed as an outer approximation of the FPS. Also, the boxes in the border give information about the percentage of consistent models inside each box and it can be used to iteratively refine the inner and outer approximations.