A recursive technique for tracking the feasible parameter set in bounded error estimation

In this paper a new recursive algorithm is proposed for tracking parameter changes of a time-varying linear system. Since a bounded error approach is adopted for modeling both the measurement noise and the parameter change process, the problem addressed amounts to the design of a procedure for updating an estimate of the feasible parameter set. The approximating regions considered are in the form of outbounding orthotopes. The novelty of the approach lies in the use of a selection technique which keeps track only of a special subset of the constraints defining the feasible set. These inequalities represent the binding constraints of suitable linear programs of limited size. The devised algorithm is tested on several numerical examples, showing remarkable performance both in terms of computational burden, which is comparable to that of classical recursive estimation algorithms like RLS, and quality of the set estimate as compared to alternative techniques available in the literature.