Development of a recursive algorithm for parameter uncertainty interval estimation

This article addresses the problem of recursively estimating the parameter uncertainty intervals for a linear discrete system, whose output measurements are contaminated with noise. The estimator provides the maximally tight bounding rectangular hyperparallelepiped, whose vertices are computed in an optimal manner so as to contain all parameter values consistent with the system structure and the l₁ norm of the error bounds. The proposed method relies on a recursive formulation of the underlying posed linear programming problem in Milanese and Belforte (1982), by exploring its distinct structure. The computational effort associated with the finding of this optimal outer box is minimal. A recursive algorithm is presented for the cases of an increasing, and a fixed size sample time-sliding window. Simulation studies are included to highlight the algorithm´s performance