A numerical parameter estimation method, based on input-output integro-differential polynomials in a bounded-error framework is investigated in this paper. More precisely, the measurement noise and parameters belong to connected sets (in the proposed work, intervals). First, this method, based on the Rosenfeld–Groebner elimination algorithm, is presented. The latter provides differential equations containing derivatives, sometimes of high order. In order to improve the numerical results, a pretreatment of the differential relations is done and consists in integration. The new relations contain, essentially, integrals depending only on the outputs. In comparison with the initial relations, they are less sensitive to measurement noise. Finally, the impact of the size of the measurement noise domain on the estimated intervals is studied.