Estimation of perturbations without modeling assumptions in second-order ordinary differential equations

Abstract

This paper is concerned with the estimation of a small perturbing function affecting a system of second-order ODEs, in order to get a solution of it fitting a given set of measurements. The classical approach consist of perturbation modeling and least-squares parameter specification. Alternative procedures are needed when no a-priori adequate perturbation model is at disposal. A general scheme for methods needing no modeling assumption is introduced and a complete error analysis of them is obtained. Tills error characterisation allows to determine methods minimising the effect of each error source; therefore, optimal schemes under different restrictions are deduced.