Algorithmic study of the algebraic parameter estimation problem for a class of perturbations

We consider the algebraic parameter estimation problem for a class of standard perturbations. We assume that the measurement z(t) of a solution x(t) of a linear ordinary differential equation -- whose coefficients depend on a set θ := {θ₁, ..., θᵣ} of unknown constant parameters -- is affected by a perturbation γ(t) whose structure is supposed to be known (e.g., an unknown bias, an unknown ramp), i.e., z(t)=x(t, θ)+γ(t). We investigate the problem of obtaining closed-form expressions for the parameters θᵢ's in terms of iterative indefinite integrals or convolutions of z. The different results are illustrated by explicit examples computed using the NonA package -- developed in Maple -- in which we have implemented our main contributions.