Algebraic estimation of a biased and noisy continuous signal via orthogonal polynomials

Many important problems in signal processing and control engineering concern the reconstitution of a noisy biased signal. For this issue, in this paper, we consider the signal written as an orthogonal polynomial series expansion and we provide an algebraic estimation of its coefficients. We specialize in Hermite polynomials. On the other hand, the dynamical system described by the noisy biased signal may be given by an ordinary differential equation associated with classical orthogonal polynomials. The signal may be recovered through the coefficients identification. As an example, we illustrate our algebraic method on the parameter estimation in the case of Hermite polynomials.