Parameter estimation for orthogonal polynomial moments

Prony's method recovers a Dirac ensemble μ = Σ i =1 M   a i δ x i with given sparsity level by separating the reconstruction of the unknown coefficients and positions. While it recovers the positions by examing the so called Prony polynomial, its reconstruction is heavily based on solving linear systems, which can be constructed by given monomial moments. The intention of this article is to propose a Prony‐like method to recover the Dirac ensemble with an upper bounded sparsity level from orthogonal polynomial moments.