Best least squares solution for Prony model

In this paper the nonlinear least-squares estimation (NLSE) of the parameters of Prony model, with condition meeting in the optimization is both necessary and sufficient, is presented. The necessary condition for stationary of the summed squared error is expressed generally with an auxiliary parameter vector then defined uniquely by some way, such that the solution is sole and globally optimal. An equivalent condition involving only the exponents, with the coefficients suppressed, is developed. This condition is interpreted in the geometric language of abstract vector spaces, thus recognition for geometric structure that the best solution would meet is acquired. The condition still in effect requires solution of nonlinear algebraic equations, and a fully effective linear iterative method is proposed for this purpose. Finally, the procedure is illustrated with a simple example, and the result compared with one´s of Pro-ESPRIT method.