An iterative subspace method for parameters estimation of Prony model (superimposed exponential signals in noise) in the sense of nonlinear least-squares is presented.With condition meeting in the optimization is both necessary and sufficient

such that the solution is sole and globally optimal.The optimal condition is interpreted in the geometric language of abstract vector spaces.In the foundation

a fully effective iterative algorithm is acquired.Thus

both the understanding for the solution is deepened and the convergence property and effectiveness is greatly improved.Finally

the procedure is illustrated with a simple example

and the result compared with one’s of Pro-ESPRIT method.