Optimal identification of discrete-time systems from impulse response data

An optimal method (OM) for estimation of the parameters of rational transfer functions from prescribed impulse response data is presented. The multidimensional nonlinear fitting error minimization problem has been theoretically decoupled into two subproblems of reduced computational complexities. The proposed approach is applicable for identifying rational models with arbitrary numbers of poles and zeros. The nonlinear denominator subproblem possesses weighted-quadratic structure which is utilized to formulate an efficient iterative minimization algorithm. The optimal numerator is found noniteratively with a linear least-squares approach that utilizes the optimized denominator. Both the decoupled subcriteria of OM posses global optimality properties. The Steiglitz-McBride (1960, SM) method is also decoupled for arbitrary numbers of poles and zeros (DSM-G). It is demonstrated that the denominator subproblem of DSM-G is theoretically optimal. For another existing decoupled SM method (DSM-J), it has been shown that only the numerator is theoretically optimal