Optimal estimation of the parameters of all-pole transfer functions

An algorithm is proposed for optimal estimation of the parameters of auto-regressive (AR) or all-pole transfer function models from prescribed impulse response data. The transfer function coefficients are estimated by minimizing the l₂-norm of the exact model fitting error. Existing methods either minimize equation errors or modify the true nonlinear error criterion. In the proposed method, the multidimensional nonlinear error criterion has been decoupled into a purely linear and a nonlinear subproblem. Global optimality properties of the decoupled estimators have been established. For data corrupted with Gaussian distributed noise, the proposed method produces maximum-likelihood estimates (MLE) of the AR-parameters. The inherent mathematical structure in the nonlinear subproblem is exploited in formulating an efficient iterative computational algorithm for its minimization. The proposed algorithm provides a useful computational tool based on an appropriate theoretical foundation for accurate modeling of all-pole systems from prescribed impulse response data. The effectiveness of the algorithm has been demonstrated with several simulation examples