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 functions from prescribed impulse-response data. The parameters are estimated by minimizing the l₂-norm of the model fitting error. The multidimensional nonlinear error criterion is theoretically decoupled into a purely linear problem and a nonlinear subproblem. Global optimality properties of the decoupled estimators have been established. For noise-corrupted data distributed in a Gaussian manner, the proposed method produces maximum-likelihood estimates of the AR parameters. The weighted-quadratic structure of the denominator criterion is exploited to formulate an iterative computational algorithm for its minimization. It is also shown that the algorithm can be utilized for identifying all-zero or moving-average systems. The effectiveness of the algorithm is demonstrated with several simulation examples