Recursive scheme for ARMA coefficient and order estimation with noisy input–output data

A novel estimation scheme for determining ARMA orders and coefficients is presented. The system is assumed to be excited by a non-Gaussian random sequence. Third-order cumulants of the input–output data are introduced to eliminate additive Gaussian noises of unknown variances at the measurement site. The proposed algorithm is performed order-recursively until the estimated coefficients converge where the defined norm of error squares (NES) nearly stays at a constant value. The system orders thereby need not be known a priori. Theoretical analyses together with experimental results indicate that the system orders can be accurately determined with the same procedures while the corresponding system coefficients are being estimated.