Order-recursive blind identification of linear models using mixed cumulants

The problem of determining the AR order and parameters of a nonminimum phase ARMA model from observations of the system output is considered. The model is driven by a sequence of random variables which is assumed unobservable. A novel identification algorithm based on the second- and third-order cumulants of the output sequences is introduced. It performs order-recursively by minimising a well defined cost function. Strong convergence and consistency of the algorithm are proved and the weight of the cost function is balanced between the second-order and the third-order cumulants of output sequences. The influence of the weight on the estimation accuracy is also evaluated. Theoretical analyses and numerical simulations show that the proposed algorithm is satisfactory for both order and parameter identification of an AR model which is subordinate to a nonminimum phase ARMA model