Fast algorithm of chandrasekhar type for ARMA model identification

Abstract

This paper presents a new fast identification algorithm based on Chandrasekhar-type equations. By appropriately defining extended state vectors and corresponding matrices, a state-space model is obtained from the ARMA representation so that the Kalman filter can be used as a parameter estimator. Because the resulting system is time-invariant it is possible to apply Chandrasekhar factorization techniques to calculate the filter gain and thus produce a fast algorithm. The sparse nature of the state-space matrices greatly facilitates the initial factorization required to launch the recursive algorithm. The new algorithm is very simple and efficient. Its computational complexity per iteration requires 14 N multiplications ( N = number of ARMA parameters); consequently, a substantial gain in computing time is obtained compared to most other algorithms partaicularly those of lattice type.