An improved recursive Frisch scheme identification algorithm

A modification for a recently developed recursive Frisch scheme algorithm to identify dynamical linear time-invariant errors-in-variables systems is proposed for the case of white measurement noise. For the update of the estimated model parameters, a recursive bias-compensating least squares algorithm is considered. The estimate of the output measurement noise variance is determined using a conjugate gradient method, which tracks the smallest eigen-value of a slowly varying matrix. The modification concerns the update of the input measurement noise variance estimate: the cost junction which is based on the high order Yule-Walker equations is approximated using linearisations of the Frisch scheme equations. For this approximated cost function, a closed form solution for its minimum can be computed directly, which forms the update equation for the input measurement noise estimate. The local convergence properties of the corresponding iterative scheme are analysed in simulation.