Two-stage parameter estimation algorithms for Box–Jenkins systems

A two-stage recursive least-squares identification method and a two-stage multi-innovation stochastic gradient method are derived for Box-Jenkins (BJ) systems. The key is to decompose a BJ system into two subsystems, one containing the parameters of the system model and the other containing the parameters of the noise model, and then to estimate the parameters of the system model and the noise model, respectively. The simulation examples indicate that the proposed algorithms can generate highly accurate parameter estimates and require small computational burden.