Robust recursive time series modeling using ARX models with optimal exogenous inputs

A new method for estimating parameters of ARX time series models, based on the approximate maximum likelihood estimation, named M-estimation, has been considered. Making use of the optimal design of exogenous inputs, the rate of estimates convergence is improved significantly. The convergence of the proposed algorithms is established theoretically using the ordinary differential equation approach. The feasibility of the approach is demonstrated with simulations.