Optimal Estimation for ARMAX Processes With Noisy Output

This paper concerns the problem of explicitly handling the additive noises that affect the output of an ARMAX process. To introduce additional information to the estimation problem, nuisances variables are employed to model the output noise as well as potentially existed outliers, which are then regularized with ℓ
₂
norm to produce estimates. The regularized estimator successfully suppresses the adverse effects of the output noise and provides minimum-variance estimates if the regularization parameter is properly chosen. Two special cases in which the regularization parameter is set to zero or infinity are also discussed.