Estimation of ARMAX processes with noise corrupted output signal observations

Auto-regressive-moving-average with exogenous input (ARMAX) models contribute significantly in representing a variety of practical systems, but neglect the measurement uncertainties on the output, which impairs the fidelity of the model. In this paper, a method to perform simultaneous state and output noise estimation for ARMAX processes with additive output noise is presented. The output noise as well as outliers are modeled as auxiliary variables, and an additional quadratic regularization term is added to the original least-squares cost function of the Kalman filter to identify them. The resultant estimator is still a Kalman-type estimator which is able to reduce the adverse effects of output noise and provides smaller estimation errors. The possibility of adaptively selecting the regularization parameter makes the derived estimator well suited to resisting output noise and outliers. Numerical examples are given to demonstrate the effectiveness of the proposed approach. & COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.