Modified Kalman filtering based multi-step-length gradient iterative algorithm for ARX models with random missing outputs

Abstract

This study presents a modified Kalman filtering-based multi-step-length gradient iterative algorithm to identify ARX models with missing outputs. The Kalman filtering method is modified to enhance the estimation of unmeasurable outputs, laying the foundation for enabling the multi-step-length gradient iterative algorithm to update effectively the ARX model parameter estimation through the estimated outputs. Compared to the classical gradient iterative algorithm, this study improves the estimation accuracy of the missing outputs by introducing a modified Kalman filter, and the parameter estimation convergence rate by deriving a new multi-step-length formulation. To validate the framework and the algorithm developed, a series of bench tests were conducted with computational experiments. The simulated numerical results are consistent with the analytically derived results in terms of the feasibility and effectiveness of the proposed procedure.