Robust $H_{2}$-OFIR Filtering: Improving Tracking of Disturbed Systems Under Initial and Data Errors
Jorge A. Ortega-Contreras, Yuriy S. Shmaliy, José Amparo Andrade-Lucio, Oscar Gerardo Ibarra-Manzano · IEEE Transactions on Aerospace and Electronic Systems · 2022
In harsh environments, tracking is organized assuming disturbances, initial errors, and data errors that requires robust algorithms. In this article, we develop, in discrete-time state space, a robusta posteriori$H_{2}$optimal finite impulse response ($H_{2}$-OFIR) filter of disturbed systems under initial and measurement errors. The derivation is provided using a novel$H_{2}$finite impulse response ($H_{2}$-FIR) state estimation approach by minimizing the squared Frobenius norm of the weighted transfer function. The robust$H_{2}$-OFIR filter is designed for full block error matrices, and its recursive forms are shown for diagonal error matrices. Also presented is the suboptimal$H_{2}$-FIR filtering algorithm using the linear matrix inequality. It is shown that, in global-positioning-system-based tracking of moving vehicles, the$H_{2}$-OFIR filter outperforms the Kalman and unbiased FIR filters in terms of accuracy and robustness. Moreover, the ability to operate on short horizons makes the$H_{2}$-OFIR filter computationally efficient.