Robust $H_{2}$-OFIR Filtering: Improving Tracking of Disturbed Systems Under Initial and Data Errors

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 robust
a 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.