Bounded-error estimator design with missing data patterns via state augmentation

In this paper, we present a bounded-error estimator that achieves equalized recovery for discrete-time time-varying affine systems subject to missing data. By augmenting the system state estimate with a Luenberger-like observer error, we formulate the equalized recovery estimator design problem as a semi-infinite optimization problem, and leverage tools from robust optimization to solve it. Due to the design freedom introduced by the Luenberger-like observer, we can place the eigenvalues of the augmented system to desired locations, which results in a more optimal intermediate level in the equalized recovery problem than existing approaches in the literature. Furthermore, as an extension of the proposed equalized recovery estimator, we consider missing data in the estimator design, where a fixed-length language is used to specify the allowable missing data patterns. Simulation examples involving an adaptive cruise control system are given to demonstrate the equalized recovery performance of the proposed estimator.