Feedback control systems, which use measured responses from the structure to alter the supplemental device in real time, can adapt to changes in the structure and loading for added seismic protection. Typically, a complete set of measurements or states are not available, so the structural system states are estimated for feedback control. With wired control systems, estimation performance and error can be determined and limited with proper assumptions of measurement and modeling error. However, with wireless feedback systems, packet loss and delay can lead to estimator and controller instability. Therefore, the estimator design and measurement feedback should account for channel loss and latency to limit instability in a wireless control system. A sparse estimation design approach that weights the constant-gain estimator error covariance as well as the number of measurements is applied to a benchmark problem. The wireless benchmark control problem offers a unique test-bed to evaluate estimator performance under packet loss. The sparse estimation feedback structure highlights the most important measurements for state estimation without requiring a trial and error approach. Additionally, a sparse form allows the control system to operate at a faster sampling rate, which can help overcome packet loss. Ultimately, the closed-loop wireless estimation performance is compared with a wired centralized system.