This paper describes an indoor navigation approach using estimation and control for horizontal translational motion and heading angle for quadrotor Unmanned Aerial Vehicles (UAVs) via Ultra-Wideband (UWB)-based localization. In particular, to cope with noisy measurements, emanating from model uncertainties, and Non-Line-Of-Sight (NLOS) conditions, a Linear Quadratic Regulator (LQR) is deployed along with a Maximum Correntropy Criterion Kalman Filter (MCC-KF). This approach has proven improved robustness compared to the traditional Kalman Filter (KF) against non-Gaussian noise. A testbed with a quadrotor was developed for evaluating the performance of our proposed approach. We demonstrate, via the experimental setup, that the MCC-KF outperforms the use of KF in the presence of shots of mixed noise and communication delays, enabling onboard robust estimation and control via UWB-based localization.