<p>Sensor fusion algorithms are of fundamental importance for the odometric pose estimation of Differential Drive Wheeled Robots (DDWR) as it can be integrated into other algorithms to localize and map the environment. Different sensors are used for odometric pose estimation and, in some cases, Virtual Sensors (VS) are also used. The purpose of this work is to present a new VS can be integrated into sensor fusion algorithms for estimating the odometric pose of the robot. For this reason, a new VS for real-time estimation of the angular speed of the wheels connected to a DC of a DDWR for indoor applications is presented. The estimated wheel angular speed is obtained by processing the vibrational signals sampled from an onboard Inertial Measurement Unit (IMU) through the Discrete Fourier Transform (DFT). This technique is named Fast Fourier Transform as Wheel Angular Speed Estimator (FFT-WASE). The estimation process, integrated with the IMU, enables the realization of a new VS. The estimated angular speed obtained through the VS-based approach is adopted for making the speed control of the DDWR, as an application to validate the proposed technique. The comparison between the estimated and the measured speed coming from the encoders, the study of the absolute percentage errors and RMSE, the reconstruction of DDWR linear speed and yaw rate, and the stability analysis of the controlled DDWR have proved the validity of VS. Further tests are provided to show the applicability of the same acquired vibrational signals for real-time wheel slip monitoring.</p>