This dissertation presents a novel approach to develop a system for real-time tracking of the position and orientation of the human hand in three-dimensional space, using MEMS inertial measurement units (IMUs) and infrared cameras. This research focuses on the study and implementation of an algorithm to correct the gyroscope drift, which is a major problem in orientation tracking using commercial-grade IMUs. An algorithm to improve the orientation estimation is proposed. It consists of: 1.) Prediction of the bias offset error while the sensor is static, 2.) Estimation of a quaternion orientation from the unbiased angular velocity, 3.) Correction of the orientation quaternion utilizing the gravity vector and the magnetic North vector, and 4.) Adaptive quaternion interpolation, which determines the final quaternion estimate based upon the current conditions of the sensor. The results verified that the implementation of the orientation correction algorithm using the gravity vector and the magnetic North vector is able to reduce the amount of drift in orientation tracking and is compatible with position tracking using infrared cameras for real-time human hand motion tracking. Thirty human subjects participated in an experiment to validate the performance of the hand motion tracking system. The statistical analysis shows that the error of position tracking is, on average, 1.7 cm in the x-axis, 1.0 cm in the y-axis, and 3.5 cm in the z-axis. The Kruskal-Wallis tests show that the orientation correction algorithm using gravity vector and magnetic North vector can significantly reduce the errors in orientation tracking in comparison to fixed offset compensation. Statistical analyses show that the orientation correction algorithm using gravity vector and magnetic North vector and the on-board Kalman-based orientation filtering produced orientation errors that were not significantly different in the Euler angles, Phi, Theta and Psi, with the p-values of 0.632, 0.262 and 0.728, respectively. The proposed orientation correction algorithm represents a contribution to the emerging approaches to obtain reliable orientation estimates from MEMS IMUs. The development of a hand motion tracking system using IMUs and infrared cameras in this dissertation enables future improvements in natural human-computer interactions within a 3D virtual environment.