Inertial sensing suites now permeate all forms of smart automation, yet a plateau exists in real-world derivation of global orientation. Magnetic field fluctuations and inefficient sensor fusion still inhibit deployment. We introduce a new algorithm, an Extended Complementary Filter (ECF), to derive 3D rigid body orientation from inertial sensing suites addressing these challenges. The ECF combines computational efficiency of classic complementary filters with improved accuracy compared to popular optimization filters. We present a complete formulation of the algorithm, including an extension to address the challenge of orientation accuracy in the presence of fluctuating magnetic fields. Performance is tested under a variety of conditions and benchmarked against the commonly used gradient decent (GDA) inertial sensor fusion algorithm. Results demonstrate improved efficiency, with the ECF achieving convergence 30% faster than standard alternatives. We further demonstrate an improved robustness to sources of magnetic interference in pitch and roll and to fast changes of orientation in the yaw direction. The ECF has been implemented at the core of a wearable rehabilitation system tracking movement of stroke patients for home telehealth. The ECF and accompanying magnetic disturbance rejection algorithm enables previously unachievable real-time patient movement feedback in the form of a full virtual human (avatar), even in the presence of magnetic disturbance. Algorithm efficiency and accuracy have also spawned an entire commercial product line released by the company x-io. We believe the ECF and accompanying magnetic disturbance routines are key enablers for future widespread use of wearable systems with the capacity for global orientation tracking