A system that efficiently estimates an object's orientation using magnetic, angular rate, and gravity sensors. The object may be for example a virtual reality headset or a user in a virtual reality environment. Magnetic and gravity data are used to correct errors that accumulate from integrating angular velocity. Unlike systems that use Kalman filter approaches, embodiments of the system apply a simple, highly efficient technique to generate magnetic and gravity error vectors; these error vectors are added directly to the angular velocity prior to integration. Error calculations are performed in the sensor reference frame rather than in the Earth reference frame. Magnetic error correction uses only the horizontal component of the magnetic field, which is efficiently calculated by subtracting off the projection of the magnetic field onto the measured gravity vector. Sensors and processors for calculating orientation may be integrated into a low-latency virtual reality display system.