Accelerometers and gyroscopes embedded in mobile devices have shown great potential for non-obtrusive gait biometrics by directly capturing a user's characteristic locomotion. Despite the success in gait analysis under controlled experimental settings using these sensors, their performance in realistic scenarios is unsatisfactory due to data dependency on sensor placement. In practice, the placement of mobile devices is unconstrained. In this paper, we propose a novel gait representation for accelerometer and gyroscope data which is both sensor-orientation-invariant and highly discriminative to enable high-performance gait biometrics for real-world applications. We also adopt the i-vector paradigm, a state-of-the-art machine learning technique widely used for speaker recognition, to extract gait identities using the proposed gait representation. Performance studies using both the naturalistic McGill University gait dataset and the Osaka University gait dataset containing 744 subjects have shown dominant superiority of this novel gait biometrics approach compared to existing methods.