Joint Magnetic Calibration and Localization Based on Expectation Maximization for Tongue Tracking

Background: Tongue tracking, which helps researchers gain valuable insights into speech mechanism, has many applications in speech therapy and language learning. The wireless localization technique, which involves tracking a small magnetic tracer within the 3-D oral space, provides a low cost and convenient approach to capture tongue kinematics. In practice, this technique requires accurate calibration of three-axial magnetic sensors used in the tracking system. The data-driven calibration depends on the trajectories of magnetic tracer and the ambient noise, which may change across time and space. Methods: In this paper, we model the kinematics of tracer movement and the noisy magnetic measurements in a Bayesian framework, then present a joint calibration and localization (JCL) algorithm based on expectation maximization (EM), where the unscented Rauch-Tung-Striebel smoother is employed for tracer localization and the curvilinear search algorithm is applied for sensor calibration. Results: Based on measurements conducted on our tongue tracking system with a small magnetic tracer (diameter: 6.05 mm, thickness: 1.25 mm, residual induction: 14 800 G), the JCL algorithm achieves averaged root mean square error of 0.45 mm for tracer position estimation and 2.33° for tracer orientation estimation, which are significantly lower than those of the separate calibration and localization algorithms. Conclusion: These results show that JCL can help improve the localization accuracy of this system. Significance: A potentially high precision tongue tracking method is demonstrated.