Estimating Linear and Rotational Head Kinematics in Ice Hockey from a Single Helmet-Mounted IMU Using Vector Autoregressive Models

Purpose Accurate estimation of head kinematics is critical for assessing brain injury risk in contact sports. This study introduces a Vector AutoRegressive (VAR) framework to jointly model linear acceleration and angular velocity during head impacts, capturing the inherent coupling between translational and rotational dynamics. Methods Controlled impacts were performed on a helmeted Hybrid III 50th percentile male headform using a pendulum impactor across multiple locations (front, front-oblique, side, rear-oblique) and three impact intensities (30°, 50°, 70° pendulum angles). Helmet-mounted Inertial Measurement Unit (IMU) signals were processed using VAR models trained on reference headform data at 30° and 50° impacts. The proposed framework was also evaluated for the estimation of head kinematics at untrained impact intensities (70°). Results At the trained intensities, the VAR approach generally improved angular velocity reconstruction across impact configurations, with PMPE and RMSE reductions of up to 20.9 pp (−81.1%) and 288.8 °/s (−85.7%), respectively, at 30°. Linear acceleration improvements were more limited, with PMPE and RMSE reductions of up to 171.8 pp (−85.7%) and 10.9 g (−74.8%), also at 30°. At the untrained 70° intensity, angular velocity PMPE decreased at all locations but significantly only at the front-oblique, while RMSE decreased significantly at the front and front-oblique (up to − 341.1 °/s, − 52.2%). In contrast, linear acceleration PMPE degraded at all locations, increasing by up to 68.6 pp (+726.4%), while RMSE showed either deterioration or non-significant improvement. Conclusion In conclusion, the VAR modeling framework offers a promising multivariate approach for reconstructing head impact kinematics from a single IMU-instrumented helmet. However, limited generalization to higher, untrained intensities highlights the need for further development before real-time head injury assessment can be supported.