An Offline Estimation Method for Hip and Knee Joint Angles of Lower Limbs Based on Quaternion and DTW Time Alignment

Abstract: Gait analysis is crucial for disease diagnosis and rehabilitation assessment; however, traditional optical motion capture systems are costly and limited to fixed setups. This study presents an "Offline Estimation Method for Hip and Knee Joint Angles of Lower Limbs Based on Quaternion and DTW Time Alignment." The method uses quaternion fusion of inertial measurement unit (IMU) orientations and employs Sakoe-Chiba constrained Dynamic Time Warping (DTW) to eliminate a 42 ms initial offset and a 150 ms cumulative drift. Combining N-pose calibration with heel velocity event detection allows for the offline calculation of hip and knee joint angles. Data were collected from eight healthy participants during flat walking and stair ascent/descent scenarios, with the Noraxon Ultium Motion system serving as the reference. Results show that DTW reduces the average root mean square error (RMSE) by 29.1%; specifically, "the RMSE for hip flexion reaches 4.1°, while the overall knee joint RMSE is 10.2°, with correlation coefficients ≥0.87. Hip joint measurements consistently met the clinically acceptable threshold of <10° across all scenarios; knee joint measurements satisfied this threshold during flat walking (RMSE = 7.8°) but exceeded it during stair negotiation (RMSE = 11.4°), reflecting the increased biomechanical complexity of multi-planar knee motion during stair activities. This study provides a low-cost, high-precision solution for the post-hoc offline estimation of hip and knee joint angles. The proposed method is specifically designed for retrospective gait data analysis rather than real-time feedback, offering a scalable strategy for early screening of gait abnormalities and clinical assessment in home and community rehabilitation settings.

Yuling Zhang, Yuejian Hua, Shengli Luo, Xiaolong Shu, Hongyan Tang and Hongliu Yu. “An Offline Estimation Method for Hip and Knee Joint Angles of Lower Limbs Based on Quaternion and DTW Time Alignment”. International Journal of Advanced Computer Science and Applications (IJACSA) 17.2 (2026). http://dx.doi.org/10.14569/IJACSA.2026.0170234

@article{Zhang2026,
title = {An Offline Estimation Method for Hip and Knee Joint Angles of Lower Limbs Based on Quaternion and DTW Time Alignment},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2026.0170234},
url = {http://dx.doi.org/10.14569/IJACSA.2026.0170234},
year = {2026},
publisher = {The Science and Information Organization},
volume = {17},
number = {2},
author = {Yuling Zhang and Yuejian Hua and Shengli Luo and Xiaolong Shu and Hongyan Tang and Hongliu Yu}
}