JC-AKF: Joint calibration and NIS-guided adaptive Kalman filtering for a low-cost MEMS IMU array

Micro-electro-mechanical systems (MEMS) inertial measurement unit (IMU) arrays composed of multiple low-cost units provide a practical way to improve inertial sensing reliability through redundancy, calibration, and data fusion. This paper focuses on two key issues in array-based inertial sensing: array-level joint calibration and fusion accuracy under time-varying motion intensity. First, a turntable-free joint calibration scheme is developed using a soccer-ball platform. The proposed scheme jointly identifies intrinsic errors, including bias, scale factor, and cross-axis coupling, as well as inter-sensor misalignments in a unified body frame. A static–dynamic objective function is further designed to refine gyroscope parameters using transition segments between adjacent static poses. Second, a normalized innovation squared (NIS)-guided adaptive Kalman filter is proposed to adjust the process-noise level online. This strategy alleviates the trade-off of fixed process-noise settings: a small value provides smooth estimates but may cause lag or even divergence under abrupt dynamics, whereas a large value improves dynamic tracking but degrades accuracy in low-dynamic conditions. Equipment-level experiments on a designed IMU array are conducted to validate the proposed framework. Compared with a single IMU and a time-invariant Kalman filter, the proposed method significantly reduces the root mean square error (RMSE) in static, low-dynamic, and step-motion regimes. The maximum RMSE reduction reaches 80% compared with a single IMU and exceeds 50% compared with the time-invariant Kalman filter. The proposed method also maintains stable performance under violent and vibration-like excitations without error bursts.