A geometrically-intuitive quaternion-based complementary attitude and heading reference system (CAHRS) proposed in our previous work estimated the attitude of a magnetic and inertial measurement unit (MIMU). The method used two correction factors, µ a , which determined the rate at which the accelerometer corrected the inclination angle, and µ m , which governed the rate at which the magnetometer corrected the yaw angle. Improvements to the filter have been made by embedding each correction factor within an error-state Kalman filter (KF), enabling the correction rates to behave adaptively. The revised filter only estimates the error in two variables, thus remaining computationally efficient (65 addition, 88 subtraction, and 214 multiplication operations) compared to established algorithms in the literature for attitude estimation that utilize a KF or extended KF. The accuracy of the attitude estimated (i.e., the pitch, roll, and yaw angle errors θby the adaptive error-state Kalman filter (AESKF) was compared to the CAHRS algorithm and a cascaded Kalman filter (CKF) that is representative of state-of-the-art methods. Each algorithm was assessed using a publicly-available dataset in which the attitude of a foot-worn MIMU was recorded by a motion capture system whilst participants walked and ran around a room for one minute or three minutes (φ • RMSE = 2.08 • , θ • RMSE = 1.98 • , ψ • RMSE = 5.25 • ).
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