Computationally Efficient Adaptive Error-State Kalman Filter for Attitude Estimation

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> that determined the rate at which the accelerometer corrected the inclination angle, and μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> that 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 with 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 θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> °, φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> °, and ψ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> °) by the adaptive error-state KF was compared with the CAHRS algorithm and a cascaded KF that is representative of state-of-the-art methods. Each algorithm was assessed using a publicly available data set in which the attitude of a foot-worn magnetic and inertial measurement units was recorded by a motion capture system while participants walked and ran around a room for one or three minutes (φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> ° = 2.08°, θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> ° = 1.98°, and ψ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</sub> ° = 5.25°).