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 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 • ).

External Disturbances Rejection for Vector Field Sensors in Attitude and Heading Reference Systems

“…Alternatively, the external disturbance can be estimated outside the attitude filter, to avoid state augmentation [ 33 , 34 , 35 , 36 , 37 ]. Hereinafter, these two approaches are referred to as ‘interior’ estimator and ‘exterior’ estimator, respectively.…”

“…The exterior estimator described by Equations (3)–(5) has been proven to be effective in [ 33 , 34 , 35 , 36 , 37 ], but it can only work with KF. Meanwhile, it still has two major problems that need further explanation.…”

“…The first problem is the interpretation of Equation (3), which was called the first-order auto-regressive process [ 36 ] or Markov chain process [ 37 ] that driven by low-pass filtered white noise [ 33 , 34 , 35 ]. However, in most cases, the external disturbances and are unpredictable, i.e., there is no sufficient a priori knowledge about their arising and changes over time.…”

“…However, in most cases, the external disturbances and are unpredictable, i.e., there is no sufficient a priori knowledge about their arising and changes over time. Therefore, Equation (3) is by no means rigorous, and it is certainly not driven by white noise (as presumed in [ 33 , 34 , 35 , 36 , 37 ]).…”

“…On the other hand, the model-based methods use certain model to estimate the external disturbance in real time, and then subtract it from the measurement of the corresponding sensor [ 2 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ].…”