A Super Fast Attitude Determination Algorithm for Consumer-Level Accelerometer and Magnetometer

Abstract

A super fast attitude solution is obtained for consumer electronics accelerometer-magnetometer combination. The quaternion parameterizing the orientation is analytically derived from a least-square optimization that maintains very simple form. Like previously developed approaches, this algorithm does not require predetermined magnetometer reference vector. It has been proven in the paper that the proposed algorithm is equivalent to two recent representative methods. Computational complexity analysis shows that the proposed algorithm has the least floating-number operations. Comparisons with recent and classical methods indicate the definite superiority of the proposed algorithm on execution time in real embedded applications.

A Novel Fuzzy-Adaptive Extended Kalman Filter for Real-Time Attitude Estimation of Mobile Robots

“…The fourth rows depict both the instantaneous external acceleration (blue curves) executed by the 6 DOF test bench and average dynamic acceleration (red curves) determined by Equation (26). Similarly, the blue curve of the fifth row of each figure shows the instantaneous magnetic perturbation generated by Equation (34), whereas the red curve indicates the average magnetic field difference calculated by Equation (27). Finally, the sixth row depicts both the instantaneous angular rate magnitude (blue curves) and the oscillation frequency of the sensor frame (red curves) determined by Equation (25).…”

“…The fundamental solutions are three-axis attitude determination (TRIAD), which produces suboptimal attitude matrix estimation by the construction of two triads of orthonormal unit vectors, and the QUaternion ESTimator (QUEST), in which the quaternion is found by minimizing a quadratic gain function based on a set of reference and observation vectors. Improved approaches have utilized the fast optimal matrix algorithm (FOAM) [22], the factored quaternion algorithm (FQA) [23], the Gauss-Newton algorithm [24], Levenberg Marquardt algorithm [25], the gradient descent algorithm [26], and the super fast least-squares optimization-based algorithm [27]. Each approach estimates the attitude based on accelerometer and magnetometer measurements and is characterized by reduced computational complexity or more robust performance.…”

Dot Product Equality Constrained Attitude Determination from Two Vector Observations: Theory and Astronautical Applications

“…From the derived results shown in last section, the quaternion calculated now only obtains roll, pitch from accelerometer, and yaw from magnetometer, respectively. The magnetometer does not influence the estimation of other two angles and neither does the accelerometer [28]. A record of accelerometer/magnetometer data along with reference angles are logged from the 3DM-GX3-25 attitude and heading reference system (AHRS).…”

“…The motion has been generated using a human-operated inertial stabilized gimbal so that the motion in all axes will be produced. The motivation of using the accelerometer and magnetometer as an experimental object is that we would like to theoretically explain why attitude estimation can be conducted in a reference-free manner as presented in previous literatures [21,28,[45][46][47]. Using MATLAB r2016b, we evaluate the attitude determination results in Figure 4.…”

“…However, the accelerometer can independently determine the roll and pitch angles, which indicates that the disturbances from magnetic sensing can be separated. In the work by the authors of [28], this is achieved by introducing an equality constraint formed by vector dot product from rigid-body motion; whereas, the two-vector attitude determination system is far beyond the single accelerometer-magnetometer one, it is believed that there might be some more generalized theory inside such two-vector system with dot product equality constraint, as some system dynamics will be interesting by incorporating external equality constraints, e.g., the works by the authors of [29][30][31].…”