Three-Axis Attitude Determination with Pseudo-Bias Estimation from Gravity/Magnetic Vector Observations

Abstract

This paper revisits the stationary alignment problem of attitude and heading reference systems (AHRSs). The investigation is initiated from the three-axis attitude determination (TRIAD)–based method, purposely chosen to use nonunitary/nonorthogonal observations of the local gravity and Earth’s magnetic flux density vectors. For the simplifying assumption of body and navigation frames aligned, a comprehensive error analysis is developed, providing additional insight into the problem. Closed-form formulas for the residual normality and orthogonality errors are used to devise innovative pseudo-bias estimation (PBE) algorithms for the x- and z-axis magnetometer biases, as well as for the z-axis accelerometer bias. As a direct consequence of applying the latter, and also figuring as the main contribution of this paper, an improved (more accurate) AHRS stationary alignment approach is obtained, herein called TRIAD-PBE. The error analysis is extended to representative state-of-the-art attitude determination techniques, confirming the relevance of TRIAD-PBE, especially in the presence of hard-iron magnetism. Results from simulated and experimental tests confirm the adequacy of the outlined verifications.