Abstract
This paper revisits the stationary attitude initialization problem, i.e., the stationary alignment, of Attitude and Heading Reference Systems (AHRSs). A detailed and comprehensive error analysis is proposed for four of the most representative accelerometer- and magnetometer-based stationary attitude determination methods, namely, the Three-Axis Attitude Determination (TRIAD), the QUaternion ESTimator (QUEST), the Factored Quaternion Algorithm (FQA), and the Arc-TANgent (ATAN). For the purpose of the error analysis, constant biases in the accelerometer and magnetometer measurements are considered (encompassing, hence, the effect of hard-iron magnetism), in addition to systematic errors in the local gravity and Earth magnetic field models (flux density magnitude, declination angle, and inclination angle). The contributions of this paper are novel closed-form formulae for the residual errors (normality, orthogonality, and alignment errors) developed in the computed Direction Cosine Matrices (DCM). As a consequence, analytical insight is provided into the problem, allowing us to properly compare the performance of the investigated alignment formulations (in terms of ultimate accuracy), as well as to remove some misleading conclusions reported in previous works. The adequacy of the proposed error analysis is validated through simulation and experimental results.
Highlights
Inertial Navigation Systems (INSs) are specialized dead-reckoning systems which provide a standalone navigation solution for attitude, velocity, and position [1]
To address the aforementioned issues, this paper presents an innovative and comprehensive analytical error description of four of the most employed attitude determination approaches for AHRS stationary alignment purposes, namely, Three-Axis Attitude Determination (TRIAD), QUaternion ESTimator (QUEST), Factored Quaternion Algorithm (FQA), and ATAN
For the purpose of the test, accelerometer and magnetometer data were generated at 100 Hz, considering the ideal scenario of body and navigation frames perfectly aligned
Summary
Inertial Navigation Systems (INSs) are specialized dead-reckoning systems which provide a standalone navigation solution for attitude, velocity, and position [1]. The very purpose of the alignment is to roughly estimate the attitude of the vehicle (or body) frame relative to the navigation frame, so that it can be used, and posteriorly corrected, by any filtering-based navigation/guidance stage deployed afterwards [4]. The local gravity and Earth rate vectors, measured by stationary accelerometers and gyros, respectively, provided by an Inertial Measurement Unit (IMU), have been chosen for INS alignment purposes [6]. When low-cost IMUs are sought, a good candidate for replacing the Earth rate vector (for stationary alignment purposes) is the Earth magnetic flux density vector, which can be adequately observed by calibrated magnetometers [8]. AHRSs have been successfully employed in a vast range of applications, including, but not limited to, Unmanned Aerial Vehicle (UAV) attitude control/stabilization [13], human body tracking [14,15], joint angle estimation [16], and mobile communications [17]
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