Analytic accelerometer–magnetometer attitude determination without reference information

Abstract

Attitude determination using the accelerometer-magnetometer combination is basically an applied mathematical problem. Commonly, such attitude determination tasks should be accomplished with reference information of sensors, e.g. the magnetometer's reference vector, from calibration processes. However, this piece of important information cannot be accurately acquired or would differ with the change of body's position. In this paper, to solve such problem, the conventional accelerometer-magnetometer combination fusion equations are transformed into a brand new set of equations, which are free of reference information. Quaternion solutions to the novel equations are obtained via analytic computation techniques. According to the unique design, the proposed attitude estimator owns very fast computation speed compared with representative methods including iterative ones and algebraic ones. Experiments and simulations are carried out to give demonstrations and comparisons, which verify the correctness and effectiveness of the proposed method. The results also show that using the proposed quaternion solution, fusion with gyroscope can be more efficiently obtained.

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

“…The overwhelming factor to obtain the proposed simple solution presented in (16) is indeed (12). In this section we are going to show that for representative existing magnetometer reference vector free algorithms, this preliminary always holds.…”

“…EQUIVALENCE ANALYSIS Equation 16is in fact a extremely simplified solution to the Wahba's problem. Therefore, combining Markley's two-vector approach or other Wahba's solutions with (12) gives the same numerical solution of attitude quaternion shown in (16).…”

“…where w is the weight of accelerometer and 1 − w belongs to magnetometer [12]. The Wahba's problem can be solved with many existing numerical methods, e.g., QUEST, FLAE, ESOQ and etc.…”

“…The most representative ones are factored quaternion algorithm (FQA) and Markley's two-vector method, which both employ the geometric relationship between sensing axes [9], [10]. Some other algorithms are proposed recently, e.g., algebraic quaternion algorithm (AQUA, [11]), symbolic accelerometermagnetometer fusion [12], singular-value-decomposition (SVD) filter [13] and etc. [14].…”

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

“…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.…”