Abstract
A novel algorithm is proposed in this paper to solve the optimal attitude determination formulation from vector observation pairs, that is, the Wahba problem. We propose here a fast analytic singular value decomposition (SVD) approach to obtain the optimal attitude matrix. The derivations and mandatory proofs are presented to clarify the theory and support its feasibility. Through simulation experiments, the proposed algorithm is validated. The results show that it maintains the same attitude determination accuracy and robustness with conventional methodologies but significantly reduces the computation time.
Highlights
In aerial applications, strapdown vector sensors are often required to directly give the rotation matrix between the body frame and inertial frame [1]
With the development of modern global navigation satellite systems (GNSS), GNSS-based attitude determination has been a vital part in spacecraft instrumentation and measurement [2]
In which Dbi and Dri are the ith pair of vector observation that was obtained in the body frame and reference frame, respectively [7]. ai is the positive weight of the ith pair with the sum of 1
Summary
Strapdown vector sensors are often required to directly give the rotation matrix between the body frame and inertial frame [1]. This leads to different algorithms of attitude determination on various platforms, for example, remote sensing and marine navigation [3, 4] In such applications, the attitude determination from vector observation pairs is usually an effective solution [5, 6]. The attitude determination from vector observation pairs is usually an effective solution [5, 6] This approach is referred to as the Wahba problem, posed in 1965, which minimizes the following loss function. Brute force calculation of such a system requires a large matrix memory and its sophisticated generalized inverse Such solution is time and space consuming, but it will cause nonorthogonality of the DCM.
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