30 November 1992 Recursive solution to quaternion-based navigation
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Abstract
Recovery of rotational parameters is a very important problem in a navigation system. A constrained least squares (CLS) method where the estimated rotation matrix is constrained to be orthonormal or a quaternion based least squares method is used to estimate the parameters. However, the solution is restricted to analyzing the motion between two successive frames only. In this paper, we propose a computationally efficient recursive scheme to estimate the rotation parameters from a long sequence of data using the quaternion formulation. The proposed method is based on the rotation of the input data at different frames to approximately align them to a given subspace. The left (the right) singular subspace defined by the running sum of the outer products of the available data points is used as the alignment matrix. The exact alignment is then obtained using the singular value decomposition (SVD) technique. The recursive estimate of the quaternions representing the constant, fixed axis rotation is shown to be given by the vector corresponding to the smallest singular value. Thus, the proposed formulation is identical to the problem of recursive updating of symmetric matrices. A recursive CLS method is also developed using a similar technique, which would yield identical estimates as in the previous method, for a given data set. The details of these methods and simulation results are presented in this paper.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Subhasis Chaudhuri, S. Ramakrishna, and Shankar Chatterjee "Recursive solution to quaternion-based navigation", Proc. SPIE 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III, (30 November 1992); doi: 10.1117/12.130930; https://doi.org/10.1117/12.130930
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