Recursive solution to quaternion-based navigation

Subhasis Chaudhuri; S. Ramakrishna; Shankar Chatterjee

doi:10.1117/12.130930

30 November 1992 Recursive solution to quaternion-based navigation

Subhasis Chaudhuri, S. Ramakrishna, Shankar Chatterjee

Proceedings Volume 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III; (1992) https://doi.org/10.1117/12.130930
Event: San Diego '92, 1992, San Diego, CA, United States

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.

Citation Download Citation

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); https://doi.org/10.1117/12.130930

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available