Rotation Vector Estimation From Noisy Angular Rate Data Using a Kalman Filter

Naum Chernoguz

Abstract:	The study deals with the problem of solving the rotation vector differential equation (RVDE). Most of presently used algorithms implement direct integration of the RVDE, a deterministic approach grounded on the Taylor series expansion. However, this method involves draw-backs such as the random walk error in the rotation vector, computational drift, sensitivity to initial conditions. The present study considers the system state observer concept as an alternative to the deterministic integration of the RVDE. In particular, an extended Kalman filter (EKF) employing either the inverse or pseudo-inverse forms of the RVDE is suggested. An important feature of this, es-sentially closed-loop filter is that it approaches the true rotation vector and rotation vector rate as it observes the angular rate data over a certain period of time. The EKF implements the second-order oscillator model as the filter dynamic equation. The adaptive constrained notch filter (ACNF) was used to identify the angular fre-quency of sinusoidal coning motion. The algorithm combining EKF and ACNF was applied to the so-called three-dimensional (3D) coning motion at dif-ferent angular frequencies, particularly, 10 and 500 Hz, and exposed stable performance. Instead of integrating the RVDE over small intervals, new algorithm may be applied over extended periods, thus de-creasing the reference frame updating rate, and, conse-quently, reducing noise, random walk and drift in the at-titude computation.
Published in:	Proceedings of the 55th Annual Meeting of The Institute of Navigation (1999) June 27 - 30, 1999 Royal Sonesta Hotel Cambridge, MA
Pages:	485 - 495
Cite this article:	Chernoguz, Naum, "Rotation Vector Estimation From Noisy Angular Rate Data Using a Kalman Filter," Proceedings of the 55th Annual Meeting of The Institute of Navigation (1999), Cambridge, MA, June 1999, pp. 485-495.
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