Experiences with an Adaptive Nonlinear Kalman Filter for the Rotation Vector Estimation From Noisy Data

Naum Chernoguz

Abstract:	The study deals with an Extended Kalman Filter (EKF) suggested for the rotation vector estimation from noisy angular rate data under the 3-D coning scenario. The filter approaches a true rotation vector and rotation vector rate as it observes the angular rate data over a certain period of time. The EKF employs either the inverse or pseudo-inverse form of the rotation vector differential equation. Both forms are comparable in performance. Using the nonrecursive representation of an EKF, one may perform the observability analysis and test the filter stability with the help of Observation Matrix (OM) and Fisher Information Matrix (FIM). At the stage of analysis we also apply the so-called Ideal Extended Kalman Filter (IEKF), the filter with ideal dynamic and observation models and zero process noise. Experimental study of the IEKF clearly demonstrates that with the 3-D coning scenario the filter is observable and stable in concept, and achieves the Cramer-Rao Lower Bound. The EKF relies on the 2nd-order oscillator model as the filter dynamic equation. As the coning frequency is unspecified beforehand, the adaptive constrained notch filter (ANF) may be used to identify this parameter. Combining the EKF and ANF results in an Adaptive Nonlinear Kalman Filter. An augmented version of this filter was applied to a scenario in which the sensors are corrupted by the deterministic bias and scale factor errors.
Published in:	Proceedings of the IAIN World Congress and the 56th Annual Meeting of The Institute of Navigation (2000) June 26 - 28, 2000 The Catamaran Resort Hotel San Diego, CA
Pages:	73 - 83
Cite this article:	Chernoguz, Naum, "Experiences with an Adaptive Nonlinear Kalman Filter for the Rotation Vector Estimation From Noisy Data," Proceedings of the IAIN World Congress and the 56th Annual Meeting of The Institute of Navigation (2000), San Diego, CA, June 2000, pp. 73-83.
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