Nonlinear Attitude Filtering Methods

Abstract

This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST, the super-iterated extended Kalman filter, the interlaced extended Kalman filter, and the second-order Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A two-step approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, including particle filters and a Bayesian filter based on a non-Gaussian, finite-parameter probability density function on S O ( 3 ) . Finally, the predictive filter, nonlinear observers and adaptive approaches are shown. The strengths and weaknesses of the various approaches are discussed.

Design of a Navigation Unit for a New Unmanned Aerial Vehicle: A Composite of a Capstone and Research Projects

“…The uncertainty in such environments can be described by either probabilistic measures, or fuzzy measures. There are many probabilistic approaches to control and navigation, including the Kalman filer (KF) [19], the extended Kalman filter (EKF) (e.g., [20] to [23]), and the unscented Kalman filter (UKF) [24]. An alternative to dealing with uncertainty is to consider a measure that is neither crisp, nor probabilistic, but is represented by a membership function (MF).…”

Effective Adaptive Kalman Filter for MEMS-IMU/Magnetometers Integrated Attitude and Heading Reference Systems

“…A major advantage of using quaternion is that the kinematics equation is linear in the quaternion and is also free of singularity (Markley et al, 2005). However, the observation model of the quaternion-based method is still non-linear (Nie et al, 2010).…”

“…With regard to the non-linear problem, Markley et al (2005) presented a review of several filtering methods for non-linear attitude estimation. Although it is possible to find different families of approaches in literature, the Extended Kalman Filter (EKF) is still the standard technique for non-linear attitude estimation in practical terms.…”

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“…In [14], attitude estimators with the star camera measurements is developed. Recently, there are many nonlinear attitude estimators [15][16][17][18], which are designed based on nonlinear theory, such as Lyapunov method. In [19], the nonlinear complementary filter is designed, which boasts computational efficiency, easily tuned parameters, and a proof of global asymptotic stability can be found in [20].…”