Nonlinear Attitude Filtering Methods

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 SO(3). Finally, the predictive filter, nonlinear observers and adaptive approaches are shown. The strengths and weaknesses of the various approaches are discussed.