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 and the backwards-smoothing extended 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 twostep 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, Associate Professor, Department of Mechanical & Aerospace Engineering. Email: johnc@eng.buffalo.edu. Associate Fellow AIAA. Aerospace Engineer, Guidance, Navigation and Control Systems Engineering Branch. Email: Landis.Markley@nasa.gov. Fellow AIAA. Postdoctoral Research Fellow, Department of Mechanical & Aerospace Engineering. Email: cheng3@eng.buffalo.edu. Member AIAA.

/pdf/survey-of-nonlinear-attitude-estimation-methods-4tcu9nk5p8.pdf

Survey of nonlinear attitude estimation methods

In this paper a novel approach is developed for relative state estimation of spacecraft flying in formation. The approach uses information from an optical sensor to provide multiple line-of-sight vectors from one spacecraft to another. The line-of-sight measurements are coupled with gyro measurements and dynamical models in an extended Kalman filter to determine relative attitude, position, and gyro biases. The quaternion is used to describe the relative kinematics, whereas general relative orbital equations are used to describe the positional dynamics. Three different attitude formulations are presented. The first estimates the relative attitude and individual gyro biases for the chief and deputy spacecraft. The second estimates the relative attitude, and the relative velocity bias and the deputy gyro bias. The third estimates the relative attitude, and the relative velocity bias and the chief gyro bias. Simulation results indicate that the combined sensor/estimator approach provides accurate relative attitude and position estimates.

Kalman filtering for relative spacecraft attitude and position estimation

http://www.math.ucsd.edu/~mleok/pdf/SaLeLeMc2006_SCL.pdf

Global Optimal Attitude Estimation using Uncertainty Ellipsoids

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.

/pdf/nonlinear-attitude-filtering-methods-1w5wirxcof.pdf

Nonlinear Attitude Filtering Methods

A novel technique for  nding a point-by-point (deterministic) attitude solution of a vehicle using Global Positioning System phase difference measurements is presented This technique transforms a general cost function into a more numerically ef cient form by determining three-dimensional vectors in either the body or reference coordinate system Covariance relationships for the new algorithm, as well as methods that minimize the general cost function, are also derived The equivalence of the general cost functionand transformed cost function is shown for the case of orthogonal baselines or sight lines Simulation results are shown that demonstrate the usefulness of the new algorithm and covariance expressions

M. D. Shuster

Papers

Kalman filtering of spacecraft attitude and the QUEST model