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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,

A new spacecraft attitude estimation approach based on the Unscented Filter is derived. For nonlinear systems the Unscented Filter uses a carefully selected set of sample points to more accurately map the probability distribution than the linearization of the standard Extended Kalman Filter, leading to faster convergence from inaccurate initial conditions in attitude estimation problems. The filter formulation is based on standard attitude-vector measurements using a gyro-based model for attitude propagation. The global attitude parameterization is given by a quaternion, while a generalized three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is derived from the local attitude error, which guarantees that quaternion normalization is maintained in the filter. Simulation results indicate that the Unscented Filter is more robust than the Extended Kalman Filter under realistic initial attitude-error conditions.

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A sigma-point Kalman filter is derived for integrating GPS measurements with inertial measurements from gyros and accelerometers to determine both the position and the attitude of a moving vehicle. Sigma-point filters use a carefully selected set of sample points to more accurately map the probability distribution than the linearization of the standard extended Kalman filter, leading to faster convergence from inaccurate initial conditions in position/attitude estimation problems. The filter formulation is based on standard inertial navigation equations. The global attitude parameterization is given by a quaternion, while a generalized three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is used to guarantee that quaternion normalization is maintained in the filter. Simulation and experimental results are shown to compare the performance of the sigma-point filter with a standard extended Kalman filter approach.