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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 (KKF), 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 EKF approach.
John L. Crassidis (Sat,) studied this question.