Sigma-Point Kalman Filtering for tightly-coupled GPS/INS

This paper proposes the fusion of GPS measurements and inertial sensor data from gyroscopes and accelerometers in tightly-coupled GPS/INS navigation systems. Usually, an extended Kalman filter (EKF) is applied for this task. However, as system dynamic model as well as the pseudorange and pseudorange rate measurement models are nonlinear, the EKF is sub-optimal choice from theoretical point of view, as it approximates the propagation of mean an covariance of Gaussian random vectors through these nonlinear models by a linear transformation, which is accurate to first-order only. The sigma-point Kalman filter (SPKF) family of algorithms use a carefully selected set of sample points to more accurately map the probability distribution than linearization of the standard EKF, leading to faster convergence from inaccurate initial conditions in position and attitude estimation problems, which achieves an accurate approximation to at least second-order. Therefore, the performance of EKF and SPKF applied to tightly-coupled GPS/INS integration is compared in numerical simulations. It is found that the SPKF approach offers better performances over standard EKF.