A novel robust progressive cubature Kalman filter with variable step size for inertial navigationsystem/global navigation satellite system tightly coupled navigation

This article investigates the state estimation problem of the nonlinear system with the large process prior uncertainty but high-accuracy measurement information, the situation is prone to occur in the inertial navigation system (INS)/global navigation satellite system (GNSS) tightly coupled navigation system. Furthermore, the unknown heavy-tailed measurement noises induced by the inaccurate prior navigation information and random measurement outliers are also considered. Given existing methods such as progressive cubature Kalman filter (PCKF) cannot effectively solve the above issues, a novel robust PCKF with variable step size (RVSS-PCKF) is proposed. First, a new Gaussian-uniform-mixing inverse Gamma (GUMIG) distribution is presented to model the variable step size and measurement noise. Next, the GUMIG distribution is expressed as a hierarchical Gaussian presentation and then RVSS-PCKF is derived with the help of the variational Bayesian (VB) inference. In the filter, the state, variable step size and noise statistic are jointly estimated by the fixed-point iterations. Finally, the simulations and real data of the tightly coupled navigation illustrate the superiority of the filter in terms of accuracy and steady-state performance.