A correlational inference-based unscented total Kalman filter for integrated navigation

Abstract

An unscented total Kalman filter (UTKF) estimator with nonlinear dynamic errors-in-variables (DEIV) model is derived based on correlational inference. The proposed UTKF considers all random errors in both system and observation equations and is a Jacobian matrix free alternative to the existing TKF estimators. In particular, this estimator is applied to the inertial navigation system (INS)/ultra-wideband (UWB) integration, in which the marginalised unscented transformation (MUT) as well as the use of generalised Rodrigues parameter (GRP) for attitude updates are embedded into the UTKF to improve the computational efficiency and deal with the dimensional mismatching problems. Furthermore, a theoretical analysis to the effects of DEIV model on total Kalman filter is given. Simulation test has been conducted to compare the performance of UTKF and standard unscented Kalman filter (UKF) in terms of attitude, velocity and position errors. The results demonstrate the feasibility and effectiveness of the proposed estimator.