Performance evaluation of Cubature Kalman filter in a GPS/IMU tightly-coupled navigation system

Abstract

In a GPS/IMU tightly-coupled navigation system, the extended Kalman filter (EKF) is widely used to estimate the navigation states, due to its simpler implementation and lower computational load. However, the EKF is a first order approximation to the nonlinear system. When the nonlinearity of the system is high, the negligibility in higher order terms of the nonlinear system will degrade the estimation accuracy. In this paper, a nonlinear filtering method Cubature Kalman filter (CKF) is introduced and analysed through Taylor expansion showing the CKF׳s capability in capturing higher-order terms of nonlinear system. The analysis indicates that the CKF benefits only when implemented with nonlinear systems. To better show the merits of the CKF, a nonlinear attitude expression is introduced to the integrated navigation system. The performance comparison between the CKF and the EKF is examined based on the observability analysis. When the observability degree is low, the CKF performs better than the EKF in the integrated navigation systems. Otherwise, the CKF has similar performance as the EKF in the tightly-coupled navigation system. The CKF is also superior to the EKF in the GPS outage and large misalignment cases when the nonlinearity of the system is high.