Stability analysis of the discrete-time cubature Kalman filter

This study analyses the estimation error behaviour of the discrete-time cubature Kalman filter (CKF) for general nonlinear systems with nonlinear measurements. First, we show that, under certain conditions, estimation error of the CKF remains bounded. Further, we show that the careful selection of noise covariance matrices can enhance the filter stability against large estimation error. A modified-CKF is then proposed to improve the stability while reducing the steady state error. The proposed modified-CKF uses adaptive process and measurement noise covariances to cope with large estimation errors, and an ellipsoidal measurement validation gate to reject measurement outliers. Theoretical findings are verified by a series of numerical simulations. The simulation results signify that when the estimation error is large, traditional-CKF may lead instability while the modified-CKF rapidly converges to the true states. Further, the results show that the use of measurement validation gate can improve the robustness of the modified-CKF against measurement outliers.