Convergence analysis of non-linear filtering based on cubature Kalman filter

This study analyses the stability of cubature Kalman filter (CKF) for non-linear systems with linear measurement. The certain conditions to ensure that the estimation error of the CKF remains bounded are proved. Then, the effect of process noise covariance is investigated and an adaptive process noise covariance is proposed to deal with large estimation error. Since adaptation law has a very important role in convergence, fuzzy logic is proposed to improve the versatility of the proposed adaptive noise covariance. Accordingly, a modified CKF (MCKF) is developed to enhance the stability and accuracy of state estimation. The performance of the modified CKF is compared to the CKF in two case studies. Simulation results demonstrate that the large estimation error may lead to instability of CKF, while the MCKF is successfully able to estimate the states. In addition, the superiority of MCKF that uses fuzzy adaptation rules is shown.