Abstract State estimation is widely used in practical engineering. However, the observation obtained by sensors may be corrupted by abnormal injected data, abnormal measurement noise, and random observation loss. Modeling uncertainty may lead to unknown process noise covariance matrices (PNCMs). The standard Cubature Kalman Filter (CKF) is poorly robust to abnormal observation and model uncertainty. Other advanced methods do not simultaneously consider that PNCM is unknown and observations contain abnormal injected data, abnormal measurement noise, and observation loss. Therefore, this paper presents an improved robust CKF using the variational Bayesian (VB) method. Especially, this paper models the observation model as a mixture of two Gaussian sub-models. One Gaussian distribution model with unknown mean and precision is used to model observation to improve the robustness for abnormal injected data, and another Gaussian distribution with variance that can be adaptively adjusted is used to model observation when measurement noise may be abnormal. In addition, the maximum likelihood estimation method is used to determine whether the observation is missing. The observation loss will be supplemented, and the introduced errors will be compensated by adjusting the parameters of the observation model. The VB method is used to estimate states and unknown parameters in real-time. Finally, simulation and indoor target-tracking experiments show that our method performs better than other methods in accuracy.
Li et al. (Wed,) studied this question.