Cubature Kalman Filtering Under Information Theoretic Criteria

In unscented Kalman filter (UKF), the choice of scaling parameter in UKF is still a challenge in practice. To ease the burden on the selection of the scaling parameter, the cubature Kalman filter (CKF) has been introduced, which is based on the spherical–radial cubature rule for numerical integration. For a nonlinear system, the CKF can obtain good performance in Gaussian noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance, the CKF and its square-root version based on MCC are provided in this chapter. The two algorithms are named as the maximum correntropy cubature Kalman filter (MCCKF) and maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filters not only retain the advantages of CKF, but also exhibit robust performance against heavy-tailed non-Gaussian noises. However, when the dynamic system suffers from complex non-Gaussian disturbances, the estimates obtained by MCCKF may be obviously biased. To address this issue, the cubature Kalman filter under minimum error entropy with fiducial points (MEEF-CKF) is presented to improve the robustness against noises. The MEEF-CKF can achieve high estimation accuracy and strong robustness in the complex non-Gaussian noises especially in multimodal distribution noise. In this chapter, the detailed derivation about these methods is presented.