Unscented Kalman Filter Under Information Theoretic Criteria

The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, which utilizes a derivative-free higher-order approximation of a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman-filter-type estimator leads to the well-known unscented Kalman filter (UKF). In general, the UKF works well in Gaussian noises, and its performance may, however, deteriorate severely when the noises are non-Gaussian, especially when the system is disturbed by noises of heavy-tailed distribution. To improve the robustness of the UKF against heavy-tailed noises, two UKF-type filters based on the maximum correntropy criterion (MCC) are presented in this chapter, namely the maximum correntropy unscented filter (MCUF) and maximum correntropy unscented Kalman filter (MCUKF). Except for MCUK and MCUKF, the unscented Kalman filter with generalized correntropy loss (GCL-UKF) is also developed, which can achieve even better performance. In addition, since the minimum error entropy (MEE) exhibits good robustness with respect to more complicated noises such as those of multimodal distributions, a unscented Kalman-type filter based on the MEE criterion, termed MEE-UKF, is also derived and discussed. In this chapter, the detailed derivation about these methods is presented.