Additional Topics in Kalman Filtering Under Information Theoretic Criteria

Besides the previously mentioned Kalman filters, some other Kalman type filters are derived based on information-theoretic criteria for specific cases. For example, to address the problem of state estimation under equality constraints, the maximum correntropy Kalman filter with state constraints (MCKF-SC) was developed, which combines the MCC and constrained estimation methodology. In addition, two novel nonlinear filters, the correntropy-based first-order divided difference (CDD1) filter and the correntropy-based second-order divided difference (CDD2) filter, are derived to solve the problem of numerical instability due to the propagation of a non-positive definite covariance matrix. When the parameters of system model are unknown a priori or varying with time, the dual Kalman filtering under minimum error entropy with fiducial points (MEEF-DEKF) provides an effective tool in estimating the model parameters and the hidden states under non-Gaussian noises. For nonlinear time-series prediction, the kernel Kalman filtering based on conditional embedding operator and maximum correntropy criterion (KKF-CEO-MCC) was also derived, which shows significant performance improvements over traditional filters in noisy nonlinear time-series prediction. In this chapter, the detailed derivation about these methods is presented.