Complex-valued Kalman filters based on Gaussian entropy

The conventional complex Kalman filter is based on the well-known mean square error criterion, which is optimal under the circular Gaussian assumption. When a real-world complex signal is involved, the state noise and the observation noise often present non-circular properties to some degree, and thus the conventional complex Kalman filter does not perform well under these circumstances. We propose a new complex Kalman filter in which the Gaussian entropy is adopted as the optimality criterion in place of the mean square error. Performance analysis shows that the steady-state error of the new algorithm decreases with the increase of the degree of non-circularity. Simulations are used to demonstrate the effectiveness of the proposed algorithm.