Kalman Filtering With Delayed Measurements in Non-Gaussian Environments

Traditionally, Kalman filter (KF) is designed with the assumptions of non-delayed measurements and additive white Gaussian noises. However, practical problems often fail to satisfy these assumptions and the conventional Kalman filter suffers from poor estimation accuracy. This paper proposes a modified Kalman filter to address both the problems of delayed measurements and non-Gaussian noises. The proposed filter is updated using correntropy maximization criterion, which is suitable for non-Gaussian noise environments. It falls short of a closed-form solution due to analytically complex equations that appear during the filtering. We use fixed-point iterative method to find an approximate solution. The delayed measurement problem is addressed by implementing a likelihood-based approach to identify the delay. Based on the identified delay information, the measurement is used to update the desired state in the subsequent past instant. To perform real-time filtering, the estimated state is further updated up to the current time instant using the process dynamics. The performance analysis validates the improved accuracy of the proposed method compared to the ordinary Kalman filter and its existing extensions.