Kalman Filtering with Queued Measurements under Non-Gaussian Noisy Environment

The Kalman filter is a widely used computational tool for estimating unknown internal states of dynamical systems using noisy measurement data. In modern technologies, measurement data is often transmitted through communication channels and networks, which introduces various irregularities that can potentially harm the accuracy. This paper particularly focuses on the queuing delay irregularity (due to the data propagation). Additionally, sensor-generated measurement data inherently contain non-Gaussian noises, whereas the standard Kalman filters approximate them as Gaussian distributed, leading to further inaccuracies. This paper develops an advanced Kalman filtering method capable of addressing both queuing delays and non-Gaussian noise. To handle the queuing delays, the proposed method reformulates the traditional measurement model to account for the potential occurrence of this irregularity. Moreover, to address non-Gaussian measurement noises, the proposed method is designed under the maximum correntropy (MC) criterion, which is more robust to non-Gaussian noises than the traditionally used minimum mean square error (MMSE) criterion. The MC-based design is performed for the reformulated measurement model to ensure that the resulting filter effectively handles both challenges. The efficacy of the proposed method is validated through two simulation problems in MATLAB, comparing its performance with the traditional Kalman filter and the relevant extensions.