A Covariance Adaptive Student's t-Based Kalman Filter

The Kalman filter (KF) employs the covariance matrices of process and measurement noise to dynamically align predicted and measurement data, enhancing adaptability. Due to the fact that the KF's performance will degrade when facing non-Gaussian noise. The Student's t-based KF (TKF) has emerged as a robust algorithm to address the limitation. The TKF leverages the covariance matrix of noise sequences, encompassing some amount of impulsive signals, which enables the TKF to mitigate the impact of impulsive noise. However, the reliance on the same covariance matrix also constrains the TKF's performance when dealing with non-impulsive noise. To address this problem, we used the Gaussian mixture model (GMM) to construct an adaptive measurement covariance matrix as a way to adaptively balance the predicted and measurement data.