Mode-matching universal Kalman filter based on closed skew-normal distribution

The universal Kalman filters based on deterministic sampling, including the unscented Kalman filter (UKF), the cubature Kalman filter (CKF), etc., are widely used for nonlinear state estimation but assumes a Gaussian state distribution, which limits the filtering accuracy since the true distribution is typically non-Gaussian, while they may still be applicable in cases where the Gaussian assumption is not strictly met. Recent work, known as the MaxUKF, attempts to address this limitation by incorporating the mode of the probability density function. However, it approximates the true state distribution using a Gaussian mixture distribution where the number of Gaussian components increases exponentially with dimensionality, making it impractical for high-dimensional systems. In this paper, we introduce the Mode-Matching Universal Kalman Filter based on the Closed Skew-Normal distribution (MMUKF-CSN), which represents the state distribution using a closed skew-normal distribution matching the computed mode and first two moments. Compared with the MaxUKF (referred to as the MMUKF-GM in this paper), the advantage of the MMUKF-CSN is that it only uses one CSN distribution for arbitrarily high-dimensional cases, offering higher computational efficiency. Simulation results demonstrate that the MMUKF-CSN achieves higher filtering accuracy than the conventional UKF and requires less computation time than the MMUKF-GM in high-dimensional settings.