Properties and Future of the Skew Kalman Filters

The Kalman filter (KF) and its variants are powerful numerical tools for estimating the unmeasured states of dynamical systems. However, traditional KFs assume Gaussian noise in measurements and processes, which may not always hold in practice. This paper reviews recent developments in non-Gaussian Kalman filters with non-zero skewness, which have received relatively little attention despite their potential benefits. This paper mainly focuses on skew Kalman filters (SKF), which replace the Gaussian assumption with the closed skew normal (CSN) distribution. This allows SKF to capture outliers in dynamical systems, resulting in improved performance and flexibility. Although there is limited literature on skew Kalman filters, tiiis study provides an overview of their potential and motivation for use in a wide range of scientific applications.