Discrete-time linear skew-Gaussian system and its recursive fixed-dimensional exact density filtering

This paper deals with modeling and exact density filtering, in a finite fixed dimension, of a discrete-time linear system with skew-Gaussian (SG) distributions. More general than a linear Gaussian system, a linear SG system is presented, where the initial state, process noise, and measurement noise are mutually independent SGs. We first investigate the SG distribution and propose an SG process. Then, we develop a linear state-space model of the SG process, which subsumes the linear Gaussian system model in an analogous form. With additional parameters beyond the linear Gaussian case, it can model some practical problems involving certain asymmetry (skewness). Finally, for the linear SG system, we derive a finite fixed-dimensional exact filter, which is similar to the Kalman filter (KF) in structure and computation. The proposed recursive filter obtains the evolving posterior distribution exactly and includes the KF as a special case. As an illustration, our proposed skew-Gaussian filter is demonstrated via a simulation study.