Kalman filter variants in the closed skew normal setting

The filtering problem, or dynamic data assimilation problem, is studied for linear and nonlinear systems with continuous state space and over discrete time steps. The paper presents filtering approaches based on the conjugate closed skew normal probability density. This distribution allows additional flexibility over the usual Gaussian approximations. With linear dynamic systems, the filtering distribution can now be computed in analytical form. With nonlinear dynamic systems, an ensemble-based version is proposed, fitting a closed skew normal distributions at each updating step. Numerical examples discuss various special cases of the methods.