Kalman filter variants in the closed skew normal setting

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