Nonlinear State Estimation Using Skew-Symmetric Representation of Distributions

Knowledge about higher moments, such as skewness and kurtosis, of the state of a stochastic system has potential benefits for state estimation. In order to model more complex nonlinear problems involving higher moments, a skew-symmetric representation of distributions is employed in this work. Based on a first-order skew-Gaussian representation, a novel method for nonlinear point estimation is developed. The proposed skew-Gaussian (SG) filter is more general than traditional Gaussian filters and LMMSE-based nonlinear filters, which propagate only the first two moments. Numerical results illustrate that our SG filter can outperform conventional nonlinear filtering methods.