A nonlinear filter based on GSK for relative navigation using relative orbital elements

Due to the sensitivity of the relative orbital elements model to the measurement noise, the non-stationary heavy-tailed noise(NSHT) induced by the time-varying environment during the relative navigation usually leads to filter divergence. To address this problem, a new nonlinear filter based on Gaussian-Student's-Multivariate K(GSK) mixture distribution is proposed in this paper. A Dirichlet stochastic mixture vector fusing Gaussian, Student's t, and Multivariate K distributions is introduced, thus proposing a GSK mixture distribution modeling measurement likelihood; then the Kullback-Leibler Divergence (KLD) of the true posteriori probability density function(PDF) and the approximate posteriori PDF are minimized by a variational Bayesian(VB) technique to solve for the state and parameter approximate a posteriori estimations, and finally a new nonlinear filter based on the GSK mixture distribution is derived for angles-only relative navigation in time-varying environments. Simulation outcomes indicate that the filter can realize state estimation in non-stationary states effectively with 45.16% higher estimation accuracy than the existing advanced filters.