Optimal and suboptimal white noise smoothers for nonlinear stochastic systems

A new approach of smoothing the white noise for nonlinear stochastic system was proposed. Through presenting the Gaussian approximation about the white noise posterior smoothing probability density function, an optimal and unifying white noise smoothing framework was firstly derived on the basis of the existing state smoother. The proposed framework was only formal in the sense that it rarely could be directly used in practice since the model nonlinearity resulted in the intractability and infeasibility of analytically computing the smoothing gain. For this reason, a suboptimal and practical white noise smoother, which is called the unscented white noise smoother (UWNS), was further developed by applying unscented transformation to numerically approximate the smoothing gain. Simulation results show the superior performance of the proposed UWNS approach as compared to the existing extended white noise smoother (EWNS) based on the first-order linearization.