Gaussian smoothers for nonlinear systems with one-step randomly delayed measurements

This technical note is concerned with the nonlinear state smoothing problem in the case that the measurements are randomly delayed by one sampling time. Under Gaussian domain, two general Gaussian approximation (GA) and Gaussian mixture approximation (GMA) smoothers are proposed in minimum mean square error (MMSE) sense. The smoothing implementation is transformed into computing some special posterior covariances, which triggers the development of the new unscented Kalman smoother (UKS) by applying unscented transformation (UT). Simulation results demonstrate the superior performance of the proposed GA-UKS and GMA-UKS algorithms.