On the ensemble Rauch‐Tung‐Striebel smoother and its equivalence to the ensemble Kalman smoother

The Rauch–Tung–Striebel (RTS) smoother is a linear‐Gaussian smoothing algorithm that is popular in the engineering community. This note is a study of its ensemble formulation (EnRTS). An on‐line expression is derived and discussed. In particular, it is used to show that the EnRTS is equivalent to the ensemble Kalman smoother (EnKS), even in the nonlinear, non‐Gaussian case. The theory is revisited under practical considerations and equability is illustrated by numerical experiments, even though equivalence is broken by inflation and localisation.