The switching linear dynamical system (SLDS) is a popular model in time-series analysis. However, the complexity of inferring the state of the latent variables scales exponentially with the length of the time-series, resulting in many approximation strategies in the literature. We focus on the recently devised expectation correction (EC) approximation which can be considered a form of Gaussian sum smoother. The algorithm has excellent numerical performance compared to a wide range of competing techniques, exploiting more fully the available information than, for example, generalised pseudo Bayes. We show that EC can be seen as an extension to the SLDS of the Rauch, Tung, Striebel inference algorithm for the linear dynamical system. This yields a simpler derivation of the EC algorithm and facilitates comparison with existing, similar approaches.