An important and well established area of quantum optics is the theory of Markovian stochastic Schrödinger equations (or by another name quantum trajectory theory). Recently stochastic Schrödinger equations have been developed for non-Markovian systems. In this paper we extend the current known stochastic Schrödinger equations for non-Markovian systems to include the position unravelling. We also discuss and illustrate that this stochastic Schrödinger equation can have an interpretation under both the orthodox and the de Broglie–Bohm hidden variable interpretation of quantum mechanics. We conclude that only the de Broglie–Bohm hidden variable theory provides a continuous-in-time interpretation of the non-Markovian stochastic Schrödinger equation.