Data Assimilation (DA) has enabled huge improvements in the skill of terrestrial operational weather forecasting. In this study, we use a variational DA scheme with a computationally efficient solar wind model and in situ observations from STEREO-A, STEREO-B and ACE. This scheme enables solar-wind observations far from the Sun, such as at 1 AU, to update and improve the inner boundary conditions of the solar wind model (at 30 solar radii). In this way, observational information can be used to improve estimates of the near-Earth solar wind, even when the observations are not directly downstream of the Earth. This allows improved initial conditions of the solar wind to be passed into forecasting models. To this effect, we employ the HUXt solar wind model to produce 27-day forecasts of the solar wind during the operational lifetime of STEREO-B (01 November 2007 - 30 September 2014). In near-Earth space, we compare the accuracy of these DA forecasts with both non-DA forecasts and simple corotation of STEREO-B observations. We find that 27-day root mean-square error (RMSE) for STEREO-B corotation and DA forecasts are comparable and both are significantly lower than non-DA forecasts. However, the DA forecast is shown to improve solar wind forecasts when STEREO-B's latitude is offset from Earth, which is an issue for corotation forecasts. And the DA scheme enables the representation of the solar wind in the whole model domain between the Sun and the Earth to be improved, which will enable improved forecasting of CME arrival time and speed.