Kalman filtering provides an elegant framework for assimilating observational data into time-dependent theoretical models. This paper explores the application of this approach to specify and forecast the radiation belt particle distribution. The Kalman filter is first outlined in a general form. A data assimilation algorithm is then derived for a simple radiation belt forecast model driven by radial diffusion. The model assimilates particle flux measurements from spacecraft in the equatorial plane, using an external magnetic field model to calculate adiabatic invariants and phase space density. The algorithm is tested in a series of virtual experiments, with data from an idealized magnetic storm simulation. Compared to assimilation by direct insertion of data, the Kalman filter more accurately reconstructs the global particle distribution from sparse observational data. We examine the response of the filter to errors in the observations, magnetic field model, and forecast model and discuss the application of this approach to more realistic models and data sets.