Using a four-dimensional stochastic model of ionosphere perturbations, simulations are made of a tomography system based on data from the Global Positioning System and a low Earth-orbiting satellite. The perturbations are departures from a simple time-independent reference state. The spatial structure is parameterized in terms of empirical orthogonal functions (EOFs) in the vertical and spherical harmonics in the horizontal. The horizontal covariance structure is specified by variance and correlation length scales as functions of latitude and longitude. Time dependence is modeled as a first-order Markov process with a 6-hour timescale and white-noise forcing. A Sun-fixed coordinate system is used so that ionospheric features are more nearly steady in time. A Kaiman filter is used to objectively assimilate the simulated data into the simple time-dependent model. In addition to solving for the three-dimensional electron density field at each time step, the procedure solves for instrumental biases. The simulations show that the fractions of resolved variance for vertical EOF modes 1, 2, and 3 are 0.99, 0.93, and 0.73, respectively. The resolution of the vertically integrated total electron content is 0.99.