A worldwide network of receivers tracking the transmissions of Global Positioning System (GPS) satellites represents a new source of ionospheric data that is globally distributed and continuously available. We describe a technique for retrieving the global distribution of vertical total electron content (TEC) from GPS-based measurements. The approach is based on interpolating TEC within triangular tiles that tessellate the ionosphere modeled as a thin spherical shell. The high spatial resolution of pixel-based methods, where widely separated regions can be retrieved independently of each other, is combined with the efficient retrieval of gradients characteristic of polynomial fitting. TEC predictions from climatological models are incorporated as simulated data to bridge significant gaps between measurements. Time sequences of global TEC maps are formed by incrementally updating the most recent retrieval with the newest data as it becomes available. This Kalman filtering approach smooths the maps in time, and provides time-resolved covariance information, useful for mapping the formal error of each global TEC retrieval. Preliminary comparisons with independent vertical TEC data, available from the TOPEX dual-frequency altimeter, suggest that the maps can accurately reproduce spatial and temporal ionospheric variations over latitudes ranging from equatorial to about ±65°.