Global Positioning System (GPS) radio occultation signals received by a low Earth orbit (LEO) satellite provide information about the global distribution of electron density in the ionosphere. We examine two radio occultation inversion algorithms. The first algorithm utilizes the Abel integral transform, which assumes spherical symmetry of the electron density field. We test this algorithm with two approaches: through the computation of bending angles and through the computation of total electron content (TEC) assuming straight line propagation. We demonstrate that for GPS frequencies and for observations in LEO, the assumption of straight-line propagation (neglecting bending) introduces small errors when monitoring the F2 layer. The second algorithm, which also assumes straight-line propagation, is a three-dimensional (3-D) inversion constrained with the horizontal structure of a priori electron density fields. As a priori fields we use tomographic solutions and the parameterized real-time ionospheric specification model (PRISM) when adjusted with ionosonde data or ground-based GPS vertical TEC maps. For both algorithms we calibrate the occultation data by utilizing observations from the part of the LEO that is closer to the GPS satellite. For inversions we use dual-frequency observational data (the difference of L1 and L2 phase observables) which cancel orbit errors (without applying precise orbit determination) and clock errors (without requiring synchronous ground data) and thus may allow inversions to be computed close to real time in the future. The Abel and 3-D constrained algorithms are validated by statistically comparing 4 days of inversions with critical frequency (f0F2) data from a network of 45 ionosonde stations and with vertical TEC data from the global network of GPS ground receivers. Globally, the Abel inversion approach agrees with the f0F2 correlative data at the 13% rms level, with a negligible mean difference. All tested 3-D constrained inversion approaches possess a statistically significant mean difference when compared with the ionosonde data. The vertical TEC correlative comparisons for both the Abel and 3-D constrained inversions are significantly biased (~30%) by the electrons above the 735-km LEO altitude. ¿ 1999 American Geophysical Union