Abstract Higher order ionospheric effects are increasingly relevant as precision requirements on GPS data and products increase. The refractive index of the ionosphere is affected by its electron content and the magnetic field of the Earth, so the carrier phase of the GPS L1 and L2 signals is advanced and the modulated code delayed. Due to system design the polarisation is unaffected. Most of the effect is removed by expanding the refractive index as a series and eliminating the first term with a linear combination of the two signals. However, the higher order terms remain. Furthermore, transiting gradients in refractive index at a non-perpendicular angle causes signal bending. In addition to the initial geometric bending term, another term allows for the difference that the curvature makes in electron content along each signal. Varying approximations have been made for practical implementation, mainly to avoid the need for a vertical profile of electron density. The magnetic field may be modelled as a tilted co-centric dipole, or using more realistic models such as the International Geomagnetic Reference Field. The largest effect is from the second term in the expansion of the refractive index. Up to several cm on L2, it particularly affects z-translation, and satellite orbits and clocks in a global network of GPS stations. The third term is at the level of the errors in modelling the second order term, while the bending terms appear to be absorbed by tropospheric parameters. Modelling improvements are possible, and three frequency transmissions will allow new possibilities.