A method is presented for the removal of ionospheric effects from single-frequency radio navigation data. It uses data from a separate single collocated dual-frequency Global Positioning System (GPS) receiver to estimate the states of a local ionospheric total electron content (TEC) model. These states can be used to estimate the TEC along lines of sight to other types of satellite-based radio navigation transmitters. Two local ionosphere models are considered. The first model is a modified version of the classical thin-shell model, where the altitude and altitude variations of the shell with respect to latitude and longitude are added as new estimable quantities. The second model is a new thick-shell model, where the thin shell has been expanded with a Chapman electron density profile. The states of the Chapman profile are allowed to vary with respect to latitude and longitude and must be estimated. States are estimated using a Kalman filter and GPS observables. Truth-model simulations are used to test the observability of the states in each of the local ionosphere models. The subset of observable local models are then tested using real GPS data. The TEC estimates produced by the local models are compared to the results produced by an existing multireceiver network and tomographic model. The local thin-shell model is shown to compare well to the tomographic model, and significant improvement is shown over the classical single-receiver fixed-altitude thin-shell model, but the thick-shell model is shown to be unobservable.