Assessment of second-order ionosphere error in GPS range observables using Arecibo incoherent scatter radar measurements

The second-order ionosphere error in GPS range measurements is determined by the electron densities and the geomagnetic field projection onto the GPS signal propagation direction along the GPS signal propagation path. It can be a delay or an advancement error. This paper presents the second-order error analysis based on an extensive collection of electron density profiles measured by the Arecibo incoherent scatter radar and geomagnetic field vectors generated using the International Geomagnetic Reference Field model. The results indicate that the 56-500 km altitude range contributes a maximum of -1.1 cm for GPS L1 signals arriving from the zenith at Arecibo. For signals coming from the north and south at 10 degree elevation angles, the maximum errors are 0.9 cm and -3.4 cm, respectively. The maximum of the mean values of the second-order error computed using the entire data set are -0.55 cm, 0.48 cm, and -1.74 cm for a signal arriving from the zenith, from the north at 10 degrees elevation, and from the south at 10 degrees elevation, respectively. The paper also discusses the diurnal patterns and geomagnetic activity dependency of the second-order error. Finally, the International Reference Ionosphere model is used to obtain an upper bound estimation of error contributions from the 500-2000 km altitude range.