GPS differential code biases considering the second-order ionospheric term

Differential code biases (DCBs) of the global positioning system (GPS) are generally estimated together with total electron content (TEC) along the signal transmission path through the ionosphere. However, better accuracy can be obtained theoretically by also considering the second-order ionospheric term, which is related to the magnetic field of the earth and TEC along the signal path. Using data from the international GNSS service tracking network stations, we built a regional TEC model by considering the second-order ionospheric term and estimated the DCBs of both GPS satellites and receivers. The geomagnetic field was calculated by IGRF-12 model. The results show that the second-order ionospheric term causes a 10(-3) ns level effect to the estimated DCBs of GPS satellites and receivers and a 10(-2) TECU (TEC unit) level change of modeled TEC. As higher accuracy is achieved, more input data such as magnetic field data of the earth are also needed. When the second-order ionospheric term is considered, the processing gets more complicated and needs more time. However, the effect of the second-order ionospheric term on DCB estimate also shows an obvious diurnal variation and showing the same monotonicity over time as local VTEC.