2 The GPS data

Each of the GPS satellites transmits on two L-band carrier frequencies, L1 at 1575.42 MHz and L2 at 1227.60 MHz. A third carrier, L3 at 1381.05 MHz, is not intended for GPS users. All of these carriers are phase locked to harmonics of a fundamental, 5.115 MHz, oscillator. By measurement of the time delay between the modulation on the L1 and L2 carriers, the ionospheric-induced delay and hence an absolute measure of the total electron content (TEC) along the line-of-sight to each visible satellite, i.e. the slant-TEC, can be determined through the simple relation

$${\rm TEC}_{\rm TU} = 0.75 \Delta T{\nu_1^2\nu_2^2\over\Delta\nu(\nu_1+\nu_2)}$$ (1)

where the frequencies are in GHz, the time difference $\Delta T$ is in nsec, and the units of the TEC are in $\rm {TU}$s, defined as $1 {\rm TU} =1.0~10^{16}~{\rm electrons/cm^2}$. With the GPS frequencies given above, the relation becomes simply ${\rm TEC_{TU}} = 2.853 \Delta T$. This measure of the total electron content is referred to as "tau-TEC''.

The relative phases of the carriers can also be measured to obtain a much more accurate determination of the TEC (the so-called phase-TEC) via the relation

$${\rm TEC}_{\rm TU} = 0.12 {\nu_1\nu_2\over\Delta\nu}\Delta\phi,$$ (2)

where the units of TEC and frequency are the same as in Eq. (1), and the phase difference is in radians. For the L1 and L2 carriers, we find TEC $_{\rm TU} = 0.67\Delta\phi$. Unfortunately, these data are subject to full-cycle ambiguities between the two carriers. The phase-TEC provides an excellent determination of the TEC variations with time and satellite position, but only the tau-TEC provides absolute values of the TEC.

Typically, our receivers would obtain data from six to nine satellites at any time, but some of these satellites were at such low elevations that their data were of little use for the correction of high elevation radio source observations. Therefore, useful data were normally obtained in about four to seven directions. Because the satellites are typically a radian or more from the astronomical source of interest, it is necessary to model the ionosphere using the GPS data and to then employ this model to estimate the TEC in the direction of the source.