I am currently undergoing a research on assessment of Seismo-electromagnetic induced perturbation in the threshold condition of the ionosphere using DEMETER Data. The estimation of TEC, Kp and Ap will help in the work.
The delay experienced by the GPS signals is directly proportional to the TEC. Moreover, this delay is dispersive, i.e. frequency dependent. So, the range measured using a signal of frequency f is Rm = Rg + 40.3 TEC/f^2. where Rm and Rg are the measured and geometric ranges respectively. Now, if you have two simultaneous measurements from the same GPs satellite using two frequencies, say f1 and f2, and difference them, the diiferential range becomes dR = 40.3 TEC [ (1/f1^2) - (1/f2^2)]. As you know dR from measurements and f1 and f2 are your known frequencies, TEC can be easily determined. Hope this helps. For, further clarification you may refer to my book: Understanding Satellite Navigation at