The ionosphere is the uppermost layer of the Earth’s atmosphere between the heights of 50 km to 1000 km above the Earth’s surface. The density of free electrons and ions is high enough to influence the propagation of satellite signals. GPS ranging can vary from a few metres to more than twenty metres within a day, depending on the user’s location and time plus variations in the ionosphere, but can reach over 150 m under extreme solar activities at midday and near the horizon (Wells et al., 1999). The ionospheric effect refracts the pseudorange and carrier-phase differently (Hofmann-Wellenhof et al., 2001; Leick, 2004), but given that the ionosphere is a dispersive medium it is possible to use an ionosphere-free pseudorange and carrier-phase combination to eliminate common ionospheric biases.

The ionospheric delay is greater at the L2 carrier frequency than that of the L1 carrier frequency. Up to 99.9% of the ionospheric delay can be eliminated through linear combination of GPS observables on L1 and L2 frequencies (Hofmann-Wellenhof et al., 2001; Collins, 2008). Though Elsobeiey et al. (2009) showed that neglecting the second-order ionospheric delay introduces an error in the order of 2 cm.

When measurements from both L1 and L2 frequencies are available, the following ionosphere-free linear combination can be formed for the pseudorange and carrier-phase in units of distance:

$$P_{IF}=\frac{f_1^2 P_1-f_2^2 P_2}{ f_1^2-f_2^2 } \tag{1}$$

$$L_{IF}=\frac{f_1^2 L_1 λ_1-f_2^2 L_2 λ_2}{f_1^2-f_2^2} \tag{2}$$

where \({f_1} = \)= 1575.42 MHz and \({f_2} = \) = 1227.60 MHz are the frequencies of the L1 and L2 signals, respectively, and \({\lambda _1}\) = 19.0 cm and \({\lambda _2}\) = 24.4 cm are the wavelengths of the L1 and L2 signals, respectively. A negative side effect of the iono-free combination is that the measurement noise is approximately tripled versus the noise on L1 or L2 (Leandro, 2009)

References

Collins P (2008) "Isolating and Estimating Undifferenced GPS Integer Ambiguities." Proc. ION NTM, pp. 720-732.

Elsobeiey M, and El-Rabbany A (2009) "Rigorous Modelling of GPS Residual Errors for Precise Point Positioning." Proceedings of the 2010 Canadian Geomatics Conference, Calgary, pp. 80-194.

Hofmann-Wellenhof B, Lichtenegger H, and Collins J (2001) GPS Theory and Practice, 5th edn. New York: Springer-Verlag Wien, 389 p.

Leandro, RF (2009) "Precise Point Positioning with GPS: A New Approach for Positioning, Atmospheric Studies, and Signal Analysis." Ph. D. dissertation,University of New Brunswick (Canada), 458 p.

Leick A (2004) GPS Satellite Surveying, 3rd edn. Wiley, 464 p.

Wells DE, Beck N, Delikaraoglou D, Kleusberg A, Krakiwsky E, Lachapelle G, Langley R, Nakiboglu M, Schwarz K, and Tranquilla J (1999) Guide to GPS Positioning, Department of Geodesy and Geomatics Engineering,Lecture Note No. 58, University of New Brunswick, NB, Canada, 601 p.

The ionospheric delay is greater at the L2 carrier frequency than that of the L1 carrier frequency. Up to 99.9% of the ionospheric delay can be eliminated through linear combination of GPS observables on L1 and L2 frequencies (Hofmann-Wellenhof et al., 2001; Collins, 2008). Though Elsobeiey et al. (2009) showed that neglecting the second-order ionospheric delay introduces an error in the order of 2 cm.

When measurements from both L1 and L2 frequencies are available, the following ionosphere-free linear combination can be formed for the pseudorange and carrier-phase in units of distance:

$$P_{IF}=\frac{f_1^2 P_1-f_2^2 P_2}{ f_1^2-f_2^2 } \tag{1}$$

$$L_{IF}=\frac{f_1^2 L_1 λ_1-f_2^2 L_2 λ_2}{f_1^2-f_2^2} \tag{2}$$

where \({f_1} = \)= 1575.42 MHz and \({f_2} = \) = 1227.60 MHz are the frequencies of the L1 and L2 signals, respectively, and \({\lambda _1}\) = 19.0 cm and \({\lambda _2}\) = 24.4 cm are the wavelengths of the L1 and L2 signals, respectively. A negative side effect of the iono-free combination is that the measurement noise is approximately tripled versus the noise on L1 or L2 (Leandro, 2009)

References

Collins P (2008) "Isolating and Estimating Undifferenced GPS Integer Ambiguities." Proc. ION NTM, pp. 720-732.

Elsobeiey M, and El-Rabbany A (2009) "Rigorous Modelling of GPS Residual Errors for Precise Point Positioning." Proceedings of the 2010 Canadian Geomatics Conference, Calgary, pp. 80-194.

Hofmann-Wellenhof B, Lichtenegger H, and Collins J (2001) GPS Theory and Practice, 5th edn. New York: Springer-Verlag Wien, 389 p.

Leandro, RF (2009) "Precise Point Positioning with GPS: A New Approach for Positioning, Atmospheric Studies, and Signal Analysis." Ph. D. dissertation,University of New Brunswick (Canada), 458 p.

Leick A (2004) GPS Satellite Surveying, 3rd edn. Wiley, 464 p.

Wells DE, Beck N, Delikaraoglou D, Kleusberg A, Krakiwsky E, Lachapelle G, Langley R, Nakiboglu M, Schwarz K, and Tranquilla J (1999) Guide to GPS Positioning, Department of Geodesy and Geomatics Engineering,Lecture Note No. 58, University of New Brunswick, NB, Canada, 601 p.