Published on *GEOG 862: GPS and GNSS for Geospatial Professionals* (https://www.e-education.psu.edu/geog862)

This same 1 percent rule of thumb can illustrate the increased precision of the carrier phase observable over the pseudorange. First, the length of a single wavelength of each carrier is calculated using this formula

$$\lambda =\frac{{c}_{a}}{f}$$

where:

$\lambda $ = the length of each complete wavelength in meters;

${c}_{a}$ = the speed of light corrected for atmospheric effects;

$f$ = the frequency in hertz.

$\begin{array}{l}\lambda =\frac{{c}_{a}}{f}\\ \lambda =\frac{300x{10}^{6}mps}{1575.42x{10}^{6}Hz}\\ \lambda =19cm\end{array}$

L1 – 1575.42 MHz carrier transmitted by GPS satellites has a wavelength of approximately 19 cm

$\begin{array}{l}\lambda =\frac{{c}_{a}}{f}\\ \lambda =\frac{300x{10}^{6}mps}{1227.60x{10}^{6}Hz}\\ \lambda =24cm\end{array}$

L2 – 1227.60 MHz carrier transmitted by GPS satellites has a wavelength of approximately 24 cm

The resolution available from a signal is approximately 1% of its wavelength. 1% of these wavelengths is approximately 2mm.

A 3m ranging precision is not adequate for most land surveying applications, not to say all. But carrier phase observations are certainly the preferred method for the higher precision work most surveyors have come to expect from GPS.

That same 1% rule of thumb can illustrate how the carrier phase observable, that second observable, comes to our rescue, so to speak, with this little formula here: the length of a complete wavelength in meters is equal to the speed of light corrected for atmospheric effects divided by the frequency in Hertz. Remember that L1 is 1575.42 megahertz. So, here is a calculation. The length of a wavelength of the L1 carrier, speed of light on top here, divided by 1575.42 times 10 to the 6th power Hertz. That shows a wavelength in L1 is approximately 19 centimeters.

Here is the same calculation in L2. The speed of light divided by 1227.60 times 10 to the 6 power Hertz shows that the wavelength in L2 is approximately 24 centimeters. Therefore, the resolution available from the carrier wave observable at 1% of the wave length of the carrier is approximately 2 millimeters.