When the codes no longer in line

The measurements based on the GPS signal are affected by errors from various sources, which can be classified according to whether they are linked to satellites, receivers or the propagation of the signal in the Earth's atmosphere. It was this last source of error that the two researchers decided to examine.

The GPS signals can be described as messages transported by electromagnetic waves, like radio waves. In a vacuum, a radio signal travels at the speed of light (300,000 km/s). This is not the case in the Earth’s atmosphere which disrupts the propagation of the signal. The latter is affected by atmospheric refraction on two levels: in the troposphere (tropospheric refraction) and in the ionosphere (ionospheric refraction) (Fig 2). In other words, explains Gilles Wautelet, “the wave that carries the signal travels the distance between the satellite and the station on the Earth’s surface. By crossing the Earth’s atmosphere, the speed of the wave is slightly less or slightly more than the speed of light (1). All in all, the delay (or advance) suffered by the GPS signal is in the order of several tens of nanoseconds, which, translated into units of length, is equal to several metres”. This delay or advance actually depends on the type of message (code or phase) and the atmospheric layer crossed (troposphere or ionosphere). Hence, the tropospheric refraction results in a delay, both in the codes and the phases, that is relatively small and stable: 2.4 metres. On the other hand, the ionospheric refraction has the contrary effect on the codes and phases. The codes are slowed down and the phases speeded up. As for the extent of the delay, this is conveyed by a far more variable an error in distance: between 1 and 50 metres. This ionospheric variability is the main source of error in GPS accuracy.

One of the ways of overcoming these errors is modelling. “While tropospheric models allows us to overcome a great deal of the tropospheric refraction, the ionospheric models are far more difficult to implement and only represent part of the actual situation”, says Gilles Wautelet.  According to René Warnant, “the study of these irregularities in the ionosphere is absolutely vital because they are at the origin of major errors in the measurements of positions made using GPS”.

The ionosphere: a battleground between waves and electrons

To understand how a GPS signal might interact with the ionosphere, we must remember that the composition of the latter results from two complex processes. First of all, there is an ionisation process which is initiated by radiation from space, mainly the sun’s ultraviolet rays and x-rays. The photons (luminous particles) in these rays contain enough energy to strip the electrons (negative charge) from the neutral atoms and atmospheric gases. Some free electrons are then captured by positive ions according to a second process known as recombination. The result is a continuous competition between the ionisation and recombination processes, thus determining the overall electronic density of the ionosphere. The concentration of electrons can therefore vary at any time and depends on two main factors: on the one hand, the density of neutral atoms and molecules (the recombination process is less pronounced at high altitudes because there is very little pressure there) and, on the other hand, the amount of sunlight received from space. While the pressure gradient (which is governed by a physical law dependent on altitude) remains stable and regular, this is far from the case for sunlight. Indeed, daytime (day/night) and seasonal (summer/winter) variations as well as solar activity (solar eruptions, 11-year cycles, etc.) will considerably modify the concentration of electrons, and consequently the propagation of the electromagnetic waves, including the GPS signals.

(1) Remember that in a given environment, a particle or a signal can travel faster than light in this environment. Therefore, it isn’t a question of exceeding the speed of light in a vacuum!