Taking a rough trip through the atmostphere
Up to now we've been treating the calculations that go into GPS very abstractly, as if the whole thing were happening in a vacuum. But in the real world there are lots of things that can happen to a GPS signal that will make its life less than mathematically perfect.
To get the most out of the system, a good GPS receiver needs to take a wide variety of possible errors into account. Here's what they've got to deal with.
First, one of the basic assumptions we've been using throughout this tutorial is not exactly true. We've been saying that you calculate distance to a satellite by multiplying a signal's travel time by the speed of light. But the speed of light is only constant in a vacuum.
As a GPS signal passes through the charged particles of the ionosphere and then through the water vapor in the troposphere it gets slowed down a bit, and this creates the same kind of error as bad clocks.
The ionosphere is the layer of the atmosphere ranging in altitude from 50 to 500 km.
It consists largely of ionized particles which can exert a perturbing effect on GPS signals.
While much of the error induced by the ionosphere can be removed through mathematical modeling, it is still one of the most significant error sources.
The troposphere is the lower part of the earth's atmosphere that encompasses our weather.
It's full of water vapor and varies in temperature and pressure.
But as messy as it is, it causes relatively little error.
There are a couple of ways to minimize this kind of error. For one thing we can predict what a typical delay might be on a typical day. This is called modeling and it helps but, of course, atmospheric conditions are rarely exactly typical.
Much of the delay caused by a signal's trip through our atmosphere can be predicted.
Mathematical models of the atmosphere take into account the charged particles in the ionosphere and the varying gaseous content of the troposphere.
On top of that, the satellites constantly transmit updates to the basic ionospheric model.
A GPS receiver must factor in the angle each signal is taking as it enters the atmosphere because that angle determines the length of the trip through the perturbing medium.
Another way to get a handle on these atmosphere-induced errors is to compare the relative speeds of two different signals. This "dual frequency" measurement is very sophisticated and is only possible with advanced receivers.
Dual Frequency Measurements
Physics says that as light moves through a given medium, low-frequency signals get "refracted" or slowed more than high-frequency signals.
By comparing the delays of the two different carrier frequencies of the GPS signal, L1 and L2, we can deduce what the medium (i.e. atmosphere) is, and we can correct for it.
Unfortunately this requires a very sophisticated receiver since only the military has access to the signals on the L2 carrier.
Civilian companies have worked around this problem with some tricky strategies.