The GPS Toolkit
Explosive is perhaps the best term to describe the growth of the Global Positioning System (GPS) market in recent years. Contributing factors are numerous, and perhaps the most dramatic are economic: access to GPS is absolutely free and the cost of hardware continues to plummet. As a result, the GPS user can choose from a variety of devices that provide a position estimate. GPS has long been used, however, to explore topics beyond positioning; space weather, precise timing and continental drift are but three examples.
In order to use GPS for advanced topics or simply for improved positioning, the raw observations collected by the GPS receiver must be processed. In the past, the nuts and bolts of such processing have been left up to proprietary software. Now, a project called the GPS Toolkit, or GPSTk, is available under the LGPL to the Open Source and research communities. GPSTk is the by-product of GPS research conducted at the Applied Research Laboratories of the University of Texas at Austin (ARL:UT) since before the first satellite launched in 1978. It is the combined effort of many software engineers and scientists. Recently, the research staff at ARL:UT has decided to open source much of their basic GPS processing software as the GPSTk.
The Global Positioning System actually is a US government satellite navigation system that provides a civilian signal. As of this writing, the signal is broadcast simultaneously by a constellation of 29 satellites, each with a 12-hour orbit. From any given position on the Earth, 8–12 satellites usually are visible at a time.
Each satellite broadcasts spread spectrum signals at 1,575.42 and 1,227.6MHz, also known as L1 and L2, respectively. Currently, the civil signal is broadcast only on L1. The signal contains two components, a time code and a navigation message. By differencing the received time code with an internal time code, the receiver can determine the distance, or range, that the signal has traveled. This range observation is offset by errors in the (imperfect) receiver clock; therefore, it is called a pseudorange. The navigation message contains the satellite ephemeris, which is a numerical model of the satellite's orbit.
GPS receivers record, besides the pseudorange, a measurement called the carrier phase, or phase. The phase also is a range observation like the pseudorange is, except it has an unknown constant added to it, the phase ambiguity. It also is much smoother, having about 100 times less measurement noise than the pseudorange, which makes it useful for precise positioning. Because of the way it is measured, the phase is subject to random, sudden jumps. These discrete changes always come in multiples of the wavelength of the GPS signal and are called cycle slips.
The standard solution for the user location requires a pseudorange measurement and an ephemeris for each satellite in view. At least four measurements are required, as there are four unknowns: three coordinates of position plus the receiver clock offset. The basic algorithm for the solution is described in the official GPS Interface Control Document, ICD-GPS-200. The position solution is corrupted due to two sources of error, errors in the observations and errors in the ephemeris.
The GPS signal travels through every layer of the Earth's atmosphere. Each layer affects the signal differently. The ionosphere, which is the high-altitude, electrically charged part of the atmosphere, introduces a delay, and therefore a range error, into the signal. The delay is frequency-dependent, so it can be computed directly if you have data on both the GPS frequencies. There also is a delay due to the troposphere, the lower part of the atmosphere. This delay also can be modeled and removed. Many other errors are associated with the GPS signal. Multipath reflections and relativistic effects are two examples.
More precise applications reduce the effect of error sources by a technique referred to as differential GPS (DGPS). By differencing measurements simultaneously collected by the user and a nearby reference receiver, the errors common to both receivers (most of them) are removed. The result of DGPS positioning is a position relative to the reference receiver; adding the reference position to the DGPS solution results in the absolute user position.
The alternative to DGPS is to model and remove errors explicitly. Creating new and robust models of phenomena that affect the GPS signal is an area of active research at ARL:UT and other laboratories. The positioning algorithm can be used to explore such models. Essentially, the basic approach is to turn the positioning algorithm inside out to look at the corrections themselves. For example, observations from a network of receivers can create a global map or model of the ionosphere.