Curious minds are the beacons of light that provide the ideas and inventions that enrich our lives and advance civilizations. One such idea was the satellite-based GPS system that has revolutionized navigation. The idea is not static, and the GPS system is continually evolving to provide more robust service and greater position accuracy. Unlike all my previous articles this one will not help you in the cockpit by pointing out features and techniques that enhance your expertise; this is for the curious mind and is intended to explain this amazingly complex system. What are its many and diverse features and how do they work? And what does the future hold?
The system in the United States was initially based on a set of 24 satellites in six orbital planes, with four satellites in each plane spread equally around the orbit. To ensure that there are at least 24 working satellites at one time, the system was expanded in 2011 to a 27-slot constellation that improves coverage around the world. Six satellites were repositioned, and three new ones added. Each orbit is about 20,000 km above the earth, or about four earth radii from the center of the earth. The satellites orbit twice during the 24-hour earth-orbit so it appears from earth they orbit once a day. Currently, there are 31 operational satellites.
The basic idea in using the system is that you determine your position from at least four satellites by triangulation. In 2D, you need to know your distance from three points to find your relative position, but in 3D you need four known positions to determine yours. Simple? Hardly!
First, how do you identify each satellite you’re receiving, where is it precisely, and what is your distance to each satellite? Each satellite sends a unique pseudo-random noise (PRN) code every millisecond, as depicted in Figure 1, on a predetermined (and very precise) schedule. Unique means that codes from the different satellites are all uncorrelated from each other. Copies of each code are stored in your receiver (each identified with a specific satellite) so you can find out which satellite you’re seeing by checking its correlation (cross-correlate) against all codes in your database. You also know precisely where it is by using almanac and ephemeris data for each satellite that you continuously receive.
Figure 1. Delay time between the received the satellite code and your code, which is then converted to distance, assuming the signal travels at the speed of light.
The tricky bit is the distance, which is determined from the delay time in receiving a particular code. From that time delay you assume the signal travels at the speed of light, which it does for most of the trip to your receiver. However, moisture in the atmosphere slows down the signal, as do electrons in the ionosphere. More on errors later.
To determine the delay time, your receiver clock and the satellite (atomic) clock must be kept perfectly in sync. You know when the message was sent (and from where) so the delay is determined from the time you receive it. But the tricky part is keeping your clock in sync with the highly accurate atomic clocks on the satellites.
Satellites also broadcast GPS time, sent to your receiver via the Navigation Message, a modulation of the carrier frequency sent at 50 bits per second in 30 second frames precisely on the minute and half minute. It takes 25 frames (12.5 min) to send the complete message, which also has the almanac and orbit (ephemeris) data. Ground stations (master control station at Falcon Air Force Base, Colorado, and stations at Cape Canaveral, Ascension Island, Diego Garcia, and Kwajalein) monitor the system and compose the Navigation message that includes data to keep your clock updated.
Now, the distance to the satellite is found, assuming the signal travels at the speed of light (300,000 kilometers per second). It takes the signal 2/30 seconds (about 67 ms) to reach your receiver, 20,000 km away. If you want to know your position with an accuracy of 3 m, that corresponds to a time accuracy of 10-8 seconds (10 ns, or nanoseconds), so the delay time needs to be determined with that accuracy. Fortunately, as stated, signal timing is done using a set of multiple atomic clocks on board each satellite, which have the requisite precision, and your receiver clock which receives updates to keep it in sync.
There are a few curious things to note about the system. First, general relativity states that space-time at each satellite is warped by the earth’s mass, but much less than at the surface of the earth. It means that clocks run slower in gravity than in space, and clocks at the surface of the earth run slower than those on the satellite (about 4 microseconds per day, 4000 ns per day) which are 4 earth radii away (less warping out there). This would make a huge timing error if not corrected, since we require 10 ns accuracy. Also, special relativity states that speeding clocks slow down, so with satellites travelling about 4 km/sec there is a time correction of 7 microseconds per day.
Finally, note that signal processing by your receiver is rather complex since the GPS signal is buried in noise. The signal level is -132 dbm (decibels below 1 milliwatt) which is about 100,000 times lower than the noise level. The satellite signal is only about 25 Watts. To extract this signal from the noise requires special techniques, as used for example in spread spectrum communications.
System Error
Errors in position have multiple causes; slight inaccuracies in time keeping, orbit changes from varying gravitation forces and radiation pressure around the orbit, multipath routes to the receiver, atmospheric effects (delay through moisture), and ionospheric delay by the electrons there. Typical errors from the various sources are as follows: ionosphere ± 5 m, troposphere ± 0.5 m, orbit data ± 2.5 m, satellite clock ± 2 m, and multipath ±1 m. These are not additive, and the actual error probability is less than the total of 11 m.
The largest error here is from signals passing through the ionosphere, where solar radiation ionizes gas in the region from 100 – 1000 km above the earth. It turns out that each electron in the beam of the signal delays the signal, and the total delay is proportional to the total number of electrons the signal penetrates. That number depends on the path the signal takes through the ionosphere, since the minimum distance through the layer is directly above you and the maximum occurs for satellites close to the horizon that penetrate on a slant course.
It turns out that if you send signals at different frequencies (over the same path) from a satellite, the “extra delay time” over the normal speed-of-light delay (for the distance travelled through the ionosphere) is less for higher frequencies than for lower frequencies by the square of the frequency ratio. Further, measuring the total delay at both frequencies, and knowing the frequency dependence of the delay, you can eliminate the ionospheric error.
In the Legacy satellite system both L1 and L2 frequencies (1575.42 MHz and 1227.60 MHz respectively) were included in each satellite, but only the military was equipped with dual receivers to use both. This improved their accuracy by eliminating the ionospheric time delay (See my web article on GPS Position Error.) The so-called Course Acquisition signal, L1 C/A, is included in all updated satellite signals.
The WAAS system consists of ground stations spaced on average roughly 500 miles apart, and 3 geosynchronous satellites (east, central, west) that broadcast to pilots the information received from the ground stations. Each of those stations know precisely where they are, and they compare that position to the erroneous position the station determines from the array of GPS satellites. That vector error is transmitted to the WAAS satellites. Your receiver is given the errors from stations around you and at your position it extrapolates the error data to find the best error correction to apply to your 3D position. The use of a WAAS receiver will correct the total position error to the range of 1 m horizontal and 2 m vertical.
Evolving Satellite Systems
Since launching the initial Block IIA system of satellites, new ones have been developed and launched, including some with the L5 frequency of 1176.45 MHz. The L1, L2, L5 signals have bandwidths of about 1 percent of their frequency. As shown in Figure 2, from www.gps.gov, the Legacy Block IIA satellites are no longer in orbit. The figure shows the different blocks now in use, and features of each. The nomenclature is IIR (replacement), IIR-M (modernized), IIF (follow-on), GPS III and IIIF (follow-on). The table in Figure 2 lists features of each block.
Figure 2. Satellite Blocks in use, from https://www.gps.gov/systems/gps/space/
Note that in addition to the L1 C/A signal, three new signals are being added: L2C, L5, and L1C (C for civilian). When combined with the C/A code on L1 (Block IIR), L2C will determine the ionospheric delay in a civilian dual-receiver unit, giving civilian users capability the military has always had. The L2C signal has higher power than the L1 C/A signal, for better reception indoors and under trees. It is available but still pre-operational.
A second new signal is L5, designed to meet safety-of-life transportation and other high-performance applications. It is broadcast in a band reserved for aviation safety services, and has higher power, greater bandwidth, and advanced signal design. A three-frequency combo of L1 C/A, L2C, and L5 may enable sub-meter position accuracy without WAAS augmentation.
Finally, a third new signal is the L1C signal, designed to enable interoperability with international GPS systems. It features so-called Multiplexed Binary Offset Carrier modulation that allows international cooperation while protecting United States security interests. It will also improve reception in cities and other challenging environments.
Clearly, to take advantage of these three new systems your GPS must have receivers for the new signals. So far, to my knowledge, the aviation GPS manufacturers are not planning to offer them soon. However, other commercial uses like surveying are already available. Also, the Apple Watch Ultra and iPhone 14 Pro/Pro Max use frequencies L1 and L5 for “precision dual-frequency GPS.” Given the capabilities and features of these new Blocks, they are a roadmap to future applications in various areas such as transportation, surveying, and many others. Hopefully these capabilities will come to general aviation in the future.
Dr. Thomassen has a PhD from Stanford and had a career in teaching (MIT, Stanford, UC Berkeley) and research in fusion energy (National Labs at Los Alamos and Livermore). He has been flying for 65 years, has the Wright Brothers Master Pilot Award, and is a current CFII. See his website (www.avionicswest.com) on all his manuals plus numerous articles on GPS and other aviation topics.
