GPS: Position and Time
The US Global Positioning System (GPS) provides position, navigation, and timing (PNT) signals that broadcast 3D positions (longitude, latitude, altitude) and time for each satellite. GPS receivers with specialized software and mapping applications determine distances used to triangulate the receiver location. The GPS receiver finds a signal, syncs to it, and then uses its own oscillator to determine the delay in reception. That delay becomes the travel time from the satellite. Multiplied by the speed of light, c, the distance from the receiver to the satellite is determined.
In addition to positioning data, GPS atomic clocks are so precise that GPS has become the time standard for many applications. GPS time is used to synchronize wireless communications and timestamp financial transactions; it's used by digital broadcasters, Doppler radars, and many scheduling apps.
Position location and satellite tracking systems did not always rely on the precise timing of the atomic clocks. The US Navy traditionally used navigation angles in reference to the stars. The first global positioning system developed by Guier and Weiffenbach was based on the Doppler shift, determining position based on the frequency changes of the satellite's broadcast signals. The Minitrack system, as it was called, compared different angles of incoming radio signals at paired antennas.
Satellite tracking systems transmitted a continuous wave from a ground-based transmitter and detected echoes from passing satellites. This required a precision timescale to measure and synchronize the transmitted and received signals. In 1964, Roger Easton realized that by putting a clock on satellites (first launched in the late 1950s) a single source could transmit time to both transmitter and receiver. Space-based timing led to a new generation of GPS, with high precision atomic clocks placed on each satellite. GPS as we know it could not exist without the atomic clock.
What Is GPS Time?
"GPS time" differs from Earth-based time systems like Coordinated Universal Time (UTC). UTC must account for the Earth's passage through the seasons and years. We are all familiar with the corrections needed for the Earth's revolutions. Our calendars have regularly scheduled "leap years" and occasionally a "leap second" is inserted (the last one in December 2016).
GPS time, by comparison, does not need to reflect the Earth's movements. Satellites have no need for a "leap" second or other corrections. From its start on midnight between January 5th and 6th of 1980, GPS time has been a continuous count of the seconds since that date.
As shown in Table 1, when GPS time was initiated in 1980, UTC and GPS time were the same, growing further apart as leap seconds accumulated through the years. GPS time is counted in Cycles, Weeks, Days, and Seconds.
Table 1. Leap Seconds and GPS Time
For the curious, you can see a live comparison of local, UTC, GPS, Loran and TAI times here.
A Matter of Time
The time standard in the USA has been set first by the National Bureau of Standards, now known as the National Institute of Standards and Technology (NIST). Timekeeping has been provided by various means as science and engineering progressed. Figure 1 shows a timeline.
Figure 1. Timekeepers through the centuries
The definition of the second, the fundamental time unit of basic physical systems, changed starting from the 1300s when the day was declared to be 24 equal hours by King Charles of France, to more precise units as mechanical clocks, pendulums, quartz clocks, and atomic clocks developed. The second has been defined as:
- a fraction of an average solar day: 1/86,000 of a mean solar day (1940s, the mean solar second)
- a fraction of the 1900 tropical year: 1/31,556,925.9747 (1956, the ephemeris second)
- a number of cycles of the cesium-133 atom: 9,192,631,770 (1967, the atomic second)
At the 1967 General Conference on Weights and Measures held in Paris, delegates from 36 countries agreed to redefine a second based on the oscillations of radiation emitted in the outer electron layer of a cesium atom. No longer tied to the Earth's movement, this second was based on an element of the Earth itself. Rooted in quantum physics and based on the difference in energy states of the outer electron of the cesium-133 atom, the definition of a second became "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium [sic] 133 atom."
The world's first cesium atomic clock, developed in 1955. Image courtesy of the National Physical Laboratory.
At the heart of all clocks is the ability to produce consistent oscillations for time units. The pendulum used mechanical checks, the quartz clock depended on electronics to control the vibrations of a crystal, keeping accurate time to the thousandths of a second. Advertisements for quartz watches of the 1970s touted its accuracy, the best at the time. Long term though, quartz clocks became inaccurate, the crystal being subject to drift and environmental issues. Also a problem for synchronizing events, each crystal was unique, with a unique frequency. Atomic clocks rely on a complex mix of circuitry to control electromagnetic fields and electron flow, forcing a change to the spins of electrons to provide frequency references. Under identical environments, each atom produces an identical frequency.
The first theories on using atomic energy levels for timing are attributed to Lord Kelvin. In the 1940s, Nobel Prize winner Isidor Rabi described the basics of an atomic clock. NIST built the first atomic clock in 1949, using ammonia molecules. Although not stable enough for use in timing, it proved the concept. In 1955 the National Physical Laboratory in England produced the first cesium-based atomic clock (pictured above with its creators, Louis Essen and Jack Parry).
Atomic Clock Frequencies
Atomic clocks have been constructed using hydrogen, ammonia, cesium, and rubidium atoms, each offering a different frequency. The basics can be described by looking at the hydrogen atom clock, the maser.
Masers (microwave amplification by stimulated emission of radiation) are based on the energy levels of the hydrogen atom. Hydrogen's electrons and protons have a spin. When they spin in the same direction, the atom as a unit has a higher energy profile. When spinning in opposite directions, the atom has a lower energy level. By controlling the spins, stable frequency oscillations occur at the frequency that is equal to the difference in energy levels divided by Planck's constant:
f = (E2 - E1) / h
where h = Planck's constant
Frequencies are approximately 1,420,405,752 Hz for the hydrogen maser, 9,192,631,770 Hz for cesium, and approximately 6,834,682,611 Hz for rubidium. The maser is the most complex and expensive, rubidium the least expensive.
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Accuracy and Timing
The algorithms used to determine an actual GPS position take into account many factors, over and above the accuracy of the clocking baseline. Errors in determining actual position are introduced by reception of the signal as well as limits on the receiving end. The signal reception is dependent on the position of the satellites, travel through the ionosphere, atmospheric conditions, and whether the signal is blocked or reflected by surrounding structures on Earth. Processing the received signal is dependent on the quality of the hardware, software, and mapping application used. At the speeds of the satellites, relativistic effects need to be accounted for as well as interpolation errors.
To isolate the effect a clock may have on position, let's look at a simple example from classical physics, removing the complexity of the GPS transmission and signal processing. The time delay is what is used to determine the satellite's distance from the receiver. Physics gives the formula for distance as:
distance = speed * time
Here on Earth, at non-relativistic speeds, doing a certain rate of travel, over a certain amount of time, will bring you so far. A car going 60 mph for an hour and a half without obstructions or accelerations, for example, should bring you 90 miles on your journey.
d = 60 mph * 1.5 hr = 90 miles
What if instead of a minute hand, however, you had a better watch and the travel time was actually 1 hour and 29.5 minutes? 89.5 miles.
A stopwatch accurate enough to indicate 29.4886 minutes would result in 89.4886 miles... over a half mile difference! For GPS, where the rate is the speed of light, a nanosecond of timing accuracy corresponds to approximately a foot of position accuracy.
GPS satellites and ground monitoring stations use hydrogen, cesium, and rubidium clocks. The master clock for GPS is provided by the United States Naval Observatory (USNO). In two facilities, with an ensemble of masers and cesium and rubidium atomic clocks, the USNO keeps GPS clocks accurate. Without intervention, GPS clocks could drift nanoseconds a day, giving errors unacceptable for navigation. With precise timing from the satellite's atomic clocks incorporated into the GPS signal, GPS receivers are able to access that precision by decoding the signal and resetting their clocks (often less accurate quartz oscillators) to sync with the atomic clocks. The receivers use their internal clocks to detect the time delay and determine distance. With signals from at least four satellites, a position is determined using trilateration. The accuracy of the receiver's positional data depends on various factors, including the number of signals used to obtain the position and errors in reception.
Time in the Trillions
Clock development continues. The NIST's Michael Lombardi said in 2011 that "The uncertainty of time measurements has improved by about 10 orders of magnitude during the past century, from parts in 106 to parts in 1016. Optical clocks should further reduce uncertainties by at least two more orders of magnitude."
Optical clocks, sometimes referred to as optical lattice clocks, use the same principle of quantum physics as atomic clocks, but with elements that have frequencies in the optical range, at laser frequencies. Optical clocks can measure time in trillionths of a second instead of the billionths of seconds of the current atomic clocks.
Clocks based on the strontium atom can split the second into 430 trillion units. The rare-earth metal ytterbium splits the second into 500 trillion. Clocks using aluminum and mercury are also being researched.
With such precision, the second may again be redefined in the future, and GPS based on these clocks will provide more-accurate positioning data.
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