TheInfoList

History

The GPS project was launched in the United States in 1973 to overcome the limitations of previous navigation systems, integrating ideas from several predecessors, including classified engineering design studies from the 1960s. The U.S. Department of Defense developed the system, which originally used 24 satellites. It was initially developed for use by the United States military and became fully operational in 1995. Civilian use was allowed from the 1980s. Roger L. Easton of the Naval Research Laboratory, Ivan A. Getting of The Aerospace Corporation, and Bradford Parkinson of the Applied Physics Laboratory are credited with inventing it. The work of Gladys West is credited as instrumental in the development of computational techniques for detecting satellite positions with the precision needed for GPS. The design of GPS is based partly on similar ground-based radio-navigation systems, such as LORAN and the Decca Navigator, developed in the early 1940s. In 1955, Friedwardt Winterberg proposed a test of general relativity – detecting time slowing in a strong gravitational field using accurate atomic clocks placed in orbit inside artificial satellites. Special and general relativity predict that the clocks on the GPS satellites would be seen by the Earth's observers to run 38 microseconds faster per day than the clocks on the Earth. The GPS calculated positions would quickly drift into error, accumulating to . This was corrected for in the design of GPS.

Predecessors

Development

Timeline and modernization

Awards

Basic concept

Fundamentals

The GPS receiver calculates its own position and time based on data received from multiple GPS satellites. Each satellite carries an accurate record of its position and time, and transmits that data to the receiver. The satellites carry very stable atomic clocks that are synchronized with one another and with ground clocks. Any drift from time maintained on the ground is corrected daily. In the same manner, the satellite locations are known with great precision. GPS receivers have clocks as well, but they are less stable and less precise. Since the speed of radio waves is constant and independent of the satellite speed, the time delay between when the satellite transmits a signal and the receiver receives it is proportional to the distance from the satellite to the receiver. At a minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and clock deviation from satellite time).

More detailed description

User-satellite geometry

Although usually not formed explicitly in the receiver processing, the conceptual time differences of arrival (TDOAs) define the measurement geometry. Each TDOA corresponds to a hyperboloid of revolution (see Multilateration). The line connecting the two satellites involved (and its extensions) forms the axis of the hyperboloid. The receiver is located at the point where three hyperboloids intersect. It is sometimes incorrectly said that the user location is at the intersection of three spheres. While simpler to visualize, this is the case only if the receiver has a clock synchronized with the satellite clocks (i.e., the receiver measures true ranges to the satellites rather than range differences). There are marked performance benefits to the user carrying a clock synchronized with the satellites. Foremost is that only three satellites are needed to compute a position solution. If it were an essential part of the GPS concept that all users needed to carry a synchronized clock, a smaller number of satellites could be deployed, but the cost and complexity of the user equipment would increase.

Structure

The current GPS consists of three major segments. These are the space segment, a control segment, and a user segment. The U.S. Space Force develops, maintains, and operates the space and control segments. GPS satellites broadcast signals from space, and each GPS receiver uses these signals to calculate its three-dimensional location (latitude, longitude, and altitude) and the current time.

Space segment

The space segment (SS) is composed of 24 to 32 satellites, or Space Vehicles (SV), in medium Earth orbit, and also includes the payload adapters to the boosters required to launch them into orbit. The GPS design originally called for 24 SVs, eight each in three approximately circular orbits, but this was modified to six orbital planes with four satellites each. The six orbit planes have approximately 55° inclination (tilt relative to the Earth's equator) and are separated by 60° right ascension of the ascending node (angle along the equator from a reference point to the orbit's intersection).GPS Overview from the NAVSTAR Joint Program Office
. Retrieved December 15, 2006.
The orbital period is one-half a sidereal day, i.e., 11 hours and 58 minutes so that the satellites pass over the same locations or almost the same locations. Retrieved October 27, 2011 every day. The orbits are arranged so that at least six satellites are always within line of sight from everywhere on the Earth's surface (see animation at right). The result of this objective is that the four satellites are not evenly spaced (90°) apart within each orbit. In general terms, the angular difference between satellites in each orbit is 30°, 105°, 120°, and 105° apart, which sum to 360°. Orbiting at an altitude of approximately ; orbital radius of approximately , each SV makes two complete orbits each sidereal day, repeating the same ground track each day. This was very helpful during development because even with only four satellites, correct alignment means all four are visible from one spot for a few hours each day. For military operations, the ground track repeat can be used to ensure good coverage in combat zones. , there are 31 satellites in the GPS constellation, 27 of which are in use at a given time with the rest allocated as stand-bys. A 32nd was launched in 2018, but as of July 2019 is still in evaluation. More decommissioned satellites are in orbit and available as spares. The additional satellites improve the precision of GPS receiver calculations by providing redundant measurements. With the increased number of satellites, the constellation was changed to a nonuniform arrangement. Such an arrangement was shown to improve accuracy but also improves reliability and availability of the system, relative to a uniform system, when multiple satellites fail. With the expanded constellation, nine satellites are usually visible from any point on the ground at any time, ensuring considerable redundancy over the minimum four satellites needed for a position.

Control segment

User segment

Applications

While originally a military project, GPS is considered a dual-use technology, meaning it has significant civilian applications as well. GPS has become a widely deployed and useful tool for commerce, scientific uses, tracking, and surveillance. GPS's accurate time facilitates everyday activities such as banking, mobile phone operations, and even the control of power grids by allowing well synchronized hand-off switching.

Civilian

Restrictions on civilian use

The U.S. government controls the export of some civilian receivers. All GPS receivers capable of functioning above above sea level and , or designed or modified for use with unmanned missiles and aircraft, are classified as munitions (weapons)—which means they require State Department export licenses. This rule applies even to otherwise purely civilian units that only receive the L1 frequency and the C/A (Coarse/Acquisition) code. Disabling operation above these limits exempts the receiver from classification as a munition. Vendor interpretations differ. The rule refers to operation at both the target altitude and speed, but some receivers stop operating even when stationary. This has caused problems with some amateur radio balloon launches that regularly reach . These limits only apply to units or components exported from the United States. A growing trade in various components exists, including GPS units from other countries. These are expressly sold as ITAR-free.

Military

thumb|right|upright|M982_Excalibur_GPS-guided_[[artillery_shell..html" style="text-decoration: none;"class="mw-redirect" title="artillery_shell.html" style="text-decoration: none;"class="mw-redirect" title="M982 Excalibur GPS-guided [[artillery shell">M982 Excalibur GPS-guided [[artillery shell.">artillery_shell.html" style="text-decoration: none;"class="mw-redirect" title="M982 Excalibur GPS-guided [[artillery shell">M982 Excalibur GPS-guided [[artillery shell. As of 2009, military GPS applications include: * Navigation: Soldiers use GPS to find objectives, even in the dark or in unfamiliar territory, and to coordinate troop and supply movement. In the United States armed forces, commanders use the ''Commander's Digital Assistant'' and lower ranks use the ''Soldier Digital Assistant''. * Target tracking: Various military weapons systems use GPS to track potential ground and air targets before flagging them as hostile. These weapon systems pass target coordinates to [[precision-guided munition]]s to allow them to engage targets accurately. Military aircraft, particularly in [[air-to-ground]] roles, use GPS to find targets. * Missile and projectile guidance: GPS allows accurate targeting of various military weapons including ICBMs, cruise missiles, precision-guided munitions and artillery shells. Embedded GPS receivers able to withstand accelerations of 12,000 ''g'' or about have been developed for use in howitzer shells. * Search and rescue. * Reconnaissance: Patrol movement can be managed more closely. * GPS satellites carry a set of nuclear detonation detectors consisting of an optical sensor called a bhangmeter, an X-ray sensor, a dosimeter, and an electromagnetic pulse (EMP) sensor (W-sensor), that form a major portion of the United States Nuclear Detonation Detection System. General William Shelton has stated that future satellites may drop this feature to save money. GPS type navigation was first used in war in the 1991 Persian Gulf War, before GPS was fully developed in 1995, to assist Coalition Forces to navigate and perform maneuvers in the war. The war also demonstrated the vulnerability of GPS to being jammed, when Iraqi forces installed jamming devices on likely targets that emitted radio noise, disrupting reception of the weak GPS signal. GPS's vulnerability to jamming is a threat that continues to grow as jamming equipment and experience grows. GPS signals have been reported to have been jammed many times over the years for military purposes. Russia seems to have several objectives for this behavior, such as intimidating neighbors while undermining confidence in their reliance on American systems, promoting their GLONASS alternative, disrupting Western military exercises, and protecting assets from drones. China uses jamming to discourage US surveillance aircraft near the contested Spratly Islands. North Korea has mounted several major jamming operations near its border with South Korea and offshore, disrupting flights, shipping and fishing operations.

Timekeeping

Leap seconds

While most clocks derive their time from Coordinated Universal Time (UTC), the atomic clocks on the satellites are set to "GPS time". The difference is that GPS time is not corrected to match the rotation of the Earth, so it does not contain leap seconds or other corrections that are periodically added to UTC. GPS time was set to match UTC in 1980, but has since diverged. The lack of corrections means that GPS time remains at a constant offset with International Atomic Time (TAI) (TAI - GPS = 19 seconds). Periodic corrections are performed to the on-board clocks to keep them synchronized with ground clocks. The GPS navigation message includes the difference between GPS time and UTC. GPS time is 18 seconds ahead of UTC because of the leap second added to UTC on December 31, 2016. Receivers subtract this offset from GPS time to calculate UTC and specific time zone values. New GPS units may not show the correct UTC time until after receiving the UTC offset message. The GPS-UTC offset field can accommodate 255 leap seconds (eight bits).

Accuracy

GPS time is theoretically accurate to about 14 nanoseconds, due to the clock drift that atomic clocks experience in GPS transmitters, relative to International Atomic Time. Most receivers lose accuracy in the interpretation of the signals and are only accurate to 100 nanoseconds.

Format

As opposed to the year, month, and day format of the Gregorian calendar, the GPS date is expressed as a week number and a seconds-into-week number. The week number is transmitted as a ten-bit field in the C/A and P(Y) navigation messages, and so it becomes zero again every 1,024 weeks (19.6 years). GPS week zero started at 00:00:00 UTC (00:00:19 TAI) on January 6, 1980, and the week number became zero again for the first time at 23:59:47 UTC on August 21, 1999 (00:00:19 TAI on August 22, 1999). It happened the second time at 23:59:42 UTC on April 6, 2019. To determine the current Gregorian date, a GPS receiver must be provided with the approximate date (to within 3,584 days) to correctly translate the GPS date signal. To address this concern in the future the modernized GPS civil navigation (CNAV) message will use a 13-bit field that only repeats every 8,192 weeks (157 years), thus lasting until 2137 (157 years after GPS week zero).

Communication

The navigational signals transmitted by GPS satellites encode a variety of information including satellite positions, the state of the internal clocks, and the health of the network. These signals are transmitted on two separate carrier frequencies that are common to all satellites in the network. Two different encodings are used: a public encoding that enables lower resolution navigation, and an encrypted encoding used by the U.S. military.

Message format

Satellite frequencies

Demodulation and decoding

Problem description

The receiver uses messages received from satellites to determine the satellite positions and time sent. The ''x, y,'' and ''z'' components of satellite position and the time sent (''s'') are designated as 'xi, yi, zi, si''where the subscript ''i'' denotes the satellite and has the value 1, 2, ..., ''n'', where ''n'' ≥ 4. When the time of message reception indicated by the on-board receiver clock is ''t̃i'', the true reception time is , where ''b'' is the receiver's clock bias from the much more accurate GPS clocks employed by the satellites. The receiver clock bias is the same for all received satellite signals (assuming the satellite clocks are all perfectly synchronized). The message's transit time is , where ''si'' is the satellite time. Assuming the message traveled at the speed of light, ''c'', the distance traveled is . For n satellites, the equations to satisfy are: :$d_i = \left\left( \tilde_i - b - s_i \right\right)c, \; i=1,2,\dots,n$ where ''di'' is the geometric distance or range between receiver and satellite ''i'' (the values without subscripts are the ''x, y,'' and ''z'' components of receiver position): :$d_i = \sqrt$ Defining ''pseudoranges'' as $p_i = \left \left( \tilde_i - s_i \right \right)c$, we see they are biased versions of the true range: :$p_i = d_i + bc, \;i=1,2,...,n$ .section 4 beginning on page 1
Geoffery Blewitt: Basics of the GPS Techique
Since the equations have four unknowns 'x, y, z, b''the three components of GPS receiver position and the clock bias—signals from at least four satellites are necessary to attempt solving these equations. They can be solved by algebraic or numerical methods. Existence and uniqueness of GPS solutions are discussed by Abell and Chaffee. When ''n'' is greater than four, this system is overdetermined and a fitting method must be used. The amount of error in the results varies with the received satellites' locations in the sky, since certain configurations (when the received satellites are close together in the sky) cause larger errors. Receivers usually calculate a running estimate of the error in the calculated position. This is done by multiplying the basic resolution of the receiver by quantities called the geometric dilution of position (GDOP) factors, calculated from the relative sky directions of the satellites used. The receiver location is expressed in a specific coordinate system, such as latitude and longitude using the WGS 84 geodetic datum or a country-specific system.

Geometric interpretation

The GPS equations can be solved by numerical and analytical methods. Geometrical interpretations can enhance the understanding of these solution methods.

Spheres

The measured ranges, called pseudoranges, contain clock errors. In a simplified idealization in which the ranges are synchronized, these true ranges represent the radii of spheres, each centered on one of the transmitting satellites. The solution for the position of the receiver is then at the intersection of the surfaces of these spheres; see trilateration (more generally, true-range multilateration). Signals from at minimum three satellites are required, and their three spheres would typically intersect at two points. One of the points is the location of the receiver, and the other moves rapidly in successive measurements and would not usually be on Earth's surface. In practice, there are many sources of inaccuracy besides clock bias, including random errors as well as the potential for precision loss from subtracting numbers close to each other if the centers of the spheres are relatively close together. This means that the position calculated from three satellites alone is unlikely to be accurate enough. Data from more satellites can help because of the tendency for random errors to cancel out and also by giving a larger spread between the sphere centers. But at the same time, more spheres will not generally intersect at one point. Therefore, a near intersection gets computed, typically via least squares. The more signals available, the better the approximation is likely to be.

Hyperboloids

If the pseudorange between the receiver and satellite ''i'' and the pseudorange between the receiver and satellite ''j'' are subtracted, , the common receiver clock bias (''b'') cancels out, resulting in a difference of distances . The locus of points having a constant difference in distance to two points (here, two satellites) is a hyperbola on a plane and a hyperboloid of revolution (more specifically, a two-sheeted hyperboloid) in 3D space (see Multilateration). Thus, from four pseudorange measurements, the receiver can be placed at the intersection of the surfaces of three hyperboloids each with foci at a pair of satellites. With additional satellites, the multiple intersections are not necessarily unique, and a best-fitting solution is sought instead.

Inscribed sphere

The receiver position can be interpreted as the center of an inscribed sphere (insphere) of radius ''bc'', given by the receiver clock bias ''b'' (scaled by the speed of light ''c''). The insphere location is such that it touches other spheres. The circumscribing spheres are centered at the GPS satellites, whose radii equal the measured pseudoranges ''p''i. This configuration is distinct from the one described above, in which the spheres' radii were the unbiased or geometric ranges ''d''i.

Hypercones

The clock in the receiver is usually not of the same quality as the ones in the satellites and will not be accurately synchronized to them. This produces pseudoranges with large differences compared to the true distances to the satellites. Therefore, in practice, the time difference between the receiver clock and the satellite time is defined as an unknown clock bias ''b''. The equations are then solved simultaneously for the receiver position and the clock bias. The solution space 'x, y, z, b''can be seen as a four-dimensional spacetime, and signals from at minimum four satellites are needed. In that case each of the equations describes a hypercone (or spherical cone), with the cusp located at the satellite, and the base a sphere around the satellite. The receiver is at the intersection of four or more of such hypercones.

Solution methods

Least squares

When more than four satellites are available, the calculation can use the four best, or more than four simultaneously (up to all visible satellites), depending on the number of receiver channels, processing capability, and geometric dilution of precision (GDOP). Using more than four involves an over-determined system of equations with no unique solution; such a system can be solved by a least-squares or weighted least squares method. :$\left\left( \hat,\hat,\hat,\hat \right\right) = \underset \sum_i \left\left( \sqrt + bc - p_i \right\right)^2$

Iterative

Both the equations for four satellites, or the least squares equations for more than four, are non-linear and need special solution methods. A common approach is by iteration on a linearized form of the equations, such as the Gauss–Newton algorithm. The GPS was initially developed assuming use of a numerical least-squares solution method—i.e., before closed-form solutions were found.

Closed-form

One closed-form solution to the above set of equations was developed by S. Bancroft. Its properties are well known;Chaffee, J. and Abel, J., "On the Exact Solutions of Pseudorange Equations", ''IEEE Transactions on Aerospace and Electronic Systems'', vol:30, no:4, pp: 1021–1030, 1994 in particular, proponents claim it is superior in low-GDOP situations, compared to iterative least squares methods. Bancroft's method is algebraic, as opposed to numerical, and can be used for four or more satellites. When four satellites are used, the key steps are inversion of a 4x4 matrix and solution of a single-variable quadratic equation. Bancroft's method provides one or two solutions for the unknown quantities. When there are two (usually the case), only one is a near-Earth sensible solution. When a receiver uses more than four satellites for a solution, Bancroft uses the generalized inverse (i.e., the pseudoinverse) to find a solution. A case has been made that iterative methods, such as the Gauss–Newton algorithm approach for solving over-determined non-linear least squares (NLLS) problems, generally provide more accurate solutions. Leick et al. (2015) states that "Bancroft's (1985) solution is a very early, if not the first, closed-form solution." Other closed-form solutions were published afterwards,Alfred Kleusberg, "Analytical GPS Navigation Solution", ''University of Stuttgart Research Compendium'',1994Oszczak, B., "New Algorithm for GNSS Positioning Using System of Linear Equations," ''Proceedings of the 26th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2013)'', Nashville, TN, September 2013, pp. 3560–3563. although their adoption in practice is unclear.

Error sources and analysis

GPS error analysis examines error sources in GPS results and the expected size of those errors. GPS makes corrections for receiver clock errors and other effects, but some residual errors remain uncorrected. Error sources include signal arrival time measurements, numerical calculations, atmospheric effects (ionospheric/tropospheric delays), ephemeris and clock data, multipath signals, and natural and artificial interference. Magnitude of residual errors from these sources depends on geometric dilution of precision. Artificial errors may result from jamming devices and threaten ships and aircraft or from intentional signal degradation through selective availability, which limited accuracy to ≈ , but has been switched off since May 1, 2000.

Accuracy enhancement and surveying

Augmentation

Integrating external information into the calculation process can materially improve accuracy. Such augmentation systems are generally named or described based on how the information arrives. Some systems transmit additional error information (such as clock drift, ephemera, or ionospheric delay), others characterize prior errors, while a third group provides additional navigational or vehicle information. Examples of augmentation systems include the Wide Area Augmentation System (WAAS), European Geostationary Navigation Overlay Service (EGNOS), Differential GPS (DGPS), inertial navigation systems (INS) and Assisted GPS. The standard accuracy of about can be augmented to with DGPS, and to about with WAAS.

Precise monitoring

Accuracy can be improved through precise monitoring and measurement of existing GPS signals in additional or alternative ways. The largest remaining error is usually the unpredictable delay through the ionosphere. The spacecraft broadcast ionospheric model parameters, but some errors remain. This is one reason GPS spacecraft transmit on at least two frequencies, L1 and L2. Ionospheric delay is a well-defined function of frequency and the total electron content (TEC) along the path, so measuring the arrival time difference between the frequencies determines TEC and thus the precise ionospheric delay at each frequency. Military receivers can decode the P(Y) code transmitted on both L1 and L2. Without decryption keys, it is still possible to use a ''codeless'' technique to compare the P(Y) codes on L1 and L2 to gain much of the same error information. This technique is slow, so it is currently available only on specialized surveying equipment. In the future, additional civilian codes are expected to be transmitted on the L2 and L5 frequencies. All users will then be able to perform dual-frequency measurements and directly compute ionospheric delay errors. A second form of precise monitoring is called ''Carrier-Phase Enhancement'' (CPGPS). This corrects the error that arises because the pulse transition of the PRN is not instantaneous, and thus the correlation (satellite–receiver sequence matching) operation is imperfect. CPGPS uses the L1 carrier wave, which has a period of $\frac = 0.63475\,\mathrm \approx 1\, \mathrm \$, which is about one-thousandth of the C/A Gold code bit period of $\frac = 977.5 \, \mathrm \approx 1000 \, \mathrm \$, to act as an additional clock signal and resolve the uncertainty. The phase difference error in the normal GPS amounts to of ambiguity. CPGPS working to within 1% of perfect transition reduces this error to of ambiguity. By eliminating this error source, CPGPS coupled with DGPS normally realizes between of absolute accuracy. ''Relative Kinematic Positioning'' (RKP) is a third alternative for a precise GPS-based positioning system. In this approach, determination of range signal can be resolved to a precision of less than . This is done by resolving the number of cycles that the signal is transmitted and received by the receiver by using a combination of differential GPS (DGPS) correction data, transmitting GPS signal phase information and ambiguity resolution techniques via statistical tests—possibly with processing in real-time (real-time kinematic positioning, RTK).

Carrier phase tracking (surveying)

Another method that is used in surveying applications is carrier phase tracking. The period of the carrier frequency multiplied by the speed of light gives the wavelength, which is about for the L1 carrier. Accuracy within 1% of wavelength in detecting the leading edge reduces this component of pseudorange error to as little as . This compares to for the C/A code and for the P code. accuracy requires measuring the total phase—the number of waves multiplied by the wavelength plus the fractional wavelength, which requires specially equipped receivers. This method has many surveying applications. It is accurate enough for real-time tracking of the very slow motions of tectonic plates, typically per year. Triple differencing followed by numerical root finding, and the least squares technique can estimate the position of one receiver given the position of another. First, compute the difference between satellites, then between receivers, and finally between epochs. Other orders of taking differences are equally valid. Detailed discussion of the errors is omitted. The satellite carrier total phase can be measured with ambiguity as to the number of cycles. Let $\ \phi\left(r_i, s_j, t_k\right)$ denote the phase of the carrier of satellite ''j'' measured by receiver ''i'' at time $\ \ t_k$. This notation shows the meaning of the subscripts ''i, j,'' and ''k.'' The receiver (''r''), satellite (''s''), and time (''t'') come in alphabetical order as arguments of $\ \phi$ and to balance readability and conciseness, let $\ \phi_ = \phi\left(r_i, s_j, t_k\right)$ be a concise abbreviation. Also we define three functions, :$\ \Delta^r, \Delta^s, \Delta^t$, which return differences between receivers, satellites, and time points, respectively. Each function has variables with three subscripts as its arguments. These three functions are defined below. If $\ \alpha_$ is a function of the three integer arguments, ''i, j,'' and ''k'' then it is a valid argument for the functions, :$\ \Delta^r, \Delta^s, \Delta^t$, with the values defined as :$\ \Delta^r\left(\alpha_\right) = \alpha_ - \alpha_$, :$\ \Delta^s\left(\alpha_\right) = \alpha_ - \alpha_$, and :$\ \Delta^t\left(\alpha_\right) = \alpha_ - \alpha_$ . Also if $\ \alpha_\ and\ \beta_$ are valid arguments for the three functions and ''a'' and ''b'' are constants then $\ \left( a\ \alpha_ + b\ \beta_ \right)$ is a valid argument with values defined as :$\ \Delta^r\left(a\ \alpha_ + b\ \beta_\right) = a \ \Delta^r\left(\alpha_\right) + b \ \Delta^r\left(\beta_\right)$, :$\ \Delta^s\left(a\ \alpha_ + b\ \beta_ \right)= a \ \Delta^s\left(\alpha_\right) + b \ \Delta^s\left(\beta_\right)$, and :$\ \Delta^t\left(a\ \alpha_ + b\ \beta_ \right)= a \ \Delta^t\left(\alpha_\right) + b \ \Delta^t\left(\beta_\right)$ . Receiver clock errors can be approximately eliminated by differencing the phases measured from satellite 1 with that from satellite 2 at the same epoch. This difference is designated as $\ \Delta^s\left(\phi_\right) = \phi_ - \phi_$ Double differencing computes the difference of receiver 1's satellite difference from that of receiver 2. This approximately eliminates satellite clock errors. This double difference is: :$\begin \Delta^r\left(\Delta^s\left(\phi_\right)\right)\,&=\,\Delta^r\left(\phi_ - \phi_\right) &=\,\Delta^r\left(\phi_\right) - \Delta^r\left(\phi_\right) &=\,\left(\phi_ - \phi_\right) - \left(\phi_ - \phi_\right) \end$ Triple differencing subtracts the receiver difference from time 1 from that of time 2. This eliminates the ambiguity associated with the integral number of wavelengths in carrier phase provided this ambiguity does not change with time. Thus the triple difference result eliminates practically all clock bias errors and the integer ambiguity. Atmospheric delay and satellite ephemeris errors have been significantly reduced. This triple difference is: :$\ \Delta^t\left(\Delta^r\left(\Delta^s\left(\phi_\right)\right)\right)$ Triple difference results can be used to estimate unknown variables. For example, if the position of receiver 1 is known but the position of receiver 2 unknown, it may be possible to estimate the position of receiver 2 using numerical root finding and least squares. Triple difference results for three independent time pairs may be sufficient to solve for receiver 2's three position components. This may require a numerical procedure.chapter on root finding and nonlinear sets of equations An approximation of receiver 2's position is required to use such a numerical method. This initial value can probably be provided from the navigation message and the intersection of sphere surfaces. Such a reasonable estimate can be key to successful multidimensional root finding. Iterating from three time pairs and a fairly good initial value produces one observed triple difference result for receiver 2's position. Processing additional time pairs can improve accuracy, overdetermining the answer with multiple solutions. Least squares can estimate an overdetermined system. Least squares determines the position of receiver 2 that best fits the observed triple difference results for receiver 2 positions under the criterion of minimizing the sum of the squares.

Regulatory spectrum issues concerning GPS receivers

To build public support of efforts to continue the 2004 FCC authorization of LightSquared's ancillary terrestrial component vs. a simple ground-based LTE service in the Mobile Satellite Service band, GPS receiver manufacturer Trimble Navigation Ltd. formed the "Coalition To Save Our GPS." The FCC and LightSquared have each made public commitments to solve the GPS interference issue before the network is allowed to operate. According to Chris Dancy of the Aircraft Owners and Pilots Association, airline pilots with the type of systems that would be affected "may go off course and not even realize it." The problems could also affect the Federal Aviation Administration upgrade to the air traffic control system, United States Defense Department guidance, and local emergency services including 911. On February 14, 2012, the FCC moved to bar LightSquared's planned national broadband network after being informed by the National Telecommunications and Information Administration (NTIA), the federal agency that coordinates spectrum uses for the military and other federal government entities, that "there is no practical way to mitigate potential interference at this time".FCC press releas
"Spokesperson Statement on NTIA Letter – LightSquared and GPS"
. February 14, 2012. Accessed 2013-03-03.
LightSquared is challenging the FCC's action.

Other systems

Other notable satellite navigation systems in use or various states of development include: * Beidou – system deployed and operated by the People's Republic of China's, initiating global services in 2019. * Galileo – a global system being developed by the European Union and other partner countries, which began operation in 2016, and is expected to be fully deployed by 2020. * GLONASSRussia's global navigation system. Fully operational worldwide. *NavIC – A regional navigation system developed by the Indian Space Research Organisation. *Michibiki – A regional navigation system receivable in the Asia-Oceania regions, with a focus on Japan.

* GPS/INS * GPS navigation software * GPS spoofing * Indoor positioning system * List of GPS satellites * Local Area Augmentation System * Local positioning system * Military invention * Mobile phone tracking * Navigation paradox * Notice Advisory to Navstar Users * S-GPS

Notes

References

* * * *
Global Positioning System
Open Courseware from MIT, 2012 *