The Global Positioning
Contents 1 History 1.1 Predecessors 1.2 Development 1.3 Timeline and modernization 1.4 Awards 2 Basic concept of GPS 2.1 Fundamentals 2.2 More detailed description 2.3 User-satellite geometry 2.4 Receiver in continuous operation 2.5 Non-navigation applications 3 Structure 3.1 Space segment 3.2 Control segment 3.3 User segment 4 Applications 4.1 Civilian 4.1.1 Restrictions on civilian use 4.2 Military 5 Communication 5.1 Message format
5.2
6
6.1 Problem description 6.2 Geometric interpretation 6.2.1 Spheres 6.2.2 Hyperboloids 6.2.3 Inscribed sphere 6.2.4 Spherical cones 6.3 Solution methods 6.3.1 Least squares 6.3.2 Iterative 6.3.3 Closed-form 7 Error sources and analysis 8 Accuracy enhancement and surveying 8.1 Augmentation 8.2 Precise monitoring 8.3 Timekeeping 8.3.1 Leap seconds 8.3.2 Accuracy 8.3.3 Format 8.4 Carrier phase tracking (surveying) 9 Regulatory spectrum issues concerning
History[edit]
The
Emblem of the 50th Space Wing TRANSIT was first successfully tested in 1960.[18] It used a
constellation of five satellites and could provide a navigational fix
approximately once per hour.
In 1967, the U.S. Navy developed the
Summary of satellites[37][38][39] Block
Launch
period
Suc- cess Fail- ure In prep- aration Plan- ned I 1978–1985 10 1 0 0 0 II 1989–1990 9 0 0 0 0 IIA 1990–1997 19 0 0 0 0 IIR 1997–2004 12 1 0 0 12 IIR-M 2005–2009 8 0 0 0 7 IIF 2010–2016 12 0 0 0 12 IIIA From 2017 0 0 0 12 0 IIIF — 0 0 0 22 0 Total 70 2 0 34 31 (Last update: March 9, 2016)
8 satellites from Block IIA are placed in reserve
In 1972, the USAF Central Inertial Guidance Test Facility (Holloman
AFB) conducted developmental flight tests of four prototype GPS
receivers in a Y configuration over White Sands Missile Range, using
ground-based pseudo-satellites.[41]
In 1978, the first experimental Block-I
Awards[edit]
On February 10, 1993, the
Ivan Getting, emeritus president of
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2015) (Learn how and when to remove this template message) Fundamentals[edit]
The
A pseudorandom code (sequence of ones and zeros) that is known to the
receiver. By time-aligning a receiver-generated version and the
receiver-measured version of the code, the time of arrival (TOA) of a
defined point in the code sequence, called an epoch, can be found in
the receiver clock time scale
A message that includes the time of transmission (TOT) of the code
epoch (in
Conceptually, the receiver measures the TOAs (according to its own
clock) of four satellite signals. From the TOAs and the TOTs, the
receiver forms four time of flight (TOF) values, which are (given the
speed of light) approximately equivalent to receiver-satellite ranges.
The receiver then computes its three-dimensional position and clock
deviation from the four TOFs.
In practice the receiver position (in three dimensional Cartesian
coordinates with origin at the Earth's center) and the offset of the
receiver clock relative to the
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2015) (Learn how and when to remove this template message) The current
Unlaunched
A visual example of a 24 satellite
The space segment (SS) is composed of 24 to 32 satellites in medium
Ground monitor station used from 1984 to 2007, on display at the Air Force Space & Missile Museum. The control segment (CS) is composed of: a master control station (MCS), an alternate master control station, four dedicated ground antennas, and six dedicated monitor stations. The MCS can also access
OCX will have the ability to control and manage
On September 14, 2011,[82] the
The first portable
The user segment (US) is composed of hundreds of thousands of U.S. and
allied military users of the secure
A typical OEM
A typical
Many
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2015) (Learn how and when to remove this template message) Main article: GNSS applications
See also:
This antenna is mounted on the roof of a hut containing a scientific experiment needing precise timing. Many civilian applications use one or more of GPS's three basic components: absolute location, relative movement, and time transfer. Agriculture:
Restrictions on civilian use[edit]
The U.S. government controls the export of some civilian receivers.
All
Attaching a
As of 2009, military
Navigation: Soldiers use
Subframes Description 1
2–3 Ephemeris (precise satellite orbit) 4–5 Almanac component (satellite network synopsis, error correction) Each
Band Frequency Description L1 1575.42 MHz Coarse-acquisition (C/A) and encrypted precision (P(Y)) codes, plus the L1 civilian (L1C) and military (M) codes on future Block III satellites. L2
1227.60 MHz
P(Y) code, plus the
L3 1381.05 MHz Used for nuclear detonation (NUDET) detection. L4 1379.913 MHz Being studied for additional ionospheric correction. L5 1176.45 MHz Proposed for use as a civilian safety-of-life (SoL) signal. All satellites broadcast at the same two frequencies, 1.57542 GHz
(L1 signal) and 1.2276 GHz (L2 signal). The satellite
network uses a CDMA spread-spectrum technique[104]:607 where the
low-bitrate message data is encoded with a high-rate pseudo-random
(PRN) sequence that is different for each satellite. The receiver must
be aware of the PRN codes for each satellite to reconstruct the actual
message data. The C/A code, for civilian use, transmits data at
1.023 million chips per second, whereas the P code, for U.S.
military use, transmits at 10.23 million chips per second. The
actual internal reference of the satellites is 10.22999999543 MHz
to compensate for relativistic effects[105][106] that make observers
on the
Demodulating and Decoding
Because all of the satellite signals are modulated onto the same L1
carrier frequency, the signals must be separated after demodulation.
This is done by assigning each satellite a unique binary sequence
known as a Gold code. The signals are decoded after demodulation using
addition of the Gold codes corresponding to the satellites monitored
by the receiver.[114][115]
If the almanac information has previously been acquired, the receiver
picks the satellites to listen for by their PRNs, unique numbers in
the range 1 through 32. If the almanac information is not in
memory, the receiver enters a search mode until a lock is obtained on
one of the satellites. To obtain a lock, it is necessary that there be
an unobstructed line of sight from the receiver to the satellite. The
receiver can then acquire the almanac and determine the satellites it
should listen for. As it detects each satellite's signal, it
identifies it by its distinct C/A code pattern. There can be a
delay of up to 30 seconds before the first estimate of position
because of the need to read the ephemeris data.
Processing of the navigation message enables the determination of the
time of transmission and the satellite position at this time. For more
information see Demodulation and Decoding, Advanced.
d i = ( t ~ i − b − s i ) c , i = 1 , 2 , … , n displaystyle d_ i =left( tilde t _ i -b-s_ i right)c,;i=1,2,dots ,n where di is the geometric distance or range between receiver and satellite: d i = ( x − x i ) 2 + ( y − y i ) 2 + ( z − z i ) 2 displaystyle d_ i = sqrt (x-x_ i )^ 2 +(y-y_ i )^ 2 +(z-z_ i )^ 2 Defining pseudoranges as p i = ( t ~ i − s i ) c displaystyle p_ i =left( tilde t _ i -s_ i right)c , we see they are biased versions of the true range: p i = d i + b c , i = 1 , 2 , . . . , n displaystyle p_ i =d_ i +bc,;i=1,2,...,n .[116][117] Since the equations have four unknowns [x, y, z, b]—the three
components of
( x ^ , y ^ , z ^ , b ^ ) = arg min ( x , y , z , b ) ∑ i ( ( x − x i ) 2 + ( y − y i ) 2 + ( z − z i ) 2 + b c − p i ) 2 displaystyle left( hat x , hat y , hat z , hat b right)= underset left(x,y,z,bright) arg min sum _ i left( sqrt (x-x_ i )^ 2 +(y-y_ i )^ 2 +(z-z_ i )^ 2 +bc-p_ i right)^ 2 Iterative[edit]
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
This article duplicates the scope of other articles, specifically, GNSS enhancement. Please discuss this issue on the talk page and edit it to conform with's Manual of Style. (November 2013) Augmentation[edit]
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
1 s 1575.42 × 10 6 = 0.63475 n s ≈ 1 n s
displaystyle frac 1,mathrm s 1575.42times 10^ 6 =0.63475,mathrm ns approx 1,mathrm ns , which is about one-thousandth of the C/A
1 s 1023 × 10 3 = 977.5 n s ≈ 1000 n s
displaystyle frac 1,mathrm s 1023times 10^ 3 =977.5,mathrm ns approx 1000,mathrm ns , to act as an additional clock signal and resolve the uncertainty.
The phase difference error in the normal
ϕ ( r i , s j , t k ) displaystyle phi (r_ i ,s_ j ,t_ k ) denote the phase of the carrier of satellite j measured by receiver i at time
t k displaystyle 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 ϕ displaystyle phi and to balance readability and conciseness, let
ϕ i , j , k = ϕ ( r i , s j , t k ) displaystyle phi _ i,j,k =phi (r_ i ,s_ j ,t_ k ) be a concise abbreviation. Also we define three functions, :
Δ r , Δ s , Δ t displaystyle 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
α i , j , k displaystyle alpha _ i,j,k is a function of the three integer arguments, i, j, and k then it is a valid argument for the functions, :
Δ r , Δ s , Δ t displaystyle Delta ^ r ,Delta ^ s ,Delta ^ t , with the values defined as
Δ r ( α i , j , k ) = α i + 1 , j , k − α i , j , k displaystyle Delta ^ r (alpha _ i,j,k )=alpha _ i+1,j,k -alpha _ i,j,k ,
Δ s ( α i , j , k ) = α i , j + 1 , k − α i , j , k displaystyle Delta ^ s (alpha _ i,j,k )=alpha _ i,j+1,k -alpha _ i,j,k , and
Δ t ( α i , j , k ) = α i , j , k + 1 − α i , j , k displaystyle Delta ^ t (alpha _ i,j,k )=alpha _ i,j,k+1 -alpha _ i,j,k . Also if
α i , j , k a n d β l , m , n displaystyle alpha _ i,j,k and beta _ l,m,n are valid arguments for the three functions and a and b are constants then ( a α i , j , k + b β l , m , n ) displaystyle (a alpha _ i,j,k +b beta _ l,m,n ) is a valid argument with values defined as
Δ r ( a α i , j , k + b β l , m , n ) = a Δ r ( α i , j , k ) + b Δ r ( β l , m , n ) displaystyle Delta ^ r (a alpha _ i,j,k +b beta _ l,m,n )=a Delta ^ r (alpha _ i,j,k )+b Delta ^ r (beta _ l,m,n ) ,
Δ s ( a α i , j , k + b β l , m , n ) = a Δ s ( α i , j , k ) + b Δ s ( β l , m , n ) displaystyle Delta ^ s (a alpha _ i,j,k +b beta _ l,m,n )=a Delta ^ s (alpha _ i,j,k )+b Delta ^ s (beta _ l,m,n ) , and
Δ t ( a α i , j , k + b β l , m , n ) = a Δ t ( α i , j , k ) + b Δ t ( β l , m , n ) displaystyle Delta ^ t (a alpha _ i,j,k +b beta _ l,m,n )=a Delta ^ t (alpha _ i,j,k )+b Delta ^ t (beta _ l,m,n ) . Receiver clock errors can be approximately eliminated by differencing the phases measured from satellite 1 with that from satellite 2 at the same epoch.[141] This difference is designated as
Δ s ( ϕ 1 , 1 , 1 ) = ϕ 1 , 2 , 1 − ϕ 1 , 1 , 1 displaystyle Delta ^ s (phi _ 1,1,1 )=phi _ 1,2,1 -phi _ 1,1,1 Double differencing[142] computes the difference of receiver 1's satellite difference from that of receiver 2. This approximately eliminates satellite clock errors. This double difference is: Δ r ( Δ s ( ϕ 1 , 1 , 1 ) ) = Δ r ( ϕ 1 , 2 , 1 − ϕ 1 , 1 , 1 ) = Δ r ( ϕ 1 , 2 , 1 ) − Δ r ( ϕ 1 , 1 , 1 ) = ( ϕ 2 , 2 , 1 − ϕ 1 , 2 , 1 ) − ( ϕ 2 , 1 , 1 − ϕ 1 , 1 , 1 ) displaystyle begin aligned Delta ^ r (Delta ^ s (phi _ 1,1,1 )),&=,Delta ^ r (phi _ 1,2,1 -phi _ 1,1,1 )&=,Delta ^ r (phi _ 1,2,1 )-Delta ^ r (phi _ 1,1,1 )&=,(phi _ 2,2,1 -phi _ 1,2,1 )-(phi _ 2,1,1 -phi _ 1,1,1 )end aligned Triple differencing[143] 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:
Δ t ( Δ r ( Δ s ( ϕ 1 , 1 , 1 ) ) ) displaystyle Delta ^ t (Delta ^ r (Delta ^ s (phi _ 1,1,1 ))) 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.[144][145] 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.
Comparison of geostationary, GPS, GLONASS, Galileo,
Other satellite navigation systems in use or various states of development include:
See also[edit] Gladys West
GPS/INS
Notes[edit] ^ Orbital periods and speeds are calculated using the relations
4π²R³ = T²GM and V²R = GM, where R = radius
of orbit in metres, T = orbital period in seconds, V = orbital speed
in m/s, G = gravitational constant ≈ 6.673×10−11 Nm²/kg²,
M = mass of
References[edit] ^ "GPS: Global Positioning
Further reading[edit] "NAVSTAR
External links[edit] Wikimedia Commons has media related to Global Positioning System. Global Positioning
v t e NAVSTAR Global Positioning
List of
Block I 1 2 3 4 5 6 7† 8 9 10 11 Block II 1 2 3 4 5 6 7 8 9 Block IIA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Block IIR 1† 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Block IIRM 1 2 3 4 5 6 7 8 Block IIF 1 2 3 4 5 6 7 8 9 10 11 12 Block IIIA 1 2 3 4 5 6 7 8 9 10 Block IIIF 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Italics indicate future missions. Signs † indicate launch failures. v t e
Operational BDS / BeiDou-2 / COMPASS
DORIS
Galileo
GLONASS
Historical BDS / BeiDou-1 Transit Timation Tsiklon GNSS augmentation EGNOS
GAGAN
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BSF
CHU
HD2IOA
HLA
JN53DV
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ROA
WWV
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