GPS signals - Knowledge

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offset in which trials of all 1,023 offsets could potentially be required, the tracking to maintain lock usually requires shifting of half a pulse width or less. To perform this tracking, the receiver observes two quantities, phase error and received frequency offset. The correlation of the received PRN code with respect to the receiver generated PRN code is computed to determine if the bits of the two signals are misaligned. Comparisons of the received PRN code with receiver generated PRN code shifted half a pulse width early and half a pulse width late are used to estimate adjustment required. The amount of adjustment required for maximum correlation is used in estimating phase error. Received frequency offset from the frequency generated by the receiver provides an estimate of phase rate error. The command for the frequency generator and any further PRN code shifting required are computed as a function of the phase error and the phase rate error in accordance with the control law used. The Doppler velocity is computed as a function of the frequency offset from the carrier nominal frequency. The Doppler velocity is the velocity component along the line of sight of the receiver relative to the satellite.

1194:(UTC). Each frame contains a part of the almanac (in subframes 4 and 5) and the complete almanac is transmitted by each satellite in 25 frames total (requiring 12.5 minutes). The almanac serves several purposes. The first is to assist in the acquisition of satellites at power-up by allowing the receiver to generate a list of visible satellites based on stored position and time, while an ephemeris from each satellite is needed to compute position fixes using that satellite. In older hardware, lack of an almanac in a new receiver would cause long delays before providing a valid position, because the search for each satellite was a slow process. Advances in hardware have made the acquisition process much faster, so not having an almanac is no longer an issue. The second purpose is for relating time derived from the GPS (called GPS time) to the international time standard of 3937: 6117:). The code gives strong autocorrelation only at offsets less than 1 in magnitude. The extent of the search space in the code phase dimension depends on the granularity of the offsets at which correlation is computed. It is typical to search for the code phase within a granularity of 0.5 chips or finer; that means 2,046 offsets. There may be more factors increasing the size of the search space of code phase. For example, a receiver may be designed so as to examine 2 consecutive windows of the digitalized signal, so that at least one of them does not contain a navigation bit transition (which worsens the correlation peak); this requires the signal windows to be at most 10 ms long. 3316: 3932:{\displaystyle {\begin{aligned}{\text{L1C}}_{i}(t)&={\text{L1C}}'(t{\bmod {10\,230}})\\{\text{L1C}}'_{i}(t')&={\begin{cases}W_{i}(t')&{\text{ if }}t'<p'_{i}\\S(t'-p'_{i})&{\text{ if }}p'_{i}\leq t'<p'_{i}+7\\W_{i}(t'-7)&{\text{ if }}t'\geq p'_{i}+7\\\end{cases}}\\S&=(0,1,1,0,1,0,0)\\W_{i}(n)&=L(n)\oplus L((n+w_{i}){\bmod {10\,223}})\\L(n)&={\begin{cases}1&{\text{ if }}n\neq 0{\text{ and there is an integer }}m{\text{ such that }}n\equiv m^{2}{\pmod {10\,223}}\\0&{\text{ otherwise}}\\\end{cases}}\end{aligned}}} 51: 2480: 1530:

new hardware on board the satellite, it is only transmitted by the so-called Block IIR-M and later design satellites. The L2C signal is tasked with improving accuracy of navigation, providing an easy to track signal, and acting as a redundant signal in case of localized interference. L2C signals have been broadcast beginning in April 2014 on satellites capable of broadcasting it, but are still considered pre-operational. As of January 2021, L2C is broadcast on 23 satellites and is expected on 24 satellites by 2023.

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message. The TLM word at the beginning of each subframe of a navigation frame enables the receiver to detect the beginning of a subframe and determine the receiver clock time at which the navigation subframe begins. The HOW word then enables the receiver to determine which specific subframe is being transmitted. 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 before computing the intersections of sphere surfaces.

20: 28: 6158:. The replica that generates the highest magnitude of dot product is likely the one that best matches the code phase and frequency of the signal; therefore, if that magnitude is above a threshold, the receiver proceeds to track the signal or further refine the estimated parameters before tracking. The threshold is used to minimize false positives (apparently detecting a signal when there is in fact no signal), but some may still occur occasionally. 2012: 3197:

bit-train is used to modulate the L5 in-phase (I5) carrier. This combined signal is called the L5 Data signal. The L5 quadrature-phase (Q5) carrier has no data and is called the L5 Pilot signal. The format used for L5 CNAV is very similar to that of L2 CNAV. One difference is that it uses 2 times the data rate. The bit fields within each message, message types, and forward error correction code algorithm are the same as those of

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diameter) and increase the local signal strength by 20 dB, or approximately 100 times stronger. A side effect of having two antennas is that the GPS satellite will appear to be two GPS satellites occupying the same position to those inside the spot beam. While the whole Earth M-code signal is available on the Block IIR-M satellites, the spot beam antennas will not be deployed until the

6918: 2475:{\displaystyle {\begin{aligned}X_{1}(t)&=d(t)\oplus d(t-2)\oplus d(t-3)\oplus d(t-5)\oplus d(t-6)\\X_{2}(t)&=d(t)\oplus d(t-1)\oplus d(t-2)\oplus d(t-3)\oplus d(t-6)\\d'(t')&={\begin{cases}X_{1}\left({\frac {t'}{2}}\right)&{\text{if }}t'\equiv 0{\pmod {2}}\\X_{2}\left({\frac {t'-1}{2}}\right)&{\text{if }}t'\equiv 1{\pmod {2}}\\\end{cases}}\end{aligned}}} 1148:

subframe will be transmitted) and identifies the specific subframe within a complete frame. The remaining eight words of the subframe contain the actual data specific to that subframe. Each word includes 6 bits of parity generated using an algorithm based on Hamming codes, which take into account the 24 non-parity bits of that word and the last 2 bits of the previous word.

6212:. Note that each frequency bin is centered on its interval and therefore covers 250 Hz in each direction; for example, the first bin has a carrier at −4.750 Hz and covers the interval −5,000 Hz to −4,500 Hz. Code phases are equivalent modulo 1,023 because the ranging code is periodic; for example, phase −0.5 is equivalent to phase 1,022.5. 5620: 6639: 1174:

when powered on, assume that the newly decoded truncated week number corresponds to the period of 1,024 weeks that starts at the last saved date. This method correctly deduces the full week number if the receiver is never allowed to remain shut down (or without a time and position fix) for more than 1,024 weeks (~19.6 years).

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of the received signal with a locally generated replica of the ranging code and detecting the highest peak or lowest valley. The offset of the highest peak or lowest valley contains information about the code phase relative to receiver time. The duration of the local replica is set by receiver design

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In CNAV, at least 1 out of every 4 packets are ephemeris data and the same lower bound applies for clock data packets. The design allows for a wide variety of packet types to be transmitted. With a 32-satellite constellation, and the current requirements of what needs to be sent, less than 75% of the

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An ephemeris is valid for only four hours, while an almanac is valid–with little dilution of precision–for up to two weeks. The receiver uses the almanac to acquire a set of satellites based on stored time and location. As the receiver acquires each satellite, each satellite’s ephemeris is decoded so

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since their epochs, starting at 0. The epoch of the LFSRs is the point at which they are at the initial state; and for the overall C/A codes it is the start of any UTC second plus any integer number of milliseconds. The output of LFSRs at negative arguments is defined consistent with the period which

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50,000 samples in the digital signal, and therefore 25,001 frequency components ranging from 0 Hz to 2.5 MHz in steps of 100 Hz (note that the 0 Hz component is real because it is the average of a real-valued signal and the 2.5 MHz component is real as well because it is the

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analogous to LNAV frames. While LNAV frames have a fixed information content, CNAV messages may be of one of several defined types. The type of a frame determines its information content. Messages do not follow a fixed schedule regarding which message types will be used, allowing the Control Segment

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which is reset periodically to a predetermined initial state. The period of the CM and CL is determined by this resetting and not by the natural period of the LFSR (as is the case with the C/A code). The initial states are designated in the interface specification and are different for different PRN

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The project involves new ground stations and new satellites, with additional navigation signals for both civilian and military users. It aims to improve the accuracy and availability for all users. The implementation goal of 2013 was established, and contractors were offered incentives if they could

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Satellites broadcast a new ephemeris every two hours. The ephemeris is generally valid for 4 hours, with provisions for updates every 4 hours or longer in non-nominal conditions. The time needed to acquire the ephemeris is becoming a significant element of the delay to first position fix, because as

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occurs every 1,024 GPS weeks (approximately every 19.6 years; 1,024 is 2), a receiver that computes current calendar dates needs to deduce the upper week number bits or obtain them from a different source. One possible method is for the receiver to save its current date in memory when shut down, and

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between SV identifiers and PRN numbers described in the interface specification. Unlike SVNs, the SV ID/PRN number of a satellite may be changed (resulting in a change to the ranging codes it uses). That is, no two active satellites can share any one active SV ID/PRN number. The current SVNs and PRN

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As the receiver continues to read successive PRN sequences, it will encounter a sudden change in the phase of the 1,023-bit received PRN signal. This indicates the beginning of a data bit of the navigation message. This enables the receiver to begin reading the 20 millisecond bits of the navigation

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per second, whereas the P code, for U.S. military use, transmits at 10.23 million chips per second. The L1 carrier is modulated by both the C/A and P codes, while the L2 carrier is only modulated by the P code. The P code can be encrypted as a so-called P(Y) code which is only available to military

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The L5 band provides additional robustness in the form of interference mitigation, the band being internationally protected, redundancy with existing bands, geostationary satellite augmentation, and ground-based augmentation. The added robustness of this band also benefits terrestrial applications.

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The M-code is transmitted in the same L1 and L2 frequencies already in use by the previous military code, the P(Y)-code. The new signal is shaped to place most of its energy at the edges (away from the existing P(Y) and C/A carriers). It does not work at every satellite, and M-code was switched off

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One of the first announcements was the addition of a new civilian-use signal, to be transmitted on a frequency other than the L1 frequency used for the coarse/acquisition (C/A) signal. Ultimately, this became the L2C signal, so called because it is broadcast on the L2 frequency. Because it requires

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In each subframe, each hand-over word (HOW) contains the most significant 17 bits of the TOW count corresponding to the start of the next following subframe. Note that the 2 least significant bits can be safely omitted because one HOW occurs in the navigation message every 6 seconds, which is equal

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GPS time is expressed with a resolution of 1.5 seconds as a week number and a time of week count (TOW). Its zero point (week 0, TOW 0) is defined to be 1980-01-06T00:00Z. The TOW count is a value ranging from 0 to 403,199 whose meaning is the number of 1.5 second periods elapsed since the beginning

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After a subframe has been read and interpreted, the time the next subframe was sent can be calculated through the use of the clock correction data and HOW. The receiver knows the receiver clock time of when the beginning of the next subframe was received from detection of the Telemetry Word thereby

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of ten 30-bit words each. Each subframe has the GPS time in 6-second increments. Subframe 1 contains the GPS date (week number), satellite clock correction information, satellite status and satellite health. Subframes 2 and 3 together contain the transmitting satellite's ephemeris data. Subframes 4

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Whereas the C/A PRNs are unique for each satellite, each satellite transmits a different segment of a master P-code sequence approximately 2.35 x 10 chips long (235,000,000,000,000 chips). Each satellite repeatedly transmits its assigned segment of the master code, restarting every Sunday

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and covering all frequencies is performed for each code phase; each such operation is more computationally expensive, but it may still be faster overall than the previous method due to the efficiency of FFT algorithms, and it recovers carrier frequency with a higher accuracy, because the frequency

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If the almanac information has previously been acquired, the receiver picks which satellites to listen for by their PRNs. If the almanac information is not in memory, the receiver enters a search mode and cycles through the PRN numbers until a lock is obtained on one of the satellites. To obtain a

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A GPS receiver processes the GPS signals received on its antenna to determine position, velocity and/or timing. The signal at antenna is amplified, down converted to baseband or intermediate frequency, filtered (to remove frequencies outside the intended frequency range for the digital signal that

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Very little has been published about this new, restricted code. It contains a PRN code of unknown length transmitted at 5.115 MHz. Unlike the P(Y)-code, the M-code is designed to be autonomous, meaning that a user can calculate their position using only the M-code signal. From the P(Y)-code's

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The initial states are described in the GPS interface specification as numbers expressed in octal following the convention that the LFSR state is interpreted as the binary representation of a number where the output bit is the least significant bit, and the bit where new bits are shifted in is the

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Having reached full operational capability on July 17, 1995 the GPS system had completed its original design goals. However, additional advances in technology and new demands on the existing system led to the effort to "modernize" the GPS system. Announcements from the Vice President and the White

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The P-code is a PRN sequence much longer than the C/A code: 6.187104 x 10 chips. Even though the P-code chip rate (10.23 Mchip/s) is ten times that of the C/A code, it repeats only once per week, eliminating range ambiguity. It was assumed that receivers could not directly acquire such a

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Likewise, as an improvement over the simple correlation method, it is possible to perform a single operation covering all code phases for each frequency bin. The operation performed for each code phase bin involves forward FFT, element-wise multiplication in the frequency domain. inverse FFT, and

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The CNAV data is an upgraded version of the original NAV navigation message. It contains higher precision representation and nominally more accurate data than the NAV data. The same type of information (time, status, ephemeris, and almanac) is still transmitted using the new CNAV format; however,

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Acquisition of a given PRN number can be conceptualized as searching for a signal in a bidimensional search space where the dimensions are (1) code phase, (2) frequency. In addition, a receiver may not know which PRN number to search for, and in that case a third dimension is added to the search

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Acquiring a signal is the process of determining the frequency and code phase (both relative to receiver time) when it was previously unknown. Code phase must be determined within an accuracy that depends on the receiver design (especially the tracking loop); 0.5 times the duration of code chips

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The L5 CNAV data includes SV ephemerides, system time, SV clock behavior data, status messages and time information, etc. The 50 bit/s data is coded in a rate 1/2 convolution coder. The resulting 100 symbols per second (sps) symbol stream is modulo-2 added to the I5-code only; the resultant

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After a subframe has been read and interpreted, the time the next subframe was sent can be calculated through the use of the clock correction data and the HOW. The receiver knows the receiver clock time of when the beginning of the next subframe was received from detection of the Telemetry Word

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shift, the points where received PRN sequences begin may not differ from O by an exact integral number of milliseconds. Because of this, carrier frequency tracking along with PRN code tracking are used to determine when the received satellite's PRN code begins. Unlike the earlier computation of

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An immediate effect of having two civilian frequencies being transmitted is the civilian receivers can now directly measure the ionospheric error in the same way as dual frequency P(Y)-code receivers. However, users utilizing the L2C signal alone, can expect 65% more position uncertainty due to

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L1C is a civilian-use signal, to be broadcast on the L1 frequency (1575.42 MHz), which contains the C/A signal used by all current GPS users. The L1C signals will be broadcast from GPS III and later satellites, the first of which was launched in December 2018. As of January 2021, L1C

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A dataless acquisition aid is an additional signal, called a pilot carrier in some cases, broadcast alongside the data signal. This dataless signal is designed to be easier to acquire than the data encoded and, upon successful acquisition, can be used to acquire the data signal. This technique

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CNAV messages begin and end at start/end of GPS week plus an integer multiple of 12 seconds. Specifically, the beginning of the first bit (with convolution encoding already applied) to contain information about a message matches the aforesaid synchronization. CNAV messages begin with an 8-bit

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Each subframe begins with a Telemetry Word (TLM), which enables the receiver to detect the beginning of a subframe and determine the receiver clock time at which the navigation subframe begins. Next is the handover word (HOW) giving the GPS time (as the time for when the first bit of the next

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In a major departure from previous GPS designs, the M-code is intended to be broadcast from a high-gain directional antenna, in addition to a full-Earth antenna. This directional antenna's signal, called a spot beam, is intended to be aimed at a specific region (several hundred kilometers in

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The second advancement is to use forward error correction (FEC) coding on the NAV message itself. Due to the relatively slow transmission rate of NAV data (usually 50 bits per second), small interruptions can have potentially large impacts. Therefore, FEC on the NAV message is a significant

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Given the previous example to be processed with this method, assume real-valued data (as opposed to complex data, which would have in-phase and quadrature components), a sampling rate of 5 MHz, a signal window of 10 ms, and an intermediate frequency of 2.5 MHz. There will be

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of the GPS week. Expressing TOW count thus requires 19 bits (2 = 524,288). GPS time is a continuous time scale in that it does not include leap seconds; therefore the start/end of GPS weeks may differ from that of the corresponding UTC day by an integer (whole) number of seconds.

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varies by roughly 5 kHz due to the Doppler effect when the receiver is stationary; if the receiver moves, the variation is higher. The code frequency deviation is 1/1,540 times the carrier frequency deviation for L1 because the code frequency is 1/1,540 of the carrier frequency (see

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lock, it is necessary that there be an unobstructed line of sight from the receiver to the satellite. The receiver can then decode 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.

722:). Advances in the technology used on both the GPS satellites and the GPS receivers has made ionospheric delay the largest remaining source of error in the signal. A receiver capable of performing this measurement can be significantly more accurate and is typically referred to as a 5848:{\displaystyle S(t)={\sqrt {P_{\operatorname {I} }}}X_{\operatorname {I} }(t)\cos \left(\omega t+\phi _{0}\right)-{\sqrt {P_{\operatorname {Q} }}}X_{\operatorname {Q} }(t)\underbrace {\sin \left(\omega t+\phi _{0}\right)} _{-\cos \left(\omega t+\phi _{0}+{\frac {\pi }{2}}\right)},} 926:

The delay for PRN numbers 34 and 37 is the same; therefore their C/A codes are identical and are not transmitted at the same time (it may make one or both of those signals unusable due to mutual interference depending on the relative power levels received on each GPS receiver).

6107:). The down conversion does not affect the frequency deviation; it only shifts all the signal frequency components down. Since the frequency is referenced to the receiver time, the uncertainty in the receiver oscillator frequency adds to the frequency range of the search space. 1963:

The GPS week number is now represented as 13 bits, or 8192 weeks, and only repeats every 157.0 years, meaning the next return to zero won't occur until the year 2137. This is longer compared to the L1 NAV message's use of a 10-bit week number, which returns to zero every 19.6

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to one another. The 1 ms period of the C/A code corresponds to 299.8 km of distance, and each chip corresponds to a distance of 293 m. Receivers track these codes well within one chip of accuracy, so measurement errors are considerably smaller than 293 m.

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The common structure of all messages consists of 3 frames, as listed in the adjacent table. The content of subframe 3 varies according to its page number which is analogous to the type number of L2 CNAV and L5 CNAV messages. Pages are broadcast in an arbitrary order.

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The details of the W-code are secret, but it is known that it is applied to the P-code at approximately 500 kHz, about 20 times slower than the P-code chip rate. This has led to semi-codeless approaches for tracking the P(Y) signal without knowing the W-code.

6470:, from the navigation message is used to calculate precisely where the satellite was at the start of the message. A more sensitive receiver will potentially acquire the ephemeris data more quickly than a less sensitive receiver, especially in a noisy environment. 2847:). Both codes are 10,230 chips long, transmitted at 10.23 Mchip/s (1 ms repetition period), and are generated identically (differing only in initial states). Then, I5 is modulated (by exclusive-or) with navigation data (called L5 CNAV) and a 10-bit 950:

at 00:00:00 GPS time. For reference, the GPS epoch was Sunday January 6, 1980 at 00:00:00 UTC, but GPS does not follow UTC exactly because GPS time does not incorporate leap seconds. Thus, GPS time is ahead of UTC by an integer (whole) number of seconds.

5370:, with the same meaning as with the other civilian signals. Each message contains the week number modulo 8,192 or equivalently, the 13 least significant bits of the week number, allowing direct specification of any date within a cycling 157-year range. 528:

and are only broadcast by newer satellites (or not yet at all). Furthermore, as of January 2021, none of these three signals are yet considered to be fully operational for civilian use. In addition to the four aforementioned signals, there are

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Every packet contains an alert flag, to be set if the satellite data can not be trusted. This means users will know within 12 seconds if a satellite is no longer usable. Such rapid notification is important for safety-of-life applications, such as

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Satellite data is updated typically every 24 hours, with up to 60 days data loaded in case there is a disruption in the ability to make updates regularly. Typically the updates contain new ephemerides, with new almanacs uploaded less frequently.

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The I5-code and Q5-code are generated using the same structure but with different parameters. These codes are the combination (by exclusive-or) of the output of 2 differing linear-feedback shift registers (LFSRs) which are selectively reset.

2785:, using a 10.23 MHz subcarrier against the 5.115 MHz code. This signal will have an overall bandwidth of approximately 24 MHz, with significantly separated sideband lobes. The sidebands can be used to improve signal reception. 5601:

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 where the low-bitrate message data is encoded with a high-rate

1144:). The two types use very similar formats. Subframes 1 to 3 are the same, while subframes 4 and 5 are almost the same. Each message type contains almanac data for all satellites using the same navigation message type but not the other. 3310:) which is expanded with a fixed 7-bit sequence to the required 10,230 bits. This 10,230-bit sequence is the ranging code and varies between PRN numbers and between the pilot and data components. The ranging codes are described by: 6123:

The lower PRN numbers range from 1 to 32 and therefore there are 32 PRN numbers to search for when the receiver does not have information to narrow the search in this dimension. The higher PRN numbers range from 33 to 66. See

6027:. This is a formula for the ideal case (which is not attained in practice) as it does not model timing errors, noise, amplitude mismatch between components or quadrature error (when components are not exactly in quadrature). 3248:(a secondary code that has a lower rate than the ranging code and is also predefined, like the ranging code). Of the total L1C signal power, 25% is allocated to the data and 75% to the pilot. The modulation technique used is 2742:

original design, users had to first lock onto the C/A code and then transfer the lock to the P(Y)-code. Later, direct-acquisition techniques were developed that allowed some users to operate autonomously with the P(Y)-code.

3244:), instead of carriers in quadrature as with L5. The PRN codes are 10,230 chips long and transmitted at 1.023 Mchip/s, thus repeating in 10 ms. The pilot component is also modulated by an overlay code called L1C 5606:(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 5403:

with the most significant bit and finally the most significant bit is appended as the most significant bit of the previous result to obtain the final 52 bits. Subframes 2 and 3 are individually expanded with a 24-bit

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Each frame contains (in subframe 1) the 10 least significant bits of the corresponding GPS week number. Note that each frame is entirely within one GPS week because GPS frames do not cross GPS week boundaries. Since

2754:. Similar to the new CNAV, this new MNAV is packeted instead of framed, allowing for very flexible data payloads. Also like CNAV it can utilize Forward Error Correction (FEC) and advanced error detection (such as a 6637:, Litton, James D.; Russell, Graham & Woo, Richard K., "Method and apparatus for digital processing in a global positioning system receiver", issued 1996-11-19, assigned to Leica Geosystems 2793:

The L5 signal provides a means of radionavigation secure and robust enough for life critical applications, such as aircraft precision approach guidance. The signal is broadcast in a frequency band protected by the

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of a window of the digitalized signal with a set of locally generated replicas. The locally generated replicas vary in carrier frequency and code phase to cover all the already mentioned search space which is the

3201:. L5 CNAV messages begin and end at start/end of GPS week plus an integer multiple of 6 seconds (this applies to the beginning of the first bit to contain information about a message, as is the case for L2 CNAV). 1466:

the receiver hardware becomes more capable, the time to lock onto the satellite signals shrinks; however, the ephemeris data requires 18 to 36 seconds before it is received, due to the low data transmission rate.

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A major component of the modernization process is a new military signal. Called the Military code, or M-code, it was designed to further improve the anti-jamming and secure access of the military GPS signals.

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thereby enabling computation of the transit time and thus the pseudorange. The receiver is potentially capable of getting a new pseudorange measurement at the beginning of each subframe or every 6 seconds.

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to the resolution of the truncated TOW count thereof. Equivalently, the truncated TOW count is the time duration since the last GPS week start/end to the beginning of the next frame in units of 6 seconds.

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length code (called CL). The CM code is 10,230 chips long, repeating every 20 ms. The CL code is 767,250 chips long, repeating every 1,500 ms. Each signal is transmitted at 511,500 chips per second (

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The following table depicts the local replicas that would be compared against the digitalized signal in this example. "•" means a single local replica while "..." is used for elided local replicas:

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In this section, one possible procedure is described for L1 C/A acquisition and tracking, but the process is very similar for the other signals. The described procedure is based on computing the

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Besides redundancy and increased resistance to jamming, a critical benefit of having two frequencies transmitted from one satellite is the ability to measure directly, and therefore remove, the

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Specifically, for all code phases in the search space, the digitalized signal window is multiplied element by element with a local replica of the code (with no carrier), then processed with a

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An interesting side effect of having each satellite transmit four separate signals is that the MNAV can potentially transmit four different data channels, offering increased data bandwidth.

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most significant bit. Using this convention, the LFSR shifts from most significant bit to least significant bit and when seen in big endian order, it shifts to the right. The states called

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rates, but the signals use encrypted coding, restricting use to authorized parties. Some limited use of restricted signals can still be made by civilians without decryption; this is called

4906: 6025: 1498: 699:) modulation technique. The P(Y)-code is transmitted on both the L1 and L2 frequencies as a 10.23 MHz signal using the same BPSK modulation, however the P(Y)-code carrier is in 6987:, § 3.3.3.1.1 (p. 39) Note that synchronization is described in the IS in terms of X1 epochs, which occur each 1.5 seconds and are synchronized with start/end of GPS week. 6161:

Using a complex carrier allows the replicas to match the digitalized signal regardless of the signal's carrier phase and to detect that phase (the principle is the same used by the

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bandwidth is used. Only a small fraction of the available packet types have been defined; this enables the system to grow and incorporate advances without breaking compatibility.

4657: 4437: 4163: 4104: 580:(BPSK). Only a limited number of central frequencies are used. Satellites using the same frequency are distinguished by using different ranging codes. In other words, GPS uses 4055: 3972: 5191: 5162: 5113: 5084: 4301: 4267: 4343: 1563:

When compared to the C/A signal, L2C has 2.7 dB greater data recovery and 0.7 dB greater carrier-tracking, although its transmission power is 2.3 dB weaker.

4837: 4077: 4544: 6393:). Only the components (or bins) within 5 kHz of the central frequency are examined, which is the range from 2.495 MHz to 2.505 MHz, and it is covered by 4129: 2642: 2615: 1210:

or dual-frequency receivers. However, it is often better than no correction, since ionospheric error is the largest error source for a single-frequency GPS receiver.

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and their arguments are the integer number of chips elapsed (starting at 0) since start/end of GPS week, or equivalently since the origin of the GPS time scale (see

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error for that satellite. Without such a measurement, a GPS receiver must use a generic model or receive ionospheric corrections from another source (such as the

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to calculate the position of each satellite in orbit and also to provide information about the time and status of the entire satellite constellation, called the

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signals are not yet broadcast, and only four operational satellites are capable of broadcasting them. L1C is expected on 24 GPS satellites in the late 2020s.

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Tracking is the process of continuously adjusting the estimated frequency and phase to match the received signal as close as possible and therefore is a

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is due to the fact it is reset 1 cycle before its natural period (which is 8,191) so that the next repetition becomes offset by 1 cycle with respect to

7605: 6048:

would alias into it) and digitalized; these steps may be chained in a different order. Note that aliasing is sometimes intentional (specifically, when

485:

GPS signals include ranging signals, which are used to measure the distance to the satellite, and navigation messages. The navigation messages include

7631: 7580: 7549: 1080:

In addition to the PRN ranging codes, a receiver needs to know the time and position of each active satellite. GPS encodes this information into the

6829: 3188:(otherwise, since both sequences would repeat, I5 and Q5 would repeat within any 1 ms period as well, degrading correlation characteristics). 6165:). The dot product is a complex number; its magnitude represents the level of similarity between the replica and the signal, as with an ordinary 410: 1967:

There is a packet that contains a GPS-to-GNSS time offset. This allows better interoperability with other global time-transfer systems, such as

2868:, provides sharper autocorrelation (in absolute terms, not relative to chip time duration) and requires a higher sampling rate at the receiver. 1088:

it onto both the C/A and P(Y) ranging codes at 50 bit/s. The navigation message format described in this section is called LNAV data (for

6390: 5377:

the integer number of 2 hour periods elapsed since the latest start/end of week. It has range 0 to 83 (inclusive), requiring 7 bits to encode.

2851:

clocked at 1 kHz. Similarly, the Q5-code is then modulated but with only a 20-bit Neuman-Hofman code that is also clocked at 1 kHz.

6150:

of the frequency search space and the code phase search space. The carrier is a complex number where real and imaginary components are both

6074:. Note that acquisition is performed to start using a particular satellite, but tracking is performed as long as that satellite is in use. 6356:

As an improvement over the simple correlation method, it is possible to implement the computation of dot products more efficiently with a

5054:

For PRN numbers 1 to 63 they are the truncated outputs of maximal period LFSRs which vary in initial conditions and feedback polynomials.

7565: 7500: 966: 771:

The C/A codes are generated by combining (using "exclusive or") two bit streams, each generated by two different maximal period 10 stage

232: 7445: 1133:

A frame begins at the start of the GPS week and every 30 seconds thereafter. Each week begins with the transmission of almanac page 1.

400: 368: 6360:. Instead of performing one dot product for each element in the Cartesian product of code and frequency, a single operation involving 7590: 7378: 7346: 6722: 6176:

As an example, assume that the granularity for the search in code phase is 0.5 chips and in frequency is 500 Hz, then there are

5340:

The L1C navigation data (called CNAV-2) is broadcast in 1,800 bits long (including FEC) frames and is transmitted at 100 bit/s.

5047:

The overlay codes are 1,800 bits long and is transmitted at 100 bit/s, synchronized with the navigation message encoded in L1C

3176:

are maximal length LFSRs. The modulo operations correspond to resets. Note that both are reset each millisecond (synchronized with

2675: 378: 6141:

The simplest way to acquire the signal (not necessarily the most effective or least computationally expensive) is to compute the

3213:

navigation band. The frequency was chosen so that the aviation community can manage interference to L5 more effectively than L2.

1560:. The long, dataless sequence provides for approximately 24 dB greater correlation (~250 times stronger) than L1 C/A-code. 7438: 1509:

Modernized GPS civilian signals have two general improvements over their legacy counterparts: a dataless acquisition aid and

743:

with a period of 1023 chips transmitted at 1.023 Mchip/s, causing the code to repeat every 1 millisecond. They are

358: 5957: 5919: 1589: 1481:

House in 1998 heralded the beginning of these changes, and in 2000, the U.S. Congress reaffirmed the effort, referred to as

2799: 611:. However, unlike typical QAM systems where a single bit stream is split into two, half-symbol-rate bit streams to improve 6052:

is used) but filtering is still required to discard frequencies not intended to be present in the digital representation.

5392:

TOI is the only content of subframe 1. The week number and ITOW are contained in subframe 2 along with other information.

615:, the in-phase and quadrature components of GPS signals are modulated by separate (but functionally related) bit streams. 7575: 5890: 5861: 5384:

the integer number of 18 second periods elapsed since the period represented by the current ITOW to the beginning of the

1979: 6063:

it as long as that satellite is in use; both are performed in the digital domain in by far most (if not all) receivers.

1994:

preamble which is a fixed bit pattern and whose purpose is to enable the receiver to detect the beginning of a message.

338: 7662: 7554: 6479: 139: 6774: 6098:

The frequency range of the search space is the band where the signal may be located given the receiver knowledge. The

576:

in the GPS interface specification documents) transmit simultaneously several ranging codes and navigation data using

7297: 1978:

The extra bandwidth enables the inclusion of a packet for differential correction, to be used in a similar manner to

1459: 438: 1593:

numbers and for CM/CL. The feedback polynomial/mask is the same for CM and CL. The ranging codes are thus given by:

5358:

The time of messages (not to be confused with clock correction parameters) is expressed in a different format than

3249: 2720:. FEC encoding is performed independently of navigation message boundaries; this follows from the above equations. 2672:

Since the FEC encoded bit stream runs at 2 times the rate than the non FEC encoded bit as already described, then

619: 2840: 1926: 608: 504:

There are four GPS signal specifications designed for civilian use. In order of date of introduction, these are:

7410: 5611:

equipment with a proper decryption key. Both the C/A and P(Y) codes impart the precise time-of-day to the user.

5413: 1934:

some versatility. However, for some message types there are lower bounds on how often they will be transmitted.

7570: 7485: 7312: 6764: 1968: 772: 224: 4865: 1130:

1 through 25 of the 25-page almanac. The almanac is 15,000 bits long and takes 12.5 minutes to transmit.

7600: 7585: 5995: 5603: 5409: 2564:

is the raw (non FEC encoded) navigation data, consisting of the simple concatenation of the 300-bit messages.

1556:

with the CNAV Navigation Message (see below), whereas CL does not contain any modulated data and is called a

953:

The P code is public, so to prevent unauthorized users from using or potentially interfering with it through

715: 581: 471: 240: 7595: 628:(SVN) which does not change during its lifetime. In addition, all operating satellites are numbered with a 600: 4713: 942:

long and fast code so they would first "bootstrap" themselves with the C/A code to acquire the spacecraft

695:

The C/A code is transmitted on the L1 frequency as a 1.023 MHz signal using a bi-phase shift keying (

604:(in reference to the fact that the sequences are predictable yet that they statistically resemble noise). 6170: 4406: 6836: 4134: 680:

For the ranging codes and navigation message to travel from the satellite to the receiver, they must be

6373: 6366: 5003: 4943: 4911: 4788: 3999: 1191: 6830:"Interface Specification IS-GPS-200, Revision D: Navstar GPS Space Segment/Navigation User Interfaces" 6634: 5399:. Specifically, the 8 least significant bits are BCH encoded to generate 51 bits, then combined using 4031: 3948: 2821:

Pre-operational signal with message set "unhealthy" until sufficient monitoring capability established

1533:

Unlike the C/A code, L2C contains two distinct PRN code sequences to provide ranging information; the

1501:

A visual example of the GPS constellation in motion with the Earth rotating. Notice how the number of

1136:

There are two navigation message types: LNAV-L is used by satellites with PRN numbers 1 to 32 (called

692:(10.23 MHz × 154) called L1; and a second at 1227.60 MHz (10.23 MHz × 120), called L2. 7495: 7016: 5167: 5138: 5089: 5060: 577: 479: 455: 203: 4613: 4272: 4238: 3833: 3430: 2306: 1475: 7480: 4730:

is the remainder of division (or modulo) operation, which differs to the notation in statements of

4326: 4082: 1946: 1510: 1170: 170: 117: 6615: 4820: 4731: 4060: 2997:

a PRN number; both phases and a single PRN are required for the L5 signal from a single satellite.

5405: 2755: 1989:

Finally, the system is designed to support 63 satellites, compared with 32 in the L1 NAV message.

1957: 636:(PRN number) which uniquely identifies the ranging codes that a satellite uses. There is a fixed 467: 308: 268: 3240:) component. These components use carriers with the same phase (within a margin of error of 100 764: 607:

Some satellites transmit several BPSK streams at the same frequency in quadrature, in a form of

7289:

The Telecommunications Handbook: Engineering Guidelines for Fixed, Mobile and Satellite Systems

6361: 6173:

of the dot product is an approximation of the corresponding carrier in the digitalized signal.

5057:

For PRN numbers 64 to 210 they are truncated Gold codes generated by combining 2 LFSR outputs (

1462:

guarantees that during normal operations a new almanac will be uploaded at least every 6 days.

946:, produce an approximate time and position fix, and then acquire the P-code to refine the fix. 569: 288: 7101: 7058: 6562: 3263:

Assured of 1.5 dB increase in minimum C/A code power to mitigate any noise floor increase

1579:

Available on 24 GPS satellites with ground segment control capability by 2023 (as of Jan 2020)

6900: 6866: 6854: 5351:

use a dedicated message type for ephemeris data, all CNAV-2 frames include that information.

2782: 775:(LFSR). Different codes are obtained by selectively delaying one of those bit streams. Thus: 431: 348: 98: 32: 6946:

Numbered starting from 1. Bit 1 is the first bit in the message and bit 300 is the last one.

6113:

The ranging code has a period of 1,023 chips each of which lasts roughly 0.977 μs (see

4519: 1186:

consists of coarse orbit and status information for each satellite in the constellation, an

759:

when they are almost exactly aligned. Each satellite uses a unique PRN code, which does not

688:. In the case of the original GPS design, two frequencies are utilized; one at 1575.42 7461: 4741: 4664: 4547: 4511: 4444: 4380: 3222: 2518: 2491: 459: 248: 198: 124: 7385: 7353: 7231: 7142: 7140: 6798: 6729: 8: 7667: 7531: 7521: 6676: 6082:

and is typically shorter than the duration of navigation data bits, which is 20 ms.

612: 160: 108: 7255: 6595: 4109: 2814:. L5 signals have been broadcast beginning in April 2014 on satellites that support it. 2622: 2595: 7621: 7137: 6990: 6966: 6810: 6654: 6605: 6603: 6155: 5118: 4983: 4842: 4768: 4691: 4593: 4573: 4553: 4493: 4471: 4386: 4362: 4306: 4206: 4170: 4057:; it is introduced only to allow a more clear notation. To obtain a direct formula for 3977: 2651: 2569: 2547: 2003: 1950: 1719: 594: 80: 50: 7167: 6786: 1505:

from a given point on the Earth's surface, in this example at 45°N, changes with time.

7541: 7293: 7267: 7243: 7157: 7155: 7113: 6928: 6700: 6688: 6514: 6502: 6423: 6357: 6166: 6162: 6147: 6099: 6078: 6071: 2835:

Two PRN ranging codes are transmitted on L5 in quadrature: the in-phase code (called

1203: 1199: 1187: 760: 711: 180: 165: 7219: 7197: 7195: 7125: 6600: 6526: 3209:

Broadcast on the L5 frequency (1176.45 MHz, 10.23 MHz × 115), which is an

763:

well with any other satellite's PRN code. In other words, the PRN codes are highly

700: 674: 424: 175: 7152: 1517:

improves acquisition of the GPS signal and boosts power levels at the correlator.

1202:

error by using a global ionospheric model. The corrections are not as accurate as

7287: 7192: 7009: 5296: 4346: 3296: 3256:(TMBOC) is BOC(1,1) for all except 4 of 33 cycles, when it switches to BOC(6,1). 2865: 954: 756: 1953:, so while the navigation message is 25-bit/s, a 50-bit/s signal is transmitted. 642: 7430: 6885: 6451: 5164:

has one of the 4 feedback polynomials used overall (among PRN numbers 64–210).

3266:

Data-less signal component pilot carrier improves tracking compared with L1 C/A

2772: 1109:

The almanac: status and low-resolution orbital information for every satellite.

669: 388: 155: 129: 2590:

navigation data bits elapsed since an arbitrary point in time (starting at 0).

524:

and is broadcast by all currently operational satellites. L2C, L5 and L1C are

7656: 7626: 7325: 7037: 6922: 6049: 6039:

Demodulating and Decoding GPS Satellite Signals using the Coarse/Acquisition

2811: 2807: 704: 492: 475: 462:. Receivers on or near the Earth's surface can determine location, time, and 19: 5400: 4224: 3210: 2978: 744: 685: 549: 113: 6582: 5193:

has the same feedback polynomial for all PRN numbers in the range 64–210.

2861:

Higher transmitted power than L1/L2 signal (~3 dB, or 2× as powerful)

6427: 6142: 5607: 3241: 2750:

A little more is known about the new navigation message, which is called

1546: 1198:. Finally, the almanac allows a single-frequency receiver to correct for 943: 899:

is a delay (by an integer number of periods) specific to each PRN number

534: 70: 7516: 4590:). It is defined in the Interface Specification (IS) as a 1-based index 3277:

Developmental signal with message set "unhealthy" and no navigation data

657:(C/A) code, which is freely available to the public, and the restricted 27: 5388:

message. It has range 0 to 399 (inclusive) and requires 9 bits of data.

5362:

of the previous civilian signals. Instead it consists of 3 components:

3180:

epochs). In addition, the extra modulo operation in the description of

1085: 553: 7414: 6467: 6040: 5343:

The frames of L1C are analogous to the messages of L2C and L5. While

3260:

Implementation will provide C/A code to ensure backward compatibility

3151:

is the initial state specified for the phase and PRN number given by

1553: 1140:) and LNAV-U is used by satellites with PRN numbers 33 to 63 (called 1103: 965:. The Y-code is what the satellites have been transmitting since the 937:

Error analysis for the Global Positioning System § Anti-spoofing

740: 681: 637: 487: 149: 75: 4839:

are the first bits the corresponding Weil code; the next 7 bits are

2827:

Scheduled to be available on 24 GPS satellites by approximately 2027

1745:

is the integer number of CM and CL chip periods since the origin of

7526: 6151: 5396: 1588:

The civil-moderate and civil-long ranging codes are generated by a

1497: 1152:

enabling computation of the transit time and thus the pseudorange.

463: 328: 145: 134: 7559: 6596:

Civilian GPS Receivers Actually do Have Access to the L2 Frequency

4468:

is an intermediate code called Weil code, with the same domain as

1716:

are the initial states for CM and CL respectively. for PRN number

7636: 7490: 6921:

This article incorporates text from this source, which is in the

6438:

in contrast with the previous method, which yields more accurate

6055:

For each satellite used by the receiver, the receiver must first

2803: 1972: 208: 65: 42: 2854:

Compared to L1 C/A and L2, these are some of the changes in L5:

1925:

instead of using a frame / subframe architecture, it uses a new

1692:) is the output of the LFSR when initialized with initial state 7475: 7207: 5614:

Each composite signal (in-phase and quadrature phase) becomes:

1542: 858:

is the output of the second LFSR whose generator polynomial is

318: 278: 216: 6416: 6035: 4859:; the remaining bits are the remaining bits of the Weil code. 836:

is the output of the first LFSR whose generator polynomial is

23:

Artist's conception of GPS Block II-F satellite in Earth orbit

7641: 4142: 3789: 3369: 2817:

The status of the L5 signal as of July 3, 2023 is:

2713:{\displaystyle t=\left\lfloor {\tfrac {t'}{2}}\right\rfloor } 1106:: precise orbital information for the transmitting satellite. 624:

Satellites are uniquely identified by a serial number called

103: 7189:, § 3.2.2.1.1 (p. 7–8) using a different notation. 3273:

The current status of the L1C signal as of July 3, 2023 is:

3252:(1,1) for the data signal and TMBOC for the pilot. The time 1566:

The current status of the L2C signal as of July 3, 2023 is:

6445: 3921: 3652: 3253: 2464: 1469: 1207: 1095:

The navigation message conveys information of three types:

719: 696: 589: 405: 298: 3161:

is the integer number of chip periods since the origin of

1941:

There are many important changes in the new CNAV message:

4738:

According to the formula above and the GPS IS, the first

2795: 1195: 961:, a cryptographically generated sequence, to produce the 910:

The arguments of the functions therein are the number of

689: 4570:

into the ranging code (specific for PRN number and code

4201:

or equivalently, since any GPS second (starting from 0).

3165:

or equivalently, since any GPS second (starting from 0).

1749:

or equivalently, since any GPS second (starting from 0).

1573:

Broadcasting from 25 GPS satellites (as of July 3, 2023)

969:

was enabled. The encrypted signal is referred to as the

923:

may have a negative argument using the above equation).

653:

The original GPS design contains two ranging codes: the

6783:, § 6.2.4 (p. 50), § 3.3.4 (p. 41). 6422:

extra processing so that overall, it computes circular

3280:

Broadcasting from 6 GPS satellites (as of July 3, 2023)

2806:(Block IIR-M), and is available on all satellites from 2648:

navigation data bits elapsed since the same epoch than

1982:

and which can be used to correct the L1 NAV clock data.

5999: 5985:{\displaystyle \scriptstyle X_{\operatorname {Q} }(t)} 5961: 5947:{\displaystyle \scriptstyle X_{\operatorname {I} }(t)} 5923: 5894: 5865: 3269:

Enables greater civil interoperability with Galileo L1

2690: 2542:

are the unordered outputs of the convolutional encoder

903:; it is designated in the GPS interface specification. 661:(P) code, usually reserved for military applications. 7083:"Satellite Navigation - GPS - Policy - Modernization" 6450:

Since the carrier frequency received can vary due to

5998: 5960: 5922: 5893: 5864: 5623: 5170: 5141: 5121: 5092: 5063: 5006: 4986: 4946: 4914: 4868: 4845: 4823: 4791: 4771: 4744: 4716: 4694: 4667: 4616: 4596: 4576: 4556: 4522: 4496: 4474: 4447: 4409: 4389: 4365: 4329: 4309: 4275: 4241: 4209: 4173: 4137: 4112: 4085: 4063: 4034: 4002: 3980: 3951: 3319: 2678: 2654: 2625: 2598: 2572: 2550: 2521: 2494: 2015: 1722: 556:. The format of civilian signals is described in the 5300: 4940:

does not account for the hypothetical case in which

4187:

is the integer number of L1C chip periods (which is

3295:

The L1C pilot and data ranging codes are based on a

919:

is 1,023 chips (this provision is necessary because

6067:(approx. 0.489 μs) is a representative value. 5909:{\displaystyle \scriptstyle P_{\operatorname {Q} }} 5880:{\displaystyle \scriptstyle P_{\operatorname {I} }} 4379:is an intermediate code: a Legendre sequence whose 2874:

Uses the Aeronautical Radionavigation Services band

641:numbers for the GPS constellation are published at 6835:. Navstar GPS Joint Program Office. Archived from 6019: 5984: 5946: 5908: 5879: 5847: 5185: 5156: 5127: 5107: 5078: 5024: 4992: 4972: 4932: 4900: 4851: 4831: 4809: 4777: 4757: 4722: 4700: 4680: 4651: 4602: 4582: 4562: 4538: 4502: 4480: 4460: 4431: 4395: 4371: 4337: 4315: 4295: 4261: 4215: 4179: 4157: 4123: 4098: 4071: 4049: 4020: 3986: 3966: 3931: 3046:The output of two 13-stage LFSRs with clock state 2858:Improved signal structure for enhanced performance 2712: 2660: 2636: 2609: 2578: 2556: 2534: 2507: 2474: 1728: 1099:The GPS date and time, and the satellite's status. 7632:United Kingdom Global Navigation Satellite System 4765:bits (equivalently, up to the insertion point of 3974:is the ranging code for PRN number and component 2729:ionospheric error than with the L1 signal alone. 1772:cycles for LM (just before reset in both cases). 1570:Pre-operational signal with message set "healthy" 1213: 1121:1,500 bits long, divided into five 6-second 7654: 7460: 6633: 2993:∈ {I, Q} for in-phase and quadrature-phase, and 1997: 1190:, and information to relate GPS derived time to 620:List of GPS satellites § PRN to SVN history 7010:"Interface Specification IS-GPS-200 Revision D" 6758:"Essentials of Satellite Navigation Compendium" 6583:"Codeless/Semi-Codeless GPS Access Commitments" 5135:is the PRN number) whose initial state varies. 2761: 1114:that the satellite can be used for navigation. 703:with the C/A carrier (meaning it is 90° out of 5590: 5504: 5470: 1342: 1228: 991: 751:and the result phase modulates the carrier as 7446: 6752: 6750: 4079:start from the right side of the formula for 3306:used to build an intermediate code (called a 1117:The navigation message consists of 30-second 432: 6717: 6715: 6624:, § 3.2.1.3, table 3-Ia (p. 4, 7). 6114: 6104: 6030: 5581: 5416:as a single unit using a block interleaver. 5344: 5196: 3286:Available on 24 GPS satellites in late 2020s 3198: 3177: 2871:Longer spreading codes (10× longer than C/A) 2775:are deployed, which began in December 2018. 2723: 1576:Began launching in 2005 with GPS Block IIR-M 1549:together to form a 1,023,000-chip/s signal. 557: 6527:"GPS Interface Specification (GPS-IS-800E)" 6515:"GPS Interface Specification (GPS-IS-705F)" 6503:"GPS Interface Specification (GPS-IS-200K)" 6417:Circular correlation with Fourier transform 3204: 2802:. It was first demonstrated from satellite 1739:mod is the remainder of division operation. 1476:GPS Block III § New navigation signals 752: 7453: 7439: 6959:message. It uses the same format than the 6895: 6893: 6747: 6006: 5419: 5348: 4688:is the Weil index for PRN number and code 3221:"L1C" redirects here. For other uses, see 2745: 1775: 1521:improvement in overall signal robustness. 1349: 1235: 998: 734: 545:access, and this is officially supported. 439: 425: 406:Spatial Reference System Identifier (SRID) 401:International Terrestrial Reference System 7379:"NAVSTAR GPS User Equipment Introduction" 7347:"NAVSTAR GPS User Equipment Introduction" 7285: 6723:"NAVSTAR GPS User Equipment Introduction" 6712: 6652: 6485: 4966: 4894: 4425: 4149: 3896: 3796: 3376: 1960:, against which integrity can be checked. 755:. These codes only match up, or strongly 563: 7286:Penttinen, Jyrki T. J. (16 March 2015). 6446:Tracking and navigation message decoding 6034: 4901:{\displaystyle 0\leq p'_{i}\leq 10\,222} 4323:is the PRN number of the satellite, and 4227:identifying a PRN number and a code (L1C 3191: 1496: 1470:Modernization and additional GPS signals 886:+ 1 and initial state is also 1111111111 668: 664: 26: 18: 7110:, tables 3-Ia, 3-Ib (p. 5 7). 6890: 6435: 6401:as in the previous case, thus in total 6125: 6020:{\displaystyle \scriptstyle (=\;\pm 1)} 1894:Ionospheric and group delay correction 748: 505: 7655: 7273: 7261: 7249: 7237: 7225: 7213: 7201: 7186: 7173: 7161: 7146: 7131: 7119: 7107: 6996: 6984: 6972: 6934: 6875:, § 40.3.3.5.1 (p. 207–208). 6872: 6863:, § 20.3.3.5.1 (p. 108–109). 6860: 6816: 6804: 6792: 6780: 6706: 6694: 6682: 6621: 6609: 6525: 6513: 6501: 7434: 6136: 5577: 5494: 5460: 4510:is a 7-bit long sequence defined for 4349:(not variables) that indicate the L1C 2800:aeronautical radionavigation services 2006:used to encode CNAV is described by: 1670:are the ranging codes for PRN number 980: 648: 6557: 6555: 6553: 6551: 6549: 6547: 6411:104,346 complex frequency components 6351: 5408:, then individually encoded using a 5395:Subframe 1 is encoded by a modified 4980:, which would cause the instance of 4723:{\displaystyle \operatorname {mod} } 3283:Began launching in 2018 with GPS III 3080:+ 1, and initial state 1111111111111 2732: 1980:satellite based augmentation systems 848:+ 1, and initial state is 1111111111 584:. The ranging codes are also called 7240:, § 6.3.1.2 (p. 110–111). 7185:The ranging codes are described in 6955:TOW count for the beginning of the 6807:, § 20.3.3.3.1.1 (p. 90). 6685:, § 20.3.4.1 (p. 63–130). 6655:"Satellite Almanac Life Expectancy" 6466:Then the orbital position data, or 5042: 4432:{\displaystyle 0\leq n\leq 10\,222} 3892: 3885: 3857: and there is an integer 3290: 3232:L1C consists of a pilot (called L1C 2824:Broadcasting from 18 GPS satellites 2617:is the FEC encoded navigation data. 2453: 2446: 2371: 2364: 1492: 729: 548:The interface to the User Segment ( 411:Universal Transverse Mercator (UTM) 373:European Terrestrial Ref. Sys. 1989 16:Signals broadcast by GPS satellites 13: 6612:, tables 3-Ia, 3-Ib (p. 6–8). 6480:In-phase and quadrature components 6365:bins are much closely spaced in a 5992:represent codes with/without data 5967: 5929: 5900: 5871: 5729: 5717: 5658: 5646: 5595:Safety-of-Life (SoL) Pilot signal 4158:{\displaystyle t{\bmod {10\,230}}} 2878: 1583: 283:Ordnance Survey Great Britain 1936 249:Discrete Global Grid and Geocoding 140:Horizontal position representation 14: 7679: 7264:, § 3.2.3.2 (p. 19–20). 6653:Petovello, Mark (November 2008). 6544: 5585:Safety-of-Life (SoL) Data signal 5025:{\displaystyle {\text{L1C}}'_{i}} 4973:{\displaystyle p'_{i}>10\,222} 4933:{\displaystyle {\text{L1C}}'_{i}} 4810:{\displaystyle {\text{L1C}}'_{i}} 4021:{\displaystyle {\text{L1C}}'_{i}} 3254:multiplexed binary offset carrier 2767:for SVN62/PRN25 on 5 April 2011. 1929:format made of 12-second 300-bit 1513:(FEC) coding of the NAV message. 930: 554:Interface Control Documents (ICD) 520:. L1 C/A is also called the 7326:"How a GPS Receiver Gets a Lock" 7149:, § 3.3.3.1.1 (p. 39). 6999:, § 3.3.3.1.1 (p. 39). 6975:, § 30.3.4.1 (p. 190). 6916: 6819:, § 20.3.4.1 (p. 130). 6169:of real-valued time series. The 5557: 4550:insertion index of the sequence 4050:{\displaystyle {\text{L1C}}_{i}} 3967:{\displaystyle {\text{L1C}}_{i}} 1419:A-S flags for PRN numbers 33–63, 466:using this information. The GPS 199:Global Nav. Sat. Systems (GNSSs) 49: 7403: 7384:. US Government. Archived from 7371: 7352:. US Government. Archived from 7339: 7318: 7306: 7279: 7179: 7176:, § 3.2.1.6.1 (p. 4). 7075: 7051: 7030: 7002: 6978: 6949: 6940: 6878: 6822: 6795:, § 20.3.3.1 (p. 87). 6728:. US Government. Archived from 6697:, § 6.4.1 (p. 63–64). 6490: 6440:carrier frequency determination 5186:{\displaystyle {\text{S2}}_{i}} 5157:{\displaystyle {\text{S1}}_{i}} 5108:{\displaystyle {\text{S2}}_{i}} 5079:{\displaystyle {\text{S1}}_{i}} 4908:. For clarity, the formula for 2864:Wider bandwidth provides a 10× 1452: 773:linear-feedback shift registers 609:quadrature amplitude modulation 533:with published frequencies and 363:N. American Vertical Datum 1988 7276:, § 3.2.3.1 (p. 18). 7252:, § 3.5.5.1 (p. 69). 7204:, table 3.2-2 (p. 10–12). 7122:, § 3.3.2.2 (p. 14). 6937:, § 30.3.3 (p. 140). 6709:, § 40.3.3 (p. 207). 6646: 6627: 6589: 6575: 6085: 6013: 6000: 5978: 5972: 5940: 5934: 5740: 5734: 5669: 5663: 5633: 5627: 5499:Encrypted precision P(Y) code 5465:Encrypted precision P(Y) code 4652:{\displaystyle p'_{i}=p_{i}-1} 4296:{\displaystyle ({\text{D}},n)} 4290: 4276: 4262:{\displaystyle ({\text{P}},n)} 4256: 4242: 4197: μs) since the origin of 3900: 3886: 3818: 3812: 3802: 3785: 3766: 3763: 3754: 3748: 3735: 3729: 3712: 3670: 3609: 3592: 3522: 3495: 3454: 3443: 3415: 3404: 3382: 3362: 3342: 3336: 2457: 2447: 2375: 2365: 2291: 2280: 2265: 2253: 2244: 2232: 2223: 2211: 2202: 2190: 2181: 2175: 2162: 2156: 2139: 2127: 2118: 2106: 2097: 2085: 2076: 2064: 2055: 2049: 2036: 2030: 1975:, both of which are supported. 1807:PRN of transmitting satellite 1214:Structure of subframes 4 and 5 560:which is a subset of the ICD. 393:Internet link to a point 2010 323:Geodetic Reference System 1980 241:Quasi-Zenith Sat. Sys. (QZSS) 1: 7228:, § 3.2.2.1 (p. 6). 7134:, § 20.3.3 (p. 41). 5475:Coarse/acquisition (C/A) code 5410:low-density parity-check code 5375:interval time of week (ITOW): 4338:{\displaystyle {\text{P, D}}} 4106:and replace all instances of 4099:{\displaystyle {\text{L1C}}'} 3035:are intermediate codes, with 1998:Forward error correction code 1949:(FEC) provided by a rate 1/2 1902:Earth orientation parameters 1758:in the IS are obtained after 716:Wide Area Augmentation System 601:pseudorandom binary sequences 582:code-division multiple access 472:2nd Space Operations Squadron 383:Chinese obfuscated datum 2002 7462:Satellite navigation systems 7059:"GPS.gov: New Civil Signals" 6901:"GPS.gov: New Civil Signals" 6430:. This yields more accurate 6229: 5561:being studied for additional 5539:Used to enforce nuclear test 5537:high-energy infrared events. 5535:signals nuclear detonations/ 4832:{\displaystyle {\text{L1C}}} 4734:, also used in this article. 4072:{\displaystyle {\text{L1C}}} 2762:M-code frequency information 1219: 1072:(satellite network synopsis, 1060:Telemetry and handover words 1037:Telemetry and handover words 1014:Telemetry and handover words 826:is the code with PRN number 558:Interface Specification (IS) 497: 491:data which are used both in 333:Geographic point coord. 1983 7: 7164:, § 3.1 (p. 2–3). 6496:GPS Interface Specification 6473: 6329: 6309: 6267: 6247: 5478:C/A, L1 Civilian (L1C), and 1409:Ionospheric correction data 1295:Ionospheric correction data 957:, the P-code is XORed with 293:Systema Koordinat 1942 goda 10: 7684: 6510:(describes L1, L2C and P). 6442:than the previous method. 6374:discrete Fourier transform 6190:10,000 Hz/500 Hz 5529:used by Nuclear Detonation 5512:L2 Civilian (L2C) code and 3220: 3101:) has feedback polynomial 3064:) has feedback polynomial 1537:code (called CM), and the 1473: 1432:Almanac data for SV 65–88 1421:health info. for SV 89–95 1375:Almanac data for SV 89–95 1307:health info. for SV 25–32 1261:Almanac data for SV 25–32 1192:Coordinated Universal Time 1177: 1049:(precise satellite orbit) 934: 617: 353:World Geodetic System 1984 35:") in a marine application 7663:Global Positioning System 7614: 7540: 7509: 7468: 7411:"AN02 Network Assistance" 7292:. John Wiley & Sons. 7017:United States Coast Guard 6960: 6436:simple correlation method 6225: 6220: 6115:§ Coarse/acquisition code 6105:§ Frequencies used by GPS 6031:Demodulation and decoding 5916:represent signal powers; 5570: 5567: 5498: 5487: 5484: 5464: 5453: 5450: 5359: 5212: 5209: 5206: 5197:CNAV-2 navigation message 4198: 3162: 3006:is the ranging codes for 2781:The modulation method is 2724:L2C frequency information 2668:(likewise starting at 0). 2644:is the integer number of 2586:is the integer number of 1746: 1675: 1440:Health info. for SV 65–88 1425: 1358: 1318:Almanac data for SV 1–24 1311: 1244: 1053: 1030: 1007: 638:one-to-one correspondence 634:pseudorandom noise number 578:binary phase-shift keying 480:United States Space Force 456:Global Positioning System 343:North American Datum 1983 313:South American Datum 1969 6538: 6432:code phase determination 5531:(NUDET) Detection System 5326:Differential correction 3236:) and a data (called L1C 3205:L5 frequency information 1956:Messages carry a 24-bit 1947:forward error correction 1878:Differential correction 1839:Cyclic redundancy check 1765:cycles for CM and after 1511:forward error correction 1393:Reserved for system use 1385:correction table (NMCT) 1326:Health info. for SV 1–24 1279:Reserved for system use 1271:correction table (NMCT) 630:space vehicle identifier 517: 509: 204:Global Pos. System (GPS) 171:Spatial reference system 31:Civilian GPS receiver (" 7089:. FAA. 13 November 2014 6395:51 frequency components 6091:space: (3) PRN number. 5563:ionospheric correction 5420:Overview of frequencies 5382:time of interval (TOI): 5235:Time of interval (TOI) 4383:is the set of integers 4028:represents a period of 3155:(designated in the IS). 3133:+ 1, and initial state 3039:not depending on phase 2746:MNAV navigation message 1776:CNAV navigation message 1442:almanac reference time 1328:almanac reference time 1155: 735:Coarse/acquisition code 724:dual frequency receiver 513: 468:satellite constellation 6486:Sources and references 6226:Code phase (in chips) 6200:to try for a total of 6044: 6021: 5986: 5948: 5910: 5881: 5849: 5187: 5158: 5129: 5109: 5080: 5026: 4994: 4974: 4934: 4902: 4853: 4833: 4811: 4779: 4759: 4724: 4702: 4682: 4653: 4604: 4584: 4564: 4540: 4539:{\displaystyle p'_{i}} 4504: 4482: 4462: 4433: 4397: 4373: 4339: 4317: 4297: 4263: 4217: 4181: 4159: 4125: 4100: 4073: 4051: 4022: 3988: 3968: 3933: 3216: 2935:mod 10 230) mod 8 190) 2714: 2662: 2638: 2611: 2580: 2558: 2536: 2509: 2476: 1730: 1524: 1506: 1337:LNAV-U frames 4 and 5 1305:A-S flags for SV 1–32, 1223:LNAV-L frames 4 and 5 1026:GPS time relationship 739:The C/A PRN codes are 677: 588:(in reference to CDMA/ 564:Common characteristics 552:) is described in the 36: 24: 7038:"GPS Antennas Thrust" 6961:truncated TOW in LNAV 6635:US patent 5576715 6380:5 MHz×10 ms 6210:40,920 local replicas 6038: 6022: 5987: 5949: 5911: 5882: 5850: 5188: 5159: 5130: 5110: 5081: 5027: 4995: 4975: 4935: 4903: 4854: 4834: 4812: 4780: 4760: 4758:{\displaystyle w_{i}} 4725: 4708:designated in the IS. 4703: 4683: 4681:{\displaystyle w_{i}} 4654: 4605: 4585: 4565: 4541: 4505: 4483: 4463: 4461:{\displaystyle W_{i}} 4434: 4398: 4374: 4340: 4318: 4298: 4264: 4235:) and is of the form 4218: 4182: 4160: 4126: 4101: 4074: 4052: 4023: 3989: 3969: 3934: 3865: such that 3192:L5 navigation message 2788: 2783:binary offset carrier 2715: 2663: 2639: 2612: 2581: 2559: 2537: 2535:{\displaystyle X_{2}} 2510: 2508:{\displaystyle X_{1}} 2477: 1918:GPS/GNSS time offset 1862:Ephemeris and health 1731: 1545:); however, they are 1500: 1489:complete it by 2011. 747:with a 50 bit/s 672: 665:Frequency information 618:Further information: 458:satellites to enable 99:Geographical distance 33:GPS navigation device 30: 22: 7328:. Gpsinformation.net 6770:on November 7, 2014. 6426:instead of circular 6126:§ Navigation message 6059:the signal and then 5996: 5958: 5920: 5891: 5862: 5621: 5168: 5139: 5119: 5090: 5061: 5004: 4984: 4944: 4912: 4866: 4862:The IS asserts that 4843: 4821: 4789: 4769: 4742: 4714: 4692: 4665: 4614: 4594: 4574: 4554: 4520: 4494: 4472: 4445: 4407: 4387: 4363: 4327: 4307: 4273: 4239: 4207: 4171: 4135: 4110: 4083: 4061: 4032: 4000: 3978: 3949: 3317: 3223:L1C (disambiguation) 3010:; also denoted as I5 2773:Block III satellites 2676: 2652: 2623: 2596: 2570: 2548: 2519: 2492: 2013: 1823:Truncated TOW count 1720: 1696:after being clocked 967:anti-spoofing module 753:previously described 626:space vehicle number 460:satellite navigation 273:Sea Level Datum 1929 125:Geodetic coordinates 6563:"New Civil Signals" 5604:pseudo-random noise 5509:unmodulated carrier 5428: 5273: 5249:Time correction and 5203: 5032:to wrap from index 5021: 4959: 4929: 4887: 4806: 4629: 4535: 4357:code, respectively. 4017: 3642: 3571: 3544: 3521: 3487: 3403: 1870:Almanac parameters 1847: 1784: 1460:The Control Segment 1338: 1224: 987: 986:GPS message format 613:spectral efficiency 470:is operated by the 303:European Datum 1950 261:Standards (history) 161:Reference ellipsoid 109:Figure of the Earth 7622:GNSS reflectometry 6413:will be examined. 6391:critical frequency 6137:Simple correlation 6045: 6017: 6016: 5982: 5981: 5944: 5943: 5906: 5905: 5877: 5876: 5845: 5841: 5786: 5514:Military (M) code 5480:Military (M) code 5424: 5271: 5201: 5183: 5154: 5125: 5105: 5076: 5022: 5007: 4990: 4970: 4947: 4930: 4915: 4898: 4875: 4849: 4829: 4807: 4792: 4775: 4755: 4732:modular congruence 4720: 4698: 4678: 4649: 4617: 4600: 4580: 4560: 4536: 4523: 4500: 4478: 4458: 4429: 4393: 4369: 4335: 4313: 4293: 4259: 4213: 4177: 4155: 4124:{\displaystyle t'} 4121: 4096: 4069: 4047: 4018: 4003: 3984: 3964: 3929: 3927: 3920: 3651: 3630: 3559: 3532: 3509: 3475: 3389: 2849:Neuman-Hofman code 2710: 2704: 2658: 2637:{\displaystyle t'} 2634: 2610:{\displaystyle d'} 2607: 2576: 2554: 2532: 2505: 2472: 2470: 2463: 2004:convolutional code 1951:convolutional code 1845: 1780: 1726: 1507: 1503:satellites in view 1383:Navigation message 1336: 1269:Navigation message 1222: 1082:navigation message 1074:error correction) 985: 981:Navigation message 906:⊕ is exclusive or. 749:navigation message 678: 655:coarse/acquisition 649:Legacy GPS signals 595:pseudorandom noise 531:restricted signals 526:modernized signals 181:Vertical positions 37: 25: 7650: 7649: 7542:GNSS augmentation 7315:Konowa.de (2005). 7019:. 7 December 2004 6399:2,046 code phases 6358:Fourier transform 6352:Fourier transform 6349: 6348: 6186:2,046 code phases 6163:Fourier transform 6148:Cartesian product 6100:carrier frequency 6072:phase locked loop 5833: 5745: 5743: 5722: 5651: 5599: 5598: 5446:Modernized usage 5338: 5337: 5272:Subframe 3 pages 5269: 5268: 5175: 5146: 5128:{\displaystyle i} 5097: 5068: 5011: 4993:{\displaystyle S} 4919: 4852:{\displaystyle S} 4827: 4796: 4778:{\displaystyle S} 4701:{\displaystyle i} 4603:{\displaystyle p} 4583:{\displaystyle i} 4563:{\displaystyle S} 4503:{\displaystyle S} 4481:{\displaystyle L} 4396:{\displaystyle n} 4372:{\displaystyle L} 4333: 4316:{\displaystyle n} 4282: 4248: 4216:{\displaystyle i} 4180:{\displaystyle t} 4090: 4067: 4039: 4007: 3987:{\displaystyle i} 3956: 3916: 3866: 3858: 3844: 3617: 3530: 3462: 3393: 3356: 3328: 3297:Legendre sequence 2733:Military (M-code) 2703: 2661:{\displaystyle t} 2579:{\displaystyle t} 2557:{\displaystyle d} 2429: 2418: 2347: 2336: 1927:pseudo-packetized 1922: 1921: 1843: 1842: 1781:Message structure 1729:{\displaystyle i} 1558:dataless sequence 1450: 1449: 1446: 1445: 1401:Special messages 1332: 1331: 1287:Special messages 1204:GNSS augmentation 1200:ionospheric delay 1188:ionospheric model 1142:upper PRN numbers 1138:lower PRN numbers 1090:legacy navigation 1078: 1077: 1070:Almanac component 712:ionospheric delay 454:are broadcast by 449: 448: 397: 396: 176:Spatial relations 166:Satellite geodesy 121: 7675: 7586:QZSS / Michibiki 7455: 7448: 7441: 7432: 7431: 7426: 7425: 7423: 7422: 7413:. Archived from 7407: 7401: 7400:Section 1.4.2.5. 7399: 7397: 7396: 7390: 7383: 7375: 7369: 7368:Section 1.4.2.4. 7367: 7365: 7364: 7358: 7351: 7343: 7337: 7336: 7334: 7333: 7322: 7316: 7310: 7304: 7303: 7283: 7277: 7271: 7265: 7259: 7253: 7247: 7241: 7235: 7229: 7223: 7217: 7211: 7205: 7199: 7190: 7183: 7177: 7171: 7165: 7159: 7150: 7144: 7135: 7129: 7123: 7117: 7111: 7105: 7099: 7098: 7096: 7094: 7079: 7073: 7072: 7070: 7069: 7055: 7049: 7048: 7046: 7044: 7034: 7028: 7027: 7025: 7024: 7014: 7006: 7000: 6994: 6988: 6982: 6976: 6970: 6964: 6953: 6947: 6944: 6938: 6932: 6926: 6920: 6919: 6915: 6913: 6911: 6897: 6888: 6882: 6876: 6870: 6864: 6858: 6852: 6850: 6848: 6847: 6841: 6834: 6826: 6820: 6814: 6808: 6802: 6796: 6790: 6784: 6778: 6772: 6771: 6769: 6763:. Archived from 6762: 6754: 6745: 6744:Section 1.4.2.6. 6743: 6741: 6740: 6734: 6727: 6719: 6710: 6704: 6698: 6692: 6686: 6680: 6674: 6673: 6671: 6669: 6659: 6650: 6644: 6643: 6642: 6638: 6631: 6625: 6619: 6613: 6607: 6598: 6593: 6587: 6586: 6579: 6573: 6572: 6570: 6569: 6559: 6534:(describes L1C). 6533: 6531: 6521: 6519: 6509: 6507: 6410: 6406: 6387: 6383: 6218: 6217: 6209: 6205: 6197: 6193: 6185: 6181: 6154:as described by 6120:PRN number space 6110:Code phase space 6026: 6024: 6023: 6018: 5991: 5989: 5988: 5983: 5971: 5970: 5953: 5951: 5950: 5945: 5933: 5932: 5915: 5913: 5912: 5907: 5904: 5903: 5886: 5884: 5883: 5878: 5875: 5874: 5854: 5852: 5851: 5846: 5840: 5839: 5835: 5834: 5826: 5821: 5820: 5787: 5782: 5781: 5777: 5776: 5775: 5733: 5732: 5723: 5721: 5720: 5711: 5706: 5702: 5701: 5700: 5662: 5661: 5652: 5650: 5649: 5640: 5592: 5579: 5553:(10.23 × 1214/9) 5506: 5496: 5472: 5462: 5429: 5427: 5423: 5310:Reduced almanac 5302: 5298: 5274: 5270: 5204: 5200: 5192: 5190: 5189: 5184: 5182: 5181: 5176: 5173: 5163: 5161: 5160: 5155: 5153: 5152: 5147: 5144: 5134: 5132: 5131: 5126: 5114: 5112: 5111: 5106: 5104: 5103: 5098: 5095: 5085: 5083: 5082: 5077: 5075: 5074: 5069: 5066: 5043:L1C overlay code 5038: 5037: 5031: 5029: 5028: 5023: 5017: 5012: 5009: 4999: 4997: 4996: 4991: 4979: 4977: 4976: 4971: 4955: 4939: 4937: 4936: 4931: 4925: 4920: 4917: 4907: 4905: 4904: 4899: 4883: 4858: 4856: 4855: 4850: 4838: 4836: 4835: 4830: 4828: 4825: 4816: 4814: 4813: 4808: 4802: 4797: 4794: 4784: 4782: 4781: 4776: 4764: 4762: 4761: 4756: 4754: 4753: 4729: 4727: 4726: 4721: 4707: 4705: 4704: 4699: 4687: 4685: 4684: 4679: 4677: 4676: 4658: 4656: 4655: 4650: 4642: 4641: 4625: 4609: 4607: 4606: 4601: 4589: 4587: 4586: 4581: 4569: 4567: 4566: 4561: 4545: 4543: 4542: 4537: 4531: 4509: 4507: 4506: 4501: 4487: 4485: 4484: 4479: 4467: 4465: 4464: 4459: 4457: 4456: 4438: 4436: 4435: 4430: 4402: 4400: 4399: 4394: 4378: 4376: 4375: 4370: 4344: 4342: 4341: 4336: 4334: 4331: 4322: 4320: 4319: 4314: 4302: 4300: 4299: 4294: 4283: 4280: 4268: 4266: 4265: 4260: 4249: 4246: 4222: 4220: 4219: 4214: 4196: 4195: 4191: 4186: 4184: 4183: 4178: 4164: 4162: 4161: 4156: 4154: 4153: 4130: 4128: 4127: 4122: 4120: 4105: 4103: 4102: 4097: 4095: 4091: 4088: 4078: 4076: 4075: 4070: 4068: 4065: 4056: 4054: 4053: 4048: 4046: 4045: 4040: 4037: 4027: 4025: 4024: 4019: 4013: 4008: 4005: 3993: 3991: 3990: 3985: 3973: 3971: 3970: 3965: 3963: 3962: 3957: 3954: 3938: 3936: 3935: 3930: 3928: 3924: 3923: 3917: 3914: 3903: 3883: 3882: 3867: 3864: 3859: 3856: 3845: 3842: 3801: 3800: 3784: 3783: 3728: 3727: 3655: 3654: 3638: 3626: 3618: 3615: 3602: 3591: 3590: 3567: 3555: 3540: 3531: 3528: 3517: 3505: 3483: 3471: 3463: 3460: 3453: 3442: 3441: 3414: 3399: 3394: 3391: 3381: 3380: 3361: 3357: 3354: 3335: 3334: 3329: 3326: 3305: 3304: 3291:L1C ranging code 2841:quadrature-phase 2719: 2717: 2716: 2711: 2709: 2705: 2699: 2691: 2667: 2665: 2664: 2659: 2643: 2641: 2640: 2635: 2633: 2616: 2614: 2613: 2608: 2606: 2585: 2583: 2582: 2577: 2563: 2561: 2560: 2555: 2541: 2539: 2538: 2533: 2531: 2530: 2514: 2512: 2511: 2506: 2504: 2503: 2481: 2479: 2478: 2473: 2471: 2467: 2466: 2460: 2438: 2430: 2427: 2423: 2419: 2414: 2407: 2398: 2392: 2391: 2378: 2356: 2348: 2345: 2341: 2337: 2332: 2324: 2318: 2317: 2290: 2279: 2155: 2154: 2029: 2028: 1848: 1844: 1815:Message type ID 1785: 1783:(common fields) 1779: 1771: 1770: 1764: 1763: 1735: 1733: 1732: 1727: 1493:General features 1351: 1346: 1339: 1335: 1237: 1232: 1225: 1221: 1218: 1217: 1024:Satellite clock, 1000: 995: 988: 984: 730:Modulation codes 675:broadcast signal 441: 434: 427: 265: 264: 244: 236: 228: 220: 212: 152: 111: 53: 39: 38: 7683: 7682: 7678: 7677: 7676: 7674: 7673: 7672: 7653: 7652: 7651: 7646: 7610: 7536: 7505: 7464: 7459: 7429: 7420: 7418: 7409: 7408: 7404: 7394: 7392: 7388: 7381: 7377: 7376: 7372: 7362: 7360: 7356: 7349: 7345: 7344: 7340: 7331: 7329: 7324: 7323: 7319: 7311: 7307: 7300: 7284: 7280: 7272: 7268: 7260: 7256: 7248: 7244: 7236: 7232: 7224: 7220: 7212: 7208: 7200: 7193: 7184: 7180: 7172: 7168: 7160: 7153: 7145: 7138: 7130: 7126: 7118: 7114: 7106: 7102: 7092: 7090: 7081: 7080: 7076: 7067: 7065: 7057: 7056: 7052: 7042: 7040: 7036: 7035: 7031: 7022: 7020: 7012: 7008: 7007: 7003: 6995: 6991: 6983: 6979: 6971: 6967: 6954: 6950: 6945: 6941: 6933: 6929: 6917: 6909: 6907: 6899: 6898: 6891: 6884:US Coast Guard 6883: 6879: 6871: 6867: 6859: 6855: 6845: 6843: 6839: 6832: 6828: 6827: 6823: 6815: 6811: 6803: 6799: 6791: 6787: 6779: 6775: 6767: 6760: 6756: 6755: 6748: 6738: 6736: 6732: 6725: 6721: 6720: 6713: 6705: 6701: 6693: 6689: 6681: 6677: 6667: 6665: 6657: 6651: 6647: 6640: 6632: 6628: 6620: 6616: 6608: 6601: 6594: 6590: 6581: 6580: 6576: 6567: 6565: 6561: 6560: 6545: 6541: 6532:. 4 March 2019. 6529: 6522:(describes L5). 6520:. 4 March 2019. 6517: 6508:. 4 March 2019. 6505: 6493: 6488: 6476: 6448: 6419: 6408: 6404: 6385: 6381: 6354: 6289: 6222: 6207: 6203: 6195: 6191: 6183: 6179: 6156:Euler's formula 6139: 6095:Frequency space 6088: 6033: 5997: 5994: 5993: 5966: 5962: 5959: 5956: 5955: 5928: 5924: 5921: 5918: 5917: 5899: 5895: 5892: 5889: 5888: 5870: 5866: 5863: 5860: 5859: 5825: 5816: 5812: 5802: 5798: 5788: 5771: 5767: 5757: 5753: 5746: 5744: 5728: 5724: 5716: 5712: 5710: 5696: 5692: 5682: 5678: 5657: 5653: 5645: 5641: 5639: 5622: 5619: 5618: 5572: 5562: 5552: 5540: 5538: 5536: 5534: 5532: 5530: 5523: 5513: 5489: 5479: 5455: 5443:Original usage 5436: 5426:GPS Frequencies 5425: 5422: 5288:UTC & IONO 5251:ephemeris data 5250: 5199: 5177: 5172: 5171: 5169: 5166: 5165: 5148: 5143: 5142: 5140: 5137: 5136: 5120: 5117: 5116: 5099: 5094: 5093: 5091: 5088: 5087: 5070: 5065: 5064: 5062: 5059: 5058: 5050: 5045: 5035: 5033: 5013: 5008: 5005: 5002: 5001: 4985: 4982: 4981: 4951: 4945: 4942: 4941: 4921: 4916: 4913: 4910: 4909: 4879: 4867: 4864: 4863: 4844: 4841: 4840: 4824: 4822: 4819: 4818: 4798: 4793: 4790: 4787: 4786: 4770: 4767: 4766: 4749: 4745: 4743: 4740: 4739: 4715: 4712: 4711: 4693: 4690: 4689: 4672: 4668: 4666: 4663: 4662: 4637: 4633: 4621: 4615: 4612: 4611: 4595: 4592: 4591: 4575: 4572: 4571: 4555: 4552: 4551: 4527: 4521: 4518: 4517: 4514:indexes 0 to 6. 4495: 4492: 4491: 4473: 4470: 4469: 4452: 4448: 4446: 4443: 4442: 4408: 4405: 4404: 4388: 4385: 4384: 4364: 4361: 4360: 4356: 4352: 4330: 4328: 4325: 4324: 4308: 4305: 4304: 4279: 4274: 4271: 4270: 4245: 4240: 4237: 4236: 4234: 4230: 4208: 4205: 4204: 4193: 4189: 4188: 4172: 4169: 4168: 4145: 4141: 4136: 4133: 4132: 4113: 4111: 4108: 4107: 4087: 4086: 4084: 4081: 4080: 4064: 4062: 4059: 4058: 4041: 4036: 4035: 4033: 4030: 4029: 4009: 4004: 4001: 3998: 3997: 3979: 3976: 3975: 3958: 3953: 3952: 3950: 3947: 3946: 3926: 3925: 3919: 3918: 3915: otherwise 3913: 3911: 3905: 3904: 3884: 3878: 3874: 3863: 3855: 3841: 3839: 3829: 3828: 3821: 3806: 3805: 3792: 3788: 3779: 3775: 3738: 3723: 3719: 3716: 3715: 3663: 3657: 3656: 3650: 3649: 3634: 3619: 3614: 3612: 3595: 3586: 3582: 3579: 3578: 3563: 3548: 3536: 3527: 3525: 3513: 3498: 3489: 3488: 3479: 3464: 3459: 3457: 3446: 3437: 3433: 3426: 3425: 3418: 3407: 3395: 3390: 3386: 3385: 3372: 3368: 3353: 3352: 3345: 3330: 3325: 3324: 3320: 3318: 3315: 3314: 3302: 3300: 3293: 3247: 3239: 3235: 3226: 3219: 3207: 3194: 3149: 3138: 3091: 3083: 3033: 3021: 3015: 3005: 2960: 2953: 2942: 2911: 2893: 2881: 2879:I5 and Q5 codes 2866:processing gain 2791: 2764: 2748: 2735: 2726: 2692: 2689: 2685: 2677: 2674: 2673: 2653: 2650: 2649: 2626: 2624: 2621: 2620: 2599: 2597: 2594: 2593: 2588:non FEC encoded 2571: 2568: 2567: 2549: 2546: 2545: 2526: 2522: 2520: 2517: 2516: 2499: 2495: 2493: 2490: 2489: 2469: 2468: 2462: 2461: 2445: 2431: 2426: 2424: 2400: 2399: 2397: 2393: 2387: 2383: 2380: 2379: 2363: 2349: 2344: 2342: 2325: 2323: 2319: 2313: 2309: 2302: 2301: 2294: 2283: 2272: 2269: 2268: 2165: 2150: 2146: 2143: 2142: 2039: 2024: 2020: 2016: 2014: 2011: 2010: 2000: 1910:UTC parameters 1782: 1778: 1768: 1766: 1761: 1759: 1721: 1718: 1717: 1714: 1707: 1669: 1663: 1644: 1630: 1616: 1602: 1586: 1584:CM and CL codes 1527: 1495: 1478: 1472: 1455: 1441: 1420: 1410: 1384: 1363: 1344: 1327: 1306: 1296: 1270: 1249: 1230: 1216: 1180: 1158: 1073: 1071: 1061: 1048: 1038: 1025: 1015: 993: 983: 939: 933: 897: 889: 851: 825: 810: 784: 737: 732: 667: 651: 622: 566: 445: 416: 415: 262: 254: 253: 242: 234: 226: 218: 210: 194: 186: 185: 144: 94: 86: 85: 61: 17: 12: 11: 5: 7681: 7671: 7670: 7665: 7648: 7647: 7645: 7644: 7639: 7634: 7629: 7624: 7618: 7616: 7615:Related topics 7612: 7611: 7609: 7608: 7603: 7598: 7593: 7588: 7583: 7578: 7573: 7568: 7563: 7557: 7552: 7546: 7544: 7538: 7537: 7535: 7534: 7529: 7524: 7519: 7517:BDS / BeiDou-1 7513: 7511: 7507: 7506: 7504: 7503: 7498: 7493: 7488: 7483: 7478: 7472: 7470: 7466: 7465: 7458: 7457: 7450: 7443: 7435: 7428: 7427: 7402: 7370: 7338: 7317: 7313:How GPS works. 7305: 7298: 7278: 7266: 7254: 7242: 7230: 7218: 7206: 7191: 7178: 7166: 7151: 7136: 7124: 7112: 7100: 7074: 7050: 7029: 7001: 6989: 6977: 6965: 6948: 6939: 6927: 6889: 6877: 6865: 6853: 6821: 6809: 6797: 6785: 6773: 6746: 6711: 6699: 6687: 6675: 6645: 6626: 6614: 6599: 6588: 6574: 6542: 6540: 6537: 6536: 6535: 6523: 6511: 6492: 6489: 6487: 6484: 6483: 6482: 6475: 6472: 6447: 6444: 6418: 6415: 6353: 6350: 6347: 6346: 6343: 6340: 6337: 6334: 6331: 6327: 6326: 6323: 6320: 6317: 6314: 6311: 6307: 6306: 6303: 6300: 6297: 6294: 6291: 6285: 6284: 6281: 6278: 6275: 6272: 6269: 6268:−4,250 Hz 6265: 6264: 6261: 6258: 6255: 6252: 6249: 6248:−4,750 Hz 6245: 6244: 6241: 6238: 6235: 6232: 6228: 6227: 6224: 6198:20 frequencies 6138: 6135: 6130: 6129: 6121: 6118: 6111: 6108: 6096: 6087: 6084: 6032: 6029: 6015: 6012: 6009: 6005: 6002: 5980: 5977: 5974: 5969: 5965: 5942: 5939: 5936: 5931: 5927: 5902: 5898: 5873: 5869: 5856: 5855: 5844: 5838: 5832: 5829: 5824: 5819: 5815: 5811: 5808: 5805: 5801: 5797: 5794: 5791: 5785: 5780: 5774: 5770: 5766: 5763: 5760: 5756: 5752: 5749: 5742: 5739: 5736: 5731: 5727: 5719: 5715: 5709: 5705: 5699: 5695: 5691: 5688: 5685: 5681: 5677: 5674: 5671: 5668: 5665: 5660: 5656: 5648: 5644: 5638: 5635: 5632: 5629: 5626: 5597: 5596: 5593: 5587: 5586: 5583: 5580: 5574: 5569: 5565: 5564: 5559: 5556: 5554: 5549: 5545: 5544: 5542: 5533:Payload (NDS): 5527: 5525: 5520: 5516: 5515: 5510: 5507: 5501: 5500: 5497: 5491: 5486: 5482: 5481: 5476: 5473: 5467: 5466: 5463: 5457: 5452: 5448: 5447: 5444: 5441: 5438: 5433: 5421: 5418: 5390: 5389: 5378: 5371: 5336: 5335: 5332: 5328: 5327: 5324: 5320: 5319: 5316: 5312: 5311: 5308: 5304: 5303: 5294: 5290: 5289: 5286: 5282: 5281: 5278: 5267: 5266: 5265:Variable data 5263: 5260: 5257: 5253: 5252: 5247: 5244: 5241: 5237: 5236: 5233: 5230: 5227: 5223: 5222: 5219: 5215: 5214: 5211: 5208: 5198: 5195: 5180: 5151: 5124: 5102: 5073: 5048: 5044: 5041: 5020: 5016: 5000:inserted into 4989: 4969: 4965: 4962: 4958: 4954: 4950: 4928: 4924: 4897: 4893: 4890: 4886: 4882: 4878: 4874: 4871: 4848: 4805: 4801: 4774: 4752: 4748: 4736: 4735: 4719: 4709: 4697: 4675: 4671: 4660: 4648: 4645: 4640: 4636: 4632: 4628: 4624: 4620: 4599: 4579: 4559: 4534: 4530: 4526: 4515: 4499: 4489: 4477: 4455: 4451: 4440: 4428: 4424: 4421: 4418: 4415: 4412: 4392: 4368: 4358: 4354: 4350: 4312: 4292: 4289: 4286: 4278: 4258: 4255: 4252: 4244: 4232: 4228: 4212: 4202: 4176: 4166: 4152: 4148: 4144: 4140: 4119: 4116: 4094: 4044: 4016: 4012: 3995: 3983: 3961: 3940: 3939: 3922: 3912: 3910: 3907: 3906: 3902: 3899: 3895: 3891: 3888: 3881: 3877: 3873: 3870: 3862: 3854: 3851: 3848: 3843: if 3840: 3838: 3835: 3834: 3832: 3827: 3824: 3822: 3820: 3817: 3814: 3811: 3808: 3807: 3804: 3799: 3795: 3791: 3787: 3782: 3778: 3774: 3771: 3768: 3765: 3762: 3759: 3756: 3753: 3750: 3747: 3744: 3741: 3739: 3737: 3734: 3731: 3726: 3722: 3718: 3717: 3714: 3711: 3708: 3705: 3702: 3699: 3696: 3693: 3690: 3687: 3684: 3681: 3678: 3675: 3672: 3669: 3666: 3664: 3662: 3659: 3658: 3653: 3648: 3645: 3641: 3637: 3633: 3629: 3625: 3622: 3616: if 3613: 3611: 3608: 3605: 3601: 3598: 3594: 3589: 3585: 3581: 3580: 3577: 3574: 3570: 3566: 3562: 3558: 3554: 3551: 3547: 3543: 3539: 3535: 3529: if 3526: 3524: 3520: 3516: 3512: 3508: 3504: 3501: 3497: 3494: 3491: 3490: 3486: 3482: 3478: 3474: 3470: 3467: 3461: if 3458: 3456: 3452: 3449: 3445: 3440: 3436: 3432: 3431: 3429: 3424: 3421: 3419: 3417: 3413: 3410: 3406: 3402: 3398: 3388: 3387: 3384: 3379: 3375: 3371: 3367: 3364: 3360: 3351: 3348: 3346: 3344: 3341: 3338: 3333: 3323: 3322: 3292: 3289: 3288: 3287: 3284: 3281: 3278: 3271: 3270: 3267: 3264: 3261: 3245: 3237: 3233: 3218: 3215: 3206: 3203: 3193: 3190: 3167: 3166: 3156: 3147: 3143: 3142: 3141: 3136: 3089: 3085: 3081: 3044: 3031: 3023: 3017: 3011: 3001: 2998: 2968: 2967: 2958: 2951: 2940: 2936: 2918: 2909: 2889: 2880: 2877: 2876: 2875: 2872: 2869: 2862: 2859: 2829: 2828: 2825: 2822: 2790: 2787: 2763: 2760: 2747: 2744: 2734: 2731: 2725: 2722: 2708: 2702: 2698: 2695: 2688: 2684: 2681: 2670: 2669: 2657: 2632: 2629: 2618: 2605: 2602: 2591: 2575: 2565: 2553: 2543: 2529: 2525: 2502: 2498: 2483: 2482: 2465: 2459: 2456: 2452: 2449: 2444: 2441: 2437: 2434: 2425: 2422: 2417: 2413: 2410: 2406: 2403: 2396: 2390: 2386: 2382: 2381: 2377: 2374: 2370: 2367: 2362: 2359: 2355: 2352: 2343: 2340: 2335: 2331: 2328: 2322: 2316: 2312: 2308: 2307: 2305: 2300: 2297: 2295: 2293: 2289: 2286: 2282: 2278: 2275: 2271: 2270: 2267: 2264: 2261: 2258: 2255: 2252: 2249: 2246: 2243: 2240: 2237: 2234: 2231: 2228: 2225: 2222: 2219: 2216: 2213: 2210: 2207: 2204: 2201: 2198: 2195: 2192: 2189: 2186: 2183: 2180: 2177: 2174: 2171: 2168: 2166: 2164: 2161: 2158: 2153: 2149: 2145: 2144: 2141: 2138: 2135: 2132: 2129: 2126: 2123: 2120: 2117: 2114: 2111: 2108: 2105: 2102: 2099: 2096: 2093: 2090: 2087: 2084: 2081: 2078: 2075: 2072: 2069: 2066: 2063: 2060: 2057: 2054: 2051: 2048: 2045: 2042: 2040: 2038: 2035: 2032: 2027: 2023: 2019: 2018: 1999: 1996: 1991: 1990: 1987: 1983: 1976: 1965: 1961: 1954: 1920: 1919: 1916: 1912: 1911: 1908: 1904: 1903: 1900: 1896: 1895: 1892: 1888: 1887: 1886:Text messages 1884: 1880: 1879: 1876: 1872: 1871: 1868: 1864: 1863: 1860: 1856: 1855: 1852: 1846:Message types 1841: 1840: 1837: 1833: 1832: 1829: 1825: 1824: 1821: 1817: 1816: 1813: 1809: 1808: 1805: 1801: 1800: 1797: 1793: 1792: 1789: 1777: 1774: 1751: 1750: 1740: 1737: 1725: 1712: 1705: 1701: 1679: 1665: 1659: 1652: 1651: 1642: 1626: 1623: 1614: 1598: 1585: 1582: 1581: 1580: 1577: 1574: 1571: 1535:civil-moderate 1526: 1523: 1494: 1491: 1471: 1468: 1454: 1451: 1448: 1447: 1444: 1443: 1438: 1434: 1433: 1430: 1427: 1423: 1422: 1417: 1413: 1412: 1407: 1403: 1402: 1399: 1395: 1394: 1391: 1387: 1386: 1381: 1377: 1376: 1373: 1369: 1368: 1365: 1360: 1356: 1355: 1352: 1347: 1333: 1330: 1329: 1324: 1320: 1319: 1316: 1313: 1309: 1308: 1303: 1299: 1298: 1293: 1289: 1288: 1285: 1281: 1280: 1277: 1273: 1272: 1267: 1263: 1262: 1259: 1255: 1254: 1251: 1246: 1242: 1241: 1238: 1233: 1215: 1212: 1179: 1176: 1157: 1154: 1126:and 5 contain 1111: 1110: 1107: 1100: 1076: 1075: 1068: 1064: 1063: 1062:(TLM and HOW) 1058: 1055: 1051: 1050: 1045: 1041: 1040: 1039:(TLM and HOW) 1035: 1032: 1028: 1027: 1022: 1018: 1017: 1016:(TLM and HOW) 1012: 1009: 1005: 1004: 1001: 996: 982: 979: 932: 931:Precision code 929: 908: 907: 904: 895: 891: 887: 853: 849: 831: 821: 814: 813: 808: 780: 745:exclusive-ored 736: 733: 731: 728: 666: 663: 650: 647: 586:chipping codes 574:space vehicles 570:GPS satellites 565: 562: 447: 446: 444: 443: 436: 429: 421: 418: 417: 414: 413: 408: 403: 395: 394: 391: 385: 384: 381: 375: 374: 371: 365: 364: 361: 355: 354: 351: 345: 344: 341: 335: 334: 331: 325: 324: 321: 315: 314: 311: 305: 304: 301: 295: 294: 291: 285: 284: 281: 275: 274: 271: 263: 260: 259: 256: 255: 252: 251: 246: 238: 230: 222: 214: 206: 201: 195: 192: 191: 188: 187: 184: 183: 178: 173: 168: 163: 158: 156:Map projection 153: 142: 137: 132: 130:Geodetic datum 127: 122: 106: 101: 95: 92: 91: 88: 87: 84: 83: 78: 73: 68: 62: 59: 58: 55: 54: 46: 45: 15: 9: 6: 4: 3: 2: 7680: 7669: 7666: 7664: 7661: 7660: 7658: 7643: 7640: 7638: 7635: 7633: 7630: 7628: 7627:Kalman filter 7625: 7623: 7620: 7619: 7617: 7613: 7607: 7604: 7602: 7599: 7597: 7594: 7592: 7589: 7587: 7584: 7582: 7579: 7577: 7574: 7572: 7569: 7567: 7564: 7561: 7558: 7556: 7553: 7551: 7548: 7547: 7545: 7543: 7539: 7533: 7530: 7528: 7525: 7523: 7520: 7518: 7515: 7514: 7512: 7508: 7502: 7501:IRNSS / NAVIC 7499: 7497: 7496:GPS / NavStar 7494: 7492: 7489: 7487: 7484: 7482: 7479: 7477: 7474: 7473: 7471: 7467: 7463: 7456: 7451: 7449: 7444: 7442: 7437: 7436: 7433: 7417:on 2010-02-21 7416: 7412: 7406: 7391:on 2013-10-21 7387: 7380: 7374: 7359:on 2013-10-21 7355: 7348: 7342: 7327: 7321: 7314: 7309: 7301: 7299:9781119944881 7295: 7291: 7290: 7282: 7275: 7270: 7263: 7258: 7251: 7246: 7239: 7234: 7227: 7222: 7215: 7210: 7203: 7198: 7196: 7188: 7182: 7175: 7170: 7163: 7158: 7156: 7148: 7143: 7141: 7133: 7128: 7121: 7116: 7109: 7104: 7088: 7084: 7078: 7064: 7060: 7054: 7039: 7033: 7018: 7011: 7005: 6998: 6993: 6986: 6981: 6974: 6969: 6962: 6958: 6952: 6943: 6936: 6931: 6924: 6923:public domain 6906: 6902: 6896: 6894: 6887: 6881: 6874: 6869: 6862: 6857: 6842:on 2012-09-08 6838: 6831: 6825: 6818: 6813: 6806: 6801: 6794: 6789: 6782: 6777: 6766: 6759: 6753: 6751: 6735:on 2013-10-21 6731: 6724: 6718: 6716: 6708: 6703: 6696: 6691: 6684: 6679: 6663: 6656: 6649: 6636: 6630: 6623: 6618: 6611: 6606: 6604: 6597: 6592: 6584: 6578: 6564: 6558: 6556: 6554: 6552: 6550: 6548: 6543: 6528: 6524: 6516: 6512: 6504: 6500: 6499: 6498: 6497: 6481: 6478: 6477: 6471: 6469: 6464: 6460: 6456: 6453: 6443: 6441: 6437: 6433: 6429: 6425: 6414: 6412: 6400: 6396: 6392: 6377: 6375: 6370: 6368: 6363: 6359: 6344: 6341: 6338: 6335: 6332: 6330:4,750 Hz 6328: 6324: 6321: 6318: 6315: 6312: 6310:4,250 Hz 6308: 6304: 6301: 6298: 6295: 6292: 6287: 6286: 6282: 6279: 6276: 6273: 6270: 6266: 6262: 6259: 6256: 6253: 6250: 6246: 6242: 6239: 6237:(more phases) 6236: 6233: 6230: 6221:Carrier freq. 6219: 6216: 6213: 6211: 6199: 6187: 6174: 6172: 6168: 6164: 6159: 6157: 6153: 6149: 6144: 6134: 6127: 6122: 6119: 6116: 6112: 6109: 6106: 6101: 6097: 6094: 6093: 6092: 6083: 6080: 6075: 6073: 6068: 6064: 6062: 6058: 6053: 6051: 6050:undersampling 6042: 6037: 6028: 6010: 6007: 6003: 5975: 5963: 5937: 5925: 5896: 5867: 5842: 5836: 5830: 5827: 5822: 5817: 5813: 5809: 5806: 5803: 5799: 5795: 5792: 5789: 5783: 5778: 5772: 5768: 5764: 5761: 5758: 5754: 5750: 5747: 5737: 5725: 5713: 5707: 5703: 5697: 5693: 5689: 5686: 5683: 5679: 5675: 5672: 5666: 5654: 5642: 5636: 5630: 5624: 5617: 5616: 5615: 5612: 5609: 5605: 5594: 5589: 5588: 5584: 5575: 5573:(10.23 × 115) 5566: 5560: 5555: 5550: 5547: 5546: 5543: 5541:ban treaties. 5528: 5526: 5524:(10.23 × 135) 5521: 5518: 5517: 5511: 5508: 5503: 5502: 5492: 5490:(10.23 × 120) 5483: 5477: 5474: 5469: 5468: 5458: 5456:(10.23 × 154) 5449: 5445: 5442: 5439: 5434: 5431: 5430: 5417: 5415: 5411: 5407: 5402: 5398: 5393: 5387: 5383: 5379: 5376: 5372: 5369: 5365: 5364: 5363: 5361: 5356: 5352: 5350: 5346: 5341: 5333: 5330: 5329: 5325: 5322: 5321: 5318:Midi almanac 5317: 5314: 5313: 5309: 5306: 5305: 5295: 5292: 5291: 5287: 5284: 5283: 5279: 5276: 5275: 5264: 5261: 5258: 5255: 5254: 5248: 5245: 5242: 5239: 5238: 5234: 5231: 5228: 5225: 5224: 5220: 5217: 5216: 5205: 5194: 5178: 5149: 5122: 5100: 5071: 5055: 5052: 5040: 5018: 5014: 4987: 4967: 4963: 4960: 4956: 4952: 4948: 4926: 4922: 4895: 4891: 4888: 4884: 4880: 4876: 4872: 4869: 4860: 4846: 4803: 4799: 4772: 4750: 4746: 4733: 4717: 4710: 4695: 4673: 4669: 4661: 4646: 4643: 4638: 4634: 4630: 4626: 4622: 4618: 4597: 4577: 4557: 4549: 4532: 4528: 4524: 4516: 4513: 4497: 4490: 4475: 4453: 4449: 4441: 4426: 4422: 4419: 4416: 4413: 4410: 4390: 4382: 4366: 4359: 4348: 4310: 4287: 4284: 4253: 4250: 4226: 4210: 4203: 4200: 4174: 4167: 4150: 4146: 4138: 4117: 4114: 4092: 4042: 4014: 4010: 3996: 3981: 3959: 3945: 3944: 3943: 3908: 3897: 3893: 3889: 3879: 3875: 3871: 3868: 3860: 3852: 3849: 3846: 3836: 3830: 3825: 3823: 3815: 3809: 3797: 3793: 3780: 3776: 3772: 3769: 3760: 3757: 3751: 3745: 3742: 3740: 3732: 3724: 3720: 3709: 3706: 3703: 3700: 3697: 3694: 3691: 3688: 3685: 3682: 3679: 3676: 3673: 3667: 3665: 3660: 3646: 3643: 3639: 3635: 3631: 3627: 3623: 3620: 3606: 3603: 3599: 3596: 3587: 3583: 3575: 3572: 3568: 3564: 3560: 3556: 3552: 3549: 3545: 3541: 3537: 3533: 3518: 3514: 3510: 3506: 3502: 3499: 3492: 3484: 3480: 3476: 3472: 3468: 3465: 3450: 3447: 3438: 3434: 3427: 3422: 3420: 3411: 3408: 3400: 3396: 3377: 3373: 3365: 3358: 3349: 3347: 3339: 3331: 3313: 3312: 3311: 3309: 3298: 3285: 3282: 3279: 3276: 3275: 3274: 3268: 3265: 3262: 3259: 3258: 3257: 3255: 3251: 3243: 3230: 3224: 3214: 3212: 3202: 3200: 3189: 3187: 3183: 3179: 3175: 3171: 3164: 3160: 3157: 3154: 3150: 3144: 3139: 3132: 3128: 3124: 3120: 3116: 3112: 3108: 3104: 3100: 3096: 3092: 3086: 3079: 3075: 3071: 3067: 3063: 3059: 3055: 3052: 3051: 3049: 3045: 3042: 3038: 3034: 3027: 3024: 3020: 3014: 3009: 3004: 2999: 2996: 2992: 2988: 2984: 2980: 2976: 2973: 2972: 2971: 2965: 2961: 2954: 2947: 2943: 2937: 2934: 2930: 2926: 2922: 2919: 2916: 2912: 2905: 2901: 2897: 2892: 2887: 2886: 2885: 2873: 2870: 2867: 2863: 2860: 2857: 2856: 2855: 2852: 2850: 2846: 2843:code (called 2842: 2838: 2833: 2826: 2823: 2820: 2819: 2818: 2815: 2813: 2809: 2805: 2801: 2797: 2786: 2784: 2779: 2776: 2774: 2768: 2759: 2757: 2753: 2743: 2739: 2730: 2721: 2706: 2700: 2696: 2693: 2686: 2682: 2679: 2655: 2647: 2630: 2627: 2619: 2603: 2600: 2592: 2589: 2573: 2566: 2551: 2544: 2527: 2523: 2500: 2496: 2488: 2487: 2486: 2454: 2450: 2442: 2439: 2435: 2432: 2420: 2415: 2411: 2408: 2404: 2401: 2394: 2388: 2384: 2372: 2368: 2360: 2357: 2353: 2350: 2338: 2333: 2329: 2326: 2320: 2314: 2310: 2303: 2298: 2296: 2287: 2284: 2276: 2273: 2262: 2259: 2256: 2250: 2247: 2241: 2238: 2235: 2229: 2226: 2220: 2217: 2214: 2208: 2205: 2199: 2196: 2193: 2187: 2184: 2178: 2172: 2169: 2167: 2159: 2151: 2147: 2136: 2133: 2130: 2124: 2121: 2115: 2112: 2109: 2103: 2100: 2094: 2091: 2088: 2082: 2079: 2073: 2070: 2067: 2061: 2058: 2052: 2046: 2043: 2041: 2033: 2025: 2021: 2009: 2008: 2007: 2005: 1995: 1988: 1984: 1981: 1977: 1974: 1970: 1966: 1962: 1959: 1955: 1952: 1948: 1944: 1943: 1942: 1939: 1935: 1932: 1928: 1917: 1914: 1913: 1909: 1906: 1905: 1901: 1898: 1897: 1893: 1890: 1889: 1885: 1882: 1881: 1877: 1874: 1873: 1869: 1866: 1865: 1861: 1858: 1857: 1853: 1850: 1849: 1838: 1835: 1834: 1830: 1827: 1826: 1822: 1819: 1818: 1814: 1811: 1810: 1806: 1803: 1802: 1798: 1795: 1794: 1790: 1787: 1786: 1773: 1757: 1748: 1744: 1741: 1738: 1723: 1715: 1708: 1702: 1699: 1695: 1691: 1687: 1683: 1680: 1677: 1673: 1668: 1662: 1657: 1656: 1655: 1649: 1645: 1638: 1634: 1629: 1624: 1621: 1617: 1610: 1606: 1601: 1596: 1595: 1594: 1591: 1578: 1575: 1572: 1569: 1568: 1567: 1564: 1561: 1559: 1555: 1550: 1548: 1544: 1540: 1536: 1531: 1522: 1518: 1514: 1512: 1504: 1499: 1490: 1486: 1484: 1477: 1467: 1463: 1461: 1439: 1436: 1435: 1431: 1428: 1424: 1418: 1415: 1414: 1408: 1405: 1404: 1400: 1397: 1396: 1392: 1389: 1388: 1382: 1379: 1378: 1374: 1371: 1370: 1366: 1361: 1357: 1353: 1348: 1341: 1340: 1334: 1325: 1322: 1321: 1317: 1314: 1310: 1304: 1301: 1300: 1294: 1291: 1290: 1286: 1283: 1282: 1278: 1275: 1274: 1268: 1265: 1264: 1260: 1257: 1256: 1252: 1247: 1243: 1239: 1234: 1227: 1226: 1220: 1211: 1209: 1206:systems like 1205: 1201: 1197: 1193: 1189: 1185: 1175: 1172: 1166: 1162: 1153: 1149: 1145: 1143: 1139: 1134: 1131: 1129: 1124: 1120: 1115: 1108: 1105: 1101: 1098: 1097: 1096: 1093: 1091: 1087: 1083: 1069: 1066: 1065: 1059: 1056: 1052: 1046: 1043: 1042: 1036: 1033: 1029: 1023: 1020: 1019: 1013: 1010: 1006: 1002: 997: 990: 989: 978: 974: 972: 968: 964: 960: 956: 951: 947: 945: 938: 928: 924: 922: 917: 913: 905: 902: 898: 892: 885: 881: 877: 873: 869: 865: 861: 857: 854: 847: 843: 839: 835: 832: 829: 824: 819: 818: 817: 811: 804: 800: 796: 792: 788: 783: 778: 777: 776: 774: 769: 766: 762: 758: 757:autocorrelate 754: 750: 746: 742: 727: 725: 721: 717: 713: 708: 706: 702: 698: 693: 691: 687: 683: 676: 671: 662: 660: 656: 646: 644: 639: 635: 631: 627: 621: 616: 614: 610: 605: 603: 602: 597: 596: 591: 587: 583: 579: 575: 571: 561: 559: 555: 551: 550:GPS receivers 546: 544: 543:semi-codeless 540: 536: 532: 527: 523: 522:legacy signal 519: 515: 511: 507: 502: 500: 499: 494: 493:trilateration 490: 489: 483: 481: 477: 476:Space Delta 8 473: 469: 465: 461: 457: 453: 442: 437: 435: 430: 428: 423: 422: 420: 419: 412: 409: 407: 404: 402: 399: 398: 392: 390: 387: 386: 382: 380: 377: 376: 372: 370: 367: 366: 362: 360: 357: 356: 352: 350: 347: 346: 342: 340: 337: 336: 332: 330: 327: 326: 322: 320: 317: 316: 312: 310: 307: 306: 302: 300: 297: 296: 292: 290: 287: 286: 282: 280: 277: 276: 272: 270: 267: 266: 258: 257: 250: 247: 245: 239: 237: 231: 229: 223: 221: 217:BeiDou (BDS) 215: 213: 207: 205: 202: 200: 197: 196: 190: 189: 182: 179: 177: 174: 172: 169: 167: 164: 162: 159: 157: 154: 151: 147: 143: 141: 138: 136: 133: 131: 128: 126: 123: 119: 118:circumference 115: 110: 107: 105: 102: 100: 97: 96: 90: 89: 82: 79: 77: 74: 72: 69: 67: 64: 63: 57: 56: 52: 48: 47: 44: 41: 40: 34: 29: 21: 7419:. Retrieved 7415:the original 7405: 7393:. Retrieved 7386:the original 7373: 7361:. Retrieved 7354:the original 7341: 7330:. Retrieved 7320: 7308: 7288: 7281: 7269: 7257: 7245: 7233: 7221: 7216:, p. 7. 7209: 7181: 7169: 7127: 7115: 7103: 7093:25 September 7091:. Retrieved 7086: 7077: 7066:. Retrieved 7062: 7053: 7041:. Retrieved 7032: 7021:. Retrieved 7004: 6992: 6980: 6968: 6956: 6951: 6942: 6930: 6908:. Retrieved 6904: 6880: 6868: 6856: 6844:. Retrieved 6837:the original 6824: 6812: 6800: 6788: 6776: 6765:the original 6737:. Retrieved 6730:the original 6702: 6690: 6678: 6666:. Retrieved 6661: 6648: 6629: 6617: 6591: 6577: 6566:. Retrieved 6495: 6494: 6491:Bibliography 6465: 6461: 6457: 6449: 6439: 6431: 6420: 6402: 6398: 6397:. There are 6394: 6378: 6371: 6355: 6290:frequencies) 6214: 6201: 6189: 6177: 6175: 6160: 6140: 6131: 6089: 6076: 6069: 6065: 6060: 6056: 6054: 6046: 5857: 5613: 5600: 5551:1379.9133... 5401:exclusive or 5394: 5391: 5385: 5381: 5374: 5367: 5357: 5353: 5342: 5339: 5280:Description 5213:Description 5056: 5053: 5046: 4861: 4737: 4610:, therefore 4225:ordered pair 3941: 3307: 3299:with length 3294: 3272: 3242:milliradians 3231: 3227: 3211:aeronautical 3208: 3195: 3185: 3181: 3173: 3169: 3168: 3158: 3152: 3145: 3134: 3130: 3126: 3122: 3118: 3114: 3110: 3106: 3102: 3098: 3094: 3087: 3077: 3073: 3069: 3065: 3061: 3057: 3053: 3047: 3040: 3036: 3029: 3025: 3018: 3012: 3007: 3002: 2994: 2990: 2986: 2982: 2979:ordered pair 2974: 2969: 2963: 2956: 2949: 2945: 2938: 2932: 2928: 2924: 2920: 2914: 2907: 2903: 2899: 2895: 2890: 2882: 2853: 2844: 2836: 2834: 2830: 2816: 2792: 2780: 2777: 2769: 2765: 2751: 2749: 2740: 2736: 2727: 2671: 2645: 2587: 2484: 2001: 1992: 1940: 1936: 1930: 1923: 1854:Description 1791:Information 1755: 1752: 1742: 1710: 1703: 1697: 1693: 1689: 1685: 1681: 1671: 1666: 1660: 1653: 1650:mod 767 250) 1647: 1640: 1636: 1632: 1627: 1619: 1612: 1608: 1604: 1599: 1590:modular LFSR 1587: 1565: 1562: 1557: 1551: 1538: 1534: 1532: 1528: 1519: 1515: 1508: 1502: 1487: 1482: 1479: 1464: 1456: 1453:Data updates 1362:1, 6, 10–12, 1354:Description 1248:1, 6, 11–12, 1240:Description 1183: 1181: 1167: 1163: 1159: 1150: 1146: 1141: 1137: 1135: 1132: 1127: 1122: 1118: 1116: 1112: 1094: 1089: 1081: 1079: 1003:Description 975: 970: 962: 958: 952: 948: 940: 925: 920: 915: 911: 909: 900: 893: 883: 879: 875: 871: 867: 863: 859: 855: 845: 841: 837: 833: 827: 822: 815: 806: 802: 798: 794: 790: 786: 781: 770: 738: 723: 709: 694: 686:carrier wave 679: 658: 654: 652: 633: 632:(SV ID) and 629: 625: 623: 606: 599: 593: 585: 573: 567: 547: 542: 538: 530: 525: 521: 503: 496: 486: 484: 451: 450: 193:Technologies 148: / 60:Fundamentals 7469:Operational 7063:www.gps.gov 6905:www.gps.gov 6662:Inside GNSS 6428:convolution 6424:correlation 6167:correlation 6143:dot product 6086:Acquisition 6079:correlation 5414:interleaved 5412:, and then 5368:week number 4353:code or L1C 2966:mod 10 230) 2646:FEC encoded 1831:Alert flag 1756:final state 1676:§ Time 1622:mod 10 230) 1547:multiplexed 944:ephemerides 506:L1 C/A 474:(2SOPS) of 452:GPS signals 71:Geodynamics 7668:Navigation 7657:Categories 7510:Historical 7421:2007-09-10 7395:2013-07-24 7363:2013-07-24 7332:2009-10-13 7274:GPS-IS-800 7262:GPS-IS-800 7250:GPS-IS-800 7238:GPS-IS-800 7226:GPS-IS-800 7214:GPS-IS-800 7202:GPS-IS-800 7187:GPS-IS-800 7174:GPS-IS-800 7162:GPS-IS-800 7147:GPS-IS-705 7132:GPS-IS-705 7120:GPS-IS-705 7108:GPS-IS-705 7068:2024-02-16 7023:2010-07-18 6997:GPS-IS-200 6985:GPS-IS-200 6973:GPS-IS-200 6935:GPS-IS-200 6873:GPS-IS-200 6861:GPS-IS-200 6846:2013-07-24 6817:GPS-IS-200 6805:GPS-IS-200 6793:GPS-IS-200 6781:GPS-IS-200 6739:2013-07-24 6707:GPS-IS-200 6695:GPS-IS-200 6683:GPS-IS-200 6622:GPS-IS-200 6610:GPS-IS-200 6568:2021-01-18 6223:deviation 5360:the format 5202:Subframes 4403:for which 2839:) and the 1867:12, 31, 37 1539:civil-long 1474:See also: 935:See also: 765:orthogonal 741:Gold codes 701:quadrature 7562:(retired) 6851:Page 103. 6468:ephemeris 6434:than the 6178:1,023/0.5 6152:sinusoids 6041:Gold code 6008:± 5828:π 5814:ϕ 5804:ω 5796:⁡ 5790:− 5784:⏟ 5769:ϕ 5759:ω 5751:⁡ 5708:− 5694:ϕ 5684:ω 5676:⁡ 5435:Frequency 5210:Bit count 4889:≤ 4873:≤ 4644:− 4420:≤ 4414:≤ 3872:≡ 3850:≠ 3758:⊕ 3628:≥ 3604:− 3546:≤ 3507:− 3308:Weil code 3050:is used: 2440:≡ 2409:− 2358:≡ 2260:− 2248:⊕ 2239:− 2227:⊕ 2218:− 2206:⊕ 2197:− 2185:⊕ 2134:− 2122:⊕ 2113:− 2101:⊕ 2092:− 2080:⊕ 2071:− 2059:⊕ 1986:aviation. 1875:13–14, 34 1799:Preamble 1554:modulated 1367:Reserved 1364:16, 19–24 1258:2–5, 7–10 1253:Reserved 1250:16, 19–24 1123:subframes 1104:ephemeris 1086:modulates 1047:Ephemeris 971:P(Y)-code 761:correlate 682:modulated 659:precision 488:ephemeris 150:Longitude 76:Geomatics 7596:StarFire 7591:SouthPAN 7527:Timation 6474:See also 6403:51×2,046 6243:1,022.5 6202:20×2,046 6171:argument 5397:BCH code 5277:Page no. 5221:Encoded 5207:Subframe 5115:, where 5019:′ 4957:′ 4927:′ 4885:′ 4804:′ 4627:′ 4533:′ 4199:GPS time 4118:′ 4093:′ 4015:′ 3640:′ 3624:′ 3600:′ 3569:′ 3553:′ 3542:′ 3519:′ 3503:′ 3485:′ 3469:′ 3451:′ 3412:′ 3401:′ 3359:′ 3178:C/A code 3163:GPS time 2989:) where 2707:⌋ 2697:′ 2687:⌊ 2631:′ 2604:′ 2436:′ 2428:if 2405:′ 2354:′ 2346:if 2330:′ 2288:′ 2277:′ 1945:It uses 1931:messages 1851:Type ID 1747:GPS time 1411:and UTC 1372:2–5, 7–9 1297:and UTC 1171:rollover 955:spoofing 572:(called 539:codeless 464:velocity 329:ISO 6709 227:(Europe) 225:Galileo 211:(Russia) 209:GLONASS 146:Latitude 135:Geodesic 93:Concepts 7637:Wavelet 7532:Tsiklon 7522:Transit 7491:GLONASS 7486:Galileo 7087:FAA.gov 7043:28 June 6910:10 June 6886:GPS FAQ 6668:17 July 6664:: 14–19 6452:Doppler 6240:1,022.0 6057:acquire 5571:1176.45 5522:1381.05 5488:1227.60 5454:1575.42 5349:L5 CNAV 5345:L2 CNAV 4548:0-based 4546:is the 4512:0-based 4347:symbols 4192:⁄ 3942:where: 3199:L2 CNAV 2970:where: 2845:Q5-code 2837:I5-code 2812:GPS III 2808:GPS IIF 2804:USA-203 2485:where: 1973:GLONASS 1969:Galileo 1836:277–300 1654:where: 1483:GPS III 1184:almanac 1178:Almanac 816:where: 684:onto a 498:almanac 389:Geo URI 359:NAVD 88 269:NGVD 29 243:(Japan) 235:(India) 219:(China) 81:History 66:Geodesy 43:Geodesy 7476:BeiDou 7296: 6641: 6409: 6405: 6386: 6382: 6208: 6204: 6196: 6192: 6184: 6180: 5858:where 5576: 5493: 5459: 5440:Phase 5437:(MHz) 5299:& 5039:to 0. 4381:domain 4303:where 4231:or L1C 4223:is an 3016:and Q5 2977:is an 1964:years. 1883:15, 36 1700:times. 1664:and CL 1552:CM is 1543:chip/s 1119:frames 963:Y-code 959:W-code 643:NAVCEN 379:GCJ-02 369:ETRS89 349:WGS 84 339:NAD 83 319:GRS 80 279:OSGB36 233:NAVIC 114:radius 7642:RINEX 7581:NTRIP 7566:JPALS 7560:GPS·C 7555:GAGAN 7550:EGNOS 7481:DORIS 7389:(PDF) 7382:(PDF) 7357:(PDF) 7350:(PDF) 7013:(PDF) 6840:(PDF) 6833:(PDF) 6768:(PDF) 6761:(PDF) 6733:(PDF) 6726:(PDF) 6658:(PDF) 6539:Notes 6530:(PDF) 6518:(PDF) 6506:(PDF) 6288:(more 6061:track 5608:chips 5432:Band 5334:Text 5246:1,200 4785:) of 4194:1.023 4131:with 1859:10–11 1820:21–37 1812:15–20 1788:Bits 1390:14–15 1345:frame 1276:14–15 1231:frame 994:frame 916:chips 705:phase 309:SAD69 289:SK-42 104:Geoid 7606:SDCM 7601:WAAS 7576:MSAS 7571:LAAS 7294:ISBN 7095:2018 7045:2022 6957:next 6912:2021 6670:2019 6305:... 6188:and 5954:and 5887:and 5386:next 5366:The 5347:and 5297:GGTO 5086:and 4961:> 4817:and 4345:are 4332:P, D 3557:< 3473:< 3172:and 3043:PRN. 3028:and 2948:) = 2927:) = 2906:) ⊕ 2898:) = 2810:and 2798:for 2752:MNAV 2515:and 2002:The 1971:and 1804:9–14 1709:and 1635:) = 1607:) = 1429:1–24 1350:Page 1343:Sub- 1315:1–24 1236:Page 1229:Sub- 1208:WAAS 1182:The 1156:Time 1128:page 1102:The 1084:and 1067:3–10 1044:3–10 1021:3–10 999:Word 992:Sub- 912:bits 797:) ⊕ 789:) = 720:WAAS 697:BPSK 673:GPS 598:and 590:DSSS 568:The 541:and 535:chip 516:and 299:ED50 116:and 6367:DFT 6362:FFT 6339:... 6319:... 6302:... 6299:... 6296:... 6293:... 6277:... 6257:... 6234:0.5 6231:0.0 5793:cos 5748:sin 5673:cos 5406:CRC 5373:An 5301:EOP 5262:548 5259:250 5243:576 5218:Raw 5036:229 5010:L1C 4968:222 4918:L1C 4896:222 4826:L1C 4795:L1C 4718:mod 4427:222 4269:or 4151:230 4143:mod 4089:L1C 4066:L1C 4038:L1C 4006:L1C 3955:L1C 3898:223 3890:mod 3798:223 3790:mod 3392:L1C 3378:230 3370:mod 3355:L1C 3327:L1C 3303:223 3250:BOC 3217:L1C 2796:ITU 2758:). 2756:CRC 2451:mod 2369:mod 1958:CRC 1796:1–8 1769:249 1767:767 1762:229 1525:L2C 1196:UTC 1092:). 1057:1–2 1054:4–5 1034:1–2 1031:2–3 1011:1–2 914:or 820:C/A 779:C/A 718:or 707:). 690:MHz 592:), 518:L1C 510:L2C 7659:: 7194:^ 7154:^ 7139:^ 7085:. 7061:. 7015:. 6903:. 6892:^ 6749:^ 6714:^ 6660:. 6602:^ 6546:^ 6376:. 6369:. 6345:• 6325:• 6283:• 6263:• 5568:L5 5548:L4 5519:L3 5485:L2 5451:L1 5380:A 5232:52 5174:S2 5145:S1 5096:S2 5067:S1 5051:. 5034:10 4964:10 4892:10 4423:10 4147:10 3894:10 3794:10 3374:10 3301:10 3129:+ 3125:+ 3121:+ 3117:+ 3113:+ 3109:+ 3105:+ 3099:t' 3088:XB 3076:+ 3072:+ 3068:+ 3062:t' 3054:XA 3048:t' 3041:or 2985:, 2962:, 2950:XB 2931:(( 2929:XA 2789:L5 1915:35 1907:33 1899:32 1891:30 1828:38 1760:10 1688:, 1678:). 1658:CM 1625:CL 1597:CM 1485:. 1437:25 1416:25 1406:18 1398:17 1380:13 1323:25 1302:25 1292:18 1284:17 1266:13 973:. 882:+ 878:+ 874:+ 870:+ 866:+ 862:→ 844:+ 840:→ 726:. 645:. 514:L5 512:, 508:, 501:. 482:. 478:, 7454:e 7447:t 7440:v 7424:. 7398:. 7366:. 7335:. 7302:. 7097:. 7071:. 7047:. 7026:. 6963:. 6925:. 6914:. 6849:. 6742:. 6672:. 6585:. 6571:. 6407:= 6384:= 6342:• 6336:• 6333:• 6322:• 6316:• 6313:• 6280:• 6274:• 6271:• 6260:• 6254:• 6251:• 6206:= 6194:= 6182:= 6128:. 6043:. 6014:) 6011:1 6004:= 6001:( 5979:) 5976:t 5973:( 5968:Q 5964:X 5941:) 5938:t 5935:( 5930:I 5926:X 5901:Q 5897:P 5872:I 5868:P 5843:, 5837:) 5831:2 5823:+ 5818:0 5810:+ 5807:t 5800:( 5779:) 5773:0 5765:+ 5762:t 5755:( 5741:) 5738:t 5735:( 5730:Q 5726:X 5718:Q 5714:P 5704:) 5698:0 5690:+ 5687:t 5680:( 5670:) 5667:t 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