Search Results for “gps signals”

Source: GPS signals

GPS signals are broadcast by Global Positioning System satellites to enable satellite navigation. Receivers on or near the Earth's surface can determine location, time, and velocity using this information. The GPS satellite constellation is operated by the 2nd Space Operations Squadron (2SOPS) of Space Delta 8, United States Space Force.
GPS signals include ranging signals, which are used to measure the distance to the satellite, and navigation messages. The navigation messages include ephemeris data which are used both in trilateration 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 almanac.
There are four GPS signal specifications designed for civilian use. In order of date of introduction, these are: L1 C/A, L2C, L5 and L1C. L1 C/A is also called the legacy signal and is broadcast by all currently operational satellites. L2C, L5 and L1C are modernized signals 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 restricted signals with published frequencies and chip 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 codeless and semi-codeless access, and this is officially supported.
The interface to the User Segment (GPS receivers) is described in the Interface Control Documents (ICD). The format of civilian signals is described in the Interface Specification (IS) which is a subset of the ICD.

Common characteristics

GPS

signals

GPS

Legacy GPS signals

GPS

= Frequency information

GPS

= Modulation codes

GPS

signals

GPS

= Navigation message

GPS

signals

Modernization and additional GPS signals

GPS

signals

= General features

GPS

signals

GPS

= L2C

signals

GPS

= Military (M-code)

= L5

GPS

signals

GPS

= L1C

where:

L1C

i

{\displaystyle {\text{L1C}}_{i}}

is the ranging code for PRN number and component

i

{\displaystyle i}

.

L1C

i

′

{\displaystyle {\text{L1C}}'_{i}}

represents a period of

L1C

i

{\displaystyle {\text{L1C}}_{i}}

; it is introduced only to allow a more clear notation. To obtain a direct formula for

L1C

{\displaystyle {\text{L1C}}}

start from the right side of the formula for

L1C

′

{\displaystyle {\text{L1C}}'}

and replace all instances of

t
′

{\displaystyle t'}

with

t

mod

10

230

{\displaystyle t{\bmod {10\,230}}}

.

t

{\displaystyle t}

is the integer number of L1C chip periods (which is 1⁄1.023 μs) since the origin of GPS time or equivalently, since any GPS second (starting from 0).

i

{\displaystyle i}

is an ordered pair identifying a PRN number and a code (L1CP or L1CD) and is of the form

(

P

,
n
)

{\displaystyle ({\text{P}},n)}

or

(

D

,
n
)

{\displaystyle ({\text{D}},n)}

where

n

{\displaystyle n}

is the PRN number of the satellite, and

P, D

{\displaystyle {\text{P, D}}}

are symbols (not variables) that indicate the L1CP code or L1CD code, respectively.

L

{\displaystyle L}

is an intermediate code: a Legendre sequence whose domain is the set of integers

n

{\displaystyle n}

for which

0
≤
n
≤
10

222

{\displaystyle 0\leq n\leq 10\,222}

.

W

i

{\displaystyle W_{i}}

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

L

{\displaystyle L}

.

S

{\displaystyle S}

is a 7-bit long sequence defined for 0-based indexes 0 to 6.

p

i

′

{\displaystyle p'_{i}}

is the 0-based insertion index of the sequence

S

{\displaystyle S}

into the ranging code (specific for PRN number and code

i

{\displaystyle i}

). It is defined in the Interface Specification (IS) as a 1-based index

p

{\displaystyle p}

, therefore

p

i

′

=

p

i

−
1

{\displaystyle p'_{i}=p_{i}-1}

.

w

i

{\displaystyle w_{i}}

is the Weil index for PRN number and code

i

{\displaystyle i}

designated in the IS.

mod

{\displaystyle \operatorname {mod} }

is the remainder of division (or modulo) operation, which differs to the notation in statements of modular congruence, also used in this article.
According to the formula above and the GPS IS, the first

w

i

{\displaystyle w_{i}}

bits (equivalently, up to the insertion point of

S

{\displaystyle S}

) of

L1C

i

′

{\displaystyle {\text{L1C}}'_{i}}

and

L1C

{\displaystyle {\text{L1C}}}

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

S

{\displaystyle S}

; the remaining bits are the remaining bits of the Weil code.
The IS asserts that

0
≤

p

i

′

≤
10

222

{\displaystyle 0\leq p'_{i}\leq 10\,222}

. For clarity, the formula for

L1C

i

′

{\displaystyle {\text{L1C}}'_{i}}

does not account for the hypothetical case in which

p

i

′

>
10

222

{\displaystyle p'_{i}>10\,222}

, which would cause the instance of

S

{\displaystyle S}

inserted into

L1C

i

′

{\displaystyle {\text{L1C}}'_{i}}

to wrap from index 10229 to 0.

L1C overlay code

The overlay codes are 1,800 bits long and is transmitted at 100 bit/s, synchronized with the navigation message encoded in L1CD.
For PRN numbers 1 to 63 they are the truncated outputs of maximal period LFSRs which vary in initial conditions and feedback polynomials.
For PRN numbers 64 to 210 they are truncated Gold codes generated by combining 2 LFSR outputs (

S1

i

{\displaystyle {\text{S1}}_{i}}

and

S2

i

{\displaystyle {\text{S2}}_{i}}

, where

i

{\displaystyle i}

is the PRN number) whose initial state varies.

S1

i

{\displaystyle {\text{S1}}_{i}}

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

S2

i

{\displaystyle {\text{S2}}_{i}}

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

CNAV-2 navigation message

The L1C navigation data (called CNAV-2) is broadcast in 1,800 bits long (including FEC) frames and is transmitted at 100 bit/s.
The frames of L1C are analogous to the messages of L2C and L5. While L2 CNAV and L5 CNAV use a dedicated message type for ephemeris data, all CNAV-2 frames include that information.
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.
The time of messages (not to be confused with clock correction parameters) is expressed in a different format than the format of the previous civilian signals. Instead it consists of 3 components:

The week number, 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.
An interval time of week (ITOW): 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.
A time of interval (TOI): the integer number of 18 second periods elapsed since the period represented by the current ITOW to the beginning of the next message. It has range 0 to 399 (inclusive) and requires 9 bits of data.
TOI is the only content of subframe 1. The week number and ITOW are contained in subframe 2 along with other information.
Subframe 1 is encoded by a modified BCH code. Specifically, the 8 least significant bits are BCH encoded to generate 51 bits, then combined using exclusive or 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 CRC, then individually encoded using a low-density parity-check code, and then interleaved as a single unit using a block interleaver.

Overview of frequencies

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 pseudo-random noise (PRN) sequence that is different for each satellite. The receiver must be aware of the PRN codes for each satellite to reconstruct the actual message data. The C/A code, for civilian use, transmits data at 1.023 million chips per second, whereas the P code, for U.S. military use, transmits at 10.23 million chips per second. The 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 equipment with a proper decryption key. Both the C/A and P(Y) codes impart the precise time-of-day to the user.
Each composite signal (in-phase and quadrature phase) becomes:

S
(
t
)
=

P

I

X

I

(
t
)
cos
⁡

(

ω
t
+

ϕ

0

)

−

P

Q

X

Q

(
t
)

sin
⁡

(

ω
t
+

ϕ

0

)

⏟

−
cos
⁡

(

ω
t
+

ϕ

0

+

π
2

)

,

{\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)},}

where

P

I

{\displaystyle \scriptstyle P_{\operatorname {I} }}

and

P

Q

{\displaystyle \scriptstyle P_{\operatorname {Q} }}

represent signal powers;

X

I

(
t
)

{\displaystyle \scriptstyle X_{\operatorname {I} }(t)}

and

X

Q

(
t
)

{\displaystyle \scriptstyle X_{\operatorname {Q} }(t)}

represent codes with/without data

(
=

±
1
)

{\displaystyle \scriptstyle (=\;\pm 1)}

. 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).

Demodulation and decoding

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 would alias into it) and digitalized; these steps may be chained in a different order. Note that aliasing is sometimes intentional (specifically, when undersampling is used) but filtering is still required to discard frequencies not intended to be present in the digital representation.
For each satellite used by the receiver, the receiver must first acquire the signal and then track it as long as that satellite is in use; both are performed in the digital domain in by far most (if not all) receivers.
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 (approx. 0.489 μs) is a representative value.
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 phase locked loop. Note that acquisition is performed to start using a particular satellite, but tracking is performed as long as that satellite is in use.
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 correlation 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 and is typically shorter than the duration of navigation data bits, which is 20 ms.

= Acquisition

=
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 space: (3) PRN number.

Frequency space
The frequency range of the search space is the band where the signal may be located given the receiver knowledge. The carrier frequency 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 § Frequencies used by GPS). 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.
Code phase space
The ranging code has a period of 1,023 chips each of which lasts roughly 0.977 μs (see § Coarse/acquisition code). 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.
PRN number space
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 § Navigation message.
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 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.

Simple correlation

The simplest way to acquire the signal (not necessarily the most effective or least computationally expensive) is to compute the dot product 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 Cartesian product of the frequency search space and the code phase search space. The carrier is a complex number where real and imaginary components are both sinusoids as described by Euler's formula. 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.
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 Fourier transform). The dot product is a complex number; its magnitude represents the level of similarity between the replica and the signal, as with an ordinary correlation of real-valued time series. The argument of the dot product is an approximation of the corresponding carrier in the digitalized signal.
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 1,023/0.5 = 2,046 code phases and 10,000 Hz/500 Hz = 20 frequencies to try for a total of 20×2,046 = 40,920 local replicas. 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.
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:

Fourier transform

As an improvement over the simple correlation method, it is possible to implement the computation of dot products more efficiently with a Fourier transform. Instead of performing one dot product for each element in the Cartesian product of code and frequency, a single operation involving FFT 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 bins are much closely spaced in a DFT.
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 discrete Fourier transform.
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 5 MHz×10 ms = 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 critical frequency). 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 51 frequency components. There are 2,046 code phases as in the previous case, thus in total 51×2,046 = 104,346 complex frequency components will be examined.

Circular correlation with Fourier transform

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 extra processing so that overall, it computes circular correlation instead of circular convolution. This yields more accurate code phase determination than the simple correlation method in contrast with the previous method, which yields more accurate carrier frequency determination than the previous method.

= Tracking and navigation message decoding

=
Since the carrier frequency received can vary due to Doppler 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 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.
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 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.
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 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.
Then the orbital position data, or ephemeris, 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.

Sources and references

= Bibliography

=
GPS Interface Specification

"GPS Interface Specification (GPS-IS-200K)" (PDF). 4 March 2019. (describes L1, L2C and P).
"GPS Interface Specification (GPS-IS-705F)" (PDF). 4 March 2019. (describes L5).
"GPS Interface Specification (GPS-IS-800E)" (PDF). 4 March 2019. (describes L1C).