Global Positioning

System (GPS)

24 satellite constellation24 satellite constellation Semi-synchronous, circular orbits Semi-synchronous, circular orbits

(~20,200 km/10,900 nautical (~20,200 km/10,900 nautical miles altitude)miles altitude)

Six orbital planes, inclined at 55 Six orbital planes, inclined at 55 degrees, four vehicles per planedegrees, four vehicles per plane

Repeating ground tracks (11 hours 58 minutes)Repeating ground tracks (11 hours 58 minutes) at least four satellites always in viewat least four satellites always in view

Cesium and/or rubidium clocks on board each Cesium and/or rubidium clocks on board each operational satelliteoperational satellite

GPS Satellite Constellation

Developed by the US Department of Defense Developed by the US Department of Defense Early GPS program driver was Trident Missile Early GPS program driver was Trident Missile

Program (Submarine launched ICBM)Program (Submarine launched ICBM) Precursors to GPSPrecursors to GPS

TransitTransit Timation (first atomic frequency standards flown in Timation (first atomic frequency standards flown in

space)space) USAF 621B Program (PRN codes for ranging)USAF 621B Program (PRN codes for ranging)

First prototype GPS satellite launched in 1978First prototype GPS satellite launched in 1978 First Block II (Operational) GPS satellite First Block II (Operational) GPS satellite

launched 1989launched 1989 Full Operational Capability declared in 1994Full Operational Capability declared in 1994

GPS History

Assume the maximum acceptable error Assume the maximum acceptable error contribution from GPS satellite clocks is 1 metercontribution from GPS satellite clocks is 1 meter Light travels 3x10Light travels 3x1088 m/s, one-meter requirement m/s, one-meter requirement

equivalent to 3.3 ns ranging errorequivalent to 3.3 ns ranging error Clock error must be maintained below this level over Clock error must be maintained below this level over

12 hour period (time between satellite uploads)12 hour period (time between satellite uploads) Requires a clock with < 1 part in 10Requires a clock with < 1 part in 101313 stability, which stability, which

can only be met by an atomic standardcan only be met by an atomic standard

Note: The frequency shift on the GPS satellite Note: The frequency shift on the GPS satellite clock due to relativistic effects (special and clock due to relativistic effects (special and general) is on the order of 4 to 5 parts in 10general) is on the order of 4 to 5 parts in 101010

Precise Timing is Fundamental to GPS

Two L-band carrier frequenciesTwo L-band carrier frequencies LL11 = 1575.42 MHz L = 1575.42 MHz L22 = 1227.60 MHz = 1227.60 MHz

Two PRN CodesTwo PRN Codes P(Y): Military Code P(Y): Military Code

267 day repeat interval267 day repeat interval Encrypted – code sequence not publishedEncrypted – code sequence not published Available on L1 and L2Available on L1 and L2

C/A: Coarse Acquisition (Civilian) CodeC/A: Coarse Acquisition (Civilian) Code 1 millisecond repeat interval1 millisecond repeat interval Available to all users, but only on L1Available to all users, but only on L1

Code modulated with Navigation Message DataCode modulated with Navigation Message Data Provides ephemeris data and clock corrections for the GPS Provides ephemeris data and clock corrections for the GPS

satellitessatellites Low data rate (50 bps)Low data rate (50 bps)

GPS Signal Structure

Space VehiclesSpace Vehicles

Block 0 (NTS)Satellite

Block II Satellite -SVN 13-21 1989-90 (2 Cs and 2 Rb) Block IIA Satellite - SVN 22-40 1990-1997

Block I Satellite –SVN 1 -12

1978-85(none in

service)

Block IIR and IIR-M Satellites -

SVN 41-621997-2005(0 Cs and 3

Rb)

Block IIF and GPSIII SatellitesSVN 63 - ?? 2005- ???? (3 Cs and 1 Rb)

Most GPSDOs receive the L1 Most GPSDOs receive the L1 carrier frequency at 1575.42 MHzcarrier frequency at 1575.42 MHz

The L1 carrier contains the C/A, The L1 carrier contains the C/A, or Coarse Acquisition Codeor Coarse Acquisition Code

1 millisecond repeat interval1 millisecond repeat interval 1023 bits1023 bits

Currently 29 satellites in orbit (all Currently 29 satellites in orbit (all slots filled except PRNs 9, 12, slots filled except PRNs 9, 12, and 32)and 32) 9 running off Cesium 9 running off Cesium

oscillatorsoscillators 20 running off Rubidium 20 running off Rubidium

oscillatorsoscillatorsBlock IIR Vehicles

Block II/IIA Vehicles

GPS Satellites

Monitor Stations: Hawaii, Ascension Island, Diego Garcia, Monitor Stations: Hawaii, Ascension Island, Diego Garcia, Kwajalein, and Colorado SpringsKwajalein, and Colorado Springs Monitor the GPS satellites for operational healthMonitor the GPS satellites for operational health Track the GPS satellites for orbit determinationTrack the GPS satellites for orbit determination Upload navigation message data including satellite almanacs, Upload navigation message data including satellite almanacs,

ephemeris messages, and clock correction parametersephemeris messages, and clock correction parameters

GPS Control Stations

GPS-based positioning is GPS-based positioning is fundamentally based on:fundamentally based on: The precise measurement of timeThe precise measurement of time The constancy of the speed of lightThe constancy of the speed of light

GPS-based positioning uses the GPS-based positioning uses the concept of trilaterationconcept of trilateration GPS satellite positions are knownGPS satellite positions are known Receiver position is notReceiver position is not GPS-to-receiver range measurements are GPS-to-receiver range measurements are

used to compute positionused to compute position

GPS Positioning

Transmitter(location known)

Receiver(location

unknown)

Locus of points on which the receiver can be located

Measured Range

Positioning Example with 1 Transmitter

True Receiver Location

T1

T2

False Receiver Location

Positioning Example with 2 Transmitters

True Receiver Location

T1

T2

T3

Positioning Example with 3 Transmitters

The position solution involves solving for The position solution involves solving for fourfour unknowns:unknowns:• Receiver position (x, y, z)Receiver position (x, y, z)• Receiver clock correctionReceiver clock correction

Remember: Remember: Position accuracy of ~10 m implies Position accuracy of ~10 m implies knowledge of the receiver clock to within ~30 nsknowledge of the receiver clock to within ~30 ns

Requires simultaneous measurements from four GPS Requires simultaneous measurements from four GPS satellitessatellites• The receiver makes a range measurement to the The receiver makes a range measurement to the

GPS satellite by measuring the signal propagation GPS satellite by measuring the signal propagation delaydelay

• The data message modulated on the GPS signals The data message modulated on the GPS signals provides the precise location of the GPS satellite provides the precise location of the GPS satellite and corrections for the GPS satellite clock errorsand corrections for the GPS satellite clock errors

GPS Positioning - II

Although the primary purpose of GPS is to serve as a positioning and radionavigation system, the entire system relies on precise timing. After the receiver position (x, y, z) is solved for, the solution is stored.

Then, given the travel time of the signals (observed) and the exact time when the signal left the satellite (given), time from the atomic clocks (either cesium or rubidium) onboard the satellites can be transferred to the receiver clock. The basic measurement made by the GPS receiver reveals the difference between the satellite clock and the receiver clock. This measurement, when multiplied by the speed of light, produces not the true geometric range but rather the pseudorange, with deviations introduced by the lack of time synchronization between the satellite clock and the receiver clock, by delays introduced by the ionosphere and troposphere, and by multipath and receiver noise. The equation for the pseudorange observable is

p = ρ + c × (dt − dT ) + dion + dtrop + rn

where p is the pseudorange, c is the speed of light, ρ is the geometric range to the satellite, dt and dT are the time offsets of the satellite and receiver clocks with respect to GPS time, dion isthe delay through the ionosphere, dtrop is the delay through the troposphere, and rn represents the effects of receiver and antenna noise, including multipath. An estimate of dion is obtained from the GPS broadcast.

GPS Signals

GPS Modulation

The carriers are pure sinusoids. Two binary codes are modulated onto them: the C/A (coarse/acquistion) code and the P (precise) code.

Binary biphase modulation (also known as binary phase shift keying [BPSK]) is the technique used to modulate the codes onto the carrier. There is a 180 degree carrier phase shift each time the code state changes.

The modulation requires a much wider frequency band than the minimum bandwidth required to transmit the information being sent. This is known as spread spectrum modulation. It allows lower power levels to be used.

““Spreads" the power spectrum of the transmitted Spreads" the power spectrum of the transmitted data over a wide frequency band data over a wide frequency band

Same principle is used for digital phones (voice is Same principle is used for digital phones (voice is the data)the data)

Each satellite is assigned unique Pseudo-Each satellite is assigned unique Pseudo-Random Noise (PRN) CodeRandom Noise (PRN) Code Allows Multiple Access – All GPS satellites transmit at Allows Multiple Access – All GPS satellites transmit at

the same frequencythe same frequency

Spread Spectrum Communication

The transmitted signal is the product of the The transmitted signal is the product of the navigation data, a spreading code, and the RF navigation data, a spreading code, and the RF carrier (either L1 or L2)carrier (either L1 or L2)

In order to detect the GPS signal and recover the In order to detect the GPS signal and recover the navigation data, the receiver must produce a navigation data, the receiver must produce a replica of the PRN code to mix with the incoming replica of the PRN code to mix with the incoming signal (PRN codes must be known)signal (PRN codes must be known)

The measured phase offset between the The measured phase offset between the incoming and replica PRN code is the GPS range incoming and replica PRN code is the GPS range measurementmeasurement

Spread Spectrum Communication - II

frequency

frequency

1. “Random” Binary Data Message Spectrum

2. Data*Spreading Code Spectrum

Signal is “Spread”

0 Hz

0 Hz

In our example, the data would be spread across 3 times the bandwidth of the data

Data Rate

Spreading Code Rate

Why the name “Spread Spectrum”?

frequency

frequency

1. Data Message Spectrum

2. Data*Code Spectrum Signal is “Spread”

3. Data*Code*Carrier Spectrum

This is the transmitted signal

0 Hz

0 Hz

0 Hz 1.57542 GHz

50 Hz

1.023 MHz

1.023 MHz

Spectrum chart of GPS L1 Signal

GPS Signal in Space

GPS Time Controlled by the United States Naval Observatory (USNO), but not

exactly the same thing as UTC(USNO). GPS time differs from UTC by the number of leap seconds that have

occurred since the origination of the GPS time scale (January 6, 1980); this value is equal to 13 s as of November 2005, it will become 14 s after the next leap second. The navigation message contains a leap second correction, however, and GPS receivers automatically correct the time-of-day solution.

It also differs from UTC(USNO) by a small number of nanoseconds that continuously changes. The current difference between the UTC(USNO) estimate and GPS time is also in the navigation message, and this correction is applied to the 1 pps signal.

After the leap second and UTC(USNO) corrections are applied, GPS time is usually within 30 nanoseconds of UTC, UTC(NIST), and UTC(USNO). This makes it the best estimate of UTC being broadcast anywhere, and it is available free of change to anyone, worldwide.

The frequency offset between the UTC(USNO) estimate and UTC(NIST) is very small, typically a few parts in 1015 or less when measured over a one month interval.

GPS Time vs. NIST and USNO

Factors limiting uncertainty of GPS Factors limiting uncertainty of GPS time received by userstime received by users

Errors in site survey, particularly errors in altitude Multipath Poor estimates of cable, antenna, and receiver

delays Ionospheric and Tropospheric corrections Changing delays in hardware and cables due to

temperature and other environmental factors

DOP depends on the geometry of satellites.

Self survey of receiver position typically waits for large number of satellites in view, and low DOP values. DOP values can range from 1 to infinity, most timing receivers want a DOP of < 3 before they accept an antenna survey.

Good (Low) DOPConditions:

Poor (High) DOPConditions:

Dilution of Precision (DOP)

GPS Transfer Techniques One Way (GPSDOs)One Way (GPSDOs) Single Channel Common-ViewSingle Channel Common-View

Tracking schedule, 1 satellite at a Tracking schedule, 1 satellite at a timetime

Multi-Channel Common-ViewMulti-Channel Common-View No schedule, all satellites in viewNo schedule, all satellites in view

Carrier PhaseCarrier Phase

One-Way Time Transfer

One-Way GPS Uses time signals from GPS receiver or frequency Uses time signals from GPS receiver or frequency

signals from GPSDO as real-time reference for a signals from GPSDO as real-time reference for a calibrationcalibration

Most receivers can provide on-time pulse and standard Most receivers can provide on-time pulse and standard frequenciesfrequencies

Receiver must complete acquisition process before useReceiver must complete acquisition process before use Time uncertainty relative to UTC or UTC(NIST) is Time uncertainty relative to UTC or UTC(NIST) is

usually less than 1 usually less than 1 s for nearly any receiver. s for nearly any receiver. Uncertainty can be much less than 100 ns if receiver Uncertainty can be much less than 100 ns if receiver and antenna delays are calibrated. and antenna delays are calibrated.

Frequency uncertainty is typically < 1 x 10Frequency uncertainty is typically < 1 x 10-12-12 after 1 day after 1 day of averaging.of averaging.

GPS Time Performance improved dramatically after May 2, 2000, when

the Selective Availability (SA) program was deactivated, removing the intentionally introduced jitter from the signal

SA had been previously implemented by the United States government for reasons of national defense.

GPS before and after SA Deactivation

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GPS Time vs. UTC(NIST)

GPS Disciplined Oscillators (GPSDO)

Operated as standalone time and frequency standards, often as the primary standard for the lab. GPSDOs discipline a local oscillator (quartz or rubidium) to GPS and serve as a self-calibrating standard that will perform at a high level if the receiver hardware and the GPS constellation are functioning normally.

Produce on-time pulse (1 pps). Produce standard frequency outputs (such as 1, 5, and 10

MHz). Some units produce frequencies used in telecommunications

(1.544 MHz, for example).

Disciplined Oscillator (steered, no synthesizer)

Disciplined Oscillator (unsteered, synthesizer)

GPS Receiver Operation Install antenna at fixed location. Make sure that

antenna gain is sufficient to drive antenna cable. Combination of high-gain antenna, low-loss cable, and inline-amplifiers might be needed in some cases.

Survey position. Position can be entered or receiver can self survey. Same position fix is used from then on, since antenna won’t be moving.

Use time and frequency outputs as measurement references.

GPS AntennasGPS Antennas Small and inexpensive,

higher gain units (> 35 dB typical) generally used for timing to drive long cables

Omnidirectional, need to have clear sky view on all sides for best results

OCXO with and without GPS

GPSDO “optimized” for short-term stability

Test of GPSDOs vs. UTC(NIST)

NIST tested four commercial GPSDOs in the spring and summer of 2005 against the UTC(NIST) time scale.

Two had rubidium time bases, two had OCXO timebases.

We measured the 1 pps and 10 MHz outputs at the same time with two different measurement systems.

Results showed very different behaviour amongst different GPSDOs.

Test of GPSDOs vs. UTC(NIST)

10 MHz Phase of GPSDOs vs. UTC(NIST)

10 MHz Stability of GPSDOs vs. UTC(NIST)

Common-View Time Transfer

Common View GPS Two users, A and B, observe SV at same time. Two data sets are recorded (one at each site):

Clock A - GPS Clock B - GPS

Data is exchanged. Subtract A from B to get difference between devices. Common errors cancel. Used for international computation of UTC.

Keys to Successful Common-View Measurements

Same type of receiver (manufacturer and model) should be Same type of receiver (manufacturer and model) should be used at each siteused at each site

All antenna, cable, and receiver delays must be calibrated All antenna, cable, and receiver delays must be calibrated and used as delay constantsand used as delay constants

Site survey at each site should have the least amount of Site survey at each site should have the least amount of uncertainty possible, ideally less than 1 meter for both 2D uncertainty possible, ideally less than 1 meter for both 2D and 3D position. A good survey of altitude is especially and 3D position. A good survey of altitude is especially important.important.

The ionospheric, tropospheric, and multipath delays should The ionospheric, tropospheric, and multipath delays should be nearly equivalent at each site. For the absolute best be nearly equivalent at each site. For the absolute best results, corrections for these delays are generate at each results, corrections for these delays are generate at each site.site.

Relative delays at both sites should be as close to zero as Relative delays at both sites should be as close to zero as possible.possible.

Common-View Common-Clock Comparisons, 10-minute averagesType 1 to Type 1 Rx (top), Type 2 to Type 2 Rx (middle), Type 1 to Type 2 Rx (bottom)

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Modified Julian Date (MJD)

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Impact of SA on GPS Time and Frequency Transfer

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REFa - GPS (difference is offset for demonstration purpose)

REFb - GPS (difference is offset for demonstration purpose)

Common-view difference (REFa - REFb)

All-In-View Common-View System

No tracking schedule, collects data from all satellites in viewNo tracking schedule, collects data from all satellites in view Stores data (10-min averages) in 32 x 144 matrixStores data (10-min averages) in 32 x 144 matrix Uploads to Internet for on-the-fly processing. Data are Uploads to Internet for on-the-fly processing. Data are

currently uploaded once per day, but more frequent uploads currently uploaded once per day, but more frequent uploads are possible and would create a near real-time common-view are possible and would create a near real-time common-view networknetwork

Collects about 400 min of data from each satellite per dayCollects about 400 min of data from each satellite per day Web-based software (CGI scripts) plots the composite and Web-based software (CGI scripts) plots the composite and

individual tracks recorded at both sites, plus does the common-individual tracks recorded at both sites, plus does the common-view data reductionview data reduction

Web-based software calculates average frequency and time Web-based software calculates average frequency and time offset, plus Allan deviation and time deviationoffset, plus Allan deviation and time deviation

Sample Common-View Track

TT

Sample Common-View Track (A-B)

One WayOne Way Multi-Channel Common-ViewMulti-Channel Common-View Direct Comparison with Time Interval CounterDirect Comparison with Time Interval Counter

Same GPS receiver used for all Same GPS receiver used for all measurements shown here.measurements shown here.

Direct Digital Synthesizer (DDS) produces 10 Direct Digital Synthesizer (DDS) produces 10 MHz sine wave, offset by either 10, 4, or 1 MHz sine wave, offset by either 10, 4, or 1 Hz. Frequency stability is a few parts in 10Hz. Frequency stability is a few parts in 1015 at at = 1 day. = 1 day.

Measurement Comparison

One-Way

Common-View

Direct Comparison

Comparison of Methods with Test Signal Offset by 10 uHz

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Comparison of Methods with Test Signal Offset by 4 uHz

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Comparison of Methods w ith Test Signal Offset by 1 uHz

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One-WayCommon-View

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Noise floor of 1 µHz offset test

Comparison Summary The one-way method can meet all existing requirements of calibration and testing

laboratories. It can measure a frequency offset as small as 4 x 10-13 in 1 day, or 1 x 10-13 in one week with high confidence.

Common-view has a lower noise floor than one-way, but perhaps not significantly lower from the viewpoint of calibration laboratories. However, common-view is a direct clock comparison with a simpler traceability chain.

Three caveats: Some GPSDOs might not be capable of duplicating the results shown here. Common-view performance over a long baseline will be worse than the near zero-baseline

results reported here. Over a 1000 km baseline, for example, it might be difficult for a calibration laboratory to detect any difference at all between the two methods.

GPS Performance Comparison

Technique Timing Uncertainty, 24 h, 2

Frequency Uncertainty, 24 h, 2

One-Way

< 50 ns < 2 x 10-13

Multi-Channel Common-View

15 ns < 1 x 10-13