civil and environmental engineering and geodetic science reference materials can be found at: more...

Civil and Environmental Engineering and Geodetic Science

Reference materials can be found at:

www.gmat.unsw.edu.au/snap/gps/about_gps.htm

More GPS links are provided on the course web page

Part II

WHAT IS GPS AND HOW IT WORKS

GS608


Global Positioning System (GPS)Global Positioning System (GPS)

The NAVSTAR Global Positioning System (GPS) is a satellite-based radio-positioning and time-transfer system, designed, financed, deployed and operated by the US Department of Defense.

However, the system has currently significantly larger number of civilian users as compared to the military users.


Global Positioning System (GPS)Global Positioning System (GPS)

The NAVSTAR Global Positioning System (GPS) program was initiated in 1973 through the combined efforts of the US Army, the US Navy, and the US Air Force.

The new system, designed as an all-weather, continuous, global radio-navigation system was developed to replace the old satellite navigation system, TRANSIT, which was not capable of providing continuous navigation data in real time on a global basis.


Suitable for all classes of platform: aircraft, ship, land-based and space (missiles and satellites),

Able to handle a wide variety of dynamics,

Real-time positioning, velocity and time determination capability to an appropriate accuracy,

The positioning results were to be available on a single global geodetic datum,

Highest accuracy to be restricted to a certain class of user,

Resistant to jamming (intentional and unintentional),

Redundancy provisions to ensure the survivability of the system,

GPS – Objectives 1/2GPS – Objectives 1/2


Passive positioning system that does not require the transmission of signals from the user to the satellite(s),

Able to provide the service to an unlimited number of users,

World-wide coverage

Low cost, low power, therefore as much complexity as possible should be built into the satellite segment, and

Total replacement of the Transit 1 satellite and other terrestrial navaid systems.

GPS – Objectives 2/2GPS – Objectives 2/2


GPS Receiver RequirementsGPS Receiver Requirements

GPS user hardware must have the ability to track and obtain any selected GPS satellite signal (a receiver will be required to track a number of satellites at the same time), in the presence of considerable ambient noise

This is now possible using spread-spectrum and pseudo-random-noise coding techniques


Spread Spectrum Radio (SSR) was almost exclusively used by military until 1985, when FCC allowed spread spectrum’s unlicensed commercial use in three frequency bands: 902-928 MHz, 2.4-2.4835 GHz and 5.725-5.850 GHz.

SSR differs from other commercial radio technologies because it spreads, rather than concentrates, its signal over a wide frequency range within its assigned bands.

A key characteristic of spread spectrum radios is that they increase the bandwidth of the transmitted signal by a significantly large ratio to the original signal bandwidth.

The main signal-spreading techniques are direct sequencing and frequency-hopping

Spread Spectrum Radio (SSR) Technique 1/2Spread Spectrum Radio (SSR) Technique 1/2


Direct sequencing continuously distributes the data signal across a broad portion of the frequency band; it modulates a carrier by a digital code with a bit rate much higher than the information signal bandwidth (used by GPS).

Alternatively, frequency-hopping radios move a radio signal from frequency to frequency in a fraction of a second.

The spread spectrum receiver has to reconstruct the original modulating signal from the spread-bandwidth signal by a process called correlation (or de-spreading). The fact that the interference remains spread across a large bandwidth allows the receiver to filter out most of their signal energy, by selectively allowing through only the bandwidth needed for the de-spread wanted signal.

Thus, the interference is reduced by SSR processing. Transmitting and receiving SSR radios must use the same spreading code, so only they can decode the true signal.

Spread Spectrum Radio (SSR) Technique 2/2Spread Spectrum Radio (SSR) Technique 2/2


TRANSIT as GPS Predecessor

• Researchers at Johns Hopkins observed Sputnik in 1957.

• Noted that the Doppler shift provided closest approach to earth.

• Developed a satellite system that achieved accurate positioning

• Called TRANSIT and provided basic ideas behind GPS


Development of Basic Navigation Satellite Concept

1964-1967

• SYSTEMATIC STUDY OF EVERY WILD IDEA

IMAGINABLE

• CONVERGED ON “PSEUDORANGING” IN 1967

• MAJOR STUDY CONTRACTS LET IN 1968 TO TUNE THE

CONCEPT


The mission of this Program is to:

1. Drop 5 bombs in the same hole, and

2. Build a cheap set that navigates (<$10,000),

and don’t you forget it!

Motto Adopted by the Joint Program Motto Adopted by the Joint Program Office on GPS ProgramOffice on GPS Program


Major Issues Identified in 1968 Studies

• CHOICE OF CARRIER FREQUENCY• L-Band• C-Band should be studied

• DESIGN OF SIGNAL STRUCTURE• Military and civilian use included

• ORBIT/CONSTELLATION SELECTION


• EXPANDED TRANSIT• Insisted on worldwide overage• 153 satellites in 400 mile polar orbits• Transit carrier frequency

• EXPANDED TIMATION• Initially only a Time Transfer System• Insisted on worldwide coverage• Expanded concept to intermediate altitude circular

orbit constellation of 30 to 40 satellites

Managed Concept Debates 1969-1972


Convergence on Final System1973-1974

• SWITCHED CONCEPT TO 12-HOUR CIRCULAR ORBITS• 3 planes, 8 satellites each• i = 63°

• RETAINED DIRECT-SHIFT KEYED SPREAD SPECTRUM PN SEQUENCE

• DUAL FREQUENCY SIGNAL ON L-BAND

• PICKED INITIAL DEPLOYMENT OF 4+2 ‘BLOCK I” SATELLITES


• BLOCK I SATELLITE CONTRACTS WITH ROCKWELL INTERNATIONAL• 6 satellites followed by 6 more• All satellite performance projections achieved. 3dB more transmitted power

then required• Exceptional (1x ) on-orbit Rubidium clock performance achieved.

PHASE I DESIGN 1974-1980

10-13

• DETAILS OF SIGNAL STRUCTURE & NAV MESSAGE DEFINED• C/A code designed with civil sector in mind • “P-Code” designed by Magnavox • Navigation message identical on both signals


• BLOCK II SATELLITES• Rockwell International• Selective Availability and Anti-Spoof (Y-Code) Implemented• Constellation downsized to 21 satellites (6 planes)• Nav message slightly modified

• OPERATIONAL CONTROL SEGMENT• Monitors at Ascension, Diego Garcia, Guam, Hawaii, and Colorado

Springs• 24-satellite ephemeris (orbit) determination

PHASE II DESIGN 1981-1989

• PHASE II/PHASE III USER EQUIPMENT• Rockwell Collins, Magnavox and Teledyne Systems• Rockwell Collins and Magnavox• Rockwell Collins


GPS Satellite System – Final Design 1/2GPS Satellite System – Final Design 1/2

24 satellites altitude ~20,000 km12-hour period 6 orbital planes, inclination 55o

Applications: practically unlimited!• Positioning and timing

• Navigation

• Mapping and GIS data collection

• Engineering and communication

• Agriculture

• ITS


continuous signal transmit fundamental frequency 10.23 MHz almost circular orbit (e = 0.02) at least 4 satellites visible at all times from

any point on the Earth’s surface (5-7 most of the time)

GPS Satellite System – Final Design 2/2GPS Satellite System – Final Design 2/2


GPS Policy Board*

• Department of Agriculture• Department of Commerce• Department of Defense• Department of Interior• Department of State• Department of Transportation• NASA

*created to give larger voice to civilian applications of GPS.


GPS Constellation

• Block I (not operational)

• Block II/IIA/IIR

• Currently

- 28 satellites Block II/IIA/IIR

- AS1/SA capability (to limit the access to the system by unauthorized users)

- multiple clocks onboard

1 The process of encrypting the P-code by modulo-2 addition of the P-code and a secret encryption W-code. The resulting code is called the Y-code. AS prevents an encryption-keyed GPS receiver from being “spoofed” by a bogus, enemy-generated GPS P-code signal. Y-code is not available to the civilian users.

2 The Department of Defense policy and procedure of denying to most non-military GPS users the full accuracy of the system. SA is achieved by dithering the satellite clock and degrading the navigation message ephemeris. Turned to zero on May 2, 2000.


GPS Constellation

Block I

• vehicle numbers (SVN) 1 through 11

• launched between 1978 and 1985

• concept validation satellites

• developed by Rockwell International

• circular orbits

• inclination 63 deg

• one Cesium and two Rubidium clocks

• design life of 5 years (majority performed well beyond their life expectancy)


GPS ConstellationBlock II


• launched between 1989 and 1990

• full scale operational satellites


• nearly circular orbits


• two Cesium and two Rubidium clocks

• design life of 7.3 years

• AS/SA capabilities


GPS ConstellationBlock IIA


• launched since 1990 (18 out of 19)

• second series of operational satellites




• two Cesium and two Rubidium clocks




GPS ConstellationBlock IIR


• total of 7 launched (1 unsuccessful)

• operational replenishment satellites

• developed by Lockheed Martin



• one Cesium and two Rubidium clocks




GPS Constellation

Block IIF

• will be launched between 2001 and 2010

• operational follow on satellites




• will carry an inertial navigation system

• will have an augmented signal structure (third frequency)


GPS Constellation

Block III

In November 2000, Lockheed Martin and Boeing were each awarded a $16-million, 12-month study contract by the Air Force to conceptualize the next generation GPS satellite, which will be known as GPS Block-3.


Current GPS Constellation LAUNCH LAUNCH FREQ

ORDER PRN SVN DATE STD PLANE

---------------------------------------------------------------

*II-1 14 14 FEB 89 Cs E1

II-2 02 13 10 JUN 89 Cs B3

*II-3 16 16 18 AUG 89 Cs E5

*II-4 19 19 21 OCT 89 Cs A4

II-5 17 17 11 DEC 89 Cs D3

^II-6 18 24 JAN 90 Cs F3

*II-7 20 26 MAR 90

II-8 21 21 02 AUG 90 Cs E2

II-9 15 15 01 OCT 90 Cs D2

IIA-10 23 23 26 NOV 90 Cs E4

IIA-11 24 24 04 JUL 91 Rb D1

IIA-12 25 25 23 FEB 92 Cs A2

*IIA-13 28 10 APR 92

IIA-14 26 26 07 JUL 92 Rb F2

IIA-15 27 27 09 SEP 92 Cs A3

IA-16 01 32 22 NOV 92 Cs F1

IIA-17 29 29 18 DEC 92 Rb F4

IIA-18 22 22 03 FEB 93 Rb B1

LAUNCH LAUNCH FREQ

ORDER PRN SVN DATE STD PLANE

---------------------------------------------------------------

IIA-19 31 31 30 MAR 93 Cs C3

IIA-20 07 37 13 MAY 93 Rb C4

IIA-21 09 39 26 JUN 93 Cs A1

IIA-22 05 35 30 AUG 93 Cs B4

IIA-23 04 34 26 OCT 93 Rb D4

IIA-24 06 36 10 MAR 94 Cs C1

IIA-25 03 33 28 MAR 96 Cs C2

IIA-26 10 40 16 JUL 96 Cs E3

IIA-27 30 30 12 SEP 96 Cs B2

IIA-28 08 38 06 NOV 97 Rb A5

**IIR-1 42 17 JAN 97

IIR-2 13 43 23 JUL 97 Rb F5

IIR-3 11 46 07 OCT 99 Rb D2

IIR-4 20 51 11 MAY 00 Rb E1

IR-5 28 44 16 JUL 00 Rb B5

IIR-6 14 41 10 NOV 00 Rb F1

IIR-7 18 54 30 JAN 01 Rb E4

* Satellite is no longer in service.

** Unsuccessful launch.TOTAL: 28 as of October 2, 2001


BLOCK I

BLOCK II/IIA


BLOCK IIF

BLOCK IIR


GPS Receiver Manufacturers

Over 67 GPS manufacturers and over 467 types of receivers, 106 antennas ! (GPS World, January 2000)

Ashtech/Magellanhttp://www.ashtech.com

Garminhttp://www.garmin.com

Leicahttp://www.leica-gps.com

NovAtel Inc.http://www.novatel.ca

Trimblehttp://www.trimble.com

Topcon/Javadhttp://www.topconps.com


Who are GPS largest customers?

• Survey & Mapping

~ 54%• Navigation

~ 20%• Tracking & Comm

~18%• Military

~ 6%• Car Navigation

~ 2%


GPS ApplicationsGPS Applications

• military

• civilian aircraft, land mobile, and marine vessel navigation

• time transfer between clocks

• spacecraft orbit determination

• geodesy (precise positioning)

• attitude determination with multiple antennas

• geophysics (ionosphere, crustal motion monitoring, etc.)

• surveying (static and kinematic, also real-time)

• Intelligent Transportation Systems

• GIS, Mobile Mapping Systems


THE DEPLOYED CONSTELLATION


GPS Antenna Coverage

Antenna has ~28° field of view

25788 km

SV 12-hour orbit

13.84°

EARTH


36

First GPS satellite Block I was launched in 1978

Air Force-launched Delta II carried the 18th GPS satellite into orbit in February 1993.


Source: http://www.nasm.edu


• Before GPS, pilots relied only on navigational beacons located across the country

• Now, with GPS fully operational, aircraft can fly the most direct routes between distant airports.


39

How accurate is GPS?

• Depending on the design of the GPS receiver and the measurement techniques employed, the accuracy is from 100 meters under Selective Availability (SA) policy (below 10 m with SA turned to zero) to better than 1 centimeter.

• In order to obtain better than 100 (10 with SA turned to zero) meter accuracy, differential GPS must be used (two simultaneously tracking receivers or differential services).


Why is GPS so accurate ?

• The key to GPS accuracy is the fact that the signal is precisely controlled by the highly accurate atomic clock

• Atomic clock’s stability is 10-13 – 10-14 per day (this means that the clock can loose 1 sec in 3,000,000 years!)

• This highly accurate frequency standard produces the fundamental GPS frequency, 10.23 MHz, which is a basis for derived frequencies L1 (1575.42 MHz = =154*10.23) and L2 (1227.60 MHz = 120*10.23)


• The basis of GPS is "triangulation" from satellites.

• To "triangulate," a GPS receiver measures distance using the travel time of radio signals.

• To measure travel time, GPS needs very accurate timing, which it achieves with some tricks

• The primary unknowns are three coordinates of the receiver antenna (user)


• Mathematically we need four satellite ranges to determine exact position.

• Three ranges are enough if we reject ridiculous answers or use other tricks.


Source: http://www.nasm.edu


Suppose we measure our distance from a satellite and find it to be 11,000 miles. Knowing that we're 11,000 miles from a particular satellite narrows down all the possible locations we could be in the whole universe to the surface of a sphere that is centered on this satellite and has a radius of 11,000 miles.

45

How distance measurements from three satellites can pinpoint you in space 1/3


46


Next, say we measure our distance to a second satellite and find out that it's 12,000 miles away. That tells us that we're not only on the first sphere but we're also on a sphere that's 12,000 miles from the second satellite. Or in other words, we're somewhere on the circle where thesetwo spheres intersect.


47


If we then make a measurement from a third satellite and find that we're 13,000 miles from that one, that narrows our position down even farther, to the two points where the 13,000 milesphere cuts through the circlethat's the intersection of the first two spheres.


Finally: In order to find the correct location (out of two points determined by the observation of three ranges to three satellites) we may need to make a fourth observation to the fourth satellite – this way we get the unique answer to our positioning problem.

But usually one of the two points is a ridiculous answer (either too far from Earth or moving at an impossible velocity) and can be rejected without a measurement.

However, a fourth measurement becomes very handy for another reason…


The dashed lines show the intersection point for ideal case (no observation errors), and the gray bands indicate the area of uncertainty

Because of errors in the receiver's internal clock, the spheres do not intersect at one point (the time measurement is used to determine the distance to the satellite, as explained next)

If three perfect measurements can locate a point in 3-dimensional space, then four imperfect measurements can do the same thing

So, the fourth measurement is used to fix the time (receiver clock) problem, and find a unique 3-D location in space


Thus: four range measurements to four GPS satellites are needed for point positioning

But how do we measure the range to the satellite?

By precise measurement of the time that the radio signal takes to travel from the satellite antenna to the receiver antenna


51

Measuring distance from a satellite 1/2

The timing problem is tricky. First, the signal travel times are going to be very short (about 0.06 seconds), so we need some really precise clocks. But assuming we have precise clocks, how do we measure travel time?

Suppose we start generating the same signal at the satellite and the receiver at the same time.

The signal (“Pseudo Random Code”) coming from the satellite is delayed because it had to travel over 11,000 miles.


52

If we wanted to see just how delayed the satellite's signal was, we delay the receiver's version of signal until they fell into perfect synchronization.

The amount we have to shift back the receiver's version is equal to the travel time of the satellite's version.

So we just multiply that time times the speed of light and BINGO! we've got our distance to the satellite.

Measuring distance from a satellite 2/2


53

A Random Code?

The Pseudo Random Code (PRC) or Pseudo Random Noise code, PRN, is a fundamental part of GPS. Physically it's just a very complicated digital code, or in other words, a complicated sequence of "on" and "off" pulses. The signal is so complicated that it almost looks like random electrical noise. Hence the name "Pseudo-Random".


54

A Random Code?

Since each satellite has its own unique Pseudo-Random Code, this complexity also guarantees that the receiver won't accidentally pick up another satellite's signal.

So all the satellites can use the same frequency without jamming each other. And it makes it more difficult for a hostile force to jam the system.

In fact the Pseudo Random Code gives the DoD a way to control access to the system.


55

A Random Code?

Another reason for the complexity of the Pseudo Random Code, is crucial to making GPS economical.

The codes make it possible to use information theory to “amplify” the GPS signal. And that's why GPS receivers don't need big satellite dishes to receive the GPS signals.


56

GPS Signal

L1 carrier

1575.42 MHz19 cm

L2 carrier

1227.60 MHz24 cm

Modulation

C/A code(SPS)

P code(PPS)

P code(PPS)

19 cm

293 m

29.3 m

29.3 m24 cm


57

Getting Perfect Timing

On the satellite side, timing isalmost perfect because they have incredibly precise atomic clocks on board.

But what about our receivers here on the ground?

Remember that both the satellite and the receiver need to be able to precisely synchronize their pseudo-random codes to make the system work.


58

Atomic clocks don't run on atomic energy. They get the name because they use the oscillations of a particular atom as their "metronome” (device for marking time by means of a series of clicks at precise intervals).

This form of timing is the most stable and accurate reference man has ever developed.

With the development of atomic clocks a new era of precise time-keeping had commenced. However, before the GPS program was launched these precise clocks had never been tested in space.

Atomic Clocks


Atomic Clock Technology

The development of reliable, stable, compact, space-qualified atomic frequency oscillators (rubidium, and then cesium) was therefore a significant technological breakthrough.

The advanced clocks now being used on the GPS satellites routinely achieve long-term frequency stability in the range of a few parts in 1014 per day (about 1 sec in 3,000,000 years!).

This long-term stability is one of the keys to GPS, as it allows for the autonomous, synchronized generation and transmission of accurate timing signals by each of the GPS satellites without continuous monitoring from the ground.


Quartz Crystal Oscillator Technology

In order to keep the cost of user equipment down, quartz crystal oscillators were proposed (similar to those used in modern digital watches),

Besides their low cost, quartz oscillators have excellent short-term stability.

However, their long-term drift must be accounted for as part of the user position determination process – this is where the fourth range measurement becomes handy!


61

If our receivers needed atomic clocks (which cost upwards of $50K to $100K) GPS would be a lame duck technology. Nobody could afford it.

Luckily the designers of GPS came up with a brilliant little trick that lets us get by with much less accurate clocks in our receivers.

The secret to perfect timing is to make an extra satellite measurement (remember the fourth range observation that we need to get precise position in space?)

By using an extra satellite range measurement and a little algebra a GPS receiver can eliminate any clock inaccuracies it might have.



62


Since any offset from universal time (UTC, the civilian time system that we use) will affect all of our measurements, the receiver looks for a single correction factor that it can subtract from all its timing measurements to make them correct.

That correction brings the receiver's clock back into sync with universal time, and BINGO! - you've got atomic accuracy time right in the palm of your hand (especially if you're using one of the hand-held receivers!)

Once it has that correction it applies to all the rest of its measurements and now we've got precise positioning.


63


One consequence of this principle is that any decent GPS receiver will need to have at least four channels so that it can make the four measurements simultaneously.

But for the triangulation to work we not only need to know distance, we also need to know exactly where the satellites are.


64

• Along with distance, you need to know exactly where the satellites are in space. High orbits and careful monitoring are the secret.

• Finally you must correct for any delays the signal experiences as it travels through the atmosphere.

What else do we need to navigate

(position) with GPS?


Successful operation of GPS depends on the precise knowledge and prediction of a satellite's position with respect to an earth-fixed reference system.

Tracking data collected by ground monitor stations are analyzed to determine the satellite orbit over the period of tracking (typically one week).

This reference ephemeris is extrapolated into the future and the data is then up-loaded to the satellites.

Prediction accuracies of the satellite coordinates, for one day, at the few meter level have been demonstrated.

Getting Satellite Position in Space 1/3


66

Getting Satellite Position in Space 2/3• The Air Force has injectedeach GPS satellite into a very precise planned orbit.

• GPS satellites are so high up that their orbits are very predictable.

• On the ground all GPS receivers have an almanac programmed into their computers that tells them where in the sky each satellite is.

• Minor variations in satellite orbits are measured by the Department of Defense (data from permanently tracking stations allow determination of satellite position and speed)


67

Getting Satellite Position in Space 3/3

These errors (variations from the ideal orbit) are caused by gravitational pulls from the moon and sun and by the pressure of solar radiation on the satellites. That information is sent back up to the satellite itself. The satellite then includes this new corrected position information in the timing signals it's broadcasting.

So a GPS signal is more than just pseudo-random code for timing purposes. It also contains a navigation message with ephemeris information as well.

Now we are almost ready for perfect positioning, but there is one more trouble...


68

Getting Errors Corrected

A GPS signal doesn’t travel in vacuum! We've been saying that you calculate distance to a satellite by multiplying a signal's travel time by the speed of light. But the speed of light is only constant in a vacuum. As a GPS signal passes through the charged particles of the ionosphere and then through the water vapor in the troposphere it gets slowed down, and this creates the same kind of error as bad clocks.


69

Getting Errors Corrected 1/2

Some errors can be factored out using mathematics and modeling. Another way to get a handle on these atmosphere-induced errors is to compare the relative speeds of two different signals. This "dual frequency" measurement is very sophisticated and is only possible with advanced receivers.

Problem on the ground -- is called multipath error and is similar to the ghosting you might see on a TV.

Good receivers use sophisticated signal rejection techniques to minimize this problem.


70

Getting Errors Corrected 2/2

Other error sources: satellite position. Intentional errors: the policy is called "Selective Availability" or "SA" and the idea behind it is to make sure that no hostile force or terrorist group can use GPS to make accurate weapons. DoD introduces some "noise" into the satellite's clock data which, in turn, adds noise (or inaccuracy) into position calculations. DoD may also be sending slightly erroneous orbital data to the satellites Military receivers use a decryption key to remove the SA errors and so they're much more accurate. Differential GPS can eliminate almost all error sources. SA was turned down to zero on May 2, 2000


Summary of GPS Error Sources [m]

SA=0 SA Satellite Clocks 2.0 20.0 Orbit Errors 2.1 20.0 Ionosphere 5.0 5.0 Troposphere 0.5 (model) 0.5 (model) Receiver Noise 0.3 0.3 Multipath 1.0 1.0 Typical Position Accuracy Horizontal 10.0 41.0 Vertical 13.0 51.0


Atmospheric Errors on GPS Range

troposphere

ionosphereGeometric distance

Actual signal path

Boundary between iono and troposphere


73

Summary of GPS Error Sources

Typical Error in Meters (per satellite) Standard GPS Differential GPS Satellite Clocks 1.5 0 Orbit Errors 2.5 0 Ionosphere 5.0 0.4 Troposphere 0.5 0.2 Receiver Noise 0.3 0.3 Multipath 0.6 0.6 SA 30 0 Typical Position Accuracy (under SA) Horizontal 50 1.3 Vertical 78 2.0 3-D 93 2.8


GPS Errors: An OverviewGPS Errors: An Overview

• Bias errors - can be removed from the direct observables, or at least significantly reduced, by using empirical models (eg., tropospheric models), or by differencing direct observables

- satellite orbital errors (imperfect orbit modeling),- station position errors- propagation media errors and receiver errors

• White noise


GPS Error SourcesGPS Error Sources

• Satellite and receiver clock errors • Satellite orbit errors• Atmospheric effects (ionosphere, troposphere)• Multipath: signal reflected from surfaces near the receiver• Selective Availability (SA)

- epsilon process: falsifying the navigation broadcast data - delta process: dithering or systematic destabilizing of the

satellite clock frequency• Antenna phase center


GPS Major Error Sources

• Timing errors: receiver and satellite, including SA

• satellite clock (as a difference between the precise and broadcast clocks ): 0.1-0.2 microseconds which corresponds to 30-60 m error in range

• first-order clock errors are removed by differencing technique



• Orbital errors and Selective Availability (SA)

• nominal error for the broadcast ephemeris: 1-5 m on average

• precise (post-mission) orbits are good up to 5-10 cm and better; available with 24-hour delay

• Selective Availability: not observed on the orbit

• first-order orbital errors are removed by differencing technique


GPS Major Error Sources• Propagation media

• ionosphere (50-1000km)

• the presence of free electrons in the geomagnetic field causes a nonlinear dispersion of electromagnetic waves traveling through the ionized medium

• group delay (code range is measured too long) and phase advance (phase range is measured too short) , frequency dependent; can reach ~150 m near the horizon;

positive always is density electron since thus][3.40constant

index refractive phase 1

signal) GPS code assuch waves,of (groupindex refractive group 1

22

22

22

ephgre

ph

gr

NnnHzNc

f

cn

f

cn


Propagation media cont.

• the propagation delay depends on the total electron content (TEC) along the signal’s path and on the frequency of the signal itself as well as on the geographic location and time (ionosphere is most active at noon, quiet at night; 11-year Sun spot cycle)

• integration of the refractive index renders the measured range, and the ionospheric terms for range and phase are as follows:

• differencing technique and ion-free combination of observations on both frequencies eliminate first-order terms, secondary effects can be neglected for the short baselines

• differential effect on the long baselines: 1-3 cm

zenith at range geometric theis where]mper electrons [10 TEC

TECcontent electron total where3.40

and 3.40

distance measured

0216

0

22

sdsN

TECf

TECf

dsns

e

ionoph

ionogr


11-year Sun Spot Cycle


Estimated Ionospheric Group Delay for GPS Signal

L1 L2 Residual Range Error

First Order: 1/f 2

16.2 m 26.7 m 0.0

Second Order: 1/f 3

~ 1.6 cm ~ 3.3 cm ~ -1.1 cm

Third Order: 1/f 4

~ 0.86 mm ~ 2.4 mm ~ -0.66 mm

Calibrated 1/f 3

Term Based on a Thin Layer Ionospheric Model

~ 1-2 mm

The phase advance can be obtained from the above table by multiplying each number by -1, -0.5 and -1/3 for the 1/f 2, 1/f 3 and 1/f 4 term, respectively



• Troposphere (up to 50 km) - frequency-independent, same for all frequencies below 15 GHz (troposphere is not dispersive for frequencies below 15 GHz )

• group and phase delay are the same

• elimination by dual frequency is not possible

• affects relative (differential) and point positioning

• empirical models (functions of temperature, pressure and relative humidity) are used to eliminate major part of the effect

• differential effect is usually estimated (neglected for the short baselines with similar atmospheric effects)

• total effect in the zenith direction reaches 2.5, and increases with the cosecant of the elevation angle up to 20-28 m at 5deg elevation


Tropospheric Effects (cont.)• The tropospheric propagation effect is usually represented as a function of temperature, pressure and relative humidity

• Obtained by integration of the refractivity Ntrop

where integration is performed along the geometric path

• It is separated into two components: dry (0-40 km) and wet (0-11km)

• Represents an example of refractivity model at the surface of the earth; c1, c2, c3 are constants, T is temperature in Kelvin (K), e is partial pressure of water vapor [mb], p is atmospheric pressure [mb]

10 6 dsN troptrop

wdtrop

23210 T

ec

T

ec

T

pcN trop


Tropospheric Effects (cont.)

• The dry component, which is proportional to the density of the gas molecules in the atmosphere and changes with their distribution, represents about 90% of the total tropospheric refraction

• It can be modeled with an accuracy of about 2% that corresponds to 4 cm in the zenith direction using surface measurement of pressure and temperature

• The wet refractivity is due to the polar nature of the water molecules and the electron cloud displacement

• Since the water vapor is less uniform both spatially and temporally, it cannot be modeled easily or predicted from the surface measurements

• As a phenomenon highly dependent on the turbulences in the lower atmosphere, the wet component is modeled less accurately than the dry

• The influence of the wet tropospheric zenith delay is about 5-30 cm that can be modeled with an accuracy of 2-5 cm



• The tropospheric refraction as a function of the satellite’s zenith distance is usually expressed as a product of a zenith delay and a mapping function

• A generic mapping function represents the relation between zenith effects at the observation site and at the spacecraft’s elevation • Several mapping functions have been developed (e.g., by Saastamoinen, Goad and Goodman, Chao, Lanyi), which are equivalent as long as the cutoff angle for the observations is at least 20o

• The tropospheric range correction can be written as follows:

wherefd(z), fw(z) - mapping functions for dry and wet components, respectively,

- vertical dry and wet components, respectively

trop d d w wf z f z 0 0

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• Tropospheric range correction is applied to correct the GSP measurement before it is used to find your position

•Tropospheric refraction accommodates only the systematic part of the effect, and some small un-modeled effects remain

• Moreover, errors are introduced into the tropospheric correction via inappropriate meteorological data (if applied) as well as via errors in the zenith mapping function

• These errors are propagated into station coordinates in the point positioning and into base components in the relative positioning

• For example, the relative tropospheric refraction errors affects mainly a baseline’s vertical component (error in the relative tropospheric delay at the level of 10 cm implies errors of a few millimeters in the horizontal components, and more than 20 cm in the vertical direction)



• If the zenith delay error is 1 cm, the effect on the horizontal coordinates will be less than 1 mm but the effect on the vertical component will be significant, about 2.2 cm

• The effect of the tropospheric refraction error increases with the latitude of the observing station and reaches its maximum for the polar sites. It is a natural consequence of a diluted observability at high latitudes where satellites are visible only at low elevation angles

• The scale of a baseline derived from observations that are not corrected for the effect of the tropospheric delay is distorted; the baseline is measured too long.




• Multipath - result of an interaction of the upcoming signal with the objects in antenna surrounding; causes multiple reflection and diffraction; as a result signal arrives via direct and indirect paths

• magnitude tends to be random and unpredictable, can reach 1-5 cm for phases and 10-20 m for code pseudoranges

• can be largely reduced by careful antenna location (avoiding reflective objects) and proper antenna design, e.g., proper signal polarization, choke-ring or ground-plane antennas


• As opposed to interference, which disrupts the signal and can virtually provide no or useless data, multipath would allow for data collection, but the results would be wrong!

• Existing multipath rejection technology (in-receiver) usually applies to the C/A code-based observable, and can increase the mapping accuracy by 50% (differential code positioning with a multipath rejection technology can be good to 30-35 cm in horizontal and 40-50 cm in vertical directions).

• Signal processing techniques, however, can reject the multipath signal only if the multipath distance (difference between the direct and the indirect paths) is more that 10 m.

• In a typical geodetic/surveying application, however, the antenna is about 2 m above the ground, thus the multipath distance reaches at most 4 m; consequently, the signal processing techniques cannot fully mitigate the effects of reflected signals.

Multipath


• However, properly designed choke ring antennas can almost entirely eliminate this problem for the signals reflected from the ground and the surface waves

• The multipath from the objects above the antenna still remains an unresolved problem

• The performance of the choke ring antennas is usually better for L2 than for L1, the reason being that the choke ring can be optimized only for one frequency. If the choke ring is design for L1, it has no effect for L2, while a choke ring designed for L3 has some benefits for L1.

• Naturally, the optimal solution would be to have choke rings optimized separately for L1 and L2, which is the expected direction of progress for the geodetic antennas.

Multipath



Interference and jamming (intentional interference)

• Radio interference can, at minimum, reduce the GPS signal’s apparent strength (that is reduce the signal to noise ratio by adding more noise) and consequently – the accuracy, or, at worse, even block the signal entirely

• Medium-level interference would cause frequent losses of lock or cycle slips, and might render virtually useless data.

• It is, therefore, important to make sure that the receiver has an interference protection mechanism, which would detect and eliminate (or suppress) the interfering signal.


Antenna Phase Center VariationAntenna Phase Center Variation

Antenna Phase Center is the point to which the received signal is referred

• It usually does not coincide with the physical center of the antenna, and for GPS receivers both the L1 and L2 phase centers are generally different

• The magnitudes of these offsets are provided by the manufacturer; however, the location of the phase center can vary with time (this variation should not exceed 1-2 cm)

• for modern microstrip antennas it reaches only a few millimeters.

• Antenna phase center offset depends on the azimuth and the elevation of the satellite as well as on the intensity of the incoming signal.

• Similarly, the satellite phase center does not coincide with the spacecraft’s center of mass. Suggested satellite center of mass corrections for GPS satellites can be found in IERS Technical Note No. 13 and 21 (IERS Conventions)

civil and environmental engineering and geodetic science reference materials can be found at: more...

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