50 GPS Basics - The University of Texas at Dallasaiken/GPSCLASS/GPSBasics.pdf · GPS Basics...

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Introduction to GPS (Global Positioning System)

GPS Basics50403020

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Contents

Preface ........................................................... 4

1. What is GPS and what does it do ? .......... 5

2. System Overview ....................................... 62.1 The Space Segment ............................................... 62.2 The Control Segment .............................................. 82.3 The User Segment ................................................. 9

3. How GPS works....................................... 103.1 Simple Navigation .................................................. 11

3.1.1 Satellite ranging .................................................... 113.1.2 Calculating the distance to the satellite ................. 133.1.3 Error Sources ........................................................ 143.1.4 Why are military receivers more accurate ? ........... 18

3.2 Differentially corrected positions (DGPS) ................193.2.1 The Reference Receiver ........................................ 203.2.2 The Rover receiver ................................................. 203.2.3 Further details ....................................................... 20

3.3 Differential Phase GPS and Ambiguity Resolution ...223.3.1 The Carrier Phase, C/A and P-codes .................... 223.3.2 Why use Carrier Phase? ....................................... 233.3.3 Double Differencing ............................................... 233.3.4 Ambiguity and Ambiguity Resolution ...................... 24

4. Geodetic Aspects..................................... 264.1 Introduction ...........................................................274.2. The GPS coordinate system .................................284.3 Local coordinate systems ......................................294.4 Problems with height .............................................304.5 Transformations .....................................................314.6 Map Projections and Plane Coordinates .................34

4.6.1 The Transverse Mercator Projection ...................... 354.6.2 The Lambert Projection ......................................... 37

5. Surveying with GPS ................................ 385.1 GPS Measuring Techniques ..................................39

5.1.1 Static Surveys ........................................................ 405.1.2 Rapid Static Surveys .............................................. 425.1.3 Kinematic Surveys ................................................. 445.1.4 RTK Surveys .......................................................... 45

5.2 Pre-survey preparation ...........................................465.3 Tips during operation .............................................46

Glossary ....................................................... 48

Further Reading .......................................... 59

Index ............................................................. 60

3GPS Basics -1.0.0en

Preface

1. What is GPS and what does it do?

2. System Overview

3. How GPS works

4. Geodetic Aspects

5. Surveying with GPS

Glossary

Index

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4 GPS Basics -1.0.0enPreface

Preface

Why have we written this book andwho should read it?

Leica manufactures, amongst otherthings, GPS hardware and software.This hardware and software is used bymany professionals in many applica-tions. One thing that almost all of ourusers have in common is that they arenot GPS scientists or experts in Geod-esy. They are using GPS as a tool tocomplete a task. Therefore, it is useful tohave background information about whatGPS is and how it works.

This book is intended to give a novice orpotential GPS user a background in thesubject of GPS and Geodesy. It is not adefinitive technical GPS or Geodesymanual. There are many texts of this sortavailable, some of which are included inthe reading list on the back pages.

This book is split into two main sections.The first explains GPS and how it works.The second explains the fundamentalsof geodesy.

5GPS Basics -1.0.0en System Overview

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1. What is GPS and what does it do ?GPS is the shortened form of NAVSTARGPS. This is an acronym for NAVigationSystem with Time And Ranging GlobalPositioning System.

GPS is a solution for one of man�slongest and most troublesome prob-lems. It provides an answer to thequestion �Where on earth am I ?�

One can imagine that this is an easyquestion to answer. You can easilylocate yourself by looking at objects thatsurround you and position yourselfrelative to them. But what if you have noobjects around you ? What if you are inthe middle of the desert or in the middleof the ocean ? For many centuries, thisproblem was solved by using the sun

and stars to navigate. Also, on land,surveyors and explorers used familiarreference points from which to base theirmeasurements or find their way.

These methods worked well withincertain boundaries. Sun and starscannot be seen when it is cloudy. Also,even with the most precise measure-ments position cannot be determinedvery accurately.

After the second world war, it becameapparent to the U.S. Department ofDefense that a solution had to be foundto the problem of accurate, absolutepositioning. Several projects andexperiments ran during the next 25 yearsor so, including Transit, Timation, Loran,Decca etc. All of these projects allowedpositions to be determined but werelimited in accuracy or functionality.

At the beginning of the 1970s, a newproject was proposed � GPS. Thisconcept promised to fulfill all the require-ments of the US government, namelythat one should be able to determineones position accurately, at any point onthe earth�s surface, at any time, in anyweather conditions.

GPS is a satellite-based system thatuses a constellation of 24 satellites togive a user an accurate position. It isimportant at this point to define �accu-rate�. To a hiker or soldier in the desert,accurate means about 15m. To a ship incoastal waters, accurate means 5m. Toa land surveyor, accurate means 1cm orless. GPS can be used to achieve all ofthese accuracies in all of these applica-tions, the difference being the type ofGPS receiver used and the techniqueemployed.

GPS was originally designed for militaryuse at any time anywhere on the surfaceof the earth. Soon after the originalproposals were made, it became clearthat civilians could also use GPS, andnot only for personal positioning (as wasintended for the military). The first twomajor civilian applications to emergewere marine navigation and surveying.Nowadays applications range from in-car navigation through truck fleet man-agement to automation of constructionmachinery.

What is GPS and what does it do ?

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6 GPS Basics -1.0.0enSystem Overview

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2. System OverviewThe total GPS configuration is com-prised of three distinct segments:

� The Space Segment � Satellitesorbiting the earth.

� The Control Segment � Stationspositioned on the earth�s equator tocontrol the satellites

� The User Segment � Anybody thatreceives and uses the GPS signal.

2.1 The Space Segment

The Space Segment is designed toconsist of 24 satellites orbiting the earthat approximately 20200km every 12hours. At time of writing there are 26operational satellites orbiting the earth.

GPS Satellite Constellation

The space segment is so designed thatthere will be a minimum of 4 satellitesvisible above a 15° cut-off angle at anypoint of the earth�s surface at any onetime. Four satellites are the minimumthat must be visible for most applica-tions. Experience shows that there areusually at least 5 satellites visible above

15° for most of the time and quite oftenthere are 6 or 7 satellites visible.

GPS satellite

Each GPS satellite has several veryaccurate atomic clocks on board. Theclocks operate at a fundamental fre-quency of 10.23MHz. This is used togenerate the signals that are broadcastfrom the satellite.


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The satellites broadcast two carrierwaves constantly. These carrier wavesare in the L-Band (used for radio), andtravel to earth at the speed of light.These carrier waves are derived from thefundamental frequency, generated by avery precise atomic clock:

• The L1 carrier is broadcast at 1575.42MHz (10.23 x 154)

• The L2 carrier is broadcast at 1227.60MHz (10.23 x 120).

The L1 carrier then has two codesmodulated upon it. The C/A Code orCoarse/Acquisition Code is modulatedat 1.023MHz (10.23/10) and the P-codeor Precision Code is modulated at10.23MHz). The L2 carrier has just onecode modulated upon it. The L2 P-codeis modulated at 10.23 MHz.

GPS receivers use the different codes todistingush between satellites. Thecodes can also be used as a basis formaking pseudorange measurementsand therefore calculate a position.

GPS Signal Structure

FundamentalFrequency10.23 Mhz

L11575.42 Mhz

C/A Code1.023 Mhz

P-Code10.23 Mhz

L21227.60 Mhz

P-Code10.32 Mhz

÷10

×154

×120

8 GPS Basics -1.0.0enSystem Overview

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2.2 The Control Segment

The Control Segment consists of onemaster control station, 5 monitor sta-tions and 4 ground antennas distributedamongst 5 locations roughly on theearth�s equator.

The Control Segment tracks the GPSsatellites, updates their orbiting positionand calibrates and sychronises theirclocks.

A further important function is to deter-mine the orbit of each satellite andpredict it�s path for the following 24hours. This information is uploaded toeach satellite and subsequently broad-cast from it. This enables the GPSreceiver to know where each satellitecan be expected to be found.

The satellite signals are read at Ascen-sion, Diego Garcia and Kwajalein. Themeasurements are then sent to theMaster Control Station in ColoradoSprings where they are processed todetermine any errors in each satellite.The information is then sent back to thefour monitor stations equipped withground antennas and uploaded to thesatellites.

H a w a i i

C o l o r a d o S p r i n g s

A s c e n s i o n D i e g o G a r c i a

K w a j a l e i n

Control Segment Station Locations


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2.3 The User Segment

The User Segment comprises of anyoneusing a GPS receiver to receive the GPSsignal and determine their position and/or time. Typical applications within theuser segment are land navigation forhikers, vehicle location, surveying,marine navigation, aerial navigation,machine control etc.

10 GPS Basics -1.0.0enHow GPS works

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3. How GPS worksThere are several different methods forobtaining a position using GPS. Themethod used depends on the accuracyrequired by the user and the type of GPSreceiver available. Broadly speaking, thetechniques can be broken down intothree basic classes:

Autonomous Navigation using a single stand-alone receiver. Used byhikers, ships that are far out at sea and the military. Position Accuracy isbetter than 100m for civilian users and about 20m for military users.

Differentially corrected positioning. More commonly knownas DGPS, this gives an accuracy of between 0.5-5m. Used forinshore marine navigation, GIS data acquisition, precisionfarming etc.

Differential Phase position. Gives an accuracy of 0.5-20mm.Used for many surveying tasks, machine control etc.

11GPS Basics -1.0.0en How GPS works

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3.1 Simple Navigation

This is the most simple techniqueemployed by GPS receivers to instanta-neously give a position and height and/or accurate time to a user. The accuracyobtained is better than 100m (usuallyaround the 30-50m mark) for civilianusers and 5-15m for military users. Thereasons for the difference betweencivilian and military accuracies are givenlater in this section. Receivers used forthis type of operation are typically small,highly portable handheld units with alow cost.

A Handheld GPS Receiver

3.1.1 Satellite ranging

All GPS positions are based on measuring the distance from the satellites to theGPS receiver on the earth. This distance to each satellite can be determined by theGPS receiver. The basic idea is that of resection, which many surveyors use in theirdaily work. If you know the distance to three points relative to your own position, youcan determine your own position relative to those three points. From the distance toone satellite we know that the position of the receiver must be at some point on thesurface of an imaginary sphere which has it�s origin at the satellite. By intersectingthree imaginary spheres the receiver position can be determined.

Intersection of three imaginary spheres


4 The problem with GPS is that onlypseudoranges and the time at which thesignal arrived at the receiver can bedetermined.

Thus there are four unknowns to deter-mine; position (X, Y, Z) and time of travelof the signal. Observing to four satellitesproduces four equations which can besolved, enabling these unknowns to bedetermined.

At least four satellites are required to obtain aposition and time in 3 dimensions


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3.1.2 Calculating the distance to the satellite

Calculating the Time

The satellite signal has two codes modulated upon it, the C/A code and theP-code (see section 2.1). The C/A code is based upon the time given by avery accurate atomic clock. The receiver also contains a clock that is used togenerate a matching C/A code. The GPS receiver is then able to �match� orcorrelate the incoming satellite code to the receiver generated code.

The C/A code is a digital code that is �pseudo random� or appears to berandom. In actual fact it is not random and repeats one thousand timesevery second.

In this way, the time taken for the radio signal to travel from the satellite tothe GPS receiver is calculated.

In order to calculate the distance to eachsatellite, one of Isaac Newton�s laws ofmotion is used:

Distance = Velocity x Time

For instance, it is possible to calculatethe distance a train has traveled if youknow the velocity it has been travellingand the time for which it has beentravelling at that velocity.

GPS requires the receiver to calculatethe distance from the receiver to thesatellite.

The Velocity is the velocity of the radiosignal. Radio waves travel at the speedof light, 290,000 km per second(186,000 miles per second).

The Time is the time taken for the radiosignal to travel from the satellite to theGPS receiver. This is a little harder tocalculate, since you need to know whenthe radio signal left the satellite andwhen it reached the receiver.


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3.1.3 Error Sources

Up until this point, it has been assumedthat the position derived from GPS is veryaccurate and free of error, but there areseveral sources of error that degrade theGPS position from a theoretical fewmetres to tens of metres. These errorsources are:

1. Ionospheric and atmosphericdelays

2. Satellite and Receiver ClockErrors

3. Multipath

4. Dilution of Precision

5. Selective Availability (S/A)

6. Anti Spoofing (A-S)

1. Ionospheric and Atmospheric delays

As the satellite signal passes throughthe ionosphere, it can be slowed down,the effect being similar to light refractedthrough a glass block. These atmo-spheric delays can introduce an error inthe range calculation as the velocity ofthe signal is affected. (Light only has aconstant velocity in a vacuum).

The ionosphere does not introduce aconstant delay on the signal. There areseveral factors that influence the amountof delay caused by the ionosphere.


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a. Satellite elevation. Signals from lowelevation satellites will be affected morethan signals from higher elevationsatellites. This is due to the increaseddistance that the signal passes throughthe atmosphere.

b. The density of the ionosphere isaffected by the sun. At night, there isvery little ionospheric influence. In theday, the sun increases the effect of theionosphere and slows down the signal.

The amount by which the density of theionosphere is increased varies withsolar cycles (sunspot activity).

Sunspot activity peaks approximatelyevery 11 years. At the time of writing, the

next peak (solarmax) will bearound the year2000.

In addition to this,solar flares canalso randomlyoccur and alsohave an effect onthe ionosphere.

Ionospheric errorscan be mitigatedby using one oftwo methods:

- The first methodinvolves taking anaverage of the

effect of the reduction in velocity of lightcaused by the ionosphere. This correc-tion factor can then be applied to therange calculations. However, this relieson an average and obviously this

average condition does not occur all ofthe time. This method is therefore notthe optimum solution to IonosphericError mitigation.

- The second method involves using�dual-frequency� GPS receivers. Suchreceivers measure the L1 and the L2frequencies of the GPS signal. It isknown that when a radio signal travelsthrough the ionosphere it slows down ata rate inversely proportional to it�sfrequency. Hence, if the arrival times ofthe two signals are compared, anaccurate estimation of the delay can bemade. Note that this is only possiblewith dual frequency GPS receivers. Mostreceivers built for navigation are singlefrequency.

c. Water Vapour also affects the GPSsignal. Water vapor contained in theatmosphere can also affect the GPSsignal. This effect, which can result in aposition degradation can be reduced byusing atmospheric models.


4 2. Satellite and Receiver clock errors

Even though the clocks in the satelliteare very accurate (to about 3 nanosec-onds), they do sometimes drift slightlyand cause small errors, affecting theaccuracy of the position. The US Depart-ment of Defense monitors the satelliteclocks using the Control Segment (seesection 2.2) and can correct any drift thatis found.

3. Multipath Errors

Multipath occurs when the receiverantenna is positioned close to alarge reflecting surface such as alake or building. The satellite signaldoes not travel directly to the antennabut hits the nearby object first and isreflected into the antenna creating afalse measurement.

Multipath can be reduced by use ofspecial GPS antennas that incorpo-rate a ground plane (a circular,metallic disk about 50cm (2 feet) indiameter) that prevent low elevationsignals reaching the antenna.

For highest accuracy, the preferred solution isuse of a choke ring antenna. A choke ringantenna has 4 or 5 concentric rings aroundthe antenna that trap any indirect signals.

Multipath only affects high accuracy, survey-type measurements. Simple handheldnavigation receivers do not employ suchtechniques.

Choke-Ring Antenna


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4. Dilution of Precision

The Dilution of Precision (DOP) is ameasure of the strength of satellitegeometry and is related to the spacingand position of the satellites in the sky.The DOP can magnify the effect ofsatellite ranging errors.

The principle can be best illustrated bydiagrams:

Well spaced satellites - low uncertaintyof position

The range to the satellite is affected byrange errors previously described. Whenthe satellites are well spaced, theposition can be determined as beingwithin the shaded area in the diagramand the possible error margin is small.

When the satellites are close together,the shaded area increases in size,increasing the uncertainty of the posi-tion.

Different types of Dilution of Precision orDOP can be calculated depending onthe dimension.

VDOP � Vertical Dilution of Precision.Gives accuracy degradation in verticaldirection.

HDOP � Horizontal Dilution of Precision.Gives accuracy degradation in horizontaldirection.

PDOP � Positional Dilution of Precision.Gives accuracy degradation in 3Dposition.

GDOP � Geometric Dilution of Precision.Gives accuracy degradation in 3Dposition and time.

The most useful DOP to know is GDOPsince this is a combination of all thefactors. Some receivers do howevercalculate PDOP or HDOP which do notinclude the time component.

The best way of minimizing the effect ofGDOP is to observe as many satellitesas possible. Remember however, thatthe signals from low elevation satellitesare generally influenced to a greaterdegree by most error sources.

As a general guide, when surveying withGPS it is best to observe satellites thatare 15° above the horizon. The mostaccurate positions will generally becomputed when the GDOP is low,(usually 8 or less).

Poorly spaced satellites - highuncertainty of position


4 5. Selective Availability (S/A)

Selective Availability is a processapplied by the U.S. Department ofDefense to the GPS signal. This isintended to deny civilian and hostileforeign powers the full accuracy of GPSby subjecting the satellite clocks to aprocess known as �dithering� whichalters their time slightly. Additionally, theephemeris (or path that the satellite willfollow) is broadcast as being slightlydifferent from what it is in reality. The endresult is a degradation in positionaccuracy.

It is worth noting that S/A affects civilianusers using a single GPS receiver toobtain an autonomous position. Usersof differential systems are not signifi-cantly affected by S/A.

Currently, it is planned that S/A will beswitched off by 2006 at the latest.

6. Anti-Spoofing (A-S)

Anti-Spoofing is similar to S/A in that it�sintention is to deny civilian and hostilepowers access to the P-code part of theGPS signal and hence force use of theC/A code which has S/A applied to it.

Anti-Spoofing encrypts the P-code into asignal called the Y-code. Only users withmilitary GPS receivers (the US and it�sallies) can de-crypt the Y-code.

3.1.4 Why are military receivers moreaccurate ?

Military receivers are more accuratebecause they do not use the C/A code tocalculate the time taken for the signal toreach the receiver. They use the P-code.

The P-code is modulated onto the carrierwave at 10.23 Hz. The C/A code ismodulated onto the carrier wave at 1.023Hz. Ranges can be calculated far moreaccurately using the P-code as this codeis occurring 10 times as often as the C/Acode per second.

The P-code is often subjected to AntiSpoofing (A/S) as described in the lastsection. This means that only themilitary, equipped with special GPSreceivers can read this encryted P-code(also known as the Y-code).

For these reasons, users of military GPSreceivers usually get a position with anaccuracy of around 5m whereas, civilianusers of comparable GPS receivers willonly get between about 15-100mposition accuracy.

A military handheld GPS receiver(courtesy Rockwell)


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3.2 Differentially corrected positions (DGPS)

Many of the errors affecting the measure-ment of satellite range can be com-pletely eliminated or at least significantlyreduced using differential measurementtechniques.

DGPS allows the civilian user to in-crease position accuracy from 100m to2-3m or less, making it more useful formany civilian applications.

DGPS Reference station broadcasting to Users


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3.2.1 The Reference Receiver

The Reference receiver antenna ismounted on a previously measuredpoint with known coordinates. Thereceiver that is set at this point is knownas the Reference Receiver or BaseStation.

The receiver is switched on and beginsto track satellites. It can calculate anautonomous position using the tech-niques mentioned in section 3.1.

Because it is on a known point, thereference receiver can estimate veryprecisely what the ranges to the varioussatellites should be.

The reference receiver can thereforework out the difference between thecomputed and measured range values.These differences are known as correc-tions.

The reference receiver is usually at-tached to a radio data link which is usedto broadcast these corrections.

3.2.2 The Rover receiver

The rover receiver is on the other end ofthese corrections. The rover receiver hasa radio data link attached to it thatenables it to receive the range correc-tions broadcast by the ReferenceReceiver.

The Rover Receiver also calculatesranges to the satellites as described insection 3.1. It then applies the rangecorrections received from the Reference.This lets it calculate a much moreaccurate position than would be possi-ble if the uncorrected range measure-ments were used.

Using this technique, all of the errorsources listed in section 3.1.3 areminimized, hence the more accurateposition.

It is also worthwhile to note that multipleRover Receivers can receive correctionsfrom one single Reference.

3.2.3 Further details

DGPS has been explained in a verysimple way in the preceding sections. Inreal life, it is a little more complex thanthis.

One large consideration is the radio link.There are many types of radio link thatwill broadcast over different ranges andfrequencies. The performance of theradio link depends on a range of factorsincluding:

� Frequency of the radio

� Power of the radio

� Type and �gain� of radio antenna

� Antenna position

Networks of GPS receivers and powerfulradio transmitters have been estab-lished, broadcasting on a �maritimeonly� safety frequency. These are knownas Beacon Transmitters. The users ofthis service (mostly marine craft navigat-ing in coastal waters) just need topurchase a Rover receiver that canreceive the beacon signal. Such sys-tems have been set up around thecoasts of many countries.


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Other devices such as mobile tele-phones can also be used for transmis-sion of data.

In addition to Beacon Systems, othersystems also exist that provide coverageover large land areas operated bycommercial, privately owned companies.There are also proposals for govern-ment owned systems such as theFederal Aviation Authority�s satellite-based Wide Area Augmentation System(WAAS) in the United States, the Euro-pean Space Agency�s (ESA) system anda proposed system from the Japanesegovernment.

There is a commonly used standard forthe format of broadcast GPS data. It iscalled RTCM format. This stands forRadio Technical Commission MaritimeServices, an industry sponsored non-profit organisation. This format iscommonly used all over the world.


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3.3 Differential Phase GPSand Ambiguity ResolutionDifferential Phase GPS is used mainly insurveying and related industries toachieve relative positioning accuraciesof typically 5-50mm (0.25-2.5 in). Thetechnique used differs from previouslydescribed techniques and involves a lotof statistical analysis.

It is a differential technique which meansthat a minimum of two GPS receivers arealways used simultaneously. This is oneof the similarities with the DifferentialCode Correction method described insection 3.2.

The Reference Receiver is alwayspositioned at a point with fixed or knowncoordinates. The other receiver(s) arefree to rove around. Thus they are knownas Rover Receivers. The baseline(s)between the Reference and Roverreceiver(s) are calculated.

The basic technique is still the same aswith the techniques mentioned previ-ously, - measuring distances to foursatellites and computing a position fromthose ranges.

The big difference comes in the waythose ranges are calculated.

3.3.1 The Carrier Phase, C/A and P-codes

At this point, it is useful to define the various components of the GPS signal.

Carrier Phase. The sine wave of the L1 or L2 signal that is created by the satellite.The L1 carrier is generated at 1575.42MHz, the L2 carrier at 1227.6 MHz.

C/A code. The Coarse Acquisition code. Modulated on the L1 Carrier at 1.023MHz.

P-code. The precise code. Modulated on the L1 and L2 carriers at 10.23 MHz.

Refer also to the diagram in section 2.1.

What does modulation mean ?

The carrier waves are designed to carry the binary C/A and P-codes in a processknown as modulation. Modulation means the codes are superimposed on thecarrier wave. The codes are binary codes. This means they can only have the values1 or -1. Each time the value changes, there is a change in the phase of the carrier.

Carrier Modulation


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3.3.2 Why use Carrier Phase?

The carrier phase is used because itcan provide a much more accuratemeasurement to the satellite than usingthe P-code or the C/A code. The L1carrier wave has a wavelength of 19.4cm. If you could measure the number ofwavelengths (whole and fractional parts)there are between the satellite andreceiver, you have a very accurate rangeto the satellite.

3.3.3 Double Differencing

The majority of the error incurred whenmaking an autonomous position comesfrom imperfections in the receiver andsatellite clocks. One way of bypassingthis error is to use a technique known asDouble Differencing.

If two GPS receivers make a measure-ment to two different satellites, the clockoffsets in the receivers and satellitescancel, removing any source of error thatthey may contribute to the equation.

Double Differencing


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3.3.4 Ambiguity and Ambiguity Resolution

1.

2.

an approximateposition. Theprecise answermust lie somewherewithin this circle.

The wavefronts froma single satellite

strike both withinand outside of thecircle. The precisepoint must liesomewhere on oneof the lines formedby these wavefrontsinside the circle.

Continued...

When a secondsatellite is observed,

After removing the clock errors by doubledifferencing, the whole number of carrierwavelengths plus a fraction of a wave-length between the satellite and receiverantenna can be determined. Theproblem is that there are many �sets� ofpossible whole wavelengths to eachobserved satellite. Thus the solution isambiguous. Statistical processes canresolve this ambiguity and determine themost probable solution.

The following explanation is an outline ofhow the ambiguity resolution processworks. Many complicating factors are notcovered by this explanation but it doesprovide a useful illustration.

Differential code can be used to obtain


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3.

4.

5.

6.

a second set ofwavefronts or phaselines are created.The point must lieon one of theintersections of thetwo sets of phaselines.

Adding a third

satellite furthernarrows the numberof possibilities. Thepoint must be on anintersection of allthree phase lines.

Adding a fourth

satellite furthernarrows thenumber ofpossibilities.

As the satellite

constellationchanges it willtend to rotatearound one point,revealing themost probablesolution.

26 GPS Basics -1.0.0enGeodetic Aspects

4. Geodetic AspectsSince GPS has become increasinglypopular as a Surveying and Navigationinstrument, surveyors and navigatorsrequire a basic understanding of howGPS positions relate to standardmapping systems.

A common cause of errors in GPSsurveys is the result of incorrectlyunderstanding these relationships.

27GPS Basics -1.0.0en Geodetic Aspects

4.1 Introduction

Determining a position with GPSachieves a fundamental goal of Geodesy- the determination of absolute positionwith uniform accuracy at all points on theearth�s surface. Using classical geodeticand surveying techniques, determinationof position is always relative to thestarting points of the survey, with theaccuracy achieved being dependent onthe distance from this point. GPStherefore, offers a significant advantageover conventional techniques.

The science of Geodesy is basic to GPS,and, conversely, GPS has become amajor tool in Geodesy. This is evident ifwe look at the aims of Geodesy:

1. Establishment and maintenance ofnational and global three-dimensionalgeodetic control networks on land,recognizing the time-varying nature ofthese networks due to plate movement.

2. Measurement and representation ofgeodynamic phenomena (polar motion,earth tides, and crustal motion).

3. Determination of the gravity field of theearth including temporal variations.

Although most users may never carry outany of the above tasks, it is essential thatusers of GPS equipment have a generalunderstanding of Geodesy.


4.2. The GPS coordinate system

Although the earth may appear to be auniform sphere when viewed fromspace, the surface is far from uniform.Due to the fact that GPS has to givecoordinates at any point on the earth�ssurface, it uses a geodetic coordinatesystem based on an ellipsoid. Anellipsoid (also known as a spheroid) is asphere that has been flattened orsquashed.

An ellipsoid is chosen that most accu-rately approximates to the shape of theearth. This ellipsoid has no physicalsurface but is a mathematically definedsurface.

There are actually many different ellip-soids or mathematical definitions of theearth�s surface, as will be discussedlater. The ellipsoid used by GPS isknown as WGS84 or World GeodeticSystem 1984.

A point on the surface of the earth (notethat this is not the surface of the ellip-soid), can be defined by using Latitude,Longitude and ellipsoidal height.

An alternative method for defining theposition of a point is the CartesianCoordinate system, using distances inthe X, Y, and Z axes from the origin orcentre of the spheroid. This is themethod primarily used by GPS fordefining the location of a point in space.

An Ellipsoid

P

0

X

Y

Z

DY

DZ

DX

Earth's Surface

Height

Latitude

Longitude

Defining coordinates of P byGeodetic and Cartesian coordinates


4.3 Local coordinate systems

Just as with GPS coordinates, localcoordinates or coordinates used in aparticular country�s maps are based ona local ellipsoid, designed to match thegeoid (see section 4.4) in the area.Usually, these coordinates will havebeen projected onto a plane surface toprovide grid coordinates (see section4.5).

The ellipsoids used in most localcoordinate systems throughout the worldwere first defined many years ago,before the advent of space techniques.These ellipsoids tend to fit the area ofinterest well but could not be applied toother areas of the earth. Hence, eachcountry defined a mapping system/reference frame based on a localellipsoid.

When using GPS, the coordinates of thecalculated positions are based on theWGS84 ellipsoid. Existing coordinatesare usually in a local coordinate systemand therefore the GPS coordinates haveto be transformed into this local system.

WGS84 EllipsoidEarth's Surface(topography)

Local Ellipsoid

The relationship between ellipsoidsand the earth�s surface


PH

Nh

4.4 Problems with height

The nature of GPS also affects themeasurement of height.

All heights measured with GPS aregiven in relation to the surface of theWGS84 ellipsoid. These are known asEllipsoidal Heights.

Existing heights are usually orthometricheights measured relative to mean sealevel.

Mean sea level corresponds to asurface known as the geoid. The Geoidcan be defined as an equipotentialsurface, i.e. the force of gravity is aconstant at any point on the geoid.

The geoid is of irregular shape anddoes not correspond to any ellipsoid.The density of the earth does howeverhave an effect on the geoid, causing it torise in the more dense regions and fallin less dense regions.

The relationship between the geoid,ellipsoid and earth�s surface is shownin the graphic below.

As most existing maps showorthometric heights (relative to thegeoid), most users of GPS also requiretheir heights to be orthometric.

This problem is solved by using geoidalmodels to convert ellipsoidal heights toorthometric heights. In relatively flatareas the geoid can be considered to beconstant. In such areas, use of certaintransformation techniques can create aheight model and geoidal heights canbe interpolated from existing data.

TopographyEllipsoidGeoid

h = H+N

whereh = Ellipsoidal HeightH = Orthometric HeightN = Geoid Separation

Relationship between Orthometricand Ellipsoidal height


4.5 Transformations

The purpose of a transformation is totransform coordinates from one systemto another.

Several different Transformation ap-proaches exist. The one that you use willdepend on the results you require.

The basic field procedure for determina-tion of transformation parameters is thesame no matter which approach istaken.

Firstly, coordinates must be available inboth coordinate systems (i.e. in WGS84and in the local system) for at least three(and preferably four) common points.The more common points you include inthe transformation, the more opportunityyou have for redundancy and errorchecking.

Common points are achieved by mea-suring points with GPS, where thecoordinates and orthometric heights areknown in the local system, (e.g. existingcontrol points).

The transformation parameters can thenbe calculated using one of the transfor-mation approaches.

It is important to note that the transfor-mation will only apply to points in thearea bounded by the common points.Points outside of this area should not betransformed using the calculatedparameters but should form part of anew transformation area.

Transformations apply within an area ofcommon points


Helmert Transformations

The Helmert 7 parameter transformationoffers a mathematically correct transfor-mation. This maintains the accuracy ofthe GPS measurements and localcoordinates.

Experience has shown that it is commonfor GPS surveys to be measured to amuch higher accuracy than older surveysmeasured with traditional opticalinstruments.

In the vast majority of cases, the previ-ously measured points will not be asaccurate as the new points measuredwith GPS. This may create non-homoge-neity in the network.

When transforming a point betweencoordinate systems, it is best to think ofthe origin from which the coordinates arederived as changing and not the surfaceon which it lies.

In order to transform a coordinate fromone system to another, the origins andaxes of the ellipsoid must be knownrelative to each other. From this informa-tion, the shift in space in X, Y and Z fromone origin to the other can be deter-

mined, followed by any rotation about theX, Y and Z axes and any change in scalebetween the two ellipsoids.

XS

YS

ZS

XL

YL

ZL

wY

wZ

wX

P

T

PS

PL

PS

PL

T

wX, wY, wZ

LocalEllipsoid

WGS84Ellipsoid= Position in WGS84

= Position in Local System= Resultant Vector from shift of origin in X, Y and Z

= Rotation angles

7 parameter Helmert transformation


Other transformation approaches

Whilst the Helmert transformationapproach is mathematically correct, itcannot account for irregularities in thelocal coordinate system and for accurateheighting, the geoid separation must beknown.

Therefore, Leica also makes a numberof other transformation approachesavailable in it�s equipment and software.

The so-called Interpolation approachdoes not rely on knowledge of the localellipsoid or map projection.

Inconsistencies in the local coordinatesare dealt with by stretching or squeezingany GPS coordinates to fit homoge-neously in the local system.

Additionally a height model can beconstructed. This compensates for lackof geoid separations, provided sufficientcontrol points are available.

As an alternative to the Interpolationapproach the One Step approach maybe used. This transformation approachalso works by treating the height andposition transformations separately. Forthe position transformation, the WGS84

coordinates are projected onto a tempo-rary Transverse Mercator projection andthen the shifts, rotation and scale fromthe temporary projection to the "real"projection are calculated. The Heighttransformation is a single dimensionheight approximation.

This transformation may be used inareas where the local ellipsoid and mapprojection are unknown and where thegeoid is reasonably constant.

Point projected ontoheight model surface

Height model

Ellipsoidal surface

Orthometric heightat common point

Height model generated from 4 known points

Both the Interpolation and the One Stepapproach should be limited to an area ofabout 15 x 15km, (10 x 10 miles).

A combination of the Helmert andInterpolation approaches may be foundin the Stepwise approach. This ap-proach uses a 2D Helmert transforma-tion to obtain position and a heightinterpolation to obtain heights. Thisapproach requires the knowledge oflocal ellipsoid and map projection.


4.6 Map Projections and Plane Coordinates

Most Surveyors measure and recordcoordinates in an orthogonal gridsystem. This means that points aredefined by Northings, Eastings andorthometric height (height above sealevel). Map Projections allow surveyorsto represent a 3 dimensional curvedsurface on a flat piece of paper.

Such map projections appear as planesbut actually define mathematical stepsfor specifying positions on an ellipsoidin the terms of a plane.

The way in which a map projectiongenerally works is shown in the dia-gram. Points on the surface of the

spheroid are projected on to a planesurface from the origin of the spheroid.

The diagram also highlights the problemthat it is not possible to represent truelengths or shapes on such a plane. Truelengths are only represented where theplane cuts the spheroid (points c and g).

0 10 20 30 40 50 60 70 80 90 100 110 E

010

20

30

40

50

60

70

80

90100110

N

o

ab

c

d

e

f

g

h

i

a'

b'

d'

e'

f'

h'

i'

A plane grid based map The basic idea behind map projections


4.6.1 The Transverse Mercator Projection

The Transverse Mercator projection is aconformal projection. This means thatangular measurements made on theprojection surface are true.

The Projection is based on a cylinderthat is slightly smaller than the spheroidand is then flattened out. The method isused by many countries and is espe-cially suited to large countries aroundthe equator.

The Transverse Mercator Projection isdefined by:

� False Easting and False Northing.

� Latitude of Origin

� Central Meridian

� Scale on Central meridian

� Zone Width

Cylinder Spheroid

Transverse Mercator projection


0

N

E

The False Easting and False Northingare defined in order that the origin of thegrid projection can be in the lower lefthand corner as convention dictates. Thisdoes away with the need for negativecoordinates.

The Latitude of Origin defines theLatitude of the axis of the cylinder. This isnormally the equator (in the northernhemisphere).

The Central Meridian defines thedirection of grid north and the longitudeof the centre of the projection.

Scale varies in an east-west direction. Asthe cylinder is usually smaller than thespheroid, the Scale on Central Meridianis too small, is correct on the ellipses ofintersection and is then too large at theedges of the projection.

The scale in the north-south directiondoes not vary. For this reason, theTransverse Mercator projection is mostsuitable for mapping areas that are longin the north-south direction.

The Zone Width defines the portion ofthe spheroid in an east-west direction towhich the projection applies.

Features of the Transverse Mercator projection

Universal Transverse Mercator (UTM)

The UTM projection covers the world between 80ºN and 80ºS latitude. It is atype of Transverse Mercator projection, with many of the defining parametersheld fixed. The UTM is split into zones of 6º longitude with adjacent zonesoverlapping by 30�. The one defining parameter is the Central Meridian orZone Number. (When one is defined, the other is implied).

Zone Width

Central Meridian

Ellipses ofIntersection


4.6.2 The Lambert Projection

The Lambert Projection is also aconformal projection based on a conethat intersects the spheroid. It is ideal forsmall, circular countries, islands andpolar regions.

0

N

E

Features of the Lambert Projection

Cone

� Latitude of 1st StandardParallel

� Latitude of 2nd Stand-ard Parallel

The False Easting andFalse Northing aredefined in order that theorigin of the grid projec-tion can be in the lowerleft hand corner asconvention dictates. Thisdoes away with the needfor negative coordinates.

The Latitude of Origindefines the latitude of theorigin of the projection.

The Central Meridiandefines the direction ofgrid north and thelongitude of the centre ofthe projection.

The Latitude of 1stStandard Paralleldefines the latitude atwhich the cone first cutsthe spheroid. This alsodefines where the

Spheroid

The Lambert Projection

The Lambert projection is defined by:

� False Easting and Northing

� Latitude of origin

� Central Meridian

influence of scale in the north-south direction is zero.

The Latitude of 2nd Standard Parallel defines thesecond latitude at which the cone cuts the pyramid. Theinfluence of scale will also be zero at this point.

The scale is too small between the standard parallelsand too large outside them, being defined by thelatitudes of the Standard Parallels at which it is zero.Scale in the east-west direction does not vary.

Zon

e W

idth

1/6

Zone

Wid

th2/3

Zone W

idth

1/6

Zone

Wid

th Standard Parallel

Central Meridian

Standard Parallel

38 GPS Basics -1.0.0enSurveying with GPS

5. Surveying with GPSProbably even more important to thesurveyor or engineer than the theorybehind GPS, are the practicalities of theeffective use of GPS.

Like any tool, GPS is only as good as it�soperator. Proper planning and prepara-tion are essential ingredients of asuccessful survey, as well as an aware-ness of the capabilities and limitationsof GPS.

Why use GPS?

GPS has numerous advantages overtraditional surveying methods:

1. Intervisibility between points is notrequired.

2. Can be used at any time of the day ornight and in any weather.

3. Produces results with very highgeodetic accuracy.

4. More work can be accomplished inless time with fewer people.

Limitations

In order to operate with GPS it is impor-tant that the GPS Antenna has a clearview to at least 4 satellites. Sometimes,the satellite signals can be blocked bytall buildings, trees etc. Hence, GPScannot be used indoors. It is alsodifficult to use GPS in town centers orwoodland.

Due to this limitation, it may prove morecost effective in some survey applica-tions to use an optical total station or tocombine use of such an instrument withGPS. Clear view to four satellites

Large objects can block the GPS signal

39GPS Basics -1.0.0en Surveying with GPS

5.1 GPS Measuring Techniques

There are several measuring techniquesthat can be used by most GPS SurveyReceivers. The surveyor should choosethe appropriate technique for the appli-cation.

Static - Used for long lines, geodeticnetworks, tectonic plate studies etc.Offers high accuracy over long distancesbut is comparatively slow.

Rapid Static - Used for establishinglocal control networks, Network densifi-cation etc. Offers high accuracy onbaselines up to about 20km and ismuch faster than the Static technique.

Kinematic - Used for detail surveys andmeasuring many points in quick succes-sion. Very efficient way of measuringmany points that are close together.However, if there are obstructions to thesky such as bridges, trees, tall buildingsetc., and less than 4 satellites aretracked, the equipment must bereinitialized which can take 5-10 min-utes.

A processing technique known as On-the-Fly (OTF) has gone a long way tominimise this restriction.

RTK - Real Time Kinematic uses a radiodata link to transmit satellite data fromthe Reference to the Rover. This enablescoordinates to be calculated anddisplayed in real time, as the survey isbeing carried out. Used for similarapplications as Kinematic. A very effec-tive way for measuring detail as resultsare presented as work is carried out.This technique is however reliant upon aradio link, which is subject to interfer-ence from other radio sources and alsoline of sight blockage.


5.1.1 Static Surveys

This was the first method to be devel-oped for GPS surveying. It can be usedfor measuring long baselines (usually20km (16 miles) and over).

One receiver is placed on a point whosecoordinates are known accurately inWGS84. This is known as the ReferenceReceiver. The other receiver is placed onthe other end of the baseline and isknown as the Rover.

Data is then recorded at both stationssimultaneously. It is important that datais being recorded at the same rate ateach station. The data collection ratemay be typically set to 15, 30 or 60seconds.

The receivers have to collect data for acertain length of time. This time isinfluenced by the length of the line, thenumber of satellites observed and thesatellite geometry (dilution of precisionor DOP). As a rule of thumb, the observa-tion time is a minimum of 1 hour for a20km line with 5 satellites and aprevailing GDOP of 8. Longer linesrequire longer observation times.

Once enough data has been collected,the receivers can be switched off. TheRover can then be moved to the nextbaseline and measurement can onceagain commence.

It is very important to introduce redun-dancy into the network that is beingmeasured. This involves measuringpoints at least twice and creates safetychecks against problems that wouldotherwise go undetected.

A great increase in productivity can berealized with the addition of an extraRover receiver. Good coordination isrequired between the survey crews inorder to maximize the potential of havingthree receivers. An example is given onthe next page.


1 32

54

The network ABCDE has to bemeasured with three receivers. Thecoordinates of A are known inWGS84. The receivers are placed onA, B and C. GPS data is recorded forthe required length of time.

After the required length of time, thereceiver that was at E moves to Dand B moves to C. The triangle ACDis measured.

Then A moves to E and C moves toB. The triangle BDE is measured.

Finally, B moves back to C and theline EC is measured.

The end result is the measurednetwork ABCDE. One point is mea-sured three times and every point hasbeen measured at least twice. Thisprovides redundancy. Any gross errorswill be highlighted and the offendingmeasurement can be removed.


5.1.2 Rapid Static Surveys

In Rapid Static surveys, a ReferencePoint is chosen and one or more Roversoperate with respect to it.

Typically, Rapid Static is used fordensifying existing networks, establish-ing control etc.

When starting work in an area where noGPS surveying has previously takenplace, the first task is to observe anumber of points, whose coordinatesare accurately known in the local system.This will enable a transformation to becalculated and all hence, points mea-sured with GPS in that area can beeasily converted into the local system.

As discussed in section 4.5, at least 4known points on the perimeter of thearea of interest should be observed. Thetransformation calculated will then bevalid for the area enclosed by thosepoints.

The Reference Receiver is usually setup at a known point and can be includedin the calculations of the transformationparameters. If no known point is avail-able, it can be set up anywhere withinthe network.

The Rover receiver(s) then visit each ofthe known points. The length of time thatthe Rovers must observe for at eachpoint is related to the baseline lengthfrom the Reference and the GDOP.

The data is recorded and post-proc-essed back at the office.

Checks should then be carried out toensure that no gross errors exist in themeasurements. This can done bymeasuring the points again at a differenttime of the day.

When working with two or more Roverreceivers, an alternative is to ensure thatall rovers operate at each occupied pointsimultaneously. Thus allows data fromeach station to be used as eitherReference or Rover during post-processing and is the most efficient wayto work, but also the most difficult tosynchronise.

Another way to build in redundancy is toset up two reference stations, and useone rover to occupy the points as shownin the lower example on the next page.


1 4 532

1 4 532

The network 1,2,3,4,5has to be measuredfrom Referencestation R with threeGPS receivers.

The reference stationis set up. One Roveroccupies point 1whilst the otheroccupies point 3.

After the requiredlength of time, oneRover moves to point2 whilst the othermoves to point 4.

Then, one Rover canreturn to the officewhilst the othermeasures point 5.

The end result is asabove. On a subse-quent day, the opera-tion will be repeatedin order to check forgross errors.

Alternatively...

Reference stationsare set up at R andpoint 1. The Roveroccupies point 2.

After the requiredlength of time, theRover moves to point3.

Similarly, the Roverthen progresses topoint 4...

...and then point 5. The end result is ameasured networkwith built-in redun-dancy.


5.1.3 Kinematic Surveys

The Kinematic technique is typicallyused for detail surveying, recordingtrajectories etc., although with the adventof RTK it�s popularity is diminishing.

The technique involves a moving Roverwhose position can be calculatedrelative to the Reference.

Firstly, the Rover has to perform what isknown as an initialization. This isessentially the same as measuring aRapid Static point and enables the post-processing software to resolve theambiguity when back in the office. TheReference and Rover are switched onand remain absolutely stationary for 5-20minutes, collecting data. (The actualtime depends on the baseline lengthfrom the Reference and the number ofsatellites observed).

After this period, the Rover may thenmove freely. The user can record posi-tions at a predefined recording rate, canrecord distinct positions, or record acombination of the two. This part of themeasurement is commonly called thekinematic chain.

A major point to watch during kinematicsurveys is to avoid moving too close toobjects that could block the satellitesignal from the Rover receiver. If at anytime, less than four satellites are trackedby the Rover receiver, you must stop,move into a position where 4 or moresatellites are tracked and perform aninitialization again before continuing.

1 2 3

Initialization is performedfrom the Reference to theRover.

The Rover can then move.Positions can be recordedat a predefined interval...

...and also at distinctpoints if required.

Kinematic on the Fly

This is a variation of the Kinematictechnique and overcomes the require-ment of initializing and subsequent re-initialization when the number ofobserved satellites drops below four.

Kinematic on the Fly is a processingmethod that is applied to the measure-ment during post-processing. At thestart of measurement, the operator cansimply begin walking with the Roverreceiver and record data. If they walkunder a tree and lose the satellites,upon emerging back into satellitecoverage, the system will automaticallyreinitialize.


5.1.4 RTK Surveys

RTK stands for Real Time Kinematic. Itis a Kinematic on the Fly survey carriedout in real time.

The Reference Station has a radio linkattached and rebroadcasts the data itreceives from the satellites.

The Rover also has a radio link andreceives the signal broadcast from theReference. The Rover also receivessatellite data directly from the satellitesvia it�s own GPS Antenna. These twosets of data can be processed togetherat the Rover to resolve the ambiguity andtherefore obtain a very accurate positionrelative to the Reference receiver.

Once the Reference Receiver has beenset up and is broadcasting data throughthe radio link, the Rover Receiver can beactivated.

When it is tracking satellites and receiv-ing data from the Reference, it can beginthe initialization process. This is similarto the initialization performed in a post-processed kinematic on the fly survey,the main difference being that it iscarried out in real-time.

Once the initialization is complete, theambiguities are resolved and the Rovercan record point and coordinate data. Atthis time, baseline accuracies will be inthe 1 - 5cm range.

It is important to maintain contact withthe Reference Receiver, otherwise theRover may lose the ambiguity. Thisresults in a far less accurate positionbeing calculated.

Additionally, problems may be encoun-tered when surveying close to obstruc-tions such as tall buildings, trees etc. asthe satellite signal may be blocked.

RTK is quickly becoming the mostcommon method of carrying out highprecision, high accuracy GPS surveys insmall areas and can be used for similarapplications as a conventional totalstation. This includes detail surveying,stakeout, COGO applications etc.

The Radio Link

Most RTK GPS systems make use ofsmall UHF radio modems. Radiocommunication is the part of the RTKsystem that most people experiencedifficulty with. It is worth considering thefollowing influencing factors when tryingto optimize radio performance:

1. Power of the transmitting radio.Generally speaking, the more power, thebetter the performance. However, mostcountries legally restrict output power to0.5 - 2W.

2. Height of transmitter antenna. Radiocommunication can be affected by line ofsight. The higher up you can position theantenna, the less likely you are to getline of sight problems. It will alsoincrease the overall range of radiocommunication. The same also appliesto the receiving antenna.

Other influencing factors affectingperformance include the length of thecable to radio antenna (longer cablesmean higher losses) and the type ofradio antenna used.


5.2 Pre-survey preparation

Before heading out into the field, thesurveyor needs to prepare for the survey.Items that must be considered are:

1. Radio Licences

2. Power - charged batteries

3. Spare cables

4. Communication between surveyparties

5. Coordinates of Reference Station

6. Memory cards - Do you have enoughspare memory?

7. Observation schedule. First objectiveshould be to get enough informationfor determination of TransformationParameters, then aim for redundancyof observations.

5.3 Tips during operation

For Static and Rapid Static surveys,always fill out a record sheet for eachpoint you survey. An example is given onthe next page.

With Static and Rapid Static surveys, it isvital that the antenna height is measuredcorrectly. This is one of the most com-mon mistakes when carrying out a GPSsurvey. Measure the height at thebeginning and end of occupation. WithKinematic and RTK Surveys, the an-tenna is usually mounted on a polewhich has a constant height.

During Static and Rapid Static surveys,the GPS antenna has to be kept totallystill. This also applies to the Rapid Staticinitialization of Kinematic surveys (butnot to Kinematic on the Fly or RTKsurveys). Any movement or vibration inthe antenna can adversely affect theresult.


Field Sheet

Point Id

Sensor Serial No

Operation Type

Antenna Type

Height Reading

Start Time

Stop Time

No. of Epochs

No. of Satellites

GDOP

Date

Operator

Notes

48 GPS Basics -1.0.0enGlossary

GlossaryAlmanac

Library of coarse satellite orbital dataused to calculate satellite position, risetime, elevation, and azimuth.

Ambiguity

The unknown integer number of cyclesof the reconstructed carrier phasecontained in an unbroken set of mea-surements from a single satellite passat a single receiver.

Anti-spoofing (A-S)

Encrypting the P-code (to form the Y-code).

Atmospheric propagation delay

Time delay affecting satellite signals dueto tropospheric layers of the earth�satmosphere.

Azimuth

A horizontal angle measured clockwisefrom a direction (such as North).

Bandwidth

A measure of the width of the spectrumof a signal (frequency domain represen-tation of a signal) expressed in Hertz.

Baseline

The length of the three-dimensionalvector between a pair of stations forwhich simultaneous GPS data has beencollected and processed with differentialtechniques.

Bearing

Term used in navigation to describe theangle between a reference direction(e.g., geographic north, magnetic north,grid north) and the trajectory.

Beat frequency

Either of the two additional frequenciesobtained when signals of two frequen-cies are mixed. The beat frequenciesare equal to the sum or difference of theoriginal frequencies, respectively.

Binary biphase modulation

Phase changes of either 0° or 180° (torepresent binary 0 or 1, respectively) ona constant frequency carrier. These canbe modelled by

y = A cos (wt + p),

where the amplitude function A is asequence of +1 and -1 values (torepresent 0° and 180° phase changesrespectively). GPS signals are biphasemodulated.

49GPS Basics -1.0.0en Glossary

C/A code

The Coarse/Acquisition GPS codemodulated on the GPS L1 signal. Thiscode is a sequence of 1023 pseudoran-dom binary biphase modulations on theGPS carrier at a chipping rate of 1.023MHz, thus having a code repetitionperiod of one millisecond.

Cartesian Coordinates

The coordinates of a point in spacegiven in three mutually perpendiculardimensions (x, y, z) from the origin.

Carrier

A radio wave having at least one charac-teristic (e.g., frequency, amplitude,phase) which may be varied from aknown reference value by modulation.

Carrier beat phase

The phase of the signal which remainswhen the incoming Doppler-shiftedsatellite carrier signal is beat (thedifference frequency signal is generated)

with the nominally constant referencefrequency generated in the receiver.

Carrier frequency

The frequency of the unmodulatedfundamental output of a radio transmit-ter. The GPS L1 carrier frequency is1575.42 MHz, the GPS L2 carrier fre-quency is 1227.60 MHz.

Chip

The time interval of either a zero or a onein a binary pulse code

Chip rate

Number of chips per second (e.g., C/Acode : 1.023*106 cps)

Clock offset

Constant difference in the time readingof two clocks.

Code

A system used for communication inwhich arbitrarily chosen strings of zerosand ones are assigned definite mean-ings.

Compacted data

Raw data compacted over a specifiedtime interval (compaction time) into onesingle observable (measurement) forrecording.

Conformal Projection

A map projection that preserves angleson the ellipsoid after they have beenmapped onto the plane.

Control segment

Ground-based GPS System equipmentoperated by the U.S. Government thattracks the satellite signals, determinesthe orbits of the satellites, and transmitsorbit definitions to the memories of thesatellites.


Cutoff angle

The minimum elevation angle belowwhich no more GPS satellites aretracked by the sensor.

Cycle slip

A discontinuity of an integer number ofcycles in the measured carrier beatphase resulting from a temporary loss oflock of a GPS satellite signal.

Data message

A message included in the GPS signalthat reports the satellite�s location, clockcorrections, and health. Included isrough information on the status of othersatellites in the constellation.

DGPS

Differential GPS. The term commonlyused for a GPS system that utilizesdifferential code corrections to achievean enhanced positioning accuracy ofaround 0.5 - 5m.

Deflection of the vertical

The angle between the normal to theellipsoid and the vertical (true plumbline). It is usually resolved into a compo-nent in the meridian and a componentperpendicular to the meridian.

Delay lock

The technique whereby the receivedcode (generated by the satellite clock) iscompared with the internal code (gener-ated by the receiver clock) and the lattershifted in time until the two codes match.

Differenced measurements

GPS measurements can be differencedacross receivers, across satellites andacross time. Although many combina-tions are possible, the present conven-tion for GPS phase measurementdifferencing is to perform the differencesin the above order: first across receiv-ers, second across satellites and thirdacross time.

A single difference measurement(across receivers) is the instantaneousdifference in phase of a received signal,measured by two receivers simultane-ously observing one satellite.

A double difference measurement(across receivers and satellites) isobtained by differencing the singledifference for one satellite with respect tothe corresponding single difference for achosen reference satellite.

A triple difference measurement (acrossreceivers, satellites and time) is thedifference between a double differenceat one epoch of time and the samedouble difference at another epoch oftime.

Differential positioning

Determination of relative coordinatesbetween two or more receivers whichare simultaneously tracking the sameGPS signals.


Dilution of precision (DOP)

A description of the purely geometricalcontribution to the uncertainty in aposition fix. The DOP factor indicates thegeometrical strength of the satelliteconstellation at the time of measure-ment. Standard terms in the case ofGPS are

GDOP three position coordinates plusclock offset

PDOP three coordinates

HDOP two horizontal coordinates

VDOP height only

TDOP clock offset only

HTDOP horizontal position and time

Doppler shift

The apparent change in frequency of areceived signal due to the rate of changeof the range between the transmitter andreceiver.

Eccentricity

The ratio of the distance from the centreof an ellipse to its focus to thesemimajor axis.

e = (1 - b2/a2)1/2

where a and b are the semimajor andsemiminor axis of the ellipse, respec-tively.

Elevation

Height above the Geoid. SeeOrthometric height.

Ellipsoid

In geodesy, unless otherwise specified,a mathematical figure formed by revolv-ing an ellipse about its minor axis(sometimes also referred to as sphe-roid). Two quantities define an ellipsoid;these are usually given as the length ofthe semimajor axis a and the flattening f.

Ellipsoid height

The vertical distance of a point above theellipsoid.

Ephemeris

A list of positions or locations of acelestial object as a function of time.

Ephemeris error

Difference between the actual satellitelocation and the location predicted by thesatellite orbital data (ephemerides).

Epoch

A particular fixed instant of time used asa reference point on a time scale.

Equipotential Surface

A mathematically defined surface wherethe gravitational potential is the same atany point on that surface. An example ofsuch a surface is the geoid.


Flattening

Relating to Ellipsoids.

f = (a-b)/a = 1-(1-e2)1/2

where a ... semimajor axis

b ... semiminor axis

e ... eccentricity

Fundamental frequency

The fundamental frequency used in GPSis 10.23 MHz. The carrier frequencies L1and L2 are integer multiples of thefundamental frequency.

L1 = 154F = 1575.42 MHz

L2 = 120F = 1227.60 MHz

GDOP

Geometric dilution of precision

�> Dilution of precision

Geocentric

Relating to the centre of the earth.

Geodesy

The study of the earth�s size and shape

Geodetic Coordinates

Coordinates defining a point withreference to an ellipsoid. GeodeticCoordinates are either defined usinglatitude, longitude and ellipsoidal heightor using Cartesian coordinates.

Geodetic Datum

A mathematical model designed to bestfit part or all of the geoid. It is defined byan ellipsoid and the relationship be-tween the ellipsoid and a point on thetopographic surface established as theorigin of datum. This relationship canbe defined by six quantities, generally(but not necessarily) the geodeticlatitude, longitude, and the height of theorigin, the two components of the

deflection of the vertical at the origin, andthe geodetic azimuth of a line from theorigin to some other point.

Geoid

The particular equipotential surfacewhich coincides with mean sea level,and which may be imagined to extendthrough the continents. This surface iseverywhere perpendicular to the direc-tion of the force of gravity.

Geoidal Height

See Geoid separation

Geoid separation

The distance from the surface of thereference ellipsoid to the geoid mea-sured outward along the normal to theellipsoid.

GPS

Global Positioning System


GPS time

A continuous time system based on theCoordinated Universal Time (UTC) from6th January 1980.

Greenwich mean time (GMT)

The mean solar time of the meridian ofGreenwich. Used as the prime basis ofstandard time throughout the world.

Great circle course

Term used in navigation. Shortestconnection between two points.

Graticule

A plane grid representing the lines ofLatitude and Longitude of an ellipsoid.

Gravitational constant

The proportionality constant in Newton�sLaw of gravitation.

G = 6.672 * 10-11 m3s-2kg-1

Inclination

The angle between the orbital plane ofan object and some reference plane(e.g., equatorial plane).

Integer bias term

See Ambiguity

Ionospheric Delay

A wave propagating through the iono-sphere (which is a non-homogeneousand dispersive medium) experiencesdelay. Phase delay depends on electroncontent and affects carrier signals.Group delay depends on dispersion inthe ionosphere as well, and affectssignal modulation (codes). The phaseand group delay are of the same magni-tude but opposite sign.

Kinematic positioning

Determination of a time series of sets ofcoordinates for a moving receiver, eachset of coordinates being determinedfrom a single data sample, and usuallycomputed in real time.

Keplerian orbital elements

Allow description of any astronomicalorbit:

a: semimajor axis

e: eccentricity

w: argument of perigee

W: right ascension of ascending node

i: inclination

n: true anomaly

Lambert Projection

A conformal conic map projection thatprojects an ellipsoid onto a planesurface by placing a cone over thesphere.

Latitude

The angle between the ellipsoidalnormal and the equatorial plane.Latitude is zero on the equator and 90°at the poles.


L-band

The radio frequency band extending from390 MHz to 1550 MHz. The frequenciesof the L1 and L2 carriers transmitted byGPS satellites lie within this L-band.

Least squares estimation

The process of estimating unknownparameters by minimizing the sum of thesquares of measurement residuals.

Local Ellipsoid

An Ellipsoid that has been defined forand fits a specific portion of the earth.Local ellipsoids usually fit single orgroups of countries.

Local Time

Local time equals to GMT time + timezone.

Longitude

Longitude is the angle between themeridian ellipse which passes throughGreenwich and the meridian ellipsecontaining the point in question. Thus,Latitude is 0° at Greenwich and thenmeasured either eastward through 360°or eastward 180° and westward 180°.

Meridian

An imaginary line joining north to southpole and passing through the equator at90°.

Multipath error

A positioning error resulting frominterference between radio waves whichhave travelled between the transmitterand the receiver by two paths of differentelectrical lengths.

NAVSTAR

Acronym for Navigation System withTime and Ranging, the original name forGPS.

NMEA

National Marine Electronics Association.Defined a standard (NMEA 0183) toenable marine electronics instruments,communication and navigation equip-ment to communicate. This standard isused to get time and position data out ofGPS instruments in many applications.

Observing Session

A period of time over which GPS data iscollected simultaneously by two or morereceivers.

Orthometric height

The distance of a point above the geoidmeasured along the plumb line throughthe point (height above mean sea level).See also Elevation.


P-code

The Precise GPS code - a very long(about 1014 bit) sequence of pseudoran-dom binary biphase modulations on theGPS carrier at a chipping rate of 10.23MHz which does not repeat itself forabout 267 days. Each one-weeksegment of the P-code is unique to oneGPS satellite, and is reset each week.Access to the P-code will be restricted bythe U.S. Government to authorized usersonly.

PDOP

Position dilution of precision.

see Dilution of Precision

Phase observable

See Reconstructed Carrier Phase

Point Positioning

The independent reduction of observa-tions made by a particular receiver usingthe pseudorange information broadcastfrom the satellites.

Post processing

The process of computing positions innon-real-time, using data previouslycollected by GPS receivers.

Precise positioning service (PPS)

The highest level of point positioningaccuracy provided by GPS. It is basedon the dual-frequency P - code.

Propagation delay

See Atmospheric propagation delay,and Ionospheric delay

Pseudolite

The ground-based differential GPSstation which transmits a signal with astructure similar to that of an actual GPSsatellite.

Pseudorandom noise (PRN) code

Any group of binary sequences that

appear to be randomly distributed likenoise, but which can be exactly distrib-uted. The most important property ofPRN codes is that the sequence has aminimum autocorrelation value, exceptat zero lag.

Pseudorange

A measure of the apparent signalpropagation time from the satellite to thereceiver antenna, scaled into distance bythe speed of light. The apparent propa-gation time is the difference between thetime of signal reception (measured inthe receiver time frame) and the time ofemission (measured in the satellite timeframe). Pseudorange differs from theactual range by the influence of satelliteand user clock.

Range

Term used in Navigation for the length ofthe trajectory between two points. Thetrajectory is normally the great circle orthe rhumb line.


Rapid static survey

Term used in connection with the GPSSystem for static survey with shortobservation times. This type of survey ismade possible by the fast ambiguityapproach that is resident in the SKIsoftware.

Raw data

Original GPS data taken and recordedby a receiver.

Receiver channel

The radio frequency and digital hard-ware and the software in a GPS receiver,required to track the signal from oneGPS satellite at one of the two GPScarrier frequencies.

Reconstructed carrier phase

The difference between the phase of theincoming Doppler-shifted GPS carrierand the phase of a nominally-constantreference frequency generated in thereceiver.

Relative positioning

See Differential positioning

Rhumb line

Term used in navigation. Trajectorybetween two points with constantbearing.

RINEX

Receiver INdependent EXchange format.A set of standard definitions and formatsto promote the free exchange of GPSdata

RTCM

Radio Technical Commission forMaritime services. Commission set upto define a differential data link to relayGPS messages from a monitor stationto a field user.

RTK

Real Time Kinematic. A term used todescribe the procedure of resolving thephase ambiguity at the GPS receiver sothat the need for post-processing isremoved.

Satellite Constellation

The arrangement in space of thecomplete set of satellites of a systemlike GPS.

Satellite Configuration

The state of the satellite constellation ata specific time, relative to a specific useror set of users.

Selective availability (SA)

Degradation of point positioning accu-racy for civil users by the U.S. Depart-ment of Defense. SA is produced byeither clock dithering or orbit degrada-tion.


Sidereal day

Time interval between two successiveupper transits of the vernal equinox.

Site

A location where a receiver has beensetup to determine coordinates.

Space segment

The part of the whole GPS system that isin space, i.e. the satellites.

Solar day

Time interval between two successiveupper transits of the Sun.

Squared reception mode

A method used for tracking GPS L2signals which doubles the carrierfrequency and does not use the P-code.

Squaring-type channel

A GPS receiver channel which multipliesthe received signal by itself to obtain asecond harmonic of the carrier whichdoes not contain the code modulation.

Standard positioning service (SPS)

Level of point positioning accuracyprovided by GPS based on the single-frequency C/A - code.

Static Survey

The expression static survey is used inconnection with GPS for all non-kine-matic survey applications. This includesthe following operation modes:

� Static survey

� Rapid static survey

Stop & Go Survey

The term Stop & Go survey is used inconnection with GPS for a special kind ofkinematic survey. After initialization(determination of ambiguities) on thefirst site, the roving receiver has to bemoved between the other sites withoutloosing lock to the satellite signal. Onlya few epochs are then necessary onthese sites to get a solution with surveyaccuracy. Once loss of lock occurred, anew initialization has to be done.

Time Zone

Time zone = Local Time - GreenwichMean Time (GMT). Note that GreenwichMean Time is approximately equal toGPS time.

Topography

The form of the land of a particularregion.


Transformation

The process of transforming coordinatesfrom one system to another.

Transit

The predecessor to GPS. A satellitenavigation system that was in servicefrom 1967 to 1996.

Transverse Mercator Projection

A conformal cylindrical map projectionwhich may be visualized as a cylinderwrapped around the earth.

Translocation

The method of using simultaneous datafrom separate stations to determine therelative position of one station withrespect to another station. See differen-tial positioning.

Universal time

Local solar mean time at GreenwichMeridian

UT Abbreviation for universal time

UT0 UT as deduced directly fromobservation of stars

UT1 UT0 corrected for polar motion

UT2 UT1 corrected for seasonalvariations in the Earth�s rotationrate

UTC Universal Time Coordinated;uniform atomic time system keptvery close to UT2 by offsets.

User equivalent range error (UERE)

The contribution to the range measure-ment error from an individual errorsource, converted into range units,assuming that error source isuncorrelated with all other error sources.

User segment

The part of the GPS system that includesthe receivers of GPS signals.

UTM

Universal Transverse Mercator Projec-tion. A form of Transverse Mercatorprojection. The projection has differentzones, each 6° wide with a central scalefactor of 0.996. Which zone is useddepends upon your location on the earth.

Y-code

An encrypted version of the P-code thatis transmitted by a GPS satellite when inthe anti-spoofing mode.

WGS 84

World Geodetic System 1984. Thesystem on which all GPS measure-ments and results are based.

Zenith angle

Vertical angle with 0° on the horizon and90° directly overhead.


Further Reading

GPS Theory and Practice -B. Hofmann-Wellenhof, H. Lichtenegger and J. Collins.ISBN 3-211-82839-7 Springer Verlag.

GPS Satellite Surveying -Alfred Leick.ISBN 0471306266 John Wiley and Sons.

Satellite Geodesy: Foundations, Methods and Applications -Gunter Seeber.ISBN 3110127539 Walter De Gruyter.

Understanding GPS: Principles and ApplicationsElliot D. Kaplan (Ed.).ISBN 0890067937 Artech House.

The Global Positioning System: Theory and ApplicationsBradford W. Parkinson and James J. Spilker (Eds.).ISBN 9997863348 American Institute of Aeronautics and Astronautics.

Further Reading


AAlmanac 48Ambiguity 24, 45, 48Ambiguity Resolution 22, 24Anti-Spoofing (A-S). See Error SourcesAtmospheric propagation delay 48Azimuth 48

BBandwidth 48Baseline 48Bearing 48Beat frequency 48Binary biphase modulation 48

CC/A code 7, 13, 18, 22, 49Carrier 49Carrier beat phase 49Carrier phase 22, 23, 49Cartesian coordinates 28, 49Central Meridian 36, 37Chip 49Chip rate 49Choke-Ring Antenna 16Clock (Satellite and Receiver) 16Clock offset 49Code 49

IndexCompacted data 49Conformal Projection 49Control segment 8, 49Coordinate system 28

Cartesian 28, 49GPS 28Local 29

Coordinate transformation 31Helmert 32Interpolation 33One Step 33Stepwise 33

Cutoff angle 50Cycle slip 50

DData message 50Deflection of the vertical 50Delay lock 50DGPS 10, 19, 20, 50Differenced measurements 50Differential positioning 50Differential phase 22Dilution of precision (DOP) 51

GDOP 17, 51, 52HDOP 17, 51HTDOP 51PDOP 17, 51, 55TDOP 51

VDOP 17, 51Distance to satellite 13Doppler shift 51Double difference 23, 50

EEccentricity 51Elevation 51Ellipsoid 28, 51Ellipsoid height 30, 51Ephemeris 51Epoch 51Equipotential Surface 51Error Sources 14

Anti-Spoofing (A-S) 18, 48Dilution of Precision 17, 51Multipath 16, 54Satellite and Receiver clock 16Selective Availability (S/A) 18, 56Water Vapour 15

FFalse Easting 36, 37False Northing 36, 37Flattening 52Fundamental frequency 52


GGDOP. See Dilution of precision (DOP)Geocentric 52Geodesy 52Geodetic Datum 52Geoid 52Geoid separation 30, 33, 52GPS 52GPS time 53Graticule 53Gravitational constant 53Great circle cours 53Greenwich mean time (GMT) 53

HHelmert Transformation 32

IInclination 53Integer bias term 53Ionospheric Delay 14, 53

KKeplerian orbital elements 53Kinematic 39, 44, 53Kinematic On the Fly (OTF) 39, 44

LL-band 54Lambert Projection 53Latitude 28, 53Latitude of Origin 36, 37Least squares estimation 54Longitude 28, 54

MMap projection 34

Lambert 37Transverse Mercator 35Universal Transverse Mercator 36

Measuring techniques (GPS) 39Kinematic 39, 44Kinematic On the Fly (OTF) 39, 44Rapid Static 39, 42Real Time Kinematic (RTK) 39, 45, 56Static 39, 40

Meridian 54Multipath error 54

NNAVSTAR 5, 54NMEA 54

OOrthometric height 30, 54

PP-code 55Phase observable 55Point Positioning 55Post processing 55Precise positioning service (PPS) 55Projection. See Map projectionPropagation delay 55Pseudolite 55Pseudorandom noise (PRN) code 55Pseudorange 55

RRadio link 45Range 55Rapid Static 39, 42Rapid static survey 56Raw data 56Real Time Kinematic (RTK) 39, 45, 56Receiver channel 56Reconstructed carrier phase 56Reference Receiver 20Relative positioning 56Rhumb line 56RINEX 56


Rover receiver 20RTCM 21, 56RTK 39, 45, 56

SSatellite Configuration 56Satellite Constellation 56Selective Availability (S/A). See Error

SourcesSidereal day 57Site 57Solar day 57Space segment 57Squared reception mode 57Squaring-type channel 57Standard Parallel 37Standard positioning service (SPS) 57Static 39, 40Static Survey 57Stop & Go Survey 57

TTime Zone 57Topography 57Transformation 31, 58

Helmert transformation 32Interpolation approach 33

One Step approach 33Stepwise approach 33

Transit 58Translocation 58Transverse Mercator Projection 58

UUniversal time 58User equivalent range error (UERE) 58User segment 58UTM 58

WWater Vapour. See Error SourcesWGS 84 58

YY-code 58

ZZenith angle 58Zone Width 36

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