20 30 40 50 GPS Basics Introduction to GPS (Global Positioning System) Version 1.
Contents Preface ........................................................... 4 4. Geodetic Aspects ..................................... 26 4.1 Introduction ...........................................................27 4.2. The GPS coordinate system ................................. 28 4.3 Local coordinate systems ......................................29 4.4 Problems with height ............................................. 30 4.5 Transformations .....................................................31 4.
View of chapters GPS Basics -1.0.0en Preface 4 1. What is GPS and what does it do? 5 2. System Overview 6 3. How GPS works 10 4. Geodetic Aspects 26 5.
Preface Why have we written this book and who should read it? Leica manufactures, amongst other things, GPS hardware and software. This hardware and software is used by many professionals in many applications. One thing that almost all of our users have in common is that they are not GPS scientists or experts in Geodesy. They are using GPS as a tool to complete a task. Therefore, it is useful to have background information about what GPS is and how it works.
1. What is GPS and what does it do ? GPS is the shortened form of NAVSTAR GPS. This is an acronym for NAVigation System with Time And Ranging Global Positioning System. and stars to navigate. Also, on land, surveyors and explorers used familiar reference points from which to base their measurements or find their way. GPS is a solution for one of mans longest and most troublesome problems. It provides an answer to the question Where on earth am I ? These methods worked well within certain boundaries.
4 2. System Overview The total GPS configuration is comprised of three distinct segments: The Space Segment Satellites orbiting the earth. 2.1 The Space Segment The Space Segment is designed to consist of 24 satellites orbiting the earth at approximately 20200km every 12 hours. At time of writing there are 26 operational satellites orbiting the earth. 15° for most of the time and quite often there are 6 or 7 satellites visible.
The satellites broadcast two carrier waves constantly. These carrier waves are in the L-Band (used for radio), and travel to earth at the speed of light. These carrier waves are derived from the fundamental frequency, generated by a very precise atomic clock: • The L1 carrier is broadcast at 1575.42 MHz (10.23 x 154) 4 5 Fundamental Frequency 10.23 Mhz ÷10 • The L2 carrier is broadcast at 1227.60 MHz (10.23 x 120). The L1 carrier then has two codes modulated upon it.
4 2.2 The Control Segment The Control Segment consists of one master control station, 5 monitor stations and 4 ground antennas distributed amongst 5 locations roughly on the earths equator. The Control Segment tracks the GPS satellites, updates their orbiting position and calibrates and sychronises their clocks. A further important function is to determine the orbit of each satellite and predict its path for the following 24 hours.
2.3 The User Segment 4 The User Segment comprises of anyone using a GPS receiver to receive the GPS signal and determine their position and/ or time. Typical applications within the user segment are land navigation for hikers, vehicle location, surveying, marine navigation, aerial navigation, machine control etc. GPS Basics -1.0.
4 3. How GPS works There are several different methods for obtaining a position using GPS. The method used depends on the accuracy required by the user and the type of GPS receiver available. Broadly speaking, the techniques can be broken down into three basic classes: Autonomous Navigation using a single stand-alone receiver. Used by hikers, ships that are far out at sea and the military. Position Accuracy is better than 100m for civilian users and about 20m for military users.
3.1 Simple Navigation This is the most simple technique employed by GPS receivers to instantaneously give a position and height and/ or accurate time to a user. The accuracy obtained is better than 100m (usually around the 30-50m mark) for civilian users and 5-15m for military users. The reasons for the difference between civilian and military accuracies are given later in this section. Receivers used for this type of operation are typically small, highly portable handheld units with a low cost. 3.1.
4 The problem with GPS is that only pseudoranges and the time at which the signal arrived at the receiver can be determined. Thus there are four unknowns to determine; position (X, Y, Z) and time of travel of the signal. Observing to four satellites produces four equations which can be solved, enabling these unknowns to be determined. At least four satellites are required to obtain a position and time in 3 dimensions How GPS works 12 GPS Basics -1.0.
3.1.2 Calculating the distance to the satellite 4 In order to calculate the distance to each satellite, one of Isaac Newtons laws of motion is used: Distance = Velocity x Time For instance, it is possible to calculate the distance a train has traveled if you know the velocity it has been travelling and the time for which it has been travelling at that velocity. 5 Calculating the Time The satellite signal has two codes modulated upon it, the C/A code and the P-code (see section 2.1).
4 3.1.3 Error Sources Up until this point, it has been assumed that the position derived from GPS is very accurate and free of error, but there are several sources of error that degrade the GPS position from a theoretical few metres to tens of metres. These error sources are: 1. Ionospheric and atmospheric delays 2. Satellite and Receiver Clock Errors 3. Multipath 4. Dilution of Precision 5. Selective Availability (S/A) 6. Anti Spoofing (A-S) How GPS works 1.
a. Satellite elevation. Signals from low elevation satellites will be affected more than signals from higher elevation satellites. This is due to the increased distance that the signal passes through the atmosphere. The amount by which the density of the ionosphere is increased varies with solar cycles (sunspot activity). Sunspot activity peaks approximately every 11 years. At the time of writing, the next peak (solar max) will be around the year 2000.
4 2. Satellite and Receiver clock errors 3. Multipath Errors Even though the clocks in the satellite are very accurate (to about 3 nanoseconds), they do sometimes drift slightly and cause small errors, affecting the accuracy of the position. The US Department of Defense monitors the satellite clocks using the Control Segment (see section 2.2) and can correct any drift that is found. Multipath occurs when the receiver antenna is positioned close to a large reflecting surface such as a lake or building.
4. Dilution of Precision The Dilution of Precision (DOP) is a measure of the strength of satellite geometry and is related to the spacing and position of the satellites in the sky. The DOP can magnify the effect of satellite ranging errors. The principle can be best illustrated by diagrams: The range to the satellite is affected by range errors previously described.
4 3.1.4 Why are military receivers more accurate ? 5. Selective Availability (S/A) 6. Anti-Spoofing (A-S) Selective Availability is a process applied by the U.S. Department of Defense to the GPS signal. This is intended to deny civilian and hostile foreign powers the full accuracy of GPS by subjecting the satellite clocks to a process known as dithering which alters their time slightly.
3.2 Differentially corrected positions (DGPS) 4 Many of the errors affecting the measurement of satellite range can be completely eliminated or at least significantly reduced using differential measurement techniques. 5 DGPS allows the civilian user to increase position accuracy from 100m to 2-3m or less, making it more useful for many civilian applications. 6 DGPS Reference station broadcasting to Users GPS Basics -1.0.
4 3.2.1 The Reference Receiver 3.2.2 The Rover receiver 3.2.3 Further details The Reference receiver antenna is mounted on a previously measured point with known coordinates. The receiver that is set at this point is known as the Reference Receiver or Base Station. The rover receiver is on the other end of these corrections. The rover receiver has a radio data link attached to it that enables it to receive the range corrections broadcast by the Reference Receiver.
4 Other devices such as mobile telephones can also be used for transmission of data. 5 In addition to Beacon Systems, other systems also exist that provide coverage over large land areas operated by commercial, privately owned companies. There are also proposals for government owned systems such as the Federal Aviation Authoritys satellitebased Wide Area Augmentation System (WAAS) in the United States, the European Space Agencys (ESA) system and a proposed system from the Japanese government.
4 3.3 Differential Phase GPS and Ambiguity Resolution 3.3.1 The Carrier Phase, C/A and P-codes Differential Phase GPS is used mainly in surveying and related industries to achieve relative positioning accuracies of typically 5-50mm (0.25-2.5 in). The technique used differs from previously described techniques and involves a lot of statistical analysis. At this point, it is useful to define the various components of the GPS signal.
3.3.2 Why use Carrier Phase? 3.3.3 Double Differencing The carrier phase is used because it can provide a much more accurate measurement to the satellite than using the P-code or the C/A code. The L1 carrier wave has a wavelength of 19.4 cm. If you could measure the number of wavelengths (whole and fractional parts) there are between the satellite and receiver, you have a very accurate range to the satellite.
4 3.3.4 Ambiguity and Ambiguity Resolution After removing the clock errors by double differencing, the whole number of carrier wavelengths plus a fraction of a wavelength between the satellite and receiver antenna can be determined. The problem is that there are many sets of possible whole wavelengths to each observed satellite. Thus the solution is ambiguous. Statistical processes can resolve this ambiguity and determine the most probable solution. 1. an approximate position.
3. 4 5. a second set of wavefronts or phase lines are created. The point must lie on one of the intersections of the two sets of phase lines. 5 satellite further narrows the number of possibilities. As the satellite Adding a third 4. 6. constellation changes it will tend to rotate around one point, revealing the most probable solution. satellite further narrows the number of possibilities. The point must be on an intersection of all three phase lines. Adding a fourth GPS Basics -1.0.
4. Geodetic Aspects Since GPS has become increasingly popular as a Surveying and Navigation instrument, surveyors and navigators require a basic understanding of how GPS positions relate to standard mapping systems. A common cause of errors in GPS surveys is the result of incorrectly understanding these relationships. Geodetic Aspects 26 GPS Basics -1.0.
4.1 Introduction Determining a position with GPS achieves a fundamental goal of Geodesy - the determination of absolute position with uniform accuracy at all points on the earths surface. Using classical geodetic and surveying techniques, determination of position is always relative to the starting points of the survey, with the accuracy achieved being dependent on the distance from this point. GPS therefore, offers a significant advantage over conventional techniques.
4.2. The GPS coordinate system An ellipsoid is chosen that most accurately approximates to the shape of the earth. This ellipsoid has no physical surface but is a mathematically defined surface. There are actually many different ellipsoids or mathematical definitions of the earths surface, as will be discussed later. The ellipsoid used by GPS is known as WGS84 or World Geodetic System 1984.
4.3 Local coordinate systems Just as with GPS coordinates, local coordinates or coordinates used in a particular countrys maps are based on a local ellipsoid, designed to match the geoid (see section 4.4) in the area. Usually, these coordinates will have been projected onto a plane surface to provide grid coordinates (see section 4.5). The ellipsoids used in most local coordinate systems throughout the world were first defined many years ago, before the advent of space techniques.
4.4 Problems with height The nature of GPS also affects the measurement of height. All heights measured with GPS are given in relation to the surface of the WGS84 ellipsoid. These are known as Ellipsoidal Heights. Existing heights are usually orthometric heights measured relative to mean sea level. This problem is solved by using geoidal models to convert ellipsoidal heights to orthometric heights. In relatively flat areas the geoid can be considered to be constant.
4.5 Transformations The purpose of a transformation is to transform coordinates from one system to another. Several different Transformation approaches exist. The one that you use will depend on the results you require. It is important to note that the transformation will only apply to points in the area bounded by the common points. Points outside of this area should not be transformed using the calculated parameters but should form part of a new transformation area.
Helmert Transformations The Helmert 7 parameter transformation offers a mathematically correct transformation. This maintains the accuracy of the GPS measurements and local coordinates. mined, followed by any rotation about the X, Y and Z axes and any change in scale between the two ellipsoids. P Experience has shown that it is common for GPS surveys to be measured to a much higher accuracy than older surveys measured with traditional optical instruments.
Other transformation approaches Whilst the Helmert transformation approach is mathematically correct, it cannot account for irregularities in the local coordinate system and for accurate heighting, the geoid separation must be known. Therefore, Leica also makes a number of other transformation approaches available in its equipment and software.
4.6 Map Projections and Plane Coordinates Such map projections appear as planes but actually define mathematical steps for specifying positions on an ellipsoid in the terms of a plane. The way in which a map projection generally works is shown in the diagram. Points on the surface of the spheroid are projected on to a plane surface from the origin of the spheroid. The diagram also highlights the problem that it is not possible to represent true lengths or shapes on such a plane.
4.6.1 The Transverse Mercator Projection The Transverse Mercator projection is a conformal projection. This means that angular measurements made on the projection surface are true. Cylinder Spheroid The Projection is based on a cylinder that is slightly smaller than the spheroid and is then flattened out. The method is used by many countries and is especially suited to large countries around the equator. The Transverse Mercator Projection is defined by: False Easting and False Northing.
The False Easting and False Northing are defined in order that the origin of the grid projection can be in the lower left hand corner as convention dictates. This does away with the need for negative coordinates. N Zone Width Central Meridian The Latitude of Origin defines the Latitude of the axis of the cylinder. This is normally the equator (in the northern hemisphere).
4.6.2 The Lambert Projection Spheroid The Lambert projection is defined by: False Easting and Northing Latitude of origin Central Meridian GPS Basics -1.0.0en The False Easting and False Northing are defined in order that the origin of the grid projection can be in the lower left hand corner as convention dictates. This does away with the need for negative coordinates. The Central Meridian defines the direction of grid north and the longitude of the centre of the projection.
5. Surveying with GPS Probably even more important to the surveyor or engineer than the theory behind GPS, are the practicalities of the effective use of GPS. Like any tool, GPS is only as good as its operator. Proper planning and preparation are essential ingredients of a successful survey, as well as an awareness of the capabilities and limitations of GPS.
5.1 GPS Measuring Techniques There are several measuring techniques that can be used by most GPS Survey Receivers. The surveyor should choose the appropriate technique for the application. Static - Used for long lines, geodetic networks, tectonic plate studies etc. Offers high accuracy over long distances but is comparatively slow. Rapid Static - Used for establishing local control networks, Network densification etc.
5.1.1 Static Surveys This was the first method to be developed for GPS surveying. It can be used for measuring long baselines (usually 20km (16 miles) and over). One receiver is placed on a point whose coordinates are known accurately in WGS84. This is known as the Reference Receiver. The other receiver is placed on the other end of the baseline and is known as the Rover. Data is then recorded at both stations simultaneously. It is important that data is being recorded at the same rate at each station.
2 3 The network ABCDE has to be measured with three receivers. The coordinates of A are known in WGS84. The receivers are placed on A, B and C. GPS data is recorded for the required length of time. After the required length of time, the receiver that was at E moves to D and B moves to C. The triangle ACD is measured. Then A moves to E and C moves to B. The triangle BDE is measured. 4 5 1 Finally, B moves back to C and the line EC is measured. GPS Basics -1.0.
5.1.2 Rapid Static Surveys In Rapid Static surveys, a Reference Point is chosen and one or more Rovers operate with respect to it. Typically, Rapid Static is used for densifying existing networks, establishing control etc. When starting work in an area where no GPS surveying has previously taken place, the first task is to observe a number of points, whose coordinates are accurately known in the local system.
1 The network 1,2,3,4,5 has to be measured from Reference station R with three GPS receivers. 2 The reference station is set up. One Rover occupies point 1 whilst the other occupies point 3. 3 After the required length of time, one Rover moves to point 2 whilst the other moves to point 4. 4 5 Then, one Rover can return to the office whilst the other measures point 5. The end result is as above. On a subsequent day, the operation will be repeated in order to check for gross errors. Alternatively...
5.1.3 Kinematic Surveys The Kinematic technique is typically used for detail surveying, recording trajectories etc., although with the advent of RTK its popularity is diminishing. 1 2 3 Initialization is performed from the Reference to the Rover. The Rover can then move. ...and also at distinct Positions can be recorded points if required. at a predefined interval... The technique involves a moving Rover whose position can be calculated relative to the Reference.
5.1.4 RTK Surveys RTK stands for Real Time Kinematic. It is a Kinematic on the Fly survey carried out in real time. The Reference Station has a radio link attached and rebroadcasts the data it receives from the satellites. The Rover also has a radio link and receives the signal broadcast from the Reference. The Rover also receives satellite data directly from the satellites via its own GPS Antenna.
5.2 Pre-survey preparation 5.3 Tips during operation Before heading out into the field, the surveyor needs to prepare for the survey. Items that must be considered are: For Static and Rapid Static surveys, always fill out a record sheet for each point you survey. An example is given on the next page. 1. Radio Licences 2. Power - charged batteries 3. Spare cables 4. Communication between survey parties 5. Coordinates of Reference Station 6. Memory cards - Do you have enough spare memory? 7.
Field Sheet Point Id Date Sensor Serial No Operator Notes Operation Type Antenna Type Height Reading Start Time Stop Time No. of Epochs No. of Satellites GDOP GPS Basics -1.0.
Glossary Almanac Azimuth Beat frequency Library of coarse satellite orbital data used to calculate satellite position, rise time, elevation, and azimuth. A horizontal angle measured clockwise from a direction (such as North). Either of the two additional frequencies obtained when signals of two frequencies are mixed. The beat frequencies are equal to the sum or difference of the original frequencies, respectively.
C/A code The Coarse/Acquisition GPS code modulated on the GPS L1 signal. This code is a sequence of 1023 pseudorandom binary biphase modulations on the GPS carrier at a chipping rate of 1.023 MHz, thus having a code repetition period of one millisecond. Cartesian Coordinates The coordinates of a point in space given in three mutually perpendicular dimensions (x, y, z) from the origin. Carrier A radio wave having at least one characteristic (e.g.
Cutoff angle Deflection of the vertical The minimum elevation angle below which no more GPS satellites are tracked by the sensor. The angle between the normal to the ellipsoid and the vertical (true plumb line). It is usually resolved into a component in the meridian and a component perpendicular to the meridian. Cycle slip A discontinuity of an integer number of cycles in the measured carrier beat phase resulting from a temporary loss of lock of a GPS satellite signal.
Dilution of precision (DOP) Eccentricity Ellipsoid height A description of the purely geometrical contribution to the uncertainty in a position fix. The DOP factor indicates the geometrical strength of the satellite constellation at the time of measurement. Standard terms in the case of GPS are The ratio of the distance from the centre of an ellipse to its focus to the semimajor axis. The vertical distance of a point above the ellipsoid.
Flattening Geocentric Relating to Ellipsoids. Relating to the centre of the earth. deflection of the vertical at the origin, and the geodetic azimuth of a line from the origin to some other point. f = (a-b)/a = 1-(1-e2)1/2 where a ... semimajor axis b ... semiminor axis Geodesy Geoid The study of the earths size and shape e ... eccentricity Geodetic Coordinates Fundamental frequency The fundamental frequency used in GPS is 10.23 MHz.
GPS time Inclination Keplerian orbital elements A continuous time system based on the Coordinated Universal Time (UTC) from 6th January 1980. The angle between the orbital plane of an object and some reference plane (e.g., equatorial plane). Allow description of any astronomical orbit: Integer bias term Greenwich mean time (GMT) The mean solar time of the meridian of Greenwich. Used as the prime basis of standard time throughout the world. Great circle course Term used in navigation.
L-band Longitude NAVSTAR The radio frequency band extending from 390 MHz to 1550 MHz. The frequencies of the L1 and L2 carriers transmitted by GPS satellites lie within this L-band. Longitude is the angle between the meridian ellipse which passes through Greenwich and the meridian ellipse containing the point in question. Thus, Latitude is 0° at Greenwich and then measured either eastward through 360° or eastward 180° and westward 180°.
P-code Post processing The Precise GPS code - a very long (about 1014 bit) sequence of pseudorandom binary biphase modulations on the GPS carrier at a chipping rate of 10.23 MHz which does not repeat itself for about 267 days. Each one-week segment of the P-code is unique to one GPS satellite, and is reset each week. Access to the P-code will be restricted by the U.S. Government to authorized users only.
Rapid static survey Relative positioning RTK Term used in connection with the GPS System for static survey with short observation times. This type of survey is made possible by the fast ambiguity approach that is resident in the SKI software. See Differential positioning Real Time Kinematic. A term used to describe the procedure of resolving the phase ambiguity at the GPS receiver so that the need for post-processing is removed. Rhumb line Term used in navigation.
Sidereal day Squaring-type channel Stop & Go Survey Time interval between two successive upper transits of the vernal equinox. A GPS receiver channel which multiplies the received signal by itself to obtain a second harmonic of the carrier which does not contain the code modulation. Level of point positioning accuracy provided by GPS based on the singlefrequency C/A - code. The term Stop & Go survey is used in connection with GPS for a special kind of kinematic survey.
Transformation Universal time UTM The process of transforming coordinates from one system to another. Local solar mean time at Greenwich Meridian Transit UT Abbreviation for universal time The predecessor to GPS. A satellite navigation system that was in service from 1967 to 1996. UT0 UT as deduced directly from observation of stars Universal Transverse Mercator Projection. A form of Transverse Mercator projection. The projection has different zones, each 6° wide with a central scale factor of 0.
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 Applications Elliot D. Kaplan (Ed.). ISBN 0890067937 Artech House. The Global Positioning System: Theory and Applications Bradford W. Parkinson and James J.
Index A Almanac 48 Ambiguity 24, 45, 48 Ambiguity Resolution 22, 24 Anti-Spoofing (A-S).
G L O GDOP.
Rover receiver 20 RTCM 21, 56 RTK 39, 45, 56 S Satellite Configuration 56 Satellite Constellation 56 Selective Availability (S/A).
GPS Basics -1.0.
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