To ensure continuous worldwide coverage, GPS Trang 37 satellites are arranged so that four satellites are placed in each of six orbitalplanes Figure 1.1.. The primary task of theoperati
Overview of GPS
GPS operates through a constellation of 24 satellites, known as the initial operational capability (IOC), which was completed in July 1993 The official announcement of this capability was made on December 8, 1993 This system is designed to provide continuous global coverage.
The TLFeBOOK satellite constellation consists of four satellites positioned in each of six orbital planes, ensuring that anywhere in the world, four to ten GPS satellites are visible with a minimum elevation angle of 10° Notably, only four satellites are required to deliver accurate positioning and location information.
GPS satellites orbit in nearly circular paths, with a slight elliptical shape and a maximum eccentricity of about 0.01, inclined at approximately 55° to the equator The semimajor axis of these orbits measures around 26,560 km, placing the satellites about 20,200 km above the Earth's surface Each GPS satellite completes an orbit in roughly 12 sidereal hours, equivalent to about 11 hours and 58 minutes The GPS system achieved full operational capability (FOC) on July 17, 1995, guaranteeing a minimum of 24 operational, nonexperimental satellites Since reaching FOC, the GPS constellation has consistently maintained more than 24 operational satellites.
GPS segments
GPS is composed of three main segments: the space segment, the control segment, and the user segment The space segment features a constellation of 24 satellites that transmit signals containing essential components, including two carrier frequencies, two digital codes, and a navigation message These codes and the navigation message are modulated onto the carrier frequencies using binary biphase modulation The primary purpose of these carriers and codes is to calculate the distance from the user's receiver to the GPS satellites.
The navigation message from TLFeBOOK satellites includes satellite coordinates that change over time, along with additional information These signals are regulated by precise atomic clocks located on the satellites For more details on GPS signals, refer to Chapter 2.
The GPS control segment comprises a global network of tracking stations, with the master control station situated in Colorado Springs, Colorado Its main responsibility is to monitor GPS satellites to ascertain and forecast their locations, ensure system integrity, analyze the behavior of atomic clocks, gather atmospheric data, and maintain the satellite almanac This critical information is subsequently transmitted to the GPS satellites via the S-band link.
The user segment encompasses both military and civilian individuals who utilize GPS technology By connecting a GPS receiver to a GPS antenna, users can access GPS signals to accurately determine their location anywhere globally Notably, GPS services are available to all users around the world free of charge.
GPS satellite generations
The GPS satellite constellation began with the launch of 11 Block I satellites, starting with the first on February 22, 1978, and concluding with the last on October 9, 1985 These satellites were primarily designed for experimental purposes, featuring an orbital inclination angle of 63 degrees relative to the equator, which was later adjusted in subsequent generations Although the intended lifespan of Block I satellites was 4.5 years, several continued to operate beyond this timeframe.
10 years The last Block I satellite was taken out of service on November 18, 1995.
The second generation of GPS satellites, known as Block II/IIA, includes the advanced Block IIA version, which enhances navigation message data storage from 14 days in Block II to 180 days in Block IIA This advancement allows Block II and Block IIA satellites to operate continuously for 14 and 180 days, respectively, without ground support From February 1989 to November 1997, a total of 28 Block II/IIA satellites were launched, with 23 currently in service Unlike their predecessor, Block I, these satellites are inclined at 55° to the equator Each Block II/IIA satellite has a design lifetime of 7.5 years, often exceeded in practice To bolster national security, features such as selective availability (SA) and antispoofing were incorporated into the Block II/IIA satellites.
The new generation of GPS satellites, known as Block IIR, is being launched to enhance navigation capabilities These 21 satellites are backward compatible with Block II/IIA, ensuring a seamless transition for users With a design life of 10 years, Block IIR satellites offer improved accuracy and can operate autonomously for up to 180 days without needing ground corrections This autonomous capability is supported by mutual satellite ranging and uploaded ephemeris and clock data for 210 days Additionally, the last 12 Block IIR satellites will incorporate more features as part of the GPS modernization program, set to begin in 2003 As of July 2001, six Block IIR satellites have already been successfully launched.
Block IIR will be followed by another system, called Block IIF (for
The Block IIF satellite constellation, comprising 33 satellites, is designed to enhance GPS capabilities with a lifespan of 15 years These satellites will significantly improve autonomous GPS positioning accuracy as part of the GPS modernization program The inaugural Block IIF satellite is set to launch in 2005 or soon thereafter.
Current GPS satellite constellation
As of July 2001, the GPS constellation comprises 29 satellites, including five Block II, 18 Block IIA, and six Block IIR satellites, surpassing the nominal requirement of 24 satellites Notably, all Block I satellites have been decommissioned and are no longer in operation.
GPS satellites are organized into six orbital planes, labeled A through F, with the current constellation exceeding the nominal 24 satellites, allowing some planes to host four or five satellites All orbital planes have five satellites except for plane C, which contains four Satellites are identified using systems like the space vehicle number (SVN) and pseudorandom noise (PRN) Block II/IIA satellites feature four onboard atomic clocks—two cesium and two rubidium—with the cesium clock serving as the primary timing source for GPS signals In contrast, Block IIR satellites utilize different technologies for timing.
Block I Block II/IIA Block IIR
Figure 1.3 GPS satellite generations (From http:\\www2.geod.hrcan.gc.ca/
TLFeBOOK rubidium clocks only It should be pointed out that two satellites, PRN05 and PRN06, are equipped with corner cube reflectors to be tracked by laser ranging (Table 1.1).
Control sites
The GPS control segment is comprised of a master control station (MCS), a global network of monitoring stations, and ground control stations The MCS, situated near Colorado Springs, Colorado, serves as the central processing hub for the control segment and operates continuously.
The five monitor stations are strategically located in Colorado Springs (featuring the MCS), Hawaii, Kwajalein, Diego Garcia, and Ascension Island, with their coordinates being precisely determined.
Table 1.1 GPS Satellite Constellation as of July 2001
Orbital Plane Clock Sequence SVN PRN
Each monitor station features advanced GPS receivers and a cesium oscillator for continuous tracking of visible GPS satellites Notably, the Kwajalein, Diego Garcia, and Ascension Island stations are equipped with ground antennas to transmit data to the GPS satellites All monitor and ground control stations are unmanned and operated remotely from the Master Control Station (MCS).
GPS observations from monitor stations are transmitted to the MCS for processing, resulting in predicted satellite navigation data This data includes satellite positions over time, clock parameters, atmospheric data, and satellite almanac information The updated navigation data is then sent to a ground control station for upload to GPS satellites via an S-band link.
Master control station Ground antenna
Monitor station Backup ground antenna
The Monitoring Control Segment (MCS) is responsible for ensuring the integrity of the GPS system by designating satellites as unhealthy during maintenance or outages This health status is communicated in real-time as part of the satellite navigation message Additionally, scheduled maintenance or outages are publicly reported through a message known as the Notice Advisory to Navstar Users (NANU), which can be accessed via platforms like the U.S Coast Guard Navigation Center.
GPS: The basic idea
GPS operates on a straightforward principle: by knowing the distances from a GPS receiver to three satellites, along with the satellites' positions, one can determine the receiver's location using the concept of resection However, the challenge lies in accurately obtaining both the distances to the satellites and their respective locations.
Each GPS satellite continuously broadcasts a microwave radio signal that includes two carriers, two codes, and a navigation message When a GPS receiver is activated, it captures the GPS signal via its antenna After acquiring the signal, the receiver processes it with its internal software, resulting in key data such as the distances to the satellites, known as pseudoranges, and the satellites' coordinates derived from the navigation message.
To accurately determine a receiver's location, three distances to simultaneously tracked satellites are theoretically sufficient, as the receiver would be positioned at the intersection of three spheres, each centered on a satellite However, in practice, a fourth satellite is essential to correct for the receiver's clock offset Further details on this process can be found in Chapter 5.
Recent advancements have significantly improved positioning accuracy, which was previously limited to 100m horizontally, 156m vertically, and 340 ns in time at a 95% probability level This limitation was primarily due to selective availability, a technique that intentionally reduced positioning accuracy for unauthorized users However, following the recent presidential decision to terminate selective availability, horizontal accuracy is anticipated to enhance to approximately 22m at the same confidence level.
To enhance GPS positioning accuracy, the differential method utilizes two receivers that simultaneously track the same GPS satellites This technique can achieve positioning accuracy levels ranging from subcentimeter to a few meters.
GPS technology serves various purposes beyond navigation, including the measurement of user velocity, primarily achieved through the analysis of Doppler frequency shifts in received signals due to the relative motion between satellites and receivers Additionally, GPS can determine the attitude of rigid bodies, such as aircraft and marine vessels, which refers to their orientation defined by three rotational angles relative to a reference system To accurately assess attitude, a minimum of three GPS receivers or a specialized receiver with three antennas arranged in a non-linear configuration is required The data collected from these receivers is then processed to derive the rigid body's orientation.
GPS positioning service
Originally designed for military use, GPS was later opened to civilian access To maintain military superiority, the U.S Department of Defense offers two tiers of GPS services: the Precise Positioning Service (PPS) and the Standard Positioning Service (SPS).
Figure 1.5 Basic idea of GPS positioning.
PPS is the leading autonomous positioning and timing service, utilizing the P(Y)-code GPS signal, which is exclusively available to authorized users such as U.S military forces It offers exceptional positioning accuracy, with a horizontal precision of 16 meters and a vertical precision of 23 meters, both at a 95% probability level.
SPS, while less precise than PPS, utilizes the freely available C/A-code for GPS positioning Initially, SPS offered a positioning accuracy of approximately 100m horizontally and 156m vertically, influenced by selective availability However, following the recent presidential decision to discontinue selective availability, SPS now achieves autonomous positioning accuracy comparable to that of PPS.
Why use GPS?
GPS has transformed surveying and navigation since its inception Initially developed for military purposes, its civilian applications have rapidly expanded Looking ahead, the potential uses for GPS technology appear boundless, limited only by creativity and innovation.
GPS technology has significantly transformed surveying by replacing traditional methods, offering a cost-effective solution with potential savings of at least 50% when utilizing real-time kinematic (RTK) GPS Additionally, RTK GPS can enhance productivity, achieving over 75% time savings compared to conventional techniques The advantage of GPS lies in its ability to function without the need for intervisibility between stations, making it a preferred choice for surveyors In urban environments where GPS signals may be obstructed, successful integration with traditional equipment ensures continued effectiveness.
GPS technology is widely utilized in land, marine, and air navigation, with vehicle tracking and navigation emerging as rapidly growing applications As a result, it is anticipated that most GPS users will increasingly rely on GPS for vehicle navigation.
The future of GPS technology will feature advancements in automatic machine guidance and control, enabling the efficient and safe mapping of hazardous areas through remotely controlled vehicles The recent U.S initiative to modernize GPS and eliminate selective availability is set to pave the way for numerous innovative applications yet to be explored.
[2] Langley, R B., Why Is the GPS Signal So Complex? GPS World, Vol 1,
[3] Hoffmann-Wellenhof, B., H Lichtenegger, and J Collins, Global
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[4] Langley, R B., The Orbits of GPS Satellites, GPS World, Vol 2, No 3, March 1991, pp 5053.
[5] Wells, D E., et al., Guide to GPS Positioning , Fredericton, New Brunswick: Canadian GPS Associates, 1987.
[6] Kaplan, E., Understanding GPS: Principles and Applications, Norwood, MA: Artech House, 1990.
[7] Shaw, M., K Sandhoo, and D Turner, Modernization of the Global Positioning System, GPS World , Vol 11, No 9, September 2000, pp 3644.
[8] U.S Coast Guard Navigation Center, GPS Status, September 17, 2001, http://www.navcen.uscg.gov/gps/.
[9] Leick, A., GPS Satellite Surveying, 2nd ed., New York: Wiley, 1995.
[10] Langley, R B., The Mathematics of GPS, GPS World, Vol 2, No 7,
[11] Conley, R., Life After Selective Availability, U.S Institute of Navigation Newsletter, Vol 10, No 1, Spring 2000, pp 34.
[12] Kleusberg, A., Mathematics of Attitude Determination with GPS, GPS World, Vol 6, No 9, September 1995, pp 7278.
[13] Berg, R E., Evaluation of Real-Time Kinematic GPS Versus Total Stations for Highway Engineering Surveys, 8th Intl Conf Geomatics: Geomatics in the Era of RADARSAT, Ottawa, Canada, May 2430, 1996, CD-ROM.
Understanding GPS positioning involves grasping the structure of GPS signals and the measurement process It's crucial to be aware of the capabilities and limitations of different GPS receivers, as they play a key role in signal reception Additionally, GPS measurements are subject to errors and biases, which can be minimized by integrating various GPS observables This chapter provides a comprehensive discussion on these topics.
GPS signal structure
Each GPS satellite broadcasts a microwave radio signal that includes two carrier frequencies modulated by digital codes and a navigation message The L1 carrier operates at a frequency of 1,575.42 MHz, while the L2 carrier operates at 1,227.60 MHz These frequencies correspond to carrier wavelengths of approximately 19 cm for L1 and 24.4 cm for L2, determined by the relationship between frequency and the speed of light.
The availability of dual carrier frequencies in GPS technology helps correct the significant issue of ionospheric delay All GPS satellites transmit the same L1 and L2 frequencies, but each satellite employs unique code modulation, which effectively reduces signal interference.
The two main GPS codes, coarse acquisition (C/A-code) and precision (P-code), are composed of binary digits, known as bits or chips These codes, often referred to as PRN codes due to their noise-like appearance, are generated through a mathematical algorithm Currently, the C/A-code is modulated only onto the L1 carrier, while the P-code is used on both the L1 and L2 carriers This modulation technique, known as biphase modulation, involves a 180-degree phase shift of the carrier when the code value transitions between zero and one.
The C/A-code consists of 1,023 binary digits that repeat every millisecond, resulting in a chipping rate of 1.023 Mbps, with each bit lasting approximately 1 ms Each GPS satellite has a unique C/A-code, allowing receivers to identify the transmitting satellite While the C/A-code offers less precise range measurements than the P-code, it is simpler and accessible to all users.
The P-code is a lengthy binary sequence that repeats every 266 days and operates at a speed of 10.23 Mbps, resulting in approximately 2.35 × 10^14 chips over its cycle This code is segmented into 38 one-week parts, with 32 segments allocated to different GPS satellites, each transmitting a unique segment initialized at midnight on Saturdays or Sundays The remaining six segments are designated for other applications Each GPS satellite is identified by its specific one-week P-code segment, such as PRN 20, which corresponds to the twentieth segment Originally designed for military use, the P-code was accessible to all users until January 31, 1994, when it became encrypted with an unknown W-code, creating a new encrypted code.
TLFeBOOK the Y-code, which has the same chipping rate as the P-code This encryp- tion is known as the antispoofing (AS).
The GPS navigation message is a low-rate data stream, transmitted at 50 kbps on L1 and L2 carriers, consisting of 25 frames of 1,500 bits each, totaling 37,500 bits The complete transmission takes 750 seconds, or 12.5 minutes This message includes essential information such as satellite coordinates over time, health status, clock corrections, almanac data, and atmospheric conditions Each satellite broadcasts its own navigation message, providing details about its status and the approximate locations of other satellites.
GPS modernization
The GPS signal structure, originally designed in the early 1970s, is set to evolve over the next 30 years with the introduction of Block IIR, IIF, and potentially Block III satellites To address future requirements, GPS decision-makers are exploring various options to modify the signal structure and system architecture of the GPS constellation The modernization program focuses on enhancing signal redundancy, positioning accuracy, signal availability, and overall system integrity.
The modernization program will introduce a civil code (C/A-code) on the L2 frequency and two new military codes (M-codes) on both the L1 and L2 frequencies, enhancing the existing system.
12 Block IIR satellites, which will be launched at the beginning of 2003. The availability of two civil codes (i.e., C/A-code on both L1 and L2
Figure 2.1 (a) A sinusoidal wave; and (b) a digital code.
The use of TLFeBOOK frequencies enables stand-alone GPS receivers to mitigate ionospheric effects, a significant source of error in GPS accuracy Following the end of selective availability, it is anticipated that with an adequate number of satellites equipped with advanced capabilities, autonomous GPS horizontal accuracy will improve to approximately 8.5 meters or better, 95% of the time.
The integration of the C/A-code to L2 enhances autonomous GPS accuracy but is inadequate for civil aviation safety applications due to potential interference from nearby ground radars To meet aviation needs, a new civil signal, L5, operating at 1,176.45 MHz, will be introduced alongside the existing signals on the first 12 Block IIF satellites This robust L5 signal will feature a higher power level, a minimum bandwidth of 20 MHz, and a chipping rate of 10.23 MHz, improving accuracy in noisy and multipath environments The longer code will minimize self-interference by enhancing auto- and cross-correlation properties, while the navigation message will adopt a more efficient structure The first Block IIF satellite is set to launch in 2005, significantly boosting autonomous GPS positioning accuracy and allowing real-time kinematic (RTK) users to resolve initial integer ambiguity parameters instantly More details on RTK positioning can be found in Chapter 5.
The GPS modernization initiative encompasses the development of next-generation Block III satellites, set to enhance GPS capabilities through 2030 Additionally, upgrades to GPS ground control facilities are integral to this modernization program, aiming to achieve a standalone GPS horizontal accuracy of 6 meters or better, 95% of the time.
Types of GPS receivers
In 1980, only one commercial GPS receiver was available on the market, at a price of several hundred thousand U.S dollars [6] This, however, has
The GPS market has evolved significantly, with over 500 different GPS receivers currently available, as highlighted in the January 2001 issue of GPS World magazine Prices for these receivers range from approximately $100 for basic handheld models to around $15,000 for advanced geodetic quality units As technology progresses, it is expected that prices will continue to decrease Each GPS receiver requires an antenna, either internal or external, to capture satellite signals and convert them into electric current for processing.
Commercial GPS receivers are classified into four main types based on their receiving capabilities: single-frequency code receivers, single-frequency carrier-smoothed code receivers, single-frequency code and carrier receivers, and dual-frequency receivers Single-frequency receivers operate on the L1 frequency, while dual-frequency receivers utilize both L1 and L2 frequencies The number of tracking channels in GPS receivers ranges from 1 to 12, with multichannel receivers being preferred for continuous satellite tracking; most modern receivers feature 9 to 12 independent channels When selecting a GPS receiver, important factors to consider include cost, ease of use, power consumption, size and weight, data storage options, interfacing capabilities, and multipath mitigation techniques.
The single-frequency code receiver, which utilizes only the C/A-code to measure pseudoranges, is the most affordable and least accurate receiver type, primarily designed for recreational use In contrast, the single-frequency carrier-smoothed code receiver also measures pseudoranges with the C/A-code but enhances accuracy by incorporating a higher-resolution carrier frequency, resulting in precise pseudorange measurements Both receiver types output raw C/A-code pseudoranges, L1 carrier-phase measurements, and navigation messages, while the carrier-smoothed code receiver can perform functions of other discussed receiver types.
Dual-frequency receivers are the most sophisticated and most expen- sive receiver type Before the activation of AS, dual-frequency receivers
TLFeBOOK was initially able to output all GPS signal components, including L1 and L2 carriers, C/A-code, P-code, and navigation messages However, following AS activation, the P-code was encrypted to Y-code, preventing traditional signal recovery methods from accessing the P-code or L2 carrier To address this challenge, GPS receiver manufacturers developed techniques that do not rely on Y-code information Currently, most receivers utilize two primary methods: Z-tracking and cross-correlation techniques While both methods successfully recover the full L2 carrier, they do so at a reduced signal strength, with the cross-correlation technique experiencing greater degradation compared to Z-tracking.
Time systems
Time is crucial for GPS positioning, as it relies on precise timing from atomic satellite clocks Accurate range measurements from the receiver to the satellites depend on synchronized timing between both the receiver and the satellites.
GPS receiver Ashtech ZX geodetic quality
GPS receiverFigure 2.2 Examples of GPS receivers (Courtesy of Magellan Corporation.)
TLFeBOOK satellite clocks GPS is also a timing system, that is, it can be used for time synchronization.
A number of time systems are used worldwide for various purposes
Coordinated Universal Time (UTC) and GPS Time are crucial for GPS users, with UTC being an atomic time scale derived from International Atomic Time (TAI) TAI is a consistent time scale based on atomic clocks worldwide, but for surveying and navigation, a time system aligned with Earth's rotation is preferred This alignment is maintained by adjusting UTC with leap seconds, which are added to ensure UTC remains within 0.9 seconds of Universal Time 1 (UT1), a measure of Earth's rotation Leap seconds are typically introduced on June 30 or December 31, with the last addition occurring on January 1, 1999, resulting in a 32-second difference where TAI is ahead of UTC For more information on leap seconds, visit the U.S Naval Observatory's website.
GPS Time is the time scale used for referencing GPS signals, computed from atomic clocks at monitoring stations and onboard satellites Unlike UTC, GPS Time does not include leap seconds, making it a continuous time scale Established to align with UTC on January 6, 1980, GPS Time advanced ahead of UTC by 13 seconds on January 1, 1999, due to the latter's leap seconds The difference between GPS and UTC is communicated in the GPS navigation message Additionally, both GPS satellites and receivers experience clock offsets from GPS Time due to inherent clock errors.
Pseudorange measurements
The pseudorange refers to the distance between a GPS receiver's antenna and that of a GPS satellite, which is crucial for determining the receiver's position Accurate measurements of these ranges from the receiver to multiple satellites are essential for effective GPS functionality.
TLFeBOOK computation Either the P-code or the C/A-code can be used for measuring the pseudorange.
The GPS range determination process, known as pseudoranging, involves the synchronization of satellite and receiver clocks When a Pseudorandom Noise (PRN) code is transmitted from the satellite, the receiver creates an exact replica of this code After a certain time, corresponding to the signal's travel time, the receiver captures the transmitted code By comparing the two codes, the receiver calculates the signal's travel time, and by multiplying this time by the speed of light (299,729,458 m/s), it determines the distance between the satellite and the receiver This process is illustrated in Figure 2.3, which details the pseudorange measurements.
The assumption that the clocks of the receiver and satellite are perfectly synchronized is inaccurate This synchronization error, along with other biases and errors, affects the measured range, leading to the term "pseudorange" being used instead of simply "range."
GPS was originally designed with the civilian C/A-code offering less precision than the military P-code, with a resolution of 300 meters compared to the P-code's finer accuracy However, advancements in receiver technology have led to surprisingly similar accuracy levels from both codes.
Identical code generated in receiver
Carrier-phase measurements
Carrier phases provide a precise method for measuring ranges to satellites by calculating the total number of full and fractional carrier cycles at both the receiver and the satellite, then multiplying this sum by the carrier wavelength This technique yields significantly more accurate range measurements compared to pseudoranges derived from codes, primarily because the carrier phase wavelength, which is 19 cm for the L1 frequency, is much smaller than that of the codes.
One challenge with GPS technology is that the carriers are pure sinusoidal waves, resulting in identical cycles that the GPS receiver cannot distinguish from one another Consequently, upon activation, the receiver is unable to ascertain the total number of complete cycles between itself and the satellite Instead, it can only measure a fraction of a cycle with remarkable precision, achieving accuracy within less than 2 mm.
The initial cycle ambiguity, often referred to as ambiguity bias, pertains to the uncertainty regarding the number of complete cycles However, the receiver can effectively monitor phase changes once activated, ensuring that the initial cycle ambiguity remains consistent over time, provided there are no signal losses or cycle slips.
Resolving initial cycle ambiguity parameters is essential for obtaining accurate range measurements, which directly contribute to precise position determination High-accuracy positioning can be achieved using relative positioning techniques, applicable in both real-time and post-processing modes However, this method necessitates the simultaneous tracking of the same satellites by two GPS receivers For further details on positioning techniques and methods to resolve ambiguity parameters, refer to Chapters 5 and 6.
Cycle slips
A cycle slip refers to a discontinuity in GPS carrier-phase measurements, caused by temporary signal loss due to obstructions like buildings, trees, or bridges This weak and noisy GPS signal can also be disrupted by radio interference, severe ionospheric disturbances, and high receiver dynamics, leading to potential receiver malfunctions Cycle slips can last from brief moments to several minutes and may impact one or multiple satellite signals, with sizes ranging from one cycle to millions To prevent significant errors in computed coordinates, it is essential to identify and correct cycle slips One effective method involves analyzing the triple difference observable, which highlights cycle slips as spikes in the data series However, in extreme conditions, such as severe ionospheric activity, accurately detecting and repairing cycle slips using this method can be challenging.
3] Visual inspection of the adjustment residuals might be useful to locate any remaining cycle slip.
In Chapter 3, a zero baseline test is utilized to identify cycle slips caused by receiver malfunctions This procedure involves connecting two receivers to a single antenna via a signal splitter, allowing for the detection of cycle slips through the analysis of adjustment residuals.
Linear combinations of GPS observables
GPS measurements are affected by various errors and biases that are challenging to fully model, which ultimately limits the accuracy of standalone GPS receivers However, GPS receivers located near each other tend to experience similar errors and biases By combining the GPS observables from these nearby receivers, a significant portion of the error can be mitigated, enhancing overall positioning accuracy.
GPS errors and biases can be categorized into three main groups: satellite-related, receiver-related, and atmospheric errors When two GPS receivers track the same satellite simultaneously, they typically exhibit similar satellite-related and atmospheric errors The closer the receivers are to each other, the more alike the errors and biases will be Consequently, by calculating the difference between the measurements from these two GPS receivers, we can minimize the impact of these common errors.
Significant reductions in satellite-related and atmospheric errors can be achieved, particularly through the effective elimination of satellite clock errors using a linear combination method This approach, referred to as between-receiver single difference, demonstrates its efficacy as illustrated in Chapter 3.
Here is a rewritten paragraph that complies with SEO rules:When tracking two satellites with a single receiver, the measurements contain identical receiver clock errors, which can be eliminated by taking the difference between the two measurements, known as the between-satellite single difference Furthermore, when two receivers track two satellites simultaneously, two between-receiver single difference observables can be formed, and subtracting these from each other generates the double difference, a linear combination that removes satellite and receiver clock errors, greatly reduces other errors, and preserves the integer nature of the ambiguity parameters, making it ideal for precise carrier-phase-based GPS positioning.
The triple difference is a significant linear combination derived from differencing two double-difference observables across two time epochs As noted earlier, ambiguity parameters remain unchanged over time, provided there are no cycle slips Consequently, when calculating the triple difference, these constant ambiguity parameters are eliminated However, the presence of a cycle slip in the data can affect the results.
Between-receiver single difference Atmosphere
Figure 2.6 Some GPS linear combinations.
TLFeBOOK impacts only one observable in the triple-difference data series, resulting in a noticeable spike This is why the triple-difference linear combination is utilized to identify cycle slips effectively.
Linear combinations can be derived from single-frequency data, including carrier phase and pseudorange observables When dual-frequency data is available, additional beneficial linear combinations can be created, such as the ionosphere-free linear combination This combination effectively mitigates ionospheric delay, which is inversely proportional to the square of the carrier frequency, by integrating L1 and L2 measurements Additionally, combining L1 and L2 carrier-phase measurements yields the wide-lane observable, an artificial signal with an effective wavelength of approximately 86 cm, aiding in the resolution of integer ambiguity parameters.
[1] Hoffmann-Wellenhof, B., H Lichtenegger, and J Collins, Global
Positioning System: Theory and Practice, 3rd ed., New York:
[2] Langley, R B., Why Is the GPS Signal So Complex? GPS World, Vol 1,
[3] Wells, D E., et al., Guide to GPS Positioning, Fredericton, New Brunswick: Canadian GPS Associates, 1987.
[4] Langley, R B., The GPS Observables, GPS World, Vol 4, No 4, April
[5] Shaw, M., K Sandhoo, and D Turner, Modernization of the Global
Positioning System, GPS World , Vol 11, No 9, September 2000, pp. 3644.
[6] Langley, R B., The GPS Receiver: An Introduction, GPS World, Vol 2,
[7] Langley, R B., Smaller and Smaller: The Evolution of the GPS Receiver, GPS World, Vol 11, No 4, April 2000, pp 5458.
[8] Langley, R B., Time, Clocks, and GPS, GPS World , Vol 2, No 10,
[9] McCarthy, D D., and W J Klepczynski, GPS and Leap Seconds: Time to Change, GPS World , Vol 10, No 11, November 1999, pp 5057.
GPS pseudorange and carrier-phase measurements are influenced by various random errors and systematic biases These errors can be categorized into three main sources: those arising from the satellites, those from the receiver, and those resulting from signal propagation, including atmospheric refraction.
Errors in GPS signals can arise from various sources, including satellite ephemeris and clock errors, as well as the now-defunct selective availability implemented by the U.S Department of Defense to reduce GPS accuracy for security purposes until it was discontinued on May 1, 2000 Additionally, receiver-related errors, such as clock discrepancies, multipath interference, noise, and antenna phase center variations, can affect accuracy Signal propagation errors also occur due to delays as GPS signals travel through the ionospheric and tropospheric layers, with the signal only traveling at the speed of light in a vacuum.
The accuracy of GPS positioning is influenced not only by errors but also by the geometric arrangement of satellites relative to the receiver Greater satellite dispersion in the sky leads to improved positioning accuracy.
Chapter 2 highlights that certain errors and biases in GPS data can be minimized by effectively combining GPS observables, such as L1 and L2, which significantly mitigates ionospheric effects Additionally, mathematical modeling offers a viable approach to addressing these errors and biases This chapter introduces the primary sources of GPS errors and explores various methods for managing them.
GPS ephemeris errors
Satellite positions over time, as conveyed in the broadcast satellite navigation message, are predicted using prior GPS observations from ground control stations The operational control system typically utilizes overlapping 4-hour GPS data spans to derive updated satellite orbital elements for each hour However, due to the complexities of modeling the forces acting on GPS satellites, ephemeris errors can occur, leading to inaccuracies in satellite position estimates Generally, these ephemeris errors range from 2 to 5 meters but can escalate to as much as 50 meters under selective availability conditions.
Ephemeris (orbital) error Selective availability Clock error
Clock error Multipath error System noise Antenna phase center variations
Figure 3.1 GPS errors and biases.
TLFeBOOK satellite clock errors is of the order of 2.3m [1 -level;s s is the standard deviation (see Appendix B)].
An ephemeris error for a specific satellite affects all GPS users globally, but its impact on range measurements and computed positions varies due to different viewing angles While combining measurements from two receivers tracking the same satellite cannot completely eliminate this error, users in close proximity will experience nearly identical range errors that can be mitigated through differencing For relative positioning, a useful guideline suggests that the baseline error relative to the baseline length is proportional to the satellite position error divided by the range to the satellite For example, with a satellite position error of 5 meters and a baseline length of 10 kilometers, the anticipated baseline error resulting from the ephemeris error would be about 2.5 millimeters.
For applications like crustal dynamics studies, precise ephemeris data is essential, surpassing the accuracy of broadcast ephemeris Institutions such as the International GPS Service for Geodynamics (IGS), the U.S National Geodetic Survey (NGS), and Geomatics Canada offer post-mission precise orbital services, utilizing GPS data from a global network coordinated by the IGS Currently, precise ephemeris data is accessible to users with a delay ranging from 12 hours for ultra-rapid orbits to approximately 12 days for the most accurate orbits, achieving accuracies of a few decimeters to 1 decimeter Users can download this precise ephemeris data for free from the IGS center at ftp://igscb.jpl.nasa.gov/igscb/product/.
Selective availability
GPS was initially developed to provide less precise real-time positioning and navigation for civilian C/A code receivers compared to military P-code receivers However, both types of receivers surprisingly achieved nearly identical accuracy levels To maintain national security, the U.S Department of Defense (DoD) implemented measures to differentiate the capabilities of these systems.
On March 25, 1990, TLFeBOOK implemented selective availability (SA) on Block II GPS satellites, restricting accurate real-time autonomous positioning for unauthorized users.
Satellite Availability (SA) introduces two main types of errors: delta error, caused by dithering the satellite clock and affecting all users globally, and epsilon error, which is a slowly varying orbital error When SA is active, the nominal horizontal and vertical errors can reach up to 100 meters and 156 meters, respectively, at a 95% probability level The impact of SA on the horizontal position of a stationary GPS receiver is illustrated in Figure 3.2, highlighting the variation over time Both delta and epsilon errors exhibit similar range errors for users in close proximity To mitigate the effects of epsilon error, differential GPS (DGPS) can be employed, offering improved accuracy compared to standalone P-code receivers by reducing common errors.
On May 1, 2000, the U.S government ended Selective Availability (SA), significantly enhancing the accuracy of autonomous GPS systems With SA disabled, the typical horizontal and vertical accuracies of autonomous GPS improved to approximately 22 meters and 33 meters, respectively, 95% of the time.
Figure 3.2 Position variation of a stationary GPS receiver due to SA.
The removal of Selective Availability (SA) significantly improves GPS accuracy, as illustrated in Figure 3.3, leading to faster growth in GPS markets such as vehicle navigation and enhanced 911 services While the impact on Differential GPS (DGPS) accuracy is minimal, it notably lowers the installation and operational costs of DGPS systems due to reduced transmission rates.
Satellite and receiver clock errors
Each GPS Block II and Block IIA satellite is equipped with four atomic clocks—two cesium and two rubidium—while the newer Block IIR satellites utilize only rubidium clocks Among these, a cesium clock is typically chosen to meet the frequency and timing requirements for GPS signal generation, with the other clocks serving as backups Despite their high accuracy, GPS satellite clocks exhibit some limitations, with stability ranging from 1 to 2 parts in 10^13 over a day, resulting in clock errors of approximately 8.64 to 17.28 nanoseconds daily This clock error translates to a range error of about 2.59 to 5.18 meters, calculated using the speed of light Notably, cesium clocks demonstrate superior long-term stability compared to rubidium clocks.
Figure 3.3 Position variation of a stationary GPS receiver after terminating SA.
Over a period of 10 days, TLFeBOOK enhances various components within a timeframe of 10 to 14 days The ground control system continuously monitors the performance of satellite clocks, calculating the amount of drift This drift information is then transmitted as part of the navigation message, represented by three coefficients of a second-degree polynomial.
Satellite clock errors can lead to inaccuracies in GPS measurements, affecting all users tracking the same satellite These errors can be mitigated by differencing between receivers or by applying the satellite clock correction provided in the navigation message However, this correction may still leave residual errors on the order of several nanoseconds, resulting in range inaccuracies of a few meters, as one nanosecond of error corresponds to approximately 30 centimeters in range.
GPS receivers utilize low-cost crystal clocks that lack the accuracy of satellite clocks, resulting in larger clock errors These errors can be mitigated by differencing between satellites or incorporated as an unknown parameter in the estimation process In certain applications, high-precision external clocks, typically cesium or rubidium, are employed instead of the internal receiver clocks While these external atomic clocks offer significantly better performance, they come with a price tag ranging from several thousand dollars for rubidium clocks to even higher for cesium clocks.
Multipath error
Multipath error significantly impacts both carrier-phase and pseudorange measurements in GPS technology This type of error arises when GPS signals reach the receiver antenna via multiple paths, including the direct line of sight and reflections from nearby objects.
Multipath interference distorts the original GPS signal by causing reflections that impact measurements at the antenna While it affects both carrier-phase and pseudorange measurements, the distortion is significantly more pronounced in pseudorange measurements The maximum carrier-phase multipath distortion can reach up to a quarter of a cycle, approximately 4.8 cm for the L1 carrier phase In contrast, pseudorange multipath can theoretically extend to several tens of meters for C/A-code measurements, highlighting the challenges posed by this phenomenon.
TLFeBOOK receiver technology significantly minimizes pseudorange multipath errors, with advancements like the Strobe correlator from Ashtech, Inc and the MEDLL from NovAtel, Inc These multipath-mitigation techniques effectively reduce pseudorange errors to just a few meters, even in challenging, highly reflective environments.
Multipath errors can be detected by analyzing the correlation of estimated residuals on a daily basis, as the satellite-reflector-antenna geometry remains consistent each sidereal day If dual-frequency observations are utilized, it becomes easier to identify these errors in undifferenced pseudorange measurements Despite the lack of a comprehensive multipath model due to varying geometries, there are effective strategies to mitigate multipath effects Selecting an observation site free from nearby reflecting objects is a simple yet effective approach.
The TLFeBOOK chock ring antenna features a ground plane with multiple concentric metal hoops designed to attenuate reflected signals This design leverages the difference in polarization, as GPS signals are right-handed circularly polarized while reflected signals are left-handed To minimize multipath effects, using an antenna that matches the GPS signal's right-handed polarization can be effective However, a key drawback is that if the multipath signal is reflected twice, its polarization reverts to right-handed, potentially diminishing the benefits of this approach.
Antenna-phase-center variation
A GPS antenna captures satellite signals and converts them into electric currents for the GPS receiver The location where the signal is received is known as the antenna phase center, which often does not align with the antenna's physical center This discrepancy varies based on the satellite's elevation, azimuth, and signal strength, leading to potential range errors.
The error caused by antenna-phase-center variation varies by antenna type and typically measures a few centimeters Modeling this variation is challenging, necessitating careful selection of antenna types For short baselines using identical antennas oriented in the same direction, phase-center errors can be canceled However, mixing different antenna types or orientations will not eliminate this error Due to its relatively small size, this error is often overlooked in practical GPS applications.
Phase-center errors can vary between L1 and L2 carrier-phase observations, impacting the accuracy of the ionosphere-free linear combination, especially in short baselines For short baselines, these errors are closely correlated over distance and can be effectively mitigated through differencing Consequently, utilizing a single frequency may be more suitable for static mode applications in short baselines.
Receiver measurement noise
Receiver measurement noise in GPS systems arises from the limitations of the receiver's electronics, and an effective GPS system should maintain a low noise level Typically, a GPS receiver conducts a self-test upon activation; however, for high-end precise GPS systems, user-initiated evaluations may be necessary Two key methods for assessing a GPS receiver's performance are the zero baseline and short baseline tests.
A zero baseline test is essential for assessing GPS receiver performance, utilizing a single antenna and preamplifier connected to multiple receivers via a signal splitter This method effectively identifies issues such as interchannel biases and cycle slips, with the expectation that the baseline solution remains zero; any deviation indicates receiver noise While the test yields valuable insights into receiver functionality, it does not account for antenna or preamplifier noise, and the impact of receiver measurement noise on range error is significantly influenced by the GPS receiver's quality.
Figure 3.5 Zero baseline test for evaluating the performance of a GPS receiver.
According to [2], typical average value for range error due to the receiver measurement noise is of the order of 0.6m (1s-level).
To accurately assess the field performance of a GPS system, it is essential to consider the antenna/preamplifier noise component This evaluation can be conducted using short baselines, typically a few meters apart, observed over two consecutive days During this process, the double difference residuals from one day will reflect the system noise and multipath effects, while other errors will largely cancel out Since the multipath signature repeats every sidereal day, differencing the double difference residuals from the two days effectively removes the multipath influence, isolating the system noise for analysis.
Ionospheric delay
In the Earth's upper atmosphere, ultraviolet and X-ray radiation from the sun interacts with gas molecules and atoms, leading to gas ionization This process generates numerous free negatively charged electrons and positively charged atoms and molecules.
The ionosphere is a region of the atmosphere characterized by gas ionization, extending from approximately 50 km to over 1,000 km in altitude The upper limit of this ionospheric region remains undefined.
Figure 3.6 Short baseline test for evaluating the performance of a GPS system.
The ionospheric region exhibits variable electron density that changes with altitude, leading to the classification of this region into distinct layers: D (50-90 km), E (90-140 km), F1 (140-210 km), and F2 (210-1,000 km), with F2 typically exhibiting the highest electron density The altitude and thickness of these layers fluctuate over time due to solar radiation and the Earth's magnetic field variations Notably, the F1 layer is absent at night and is more prominent during summer months compared to winter.
The ionosphere significantly impacts GPS measurements by acting as a dispersive medium that bends GPS radio signals and alters their speed as they traverse various ionospheric layers This bending results in minimal range errors, especially when satellite elevation angles exceed 5 degrees However, the change in propagation speed leads to substantial range errors that must be considered Specifically, the ionosphere accelerates the carrier phase beyond the speed of light while simultaneously slowing down the PRN code and navigation message, resulting in shorter distance measurements via the carrier phase and longer measurements via the code compared to the actual distance The ionospheric delay is linked to the total electron content (TEC), which varies based on factors such as the time of day—reaching peak electron density in the early afternoon and a minimum around midnight—and the time of year, with higher electron density levels observed in winter than in summer.
The 11-year solar cycle significantly influences electron density levels, peaking approximately every 11 years, with the current peak occurring around 2001 during solar cycle number 23 Additionally, geographic location affects electron density, with minimum levels found in midlatitude regions and irregular patterns in polar, auroral, and equatorial areas The ionosphere acts as a dispersive medium, causing frequency-dependent delays; lower frequencies experience greater delays, with L2 exhibiting more delay than L1 Typically, ionospheric delay ranges from 5 to 15 meters but can exceed 150 meters during extreme solar activity, particularly at midday and near the horizon.
The electron density level in the ionosphere fluctuates over time and location, but it shows strong correlation over short distances, allowing for significant reduction of ionospheric delay through differencing GPS observations between closely spaced users By leveraging the ionosphere's dispersive characteristics, accurate determination of ionospheric delay can be achieved using P-code pseudorange measurements on both L1 and L2 frequencies, although access to P-code is restricted to authorized users The introduction of a second C/A-code on L2 as part of modernization efforts will alleviate this limitation Additionally, users with dual-frequency receivers can combine L1 and L2 carrier-phase measurements to create an ionosphere-free linear combination, effectively eliminating ionospheric delay However, this method has drawbacks, including increased observation noise and the loss of integer ambiguity parameters.
The ionosphere-free linear combination is not advisable for short baselines, as single-frequency users cannot leverage the ionosphere's dispersive properties However, they can apply empirical ionospheric models, like the Klobuchar model, to correct up to 60% of the delay, with its coefficients included in the navigation message Another effective solution for single-frequency GPS users is to obtain real-time corrections from regional networks via communication links.
Tropospheric delay
The troposphere is the electrically neutral layer of the atmosphere, reaching approximately 50 km above the Earth's surface It serves as a nondispersive medium for radio frequencies below 15 GHz, making it essential for various communication technologies.
Tropospheric delay impacts GPS signals by causing both carriers and codes to be delayed equally, resulting in an overestimation of the satellite-to-receiver range Consequently, the distance measured between two receivers appears longer than the true geometric distance Unlike ionospheric delay, tropospheric delay cannot be mitigated by combining L1 and L2 observations due to its frequency-independent nature.
Tropospheric delay is influenced by temperature, pressure, and humidity along the signal path in the troposphere Signals from satellites at lower elevation angles experience a longer path, resulting in increased delay, which is minimized at the user's zenith and maximized near the horizon Specifically, the tropospheric delay measures approximately 2.3 meters at zenith, around 9.3 meters at a 15° elevation angle, and between 20 to 28 meters at a 5° elevation angle.
Tropospheric delay consists of two main components: dry and wet The dry component accounts for approximately 90% of the total delay and can be accurately predicted using mathematical models In contrast, the wet component, influenced by water vapor along the GPS signal path, is more challenging to forecast Various mathematical models rely on surface meteorological measurements, such as atmospheric pressure, temperature, and partial water vapor pressure, to estimate this component However, the weak correlation between the wet component and surface meteorological data limits prediction accuracy Despite this, using default meteorological values—1,010 mb for atmospheric pressure, 20°C for temperature, and 50% for relative humidity—often yields satisfactory results.
Satellite geometry measures
The accuracy of computed GPS positions is significantly influenced by various types of errors and biases, necessitating proper modeling and combinations of GPS observables for improvement Additionally, satellite geometry, which refers to the spatial arrangement of GPS satellites relative to the receiver, plays a crucial role in determining overall positioning accuracy Stronger satellite geometry leads to enhanced positioning precision, highlighting that GPS accuracy is a result of both unmodeled measurement errors and satellite geometry effects.
Good satellite geometry is obtained when the satellites are spread out in the sky [19] In general, the more spread out the satellites are in the sky,
Satellite geometry significantly impacts the accuracy of receiver positioning In a two-dimensional scenario, the receiver's location is determined by the intersection of arcs from two satellites, each representing the receiver-satellite distance Measurement errors introduce an uncertainty region around the estimated distance, indicating that the receiver is likely within this area Statistical principles indicate that a smaller uncertainty area correlates with higher positional precision As illustrated, when satellites are spaced widely apart, the uncertainty area diminishes, leading to improved satellite geometry Conversely, when satellites are closely positioned, the uncertainty area expands, resulting in degraded satellite geometry.
The dilution of precision (DOP) is a key dimensionless metric that quantifies the impact of satellite geometry on positioning accuracy A lower DOP value indicates stronger geometric strength, enhancing measurement reliability This value is calculated using the relative positions of the receiver and satellites at any given moment, necessitating precise coordinates for both.
Figure 3.7 (a) Good satellite geometry; and (b) bad satellite geometry.
The DOP (Dilution of Precision) value can typically be determined without measurements, as it is generally sufficient However, the DOP value fluctuates over time due to the relative motion between satellites and receivers These changes are usually gradual, except in specific situations: when a satellite is either rising or falling in the receiver's view, or when an obstruction, such as a bridge, blocks the line of sight between the receiver and the satellite.
In practice, various DOP forms are used, depending on the users need
When assessing GPS positioning accuracy, users should consider the impact of satellite geometry on the three-dimensional (3-D) position, which is quantified by the position dilution of precision (PDOP) PDOP is divided into two components: horizontal dilution of precision (HDOP), reflecting the accuracy of the horizontal position, and vertical dilution of precision (VDOP), indicating the accuracy of the vertical position Due to the limitation of tracking only satellites above the horizon, VDOP is typically greater than HDOP, leading to less precise height solutions compared to horizontal ones To enhance VDOP, users can integrate additional sensors, such as pseudolites Other relevant forms of dilution of precision include time dilution of precision (TDOP) and geometric dilution of precision (GDOP), the latter combining the effects of PDOP and TDOP.
For optimal GPS positioning accuracy, it is essential to choose an appropriate observation time, aiming for a PDOP of five or lower, with typical values around two Most GPS software can forecast satellite geometry based on the user's location and recent satellite data from an almanac file, which is available for free online, such as from the U.S Coast Guard Navigation Center.
GPS mission planning
Despite the presence of 24 GPS satellites, there are instances when only four satellites are visible above a certain elevation angle, which may not suffice for specific GPS applications This visibility issue is more pronounced at high latitudes (above 55°) due to the configuration of the GPS constellation, but it can also occur in low- or mid-latitude regions, particularly in urban and forested areas where buildings and trees obstruct the receiver's sky view As satellite geometry varies over time, users can mitigate visibility problems by selecting optimal observation times that maximize the number of visible satellites and minimize the Dilution of Precision (DOP) values To assist users in determining the best observation periods, GPS manufacturers have created mission-planning software that forecasts satellite visibility and geometry for any location.
Mission-planning software offers various plots essential for organizing GPS surveys or missions Among these, the sky plot stands out, illustrating the user's sky window through a series of concentric circles For instance, Figure 3.8 depicts the sky plot for Toronto on April 13, 2001.
Figure 3.8 GPS sky plot for Toronto on April 13, 2001.
The TLFeBOOK, developed by the Ashtech Locus processor software, visually represents satellite positions in relation to the user's location The center point indicates the user's zenith, while the outer circle illustrates the horizon, with intermediate circles denoting various elevation angles The outer circle is marked from 0 to 360 degrees to indicate satellite azimuth (direction) By entering their approximate location and desired observation period, users can view the paths of visible satellites on a sky plot, providing information on satellite locations, azimuth, and elevation Additionally, users can set a mask angle, typically 10 or 15 degrees, below which the receiver will not track any satellites, ensuring effective satellite tracking.
Key plots in satellite data analysis include the satellite availability plot, which indicates the total number of visible satellites above a user-defined mask angle, and the satellite geometry plot For example, Figure 3.9 illustrates satellite availability and geometry for Toronto on April 13, 2001 The satellite geometry is typically represented by parameters such as PDOP, HDOP, and VDOP, which are crucial for understanding satellite positioning accuracy.
Figure 3.9 Satellite availability and geometry for Toronto on April 13, 2001.
User equivalent range error
GPS positioning accuracy is influenced by unmodeled measurement errors and satellite geometry These errors vary across satellites due to different view angles, and their ranging errors can exhibit correlation To accurately assess GPS positioning accuracy, techniques like the least-squares method can be employed, which estimates the user's location and provides a covariance matrix This matrix indicates the reliability of the user's position by reflecting the interplay between measurement errors and satellite geometry.
User Equivalent Range Error (UERE) simplifies the assessment of GPS positioning accuracy by quantifying measurement errors across satellites as identical and independent It is calculated as the root-sum-square of various errors and biases By multiplying the UERE with the relevant Dilution of Precision (DOP) value, one can determine the expected precision of GPS positioning at the one-sigma (1-σ) level.
To achieve 95% positional accuracy at the 2-level, we multiply the UERE by a factor of two For instance, with a UERE of 8m for a standalone GPS receiver and an HDOP of 1.5, the resulting accuracy is calculated as 8m × 1.5 × 2, equating to 24m.
[1] Kleusberg, A., and R B Langley, The Limitations of GPS, GPS World, Vol 1, No 2, March/April 1990, pp 5052.
[2] Shaw, M., K Sandhoo, and D Turner, Modernization of the Global
Positioning System, GPS World , Vol 11, No 9, September 2000, pp. 3644.
[3] Hoffmann-Wellenhof, B., H Lichtenegger, and J Collins, Global
Positioning System: Theory and Practice, 3rd ed., New York:
[4] El-Rabbany, A., The Effect of Physical Correlations on the Ambiguity
Resolution and Accuracy Estimation in GPS Differential Positioning,
Technical Report No 170, Department of Geodesy and Geomatics
Engineering, Fredericton, New Brunswick, Canada: University of New Brunswick, 1994.
[5] Wells, D E., et al., Guide to GPS Positioning, Fredericton, New Brunswick: Canadian GPS Associates, 1987.
[6] Georgiadou, Y., and K D Doucet, The Issue of Selective Availability, GPS World, Vol 1, No 5, September/October 1990, pp 5356.
[7] Langley, R B., Time, Clocks, and GPS, GPS World , Vol 2, No 10,
[8] Kaplan, E., Understanding GPS: Principles and Applications, Norwood, MA: Artech House, 1996.
[9] Weill, L R., Conquering Multipath: The GPS Accuracy Battle, GPS World, Vol 8, No 4, April 1997, pp 5966.
[10] Langley, R B., The GPS Receiver: An Introduction, GPS World, Vol 2,
[11] Schupler, B R., and T A Clark, How Different Antennas Effect the GPS Observable, GPS World , Vol 2, No 10, November/December 1991, pp 3236.
[12] Nolan, J., S Gourevitch, and J Ladd, Geodetic Processing Using Full Dual Band Observables, Proc ION GPS-92, 5th Intl Technical Meeting, Satellite Div., Institute of Navigation, Albuquerque, NM, September
[13] Klobuchar, J A., Ionospheric Effects on GPS, GPS World, Vol 2, No 4, April 1991, pp 4851.
In his 1997 Ph.D dissertation, "Global Ionospheric Total Electron Content Mapping Using the Global Positioning System," A Komjathy presents a comprehensive study conducted at the University of New Brunswick This research, documented as Technical Report No 188, focuses on utilizing GPS technology to map total electron content in the ionosphere, contributing valuable insights to the field of geodesy and geomatics engineering.
[15] Langley, R B., GPS, the Ionosphere, and the Solar Maximum, GPS
World, Vol 11, No 7, July 2000, pp 4449.
[16] Hay, C., and J Wong, Enhancing GPS: Tropospheric Delay Prediction at the Master Control Station, GPS World , Vol 11, No 1, January 2000, pp 5662.
[17] Brunner, F K., and W M Welsch, Effect of the Troposphere on GPS Measurements, GPS World , Vol 4, No 1, January 1993, pp 4251.
[18] Leick, A., GPS Satellite Surveying, 2nd ed., New York: Wiley, 1995.
[19] Langley, R B., Dilution of Precision, GPS World, Vol 10, No 5, May
[20] U.S Coast Guard Navigation Center, accessed 2001, http://www.navcen.uscg.gov/GPS/default.htm#almanacs.
GPS technology has revolutionized location tracking, attracting millions of users globally due to its ability to pinpoint precise locations in any weather Advances in GPS and computer technology have led to the development of user-friendly systems However, newcomers often struggle with understanding datums and coordinate systems, which necessitate some geodetic knowledge This chapter provides a comprehensive overview of these concepts without delving into complex mathematics It focuses on the horizontal component of GPS positioning and introduces map projections, while also addressing height systems for a complete understanding.
What is a datum?
The irregular topography of the Earth complicates geodetic calculations, such as determining a user's location To address this challenge, geodesists utilize a smooth mathematical surface known as the reference surface to approximate the Earth's shape, specifically the global mean sea level or geoid While a sphere is suitable for low-accuracy positioning, high-accuracy systems like GPS require a more precise model The biaxial ellipsoid, created by rotating an ellipse around its minor axis, serves as the ideal reference ellipsoid for simplifying calculations while providing accurate positioning.
[2] Similar to the ellipse, the biaxial reference ellipsoid can be defined by the semiminor and semimajor axes (a, b) or the semimajor axis and the flattening (a, f ), where f = 1 −( / b a).
A geodetic datum is a mathematically defined reference ellipsoid that has a specific origin and orientation For instance, a geocentric geodetic datum aligns its origin with the Earth's center Since there are countless geocentric datums with varying orientations, a geodetic datum is uniquely identified by eight parameters: two for the ellipsoid's dimensions, three for the origin's position, and three for the orientation of its axes relative to the Earth Examples of common reference systems and their corresponding ellipsoids are detailed in Table 4.1.
The vertical datum serves as a crucial reference surface for measuring heights (elevations) of points, with the height of any point directly on this datum defined as zero Commonly referred to as the surface of zero height, the vertical datum is frequently chosen to be the geoid, which approximates the mean sea level globally.
In the past, positions with respect to horizontal and vertical datums have been determined independent of each other [2] However, with the
TLFeBOOK advent of space geodetic positioning systems such as GPS, it is possible to determine the 3-D positions with respect to a 3-D reference system.
Geodetic coordinate system
Conventional Terrestrial Reference System
The Conventional Terrestrial Reference System (CTRS) is a 3-D geocentric coordinate system, that is, its origin coincides with the center of the Earth
Meridian plane through z Equatorial plane of ellipsoid
The CTRS, or Earth-centered, Earth-fixed (ECEF) coordinate system, is firmly connected to the Earth and rotates in unison with it.
The orientation of the axes in the Conventional Terrestrial Reference System (CTRS) is defined with the z-axis pointing toward the Conventional Terrestrial Pole (CTP), which represents the average pole location from 1900 to 1905 The x-axis is determined by the intersection of the terrestrial equatorial plane and the meridional plane that includes the mean location of the Greenwich Observatory, known as the mean Greenwich meridian Consequently, the xz-plane encompasses the mean Greenwich meridian The y-axis is established to ensure a right-handed coordinate system, positioned 90 degrees east of the x-axis within the equatorial plane All three axes converge at the Earth's center.
The Coordinate Time Reference System (CTRS) must be accurately positioned relative to the Earth, a process known as realization, to be effectively utilized in positioning This involves assigning coordinate values to a strategically selected set of well-distributed reference stations A key component of this system is the International Terrestrial Reference System (ITRS), realized through the International Terrestrial Reference Frame (ITRF) The ITRF is recognized as the most precise coordinate system, relying on data from globally distributed reference stations utilizing GPS and other space geodetic technologies To maintain its accuracy, the ITRF is updated every 1 to 3 years, with the latest version being ITRF2000 at the time of writing.
Datums, Coordinate Systems, and Map Projections 51
Figure 4.3 (a) Concept of geodetic coordinates; and (b) geodetic and Cartesian coordinates.
The WGS 84 and NAD 83 systems
The World Geodetic System of 1984 (WGS 84) is a 3-D, Earth-centered reference system developed by the U.S Defense Mapping Agency, now part of the National Imagery and Mapping Agency (NIMA), and serves as the official GPS reference system GPS users obtain their coordinates in the WGS 84 system by utilizing the broadcast ephemeris WGS 84 employs a combined terrestrial reference system (CTRS) and a reference ellipsoid closely aligned with the Geodetic Reference System of 1980 (GRS 80), which is recommended for geodetic applications Initially established using multiple Doppler stations, WGS 84 has undergone several updates to align with the International Terrestrial Reference Frame (ITRF), achieving subdecimeter accuracy with the latest revision.
The North American Datum of 1983 (NAD 83) serves as the legal datum for spatial positioning in North America, utilizing the GRS 80 ellipsoid, which closely resembles WGS 84 in size and shape Originally established in 1986, NAD 83 was based on classical geodetic observations connecting a network of horizontal control stations across North America, supplemented by observed Doppler positions Although intended as an Earth-centered reference system, further advancements revealed that NAD 83's origin is approximately 2 meters off from the true center of the Earth Access to NAD 83 was primarily through a horizontal control network, which has inherent accuracy limitations due to error accumulation To enhance its precision, NAD 83 was linked to the International Terrestrial Reference Frame (ITRF) using 12 common very long baseline interferometry (VLBI) stations in Canada and the U.S., resulting in improved versions known as NAD 83 (CSRS) and NAD 83 (NSRS) The acronyms CSRS and NSRS stand for the Canadian Spatial Reference System and National Spatial Reference System, respectively, highlighting the need to specify the epoch of ITRF coordinates due to variations in its versions.
What coordinates are obtained with GPS?
The satellite coordinates provided in the broadcast ephemeris are based on the WGS 84 reference system, meaning that GPS users utilizing this data will receive their coordinates in the same system In contrast, users who access precise ephemeris data from the IGS service will have their solutions referenced to the ITRF system Additionally, some organizations, such as Geomatics Canada, offer precise ephemeris data in multiple formats, including both ITRF and NAD.
When using reference station coordinates in NAD 83 instead of WGS 84, the impact varies based on whether the old or improved NAD 83 system is employed Although the reference ellipsoids of WGS 84 and old NAD 83 are nearly identical in size and shape, their origins differ by over 2 meters, leading to discrepancies in absolute coordinates This means that a point's coordinates will differ between the two systems, with the most significant variation occurring in the height component, approximately 0.5 meters However, this shift has a minimal effect on relative GPS positioning, resulting in negligible errors, typically at the millimeter level, when using NAD 83 coordinates for reference stations Importantly, the improved WGS 84 and NAD 83 systems are compatible.
Datum transformations
Historically, horizontal and vertical datums were determined independently, with horizontal datums being non-geocentric and tailored to specific regions, often referred to as local datums Over 150 local datums have been utilized globally, including the North American Datum of 1927 (NAD 27).
Datums, Coordinate Systems, and Map Projections 53
TLFeBOOK geodetic positioning systems such as GPS, it is now possible to determine global 3-D geocentric datums.
Old maps utilized local datums, while contemporary maps predominantly employ geocentric datums like WGS 84 To maintain consistency, it is essential to establish relationships between local and geocentric datums through a process known as datum transformation NIMA has published transformation parameters for various local datums, which many GPS manufacturers incorporate into their software However, these parameters are approximate and unsuitable for precise GPS applications For instance, in Toronto, using NIMA's parameters can result in horizontal coordinate differences of several meters compared to the more accurate National Transformation software (NTv2) from Geomatics Canada, with potential discrepancies being even greater in other areas The most reliable method for obtaining transformation parameters involves comparing coordinates of well-distributed common points across both datums.
Figure 4.4 Geocentric and local datums.
Map projections
Transverse Mercator projection 56viiiIntroduction to GPS
Transverse Mercator projection (also known as Gauss-Krüger projection) is a conformal map projection invented by Johann Lambert (Germany) in
The transverse Mercator projection, developed in 1772, mathematically projects points from an ellipsoidal surface onto an imaginary transverse cylinder positioned in the equatorial plane This cylinder can either be tangent to the ellipsoid along a central meridian or act as a secant, resulting in two small complex curves equidistant from the central meridian By cutting and unfolding this imaginary cylinder, a flat map is created, emphasizing that the transverse cylinder is purely theoretical.
TLFeBOOK explained earlier, the projection is made mathematically through the trans- formation of the geodetic coordinates into the grid coordinates.
In a tangent cylinder projection, features along the central meridian are accurately represented without distortion, maintaining a true scale of one However, as we move away from this central line, distortion increases, with the scale factor rising symmetrically This characteristic makes the tangent cylinder projection particularly effective for regions that extend predominantly in a north-south orientation.
In a secant cylinder, the mapping of features along the two small complex curves occurs without distortion, ensuring true scale along these curves rather than the central meridian As with the tangent cylinder, distortion becomes more pronounced as one moves away from the two small complex curves.
Universal transverse Mercator projection
The Universal Transverse Mercator (UTM) is a map projection derived from the original transverse Mercator, utilizing a secant cylinder It divides the Earth into 60 equally-sized zones, each centered around its own central meridian located in the middle of the zone Each UTM zone spans 6° of longitude, with 3° on either side of the central meridian, and each zone is projected independently, allowing for accurate mapping across different regions.
Datums, Coordinate Systems, and Map Projections 57
C en tr al m er id ia n (Equator)
Figure 4.7 Transverse Mercator map projection.
The Transverse Mercator projection minimizes distortion by dividing the Earth into 60 zones, each assigned a number from 1 to 60, starting at 180° W and increasing eastward For example, zone 1 spans from 180° W to 174° W, with its central meridian located at 177° W.
The Universal Transverse Mercator (UTM) system employs a scale factor of 0.9996 at the central meridian of each zone to achieve a more uniform scale distribution This choice minimizes deviations from one across the entire zone, ensuring accuracy in mapping For instance, at the equator, the scale factor varies from 0.9996 at the central meridian to 1.00097 at the zone's edge, demonstrating the importance of this scale factor in maintaining consistency in measurements.
Imaginary secant cylinder Central meridian
TLFeBOOK midlatitude (f = 45° Ν), the scale changes from 0.9996 at the central meridian to 1.00029 at the edge of the zone This shows how the distortion is kept at a minimal level with UTM.
To prevent negative coordinates in grid systems, the true origin, where the equator intersects the central meridian of a zone, is adjusted using false northing and false easting In the northern hemisphere, these values are set at 0.0 km for false northing and 500 km for false easting, while in the southern hemisphere, they are modified to 10,000 km for false northing and 500 km for false easting.
It is important to note that the Universal Transverse Mercator (UTM) projection is not ideal for polar regions due to the complexities of multiple zones required for small polar areas Instead, alternative projection methods like the stereographic double projection can be utilized for more accurate representation in these regions.
Modified transverse Mercator projection
The modified transverse Mercator (MTM) projection, similar to the UTM, utilizes a secant cylinder and is employed in several Canadian provinces, including Ontario This projection divides regions into zones of 3 degrees of longitude, with each zone projected separately to minimize distortion In Canada, the first MTM zone begins just east of Newfoundland at 51° 30' W and extends westward, encompassing a total of 32 zones Ontario specifically includes 10 zones, ranging from zones 8 to 17, with zone 10 being home to the city of Toronto.
MTM employs a scale factor of 0.9999 along the central meridian of the zone, significantly reducing distortion compared to UTM For instance, at a latitude of 43.5 N, the scale factor varies from 0.9999 at the central meridian to 1.0000803 at the zone's boundary, demonstrating how MTM minimizes scale variation and distortion However, this approach results in a doubling of the number of zones.
To prevent negative coordinates in grid systems like UTM, a false northing and false easting are introduced to shift the true origin of the coordinates Since Canada is entirely situated in the northern hemisphere, this adjustment is essential for accurate mapping.
Datums, Coordinate Systems, and Map Projections 59
TLFeBOOK only one false northing and one false easting of 0.0m and 304,800m,respectively (see Figure 4.10).
Lambert conical projection
The Lambert conical projection, created by Johann Lambert in 1772, is a conformal map projection that mathematically projects points from an ellipsoidal surface onto an imaginary cone This cone can either touch the ellipsoid at one parallel or intersect it at two parallels, resulting in one or two standard parallels, respectively By cutting and unfolding the cone, a flat map is generated, effectively representing geographic features.
The transverse Mercator projection accurately represents all features along the standard parallels without distortion However, as one moves away from these standard parallels, the projected features begin to experience increasing distortion.
TLFeBOOK distortion This means that this projection is more suitable for areas that extend in the east-west direction.
This projection features parallels represented as concentric circles centered at the cone's apex, while meridians are depicted as straight lines that converge at the apex.
The meridians act as the radii of concentric circles, with a central meridian chosen to define the grid north direction (y-axis) for the mapped area To prevent negative coordinates, the grid's origin is adjusted by adding two constants, C1 and C2 The mapping authorities determine the values of C1, C2, and the latitude of the standard parallels.
Stereographic double projection
The stereographic double projection is a specific map projection utilized in regions like New Brunswick, Canada This technique involves a two-step process where points on a reference ellipsoid are first projected onto an imaginary sphere and then onto a tangent or secant plane, resulting in a conformal map The initial projection onto the sphere is followed by the stereographic projection onto the plane, which is essential for creating accurate representations of geographic features.
Datums, Coordinate Systems, and Map Projections 61 y
Stereographic projection can be categorized into three types based on the position of the projection plane relative to the sphere When the origin is at one of the sphere's poles, it is known as polar stereographic projection If the origin is located on the equator, it is referred to as transverse or equatorial stereographic projection The general case, where the origin is at an arbitrary point, is called oblique stereographic projection In oblique stereographic projection, the meridian through the map's origin appears as a straight line, while other meridians and parallels are represented as circles In New Brunswick, a secant projection plane is utilized with the origin set at 46°30'N latitude and 66°30'W longitude.
In stereographic projection, a perspective point (P) is chosen opposite the origin (O) Using a secant projection plane, a point (A) on the sphere's surface is projected by extending a line from P to A on the projection plane Points located inside the secant circle, like point B, are projected inward.
In New Brunswick, features along the secant circle are accurately projected without distortion, whereas other features may experience distortion To enhance the projection's accuracy, a scale factor of 0.999912 is applied at the origin Additionally, to prevent negative coordinates, a false northing and a false easting are incorporated, similar to the approach used in the previous three map projections.
Marine nautical charts
Marine nautical charts are maps used by mariners for navigation purposes. They contain information such as aids to navigation and hazards Until
In the past, mariners relied solely on paper charts for navigation However, the introduction of the Electronic Chart Display and Information System (ECDIS) over a decade ago has transformed marine navigation, offering a modern and efficient alternative.
ECDIS, or Electronic Chart Display and Information System, is an advanced computerized navigation system that integrates geographic data with navigation tools It features a computer processor, a digital database, and navigation sensors, allowing for real-time display of navigation-related information ECDIS supports various advanced functions, including route planning, route monitoring, and automatic alarms Additionally, it can be combined with Radar/Automatic Radar Plotting Aid (ARPA) on a single display for enhanced collision avoidance capabilities Established by the International Maritime Organization (IMO) in November 1995, the performance standards for ECDIS mandate the use of two independent positioning sources to ensure accuracy and reliability.
Several hydrographic offices are engaged in creating ECDIS databases by digitizing traditional paper charts, which poses challenges due to the reliance on local datums To ensure consistency, it is essential to apply appropriate datum shifts Additionally, many paper charts were created using outdated survey methods, resulting in inaccuracies that do not meet current standards Consequently, a comprehensive resurvey of these regions may be necessary to address these issues effectively.
Datums, Coordinate Systems, and Map Projections 63
Figure 4.13 Marine nautical chart system.
Local arbitrary mapping systems
When surveying small areas, utilizing a user-defined local plane coordinate system is often more suitable This approach allows the curved surface of the Earth to be treated as a nearly flat plane with minimal distortion To create an effective local coordinate system using GPS, it is essential to have a set of reference points with known coordinates in both the WGS 84 and the local system.
To obtain transformation parameters for converting GPS-derived coordinates into a local coordinate system, the least squares technique is applied by comparing the coordinates of common points known in both the local and WGS 84 systems The accuracy of the transformation improves with the optimal distribution of these common points, and a higher quantity of common points further enhances the solution's reliability.
Establishing a local coordinate system is usually done in either of two ways One way is to supply the transformation parameters software
Figure 4.14 Local arbitrary mapping system.
To accurately transform GPS coordinates into a local coordinate system, manufacturers typically provide common point coordinates for both systems The software computes transformation parameters that, once uploaded to the GPS data collector, facilitate the automatic conversion of new coordinates Alternatively, if a user only knows coordinates in the local system, they can utilize a rover receiver at those points to obtain WGS 84 system coordinates Real-time kinematic (RTK) GPS surveying is commonly employed for this purpose, enabling the determination of transformation parameters directly in the field.
Height systems
The height of a point is the vertical distance from a vertical datum, commonly defined by the geoid The orthometric height refers to the distance of a point above the geoid, which can be either positive or negative based on its location Orthometric heights are significant in practical applications and are typically represented on topographic maps.
In certain applications, such as GPS, heights are measured relative to a reference ellipsoid rather than the geoid, resulting in what are known as ellipsoidal heights These heights can be either positive or negative, indicating whether a point is situated above or below the reference ellipsoid's surface However, ellipsoidal heights are purely geometric and lack physical significance, making it impossible for various geomatics instruments, like total stations, to directly measure them.
The geoid-ellipsoid separation, referred to as geoidal height or undulation, can vary significantly, reaching up to 100 meters, and can be either positive or negative based on the geoid's position relative to the reference ellipsoid Understanding geoidal height is crucial for accurately determining orthometric height from ellipsoidal height and vice versa Comprehensive geoid models have been created to represent geoidal heights globally.
Datums, Coordinate Systems, and Map Projections 65
The accuracy of geoid models varies significantly across different regions due to insufficient local gravity data and height information While many GPS receivers and software include geoid models for automatic conversions between orthometric and ellipsoidal heights, users should exercise caution, as these models often have low accuracy.
[1] Torge, W., Geodesy, New York: Walter de Gruyter, 1991.
[2] Vanicek, P., and E J Krakiwsky, Geodesy: The Concepts , 2nd ed., New York: North Holland, 1986.
[3] Leick, A., GPS Satellite Surveying, 2nd ed., New York: Wiley, 1995.
[4] National Geodetic Survey, Geodetic Glossary, U.S Department of
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[5] Hoffmann-Wellenhof, B., H Lichtenegger, and J Collins, Global
Positioning System: Theory and Practice, 3rd ed., New York:
[6] Boucher, C., and Z Altamimi, International Terrestrial Reference
Frame, GPS World, Vol 7, No 9, September 1996, pp 7174.
[7] Malys, S., et al., Refinements to the World Geodetic System 1984, Proc. ION GPS-97, 10th Intl Technical Meeting, Satellite Division, Institute of Navigation, Kansas City, MO, September 1619, 1997, pp 841850.
[8] Craymer, M., R Ferland, and R Snay, Realization and Unification of NAD83 in Canada and the U.S Via the ITRF, Proc Intl Symp Intl Assoc.
TLFeBOOK of Geodesy, Sec 2, Towards an Integrated Geodetic Observing System (IGGOS), Munich, Germany, October 59, 1998.
[9] Krakiwsky, E J., Conformal Map Projections in Geodesy, Department of Geodesy and Geomatics Engineering, L.N No 37, University of New Brunswick, Fredericton, New Brunswick, Canada, 1973.
[10] Alexander, L., What Is an ENC? Hydro International, Vol 2, No 5,
[11] Casey, M J., and P Kielland, Electronic Charts and GPS, GPS World, Vol 1, No 4, July/August 1990, pp 5659.
[12] Schwarz, K P., and M G Sideris, Heights and GPS, GPS World, Vol 4,
Datums, Coordinate Systems, and Map Projections 67
GPS positioning can be achieved through point positioning or relative positioning Point positioning utilizes a single GPS receiver to measure code pseudoranges, allowing for instantaneous determination of the user's location when at least four satellites are visible The accuracy of civilian C/A-code receivers has improved significantly, decreasing from approximately 100 meters to around 22 meters in the absence of selective availability This method is primarily employed in applications requiring lower accuracy, such as recreational activities and basic navigation.
GPS relative positioning utilizes two GPS receivers that simultaneously track the same satellites, achieving positioning accuracy from subcentimeter to a few meters when at least four common satellites are monitored This method can employ carrier-phase or pseudorange measurements, with carrier-phase offering the highest accuracy GPS relative positioning can be conducted in real-time or post-mission modes and is essential for high-accuracy applications, including surveying, mapping, GIS, and precise navigation.
GPS point positioning
GPS point positioning, or standalone positioning, utilizes a single GPS receiver to determine its coordinates by simultaneously tracking four or more satellites This method allows the receiver to calculate its position relative to the Earth's center Most GPS receivers on the market today can display these point-positioning coordinates effectively.
To accurately determine the receiver's position at any given time, it is essential to have the coordinates of at least four satellites and their respective ranges The receiver acquires satellite coordinates from the navigation message, while ranges are derived from the C/A-code or P(Y)-code, depending on whether the receiver is civilian or military Due to synchronization errors in satellite and receiver clocks, measured pseudoranges require correction; satellite clock errors can be adjusted using the navigation message, while the receiver clock error is treated as an unknown parameter This results in four unknown parameters: three for receiver coordinates and one for the receiver clock error, necessitating a minimum of four satellites for accurate positioning When tracking more than four satellites, techniques such as least-squares estimation or Kalman filtering are employed The resulting receiver coordinates will be expressed in the WGS 84 coordinate system.
Horizontal accuracy: 22m (95% of the time)
Figure 5.1 Principle of GPS point positioning.
TLFeBOOK well, as explained in Chapter 4 However, most GPS receivers provide the transformation parameters between WGS 84 and many local datums used around the world.
GPS relative positioning
GPS relative positioning, also known as differential positioning, utilizes two GPS receivers that track the same satellites to calculate their relative coordinates One receiver acts as a reference or base station, remaining stationary at a location with known coordinates, while the other, referred to as the rover or remote receiver, has unknown coordinates and can be either stationary or mobile, depending on the GPS operation type.
To achieve accurate relative positioning, at least four common satellites are essential, although tracking additional satellites can enhance the precision of GPS solutions Both carrier-phase and pseudorange measurements are utilized in relative positioning, employing various techniques to optimize accuracy.
Figure 5.2 Principle of GPS relative positioning.
TLFeBOOK offers postprocessing or real-time solutions for relative positioning techniques, detailed in Sections 5.3 to 5.7 GPS relative positioning significantly enhances accuracy compared to autonomous positioning, achieving levels from subcentimeter to a few meters based on carrier-phase or pseudorange measurements This improved accuracy arises because multiple receivers tracking the same satellite share similar errors and biases Consequently, by calculating the differences in measurements between two closely positioned receivers, these common errors can be minimized, a method known as differential positioning.
Static GPS surveying
Static GPS surveying is a precise relative positioning method that utilizes carrier-phase measurements This technique involves two or more stationary receivers that simultaneously track the same satellites One of these receivers, known as the base receiver, is positioned over a point with known coordinates, such as a survey monument The other, referred to as the remote receiver, is placed over a point with unknown coordinates The base receiver can accommodate multiple remote receivers, provided that at least four common satellites are visible from both the base and remote locations.
This method involves simultaneous measurements from both base and remote receivers over a period that can range from 20 minutes to several hours, influenced by factors such as baseline length, satellite visibility, and geometry Typically, measurements are recorded every 15 or 20 seconds Once field measurements are completed, the data is downloaded to a PC for processing, with various options available based on user needs and baseline length, particularly when the baseline is short.
To achieve high-precision positioning over short baselines of 15 to 20 km, fixing ambiguity parameters is crucial For longer baselines, users should consider the ionosphere-free linear combination to mitigate ionospheric errors, as ambiguity parameters may not be reliably fixed For very long baselines exceeding 1,000 km, it is advisable to utilize scientific software like BERENSE from the University of Bern, as opposed to commercial options Additionally, employing precise ephemeris is essential due to significant orbital error effects at both ends of the baseline.
Static GPS surveying utilizing carrier-phase measurements is the most precise positioning method, primarily due to the substantial variation in satellite geometry during extended observation periods While both single- and dual-frequency receivers are applicable for static positioning, dual-frequency receivers are typically preferred, particularly for baselines longer than 20 km.
The expected accuracy from a geodetic quality receiver is typically 5 mm +
In static GPS surveying, a baseline of 10 kilometers typically yields an accuracy of 1.5 cm (rms), with "ppm" referring to parts per million and "rms" to root-mean-square Enhanced accuracy can be achieved by utilizing precise ephemeris data.
Fast (rapid) static
Rapid static surveying is a carrier-phase-based relative positioning technique akin to static GPS surveying, utilizing two or more receivers that track the same satellites In this method, the base receiver remains fixed over a known point throughout the observation session, while the rover receiver is stationary over an unknown point for a brief period before moving to another location to determine its coordinates.
[2] Similar to the static GPS surveying, the base receiver can support any number of rovers.
This method is effective for surveys involving multiple unknown points situated within approximately 15 km of a known reference point The process begins by establishing the base receiver at the known location.
Rover(moving)Figure 5.4 Fast (rapid) static GPS surveying.
When establishing the rover receiver at the initial unknown point, the base receiver remains fixed and continuously gathers data Meanwhile, the rover receiver collects data for a specified duration to ensure accurate measurements.
The time taken for the rover receiver to collect data ranges from 2 to 10 minutes, influenced by the distance to the base and satellite geometry After gathering the data, the user proceeds to the next point with unknown coordinates and repeats the process Notably, the rover receiver can be turned off while moving, and due to the brief occupation time, the recording interval is minimized.
After downloading field data from both receivers, PC software processes the information to determine positioning accuracy If sufficient common data is available, the software produces a fixed solution, indicating that ambiguity parameters are set at integer values, leading to centimeter-level accuracy Conversely, a float solution arises when data is insufficient, resulting in real-valued ambiguity parameters and lower accuracy, typically at the decimeter or submeter level While both single- and dual-frequency receivers are suitable for fast static surveying, dual-frequency receivers have a higher likelihood of achieving a fixed solution.
Stop-and-go GPS surveying
Stop-and-go surveying is a carrier-phase-based relative positioning technique that utilizes two or more GPS receivers tracking the same satellites This method involves a stationary base receiver positioned over a known point and one or more rover receivers that travel to unknown points, stopping briefly to collect GPS data Typically, data is recorded at a rate of 1 to 2 seconds for about 30 seconds at each stop The base receiver can support multiple rovers, making this technique ideal for surveying numerous unknown points within 10 to 15 km of a known location.
The survey begins with receiver initialization to establish the initial integer ambiguity parameters, which can be achieved through various methods detailed in the next chapter Successful initialization allows for instantaneous centimeter-level positioning accuracy, provided that both the base and rover receivers simultaneously track at least four common satellites If this condition is not met at any point during the survey, the initialization process must be repeated to maintain centimeter-level accuracy.
After initialization, the rover proceeds to the first unknown point and collects data for approximately 30 seconds before moving to the second point, all while remaining powered on It is crucial to maintain tracking of at least four satellites during movement; otherwise, the initialization process must be repeated, potentially requiring reoccupation of the previous point Manufacturers like Ashtech Inc recommend reoccupying the initial point at the end of the survey, which aids in achieving a fixed solution, especially when using processing software that supports both forward and backward processing functions Once data collection is complete, PC software is utilized for processing, with certain packages offering these functions to enhance the accuracy of the results.
Rover(moving)Figure 5.5 Stop-and-go GPS surveying.
TLFeBOOK or centimeter-level accuracy Both single- and dual-frequency receivers may use the stop-and-go surveying method.
Kinematic GPS surveying is a specialized form of stop-and-go surveying that operates on the same principles but allows for continuous movement without halting at unknown points While both methods aim to determine positional accuracy, stop-and-go surveying typically achieves higher precision as it averages out errors when the receiver pauses at these unknown locations.
RTK GPS
RTK surveying is a carrier phase-based relative positioning technique that utilizes two or more receivers tracking the same satellites simultaneously This method is ideal for surveys involving numerous unknown points near a known location, typically within 10-15 km It is particularly effective when real-time coordinate data is needed and when the line of sight for signal propagation is relatively unobstructed.
TLFeBOOK of its ease of use as well as its capability to determine the coordinates in real time, this method is the preferred method by many users.
In this method, a stationary base receiver, connected to a radio transmitter, sends data to a rover receiver typically carried in a backpack This setup requires a high data rate of up to 1 Hz, similar to conventional kinematic GPS The base receiver's measurements and coordinates are transmitted via a radio link, while the rover receiver's built-in software processes the GPS data from both receivers to determine the rover's coordinates.
The initial ambiguity parameters are quickly established through on-the-fly (OTF) ambiguity resolution, allowing the receiver to display rover coordinates in real-time without the need for postprocessing This method achieves positioning accuracy of approximately 2 to 5 cm (rms), which can be enhanced by averaging the position over a brief period, such as 30 seconds The rover coordinates can be stored and later downloaded into CAD software for detailed analysis, primarily utilizing dual-frequency receivers However, the positioning accuracy of the RTK method is slightly lower than that of conventional kinematic GPS due to data latency, which arises from the time delay in processing and transmitting base receiver data to the rover.
[7] To match the time tag of the rover data, the base data must be extrapo- lated, which degrades the positioning accuracy.
Real-time differential GPS
Real-time differential GPS (DGPS) is a positioning method that utilizes multiple receivers to track the same satellites simultaneously, achieving meter-level accuracy in real-time.
TLFeBOOK provides a reliable method for GPS measurements, leveraging the principle that GPS errors in measured pseudoranges remain consistent between both the base station and the rover This method is effective as long as the distance between them is within a few hundred kilometers.
The base receiver remains stationary at a known location and utilizes built-in software to calculate the ranges to visible satellites using their precise coordinates and the navigation message This software determines pseudorange errors by comparing computed ranges with measured code pseudoranges, generating DGPS corrections These corrections are transmitted to the rover in a standard format known as RTCM The rover then applies these DGPS corrections to adjust its measured pseudoranges, which are ultimately used to compute accurate rover coordinates.
The accuracy of this method ranges from submeter precision to approximately 5 meters, influenced by factors such as the distance between the base and rover, the transmission rate of RTCM DGPS corrections, and the capabilities of C/A-code receivers Shorter base-rover separations yield higher accuracy.
Figure 5.7 Real-time differential GPS operation.
The TLFeBOOK system offers a high transmission rate and carrier-smoothed C/A-code ranges With the end of selective availability, data rates can be reduced to 10 seconds or less without compromising accuracy Further accuracy enhancements are possible if receivers can store raw pseudorange measurements for later postprocessing Real-time DGPS is increasingly utilized, with various governmental agencies and private companies providing RTCM DGPS corrections, often at no cost or for a fee Additional details about these services will be discussed in Chapter 7.
Real time versus postprocessing
Real-time refers to the immediate acquisition of results, whereas postprocessing involves collecting measurements in the field and analyzing them later for outcomes Both methods offer distinct advantages and disadvantages.
The primary benefit of real-time mode in RTK surveying is the immediate availability of results and accuracy measures in the field, which enhances productivity by collecting only the necessary GPS data for a fixed solution This eliminates the need for post-processing software training, as the built-in software automatically processes the GPS data on-site, saving users valuable time typically spent on data processing.
Postprocessing mode offers several advantages, primarily resulting in more accurate outcomes due to enhanced flexibility in editing and cleaning GPS data This method eliminates accuracy degradation associated with data latency and circumvents communication link issues, such as the need for a clear line-of-sight Additionally, it allows for the correction of input parameter errors, such as base station coordinates or antenna height, which can otherwise lead to inaccuracies in computed rover coordinates.
TLFeBOOK postprocessing mode, while they cannot be completely corrected in the real-time mode.
Communication (radio) link
RTK and real-time DGPS operations rely on a communication link to transmit data from the base receiver to the rover receiver, with RTK data typically sent at a baud rate of 9,600 and DGPS corrections at 200 Kbps Various radio links operating across different parts of the electromagnetic spectrum support these operations, primarily utilizing low/medium frequency (LF/MF) bands (30 kHz to 3 MHz) and very high/ultrahigh frequency (VHF/UHF) bands (30 MHz to 3 GHz) Many GPS users prefer dedicated radio links for transmitting base station information.
Dedicated ground-based GPS radio links primarily utilize the VHF/UHF band, offering line-of-sight coverage and the ability to penetrate buildings and obstructions The RFM96W from Pacific Crest Corporation is a notable example, available in various models requiring a license to operate Recently introduced is the Position Data Link (PDL), which supports a baud rate of 19,200 and features low power consumption and an improved user interface Additionally, a license-free spread-spectrum radio transceiver operates in the 902-928 MHz range, providing coverage of 1-5 km in urban areas and 3-15 km in rural settings Furthermore, some GPS manufacturers are now leveraging cellular technology, specifically digital Personal Communication Services (PCS), as an alternative communication link In the near future, widespread use of third-generation (3G) wideband digital networks is anticipated, as this technology employs global standards to reduce service costs and allows devices to remain constantly connected for efficient data transmission.
Obstructions like buildings and terrain can significantly attenuate transmitted signals, resulting in limited coverage Additionally, factors such as ground reflection and the transmitting antenna contribute to signal attenuation To enhance radio link coverage, users can take specific measures.
Figure 5.8 Examples of radio modems (Courtesy of Magellan Corporation.)
Figure 5.9 Use of repeaters to increase radio coverage.
To enhance radio transmission, users can utilize a power amplifier, high-quality coaxial cables, or elevate the height of their transmitting and receiving antennas However, caution is advised when using a power amplifier, as signal overload may occur if the transmitting and receiving radios are positioned too closely together.
A user may also increase the signal coverage by using a repeater station.
In this case, it might be better to use a unidirectional antenna, such as a Yagi, at the base station and an omnidirectional antenna at the repeater sta- tion (see Figure 5.9) [8].
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[3] Leick, A., GPS Satellite Surveying, 2nd ed., New York: Wiley, 1995.
[4] Levy, L J., The Kalman Filter: Navigations Integration Workhorse, GPS World, Vol 8, No 9, September 1997, pp 6571.
[5] Langley, R B., The GPS Observables, GPS World, Vol 4, No 4, April
[6] Langley, R B., RTK GPS, GPS World, Vol 9, No 9, September 1998, pp 7076.
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