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With origin dating back to the mid-1990s, [[Real Time Kinematics]] (RTK) is a [[Differential GNSS|differential GNSS]] technique which provides high positioning performance in the vicinity of a base station. The technique is based on the use of carrier measurements and the transmission of corrections from the base station, whose location is well known, to the rover, so that the main errors that drive the stand-alone positioning cancel out. A RTK base station covers a service area spreading about 10 or 20 kilometres, and a real time communication channel is needed connecting base and rover. RTK, which achieves performances in the range of a few centimetres, is a technique commonly used in surveying applications.<ref name="RTKIAG">[http://www.wasoft.de/e/iagwg451/ International Association of Geodesy (IAG) Working Group 4.5.1: Network RTK ] </ref><ref name="RTK_WIKI">[http://en.wikipedia.org/wiki/Real_Time_Kinematic RTK in Wikipedia]</ref><ref name="RTKWPNC06">[http://www.wpnc.net/fileadmin/WPNC06/Proceedings/34_Precise_Positioning_in_Real-Time_using_Navigation_Satellites_and.pdf Remote Sensing 2009, A. Rietdorf et al., ''Precise Positioning in Real-Time using Navigation Satellites and Telecommunication'', Proceedings of the 3rd Workshop on Positioning, Navigation and Communication (WPNC’06) ]</ref>
Real Time Kinematic (RTK) satellite navigation is a DGNSS technique used in land survey and in hydrographic survey based on the use of carrier phase measurements of the GPS, GLONASS and/or Galileo signals where a single reference station provides the real-time corrections, providing up to centimeter-level accuracy. When referring to GPS in particular, the system is also commonly referred to as Carrier-Phase Enhancement, CPGPS.<ref name="RTK_WIKI"/>


==RTK Technique==
==RTK Technique==
From an architectural point of view, RTK consists of a base station, one or several rover users, and a communication channel with which the base broadcasts information to the users at real time.


The classical GNSS receivers compare a C/A code pseudoranges signal being sent from the satellite with an internally generated copy of the same signal. Since the signal from the satellite takes time to reach the receiver, the two signals do not "line up" properly; the satellite's copy is delayed in relation to the local copy. By progressively delaying the local copy more and more, the two signals will eventually line up properly. That delay is the time needed for the signal to reach the receiver, and from this the distance from the satellite can be calculated.<ref name="RTK_WIKI"/>
The technique is based on the following high-level principles:
*In the neighbourhood of a clean-sky location, the main errors in the GNSS signal processing are constant, and hence they cancel out when differential processing is used. This includes the error in the satellite clock bias, the satellite orbital error, the ionospheric delay and the tropospheric delay. The main errors left without correction are multipath, interference and receiver thermal noise. Of the errors listed above, the only one which is truly constant with respect to the user location is the satellite clock bias; the rest will show a given dependency with the location as the rover moves away from the base station, being the tropospheric error the first to be fully de-correlated in a few kilometres from the base.
*The noise of carrier measurements is much smaller than the one of the pseudo-code measurements. The typical error of code pseudorange measurements is around 1 m, to compare with 5 mm for carrier phase measurements. However, the processing of carrier measurements is subject to the so-called carrier phase ambiguity, an unknown integer number of times the carrier wave length, that needs to be fixed in order to rebuild full range measurements from carrier ones.
*The phase ambiguities can be fixed using differential measurements between two reference stations. There are different techniques available to fix them, some based on single frequency measurements with long convergence times, other taking benefit of dual frequency observables with shorter convergence. In general, the techniques either depend on a high precision knowledge of the ionosphere, or assume that the two stations are close enough so that the ionospheric differential delay is negligible when compared with the wave-length of the carriers, around 20 cm. The latter is the approached followed in RTK, limiting the service area to 10 or 20 km; the former is used in [[Wide Area RTK (WARTK)|WARTK]] to cover big service areas with base stations separated around hundreds of kilometres away. The RTK approach needs continuity in the tracked measurements to avoid re-initialization of the phase-ambiguity filters; this is a severe limitation in urban environments due to the big number of obstructions.


The accuracy of the resulting range measurement is generally a function of the ability of the receiver's electronics to accurately compare the two signals. In general receivers are able to align the signals to about 1% of one bit-width. For instance, the coarse-acquisition (C/A) code sent on the GPS system sends a bit every 0.98 microsecond, so a receiver is accurate to 0.01 microsecond, or about 3 metres in terms of distance. The military-only P(Y) signal sent by the same satellites is clocked ten times as fast, so with similar techniques the receiver will be accurate to about 30 cm. Other effects introduce errors much greater than this, and accuracy based on an uncorrected C/A signal is generally about 15 m.<ref name="RTK_WIKI"/>
The base station broadcasts its well-known location together with the code and carrier measurements at frequencies L1 and L2 for all in-view satellites. With this information, the rover equipment is able to fix the phase ambiguities and determine its location relative to the base with high precision. By adding up the location of the base, the rover is positioned in a global coordinate framework.


RTK follows the same general concept, but uses the satellite's carrier phase as its signal, not the messages contained within. The improvement possible using this signal is potentially very high if one continues to assume a 1% accuracy in locking. For instance, the GPS coarse-acquisition (C/A) code broadcast in the L1 signal changes phase at 1.023 MHz, but the L1 carrier itself is 1575.42 MHz, over a thousand times as fast. This frequency corresponds to a wavelength of 19 cm for the L1 signal. Thus a ±1% error in L1 carrier phase measurement corresponds to a ±1.9mm error in baseline estimation.<ref name="RTK_WIKI">[http://en.wikipedia.org/wiki/Real_Time_Kinematic RTK in Wikipedia]</ref>
The RTK technique can be used for distances of up to 10 or 20 kilometres,<ref name="RTKIAG"/><ref name="RTKWPNC06"/> yielding accuracies of a few centimetres in the rover position, to be compared with 1 m that is achieved with code-based [[Differential GNSS|differential GPS]]. Because of its high precision in controlled environments, RTK is extensively used in surveying applications.


==RTK Algorithm==
==RTK Algorithm==


The difficulty in making an RTK system is properly aligning the signals.<ref name="RTK_WIKI"/> As stated in [http://www.septentrio.com/ Septentrio] homepage, ''the carrier phase measurements are extremely precise (down to the fractions of millimeter), but they contain an unknown integer initialization constant, the so-called “phase ambiguity”. Therefore RTK positioning has to resolve integer ambiguities to achieve the high level of precision.''<ref>[http://www.septentrio.com/support/about-gnss/dgps-vs-rtk DGPS vs RTK, Septentrio]</ref>
As stated in the previous section, one of the main problems in the RTK technique is fixing the phase ambiguities.


The RTK Algorithm is based on double differenced observables that can eliminate selective availability effects as well as other biases. The highlights of the algorithm are described next. At a given epoch, and for a given satellite, the simplified carrier phase observation equation is the following:
The RTK Algorithm is based on double differenced observables that can eliminate selective availability effects as well as other biases. The highlights of the algorithm are described next. At a given epoch, and for a given satellite, the simplified carrier phase observation equation is the following:
Line 54: Line 57:




In the above equation receiver and satellite clock offsets and hardware biases cancel, since double differencing is effectively differencing between satellites and between receivers. The single difference ambiguities difference <math>N_a^{12}-N_b^{12}</math> is commonly parameterized as a new ambiguity parameter <math>N_a^{12}</math>. The advantage of double differencing is that the new ambiguity parameter <math>N_a^{12}</math> is an integer because the non-integer terms in the GPS carrier phase observation, due to clock and hardware delays in the transmitter and receiver, are eliminated.
In the above equation receiver and satellite clock offsets and hardware biases cancel out. The single difference ambiguities difference <math>N_a^{12}-N_b^{12}</math> is commonly parameterized as a new ambiguity parameter <math>N_{ab}^{12}</math>. The advantage of double differencing is that the new ambiguity parameter <math>N_{ab}^{12}</math> is an integer because the non-integer terms in the GPS carrier phase observation, due to clock and hardware delays in the transmitter and receiver, are eliminated.  
 
Among the different challenges to achieve high-level precision, i.e. cm-level positioning, there is the ''Integer Ambiguity Resolution'', as the method used to solve the unknown integer ambiguities of the double-differenced carrier phase observables, that is the key in RTK algorithm.


Although it would be possible to estimate the double difference ambiguity using a float approach instead of an integer one, this would lead to dm-level accuracy instead of cm-level. Hence, standard RTK fixes the ambiguities to integer figures.


===Ambiguity Resolution===
===Ambiguity Resolution===
As stated in the section above, one of the keys to obtain the best accuracy from RTK is to fix the carrier phase ambiguities to integer numbers. Normally, this is done in three steps:<ref name="GPS_WORLD_LAMBDA"> Bernd Eissfeller, Thomas Pany, Günter Heinrichs, Christian Tiberius, ''Real-Time Kinematic in the Light of GPS Modernization and Galileo'', Oct. 1, 2002, GPS Word</ref>
* The ambiguities are first fixed to float numbers using standard least-square techniques.
* The set of integer ambiguities is set to the one that optimizes the residuals in the surroundings of the float solution.
* The carrier measurements are corrected with the integer ambiguities and they are used to obtain the relative position of the rover to the base station.


As it was said above the ambiguity resolution is the key of positioning precision in RTK Technique. It can be divided in mainly three steps, as shown in the figure.
Of these three steps, the second one is quite complex, because the float ambiguity covariance ellipsoid in the measurement space is extremely elongated. As a consequence, the brute-force search process is inefficient, normally beyond the computational capabilities of the rover equipment. Several techniques have been developed to deal with this problem; please consult the [[Carrier Phase Ambiguity Fixing]] article for more information.
[[File:LambdaMethod.PNG|700px|center]]
 
The first step is an "ordinary" least-squares, that can be done either in a batch implementation or a Kalman filter. In this process the integer nature of the ambiguities is not considered, and therefore, the solution of the process are real-valued estimates; the so-called 'float' solution, that includes baseline coordinates, differential atmospheric delays and carrier phase ambiguities.<ref name="GPS_WORLD_LAMBDA">[http://chromatographyonline.findanalytichem.com/lcgc/article/articleDetail.jsp?id=584852&sk=&date=&pageID=3 Bernd Eissfeller, Thomas Pany, Günter Heinrichs, Christian Tiberius, ''Real-Time Kinematic in the Light of GPS Modernization and Galileo'', Oct. 1, 2002, GPS Word]</ref>
 
The second step is the LAMBDA method itself <ref>[http://enterprise.lr.tudelft.nl/publications/files/PT_BEIJING93.PDF ''Least-Squares Estimation of the Integer GPS Ambiguities''] by P. Teunissen, 1993.</ref><ref>[http://enterprise.lr.tudelft.nl/publications/files/Teunissen_JoG_1995_V70N1-2.pdf ''The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation''] by P. Teunissen, 1995.</ref><ref>[http://enterprise.lr.tudelft.nl/publications/files/lgr12.pdf ''The LAMBDA method for integer ambiguity estimation: implementation aspects''] by P. de Jonge and C. Tiberius, 1996.</ref> , developed by [http://lr.tudelft.nl/index.php?id=26369&L=1 Delft University of Technology]. It consists mainly in the decorrelation of the ambiguities, taking into account their integer nature. This decorrelation gives a fast and efficiently integer least-squares computation.<ref name="TU_Delf_Lambda">[http://lr.tudelft.nl/index.php?id=26369&L=1  Lambda Method homepage by Delft University of Technology.]</ref>
 
Finally, in the last step, the solution of the remaining parameters, i.e. the baseline coordinates and additional parameters such as atmospheric delays, is computed keeping the ambiguities fixed to the integer values obtained in second step. This final solution is known as the 'fixed' solution and the obtained values generally have centimeter level precision or less.<ref name="GPS_WORLD_LAMBDA"/> <ref name="TU_Delf_Lambda"/>
 
As it was stated in the article ''Real-Time Kinematic in the Light of GPS Modernization and Galileo'' <ref name="GPS_WORLD_LAMBDA"/>: ''The LAMBDA method has been demonstrated to be optimal. The integer least-squares estimator is best in the sense of maximizing the probability of correct integer estimation, i.e. in maximizing the ambiguity success-rate.'' 
 
The LAMBDA method can be used as a separate, generally applicable module for integer estimation. The TU Delft University can provide Matlab and Fortran 77 source code of the subroutines for the LAMBDA method <ref name="TU_Delf_Lambda"/>. The subroutine is flexible in terms of output and number of candidates; it does not matter the number of GNSS frequencies or the absence of pseudorange code measurements on a particular frequency or incidentally missing measurements for some of the satellites.<ref name="GPS_WORLD_LAMBDA"/>
 
==RTK on-going Research ==
 
Once the ambiguity fixing is solved by LAMBDA Method explained above, the problem comes when baseline distance is larger than a few tens of kms. In this case, the compensation of atmospheric effects is not complete and the ambiguity fixing is less reliable due to error decorrelation, which increases proportionately with baseline distance. There exist the so-called Network RTK techniques, where information from a network of base stations is used to better predict the variations of ionosphere delays and orbit errors.
 
As stated in the article ''Introduction to Network RTK'':<ref name=NET_RTK>[http://www.wasoft.de/e/iagwg451/ ''Introduction to Network RTK '', International Association of Geodesy (IAG) Working Group 4.5.1: Network RTK ] </ref>
 
''In recent years first-generation Network RTK services have been developed and they have been established in several countries. These services have proven the practical feasibility of the Network RTK technique and they gained wide acceptance by the user community. Network RTK is emerging as the leading method for precise satellite-based positioning. Based on these experiences the development of second-generation Network RTK systems is under way which will make use of improved algorithms and new transmission standards. A wide range of ongoing and anticipated research is related to Network RTK. Research topics are:''
*''hierarchical network design: the contribution of global and regional real-time networks to small-scale Network RTK services''
*''content and format of Network RTK correction messages: Virtual Reference Station (VRS) concept versus broadcast Network RTK concepts''
*''substitution of observation corrections (RTK) by state space information (PPP – Precise Point Positioning)''
*''improvement of algorithms for the prediction of atmospheric corrections''
*''mitigation of station-dependent errors (mainly multipath) at the reference stations''
*''development of quality indicators for network RTK corrections either from the correction computation itself or based on the observations of additional monitor sites''
*''new data communication systems (e.g. internet-based, or Digital Audio Broadcast)''
*''inclusion of the future third GPS frequency and the future Galileo system''
*''extraction and processing of Network RTK by-products: tropospheric and ionospheric delays, local crustal deformations.''
 
==Credits==
Edited by GMV. The text in the introduction and the section ''RTK Technique'' is  mostly taken from Wikipedia with minor adaptation,<ref name="RTK_WIKI"/> provided under [http://creativecommons.org/licenses/by-sa/3.0/ Creative Commons Attribution-ShareAlike License].
 
The section ''Ambiguity Resolution'' has been taken from the article ''Real-Time Kinematic in the Light of GPS Modernization and Galileo''<ref name="GPS_WORLD_LAMBDA"/>
 
The section ''RTK on-going Research'' has been taken from the article ''Introduction to Network RTK''.<ref name=NET_RTK/>


==Notes==
==Notes==

Latest revision as of 14:30, 26 July 2018


FundamentalsFundamentals
Title RTK Fundamentals
Edited by GMV
Level Basic
Year of Publication 2011
Logo GMV.png

With origin dating back to the mid-1990s, Real Time Kinematics (RTK) is a differential GNSS technique which provides high positioning performance in the vicinity of a base station. The technique is based on the use of carrier measurements and the transmission of corrections from the base station, whose location is well known, to the rover, so that the main errors that drive the stand-alone positioning cancel out. A RTK base station covers a service area spreading about 10 or 20 kilometres, and a real time communication channel is needed connecting base and rover. RTK, which achieves performances in the range of a few centimetres, is a technique commonly used in surveying applications.[1][2][3]

RTK Technique

From an architectural point of view, RTK consists of a base station, one or several rover users, and a communication channel with which the base broadcasts information to the users at real time.

The technique is based on the following high-level principles:

  • In the neighbourhood of a clean-sky location, the main errors in the GNSS signal processing are constant, and hence they cancel out when differential processing is used. This includes the error in the satellite clock bias, the satellite orbital error, the ionospheric delay and the tropospheric delay. The main errors left without correction are multipath, interference and receiver thermal noise. Of the errors listed above, the only one which is truly constant with respect to the user location is the satellite clock bias; the rest will show a given dependency with the location as the rover moves away from the base station, being the tropospheric error the first to be fully de-correlated in a few kilometres from the base.
  • The noise of carrier measurements is much smaller than the one of the pseudo-code measurements. The typical error of code pseudorange measurements is around 1 m, to compare with 5 mm for carrier phase measurements. However, the processing of carrier measurements is subject to the so-called carrier phase ambiguity, an unknown integer number of times the carrier wave length, that needs to be fixed in order to rebuild full range measurements from carrier ones.
  • The phase ambiguities can be fixed using differential measurements between two reference stations. There are different techniques available to fix them, some based on single frequency measurements with long convergence times, other taking benefit of dual frequency observables with shorter convergence. In general, the techniques either depend on a high precision knowledge of the ionosphere, or assume that the two stations are close enough so that the ionospheric differential delay is negligible when compared with the wave-length of the carriers, around 20 cm. The latter is the approached followed in RTK, limiting the service area to 10 or 20 km; the former is used in WARTK to cover big service areas with base stations separated around hundreds of kilometres away. The RTK approach needs continuity in the tracked measurements to avoid re-initialization of the phase-ambiguity filters; this is a severe limitation in urban environments due to the big number of obstructions.

The base station broadcasts its well-known location together with the code and carrier measurements at frequencies L1 and L2 for all in-view satellites. With this information, the rover equipment is able to fix the phase ambiguities and determine its location relative to the base with high precision. By adding up the location of the base, the rover is positioned in a global coordinate framework.

The RTK technique can be used for distances of up to 10 or 20 kilometres,[1][3] yielding accuracies of a few centimetres in the rover position, to be compared with 1 m that is achieved with code-based differential GPS. Because of its high precision in controlled environments, RTK is extensively used in surveying applications.

RTK Algorithm

As stated in the previous section, one of the main problems in the RTK technique is fixing the phase ambiguities.

The RTK Algorithm is based on double differenced observables that can eliminate selective availability effects as well as other biases. The highlights of the algorithm are described next. At a given epoch, and for a given satellite, the simplified carrier phase observation equation is the following:

[math]\displaystyle{ \qquad \phi =\rho-I+Tr+c(b_{Rx}-b_{Sat} )+〖N\lambda+\varepsilon〗_\phi \qquad \mbox{(1)} }[/math]

Where:

[math]\displaystyle{ I }[/math] is the signal path delay due to the ionosphere;

[math]\displaystyle{ Tr }[/math] is the signal path delay due to the troposphere;

[math]\displaystyle{ b_{Rx} }[/math] is the receiver clock offset from the reference (GPS) time;

[math]\displaystyle{ b_{Sat} }[/math] is the satellite clock offset from the reference (GPS) time;

[math]\displaystyle{ c }[/math] is the vacuum speed of light;

[math]\displaystyle{ \lambda }[/math] is the carrier nominal wavelength;

[math]\displaystyle{ N }[/math] is the ambiguity of the carrier-phase (integer number);

[math]\displaystyle{ \varepsilon_\phi }[/math] are the measurement noise components, including multipath and other effects;

[math]\displaystyle{ \rho }[/math] is the geometrical range between the satellite and the receiver, computed as a function of the satellite [math]\displaystyle{ (x_{Sat}, y_{Sat},z_{Sat}) }[/math] and receiver [math]\displaystyle{ (x_{Rx}, y_{Rx},z_{Rx}) }[/math] coordinates as:

[math]\displaystyle{ \qquad \rho=\sqrt{〖(x_{Sat}-x_{Rx})〗^2+〖(y_{Sat}-y_{Rx})〗^2+〖(z_{Sat}-z_{Rx})〗^2 } \qquad \mbox{(2)} }[/math].

For two receivers a and b making simultaneous measurements at the same nominal time to satellites 1 and 2, the double difference observable is:


[math]\displaystyle{ \qquad \phi_a^{12} - \phi_b^{12} =\rho_a^{12}-\rho_b^{12}-I_a^{12}+I_b^{12}+Tr_a^{12}-Tr_b^{12}+\lambda(N_a^{12}-N_b^{12})+\varepsilon_a^{12}- \varepsilon_b^{12} \qquad \mbox{(3)} }[/math]


In the above equation receiver and satellite clock offsets and hardware biases cancel out. The single difference ambiguities difference [math]\displaystyle{ N_a^{12}-N_b^{12} }[/math] is commonly parameterized as a new ambiguity parameter [math]\displaystyle{ N_{ab}^{12} }[/math]. The advantage of double differencing is that the new ambiguity parameter [math]\displaystyle{ N_{ab}^{12} }[/math] is an integer because the non-integer terms in the GPS carrier phase observation, due to clock and hardware delays in the transmitter and receiver, are eliminated.

Although it would be possible to estimate the double difference ambiguity using a float approach instead of an integer one, this would lead to dm-level accuracy instead of cm-level. Hence, standard RTK fixes the ambiguities to integer figures.

Ambiguity Resolution

As stated in the section above, one of the keys to obtain the best accuracy from RTK is to fix the carrier phase ambiguities to integer numbers. Normally, this is done in three steps:[4]

  • The ambiguities are first fixed to float numbers using standard least-square techniques.
  • The set of integer ambiguities is set to the one that optimizes the residuals in the surroundings of the float solution.
  • The carrier measurements are corrected with the integer ambiguities and they are used to obtain the relative position of the rover to the base station.

Of these three steps, the second one is quite complex, because the float ambiguity covariance ellipsoid in the measurement space is extremely elongated. As a consequence, the brute-force search process is inefficient, normally beyond the computational capabilities of the rover equipment. Several techniques have been developed to deal with this problem; please consult the Carrier Phase Ambiguity Fixing article for more information.

Notes


References