RTK Fundamentals

Fundamentals
Title	RTK Fundamentals
Edited by	GMV
Level	Basic
Year of Publication	2011

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.

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 truely constant with respect to the user location is the satellite clock bias; the rest will show a given dependency with the location as one moves away from the base station, being the tropospheric error the first to be fully decorrelated 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 kilometers 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, 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 inthe previous section, ofe 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 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.

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.

The second step is the LAMBDA method itself , developed by 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.

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.

As it was stated in the article Real-Time Kinematic in the Light of GPS Modernization and Galileo : 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 . 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.

Network RTK

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. To solve this issue, information from a network of base stations is used, this is known as Network RTK techniques.

Network RTK has been established in several countries during the last years. The first-generation of Network RTK systems is consolidated, and the objectives of the International Association of Geodesy Commission 4: Positioning & Applications to develop the next generation RTK are mainly:

• investigation on important technical issues for next generation RTK system development: e.g. the improvement of algorithms for the prediction of atmospheric corrections or the mitigation of station-dependent errors (mainly multipath) at the reference stations
• development of data standards and operational procedures, including the communication protocols and message formats.
• establishment of strong collaborations with other international organizations, such as IGS, and also with the industry sector.

Credits

The section Ambiguity Resolution has been taken from the article Real-Time Kinematic in the Light of GPS Modernization and Galileo and TU Delft University web-page dedicated to the LAMBDA Method .

The section RTK on-going Research has been taken from the article Introduction to Network RTK and the International Association of Geodesy Commission 4 (Positioning & Applications) web-page.