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July 11, 2011

What is a virtual reference station and how does it work?

Q: What is a virtual reference station and how does it work?

A: To reach centimeter-level — or even better — accuracy of positioning typically requires use of precise dual-frequency carrier phase observations. Furthermore, these observations are usually processed using a differential GNSS (DGNSS) algorithm, such as real time kinematic (RTK) or post-processing (PP). Regardless of the specific differential algorithm, however, implicit in the process is an assumption that the quality of the reference station data is consistent with the desired level of positioning accuracy.

The virtual reference station (VRS) concept can help to satisfy this requirement using a network of reference stations. As a quick review, a typical DGNSS setup consists of a single reference station from which the raw data (or corrections) are sent to the rover receiver (i.e., the user). The user then forms the carrier phase differences (or corrects their raw data) and performs the data processing using the differential corrections.

What is a virtual reference station and how does it work?

FIGURE 2: The Automated GNSS Network for Switzerland (AGNES) as of 2011

In contrast, GNSS network architectures often make use of multiple reference stations. This approach allows a more precise modeling of distance-dependent systematic errors principally caused by ionospheric and tropospheric refractions, and satellite orbit errors. More specifically, a GNSS network decreases the dependence of the error budget on the distance of nearest antenna.

The general concept of network-based processing is shown in Figure 1 (above). The network of receivers is linked to a computation center, and each station contributes its raw data to help create network-wide models of the distance-dependent errors. The computation of errors based on the full network’s carrier phase measurements involves, first of all, the resolution of carrier phase ambiguities and requires knowledge of the reference station positions. (The latter is usually determined as part of the network setup.)

At the same time the rover calculates its approximate position and transmits this information to the computation server, for example, via GSM or GPRS using a standard National Marine Electronics Association (NMEA) format. The computation center generates in real time a virtual reference station at or near the initial rover position. This is done by geometrically translating the pseudorange and carrier phase data from the closest reference station to the virtual location and then adding the interpolated errors from the network error models.

This generated VRS data is then sent to the user through a wireless connection, often using the Networked Transport of RTCM via Internet Protocol (NTRIP). Finally, just as if the VRS data had come from a physical reference station, the rover receiver uses standard single-baseline algorithms to determine the coordinates of the user’s receiver, in near-real-time kinematic or post-processed modes.

The main purpose of a VRS station is to reduce the baseline distance between the rover and the reference station in order to efficiently remove spatially correlated errors using differential processing, and to incorporate error corrections obtained from the reference stations network.

To this end, the position of the VRS plays a critical role. In particular, because the user receiver cannot, by design, distinguish a real reference station and a VRS, the distance of the VRS from the user must be commensurate with the level of errors present in the VRS data. This is what allows the receiver to use its standard data processing algorithms, which vary as a function of the baseline length (i.e., distance) to the reference station.

To illustrate, let’s consider a simple example. Assume the user receiver performs L1-ony processing for baselines up to, say, 8 kilometers and wide-lane dual-frequency (L1/L2) combinations for longer baselines. (This is somewhat simplistic, but it serves our purpose here.)

Now, imagine if the errors in the VRS data were similar to a 20-kilometer baseline, but the VRS position was situated only 2 kilometers from the user. In this case, the user’s receiver would attempt to use L1-only processing, but the level of errors in the data would almost certainly not allow reliable results using this approach.

From this example we can see that the VRS concept basically needs the resource of a physical GNSS network surrounding the measurement area of the rover, with a minimum of three reference stations to enable the modeling of errors. However, the estimation accuracy increases as more physical reference stations are added to the network, especially as the number of stations exceeds five, at which point the increased redundancy and improved network geometry provide more accurate error modeling.

To conduct a survey employing a VRS network, the physical stations themselves must be installed over stable sites, preferably distributed homogeneously over the operational area. If possible, the antennas must be fixed in bedrock to ensure long term stability of the receiver’s position.

As an example, Figure 2 (above, right) shows the Swiss Automated GNSS Network for Switzerland (AGNES) established by the Federal Office of Topography (swisstopo), which contains 30 stations with dual-frequency GPS/GLONASS receivers covering the entire 41,290-squarekilometer surface area of Switzerland. AGNES incorporates an additional 19 foreign stations with the data from all 49 sites processed together to generate VRS solutions for the whole of Switzerland. At any location an average length of 30 kilometers to the AGNES reference station is guaranteed across the country.

A difficulty in Switzerland is the height variation from the lowest point at 193 meters (above mean sea level) in Lake Maggiore to 4,634 meters on the peak of Monte Rosa. To best model the atmospheric errors, the stations should have similar altitudes because of the strong dependence of the troposphere error on receiver height. To this end, typically the Jungfrauhoch (JUJO) station is not integrated into the error modelling, because its elevation of 3,582 meters is too high in comparison with the other stations in the surrounding area.

Although the VRS approach generally provides an overall improvement relative to single reference station systems, it poses some challenges. First is a dependence of the VRS service on a communication system, such as the mobile phone network in the case of Switzerland (which is quite reliable).

Moreover this technique requires a bi-directional communication link between the receiver and the computation center, because the rover has to send information about its current position and has to receive the VRS data. This telecommunication link must provide high bandwidth communication between all the elements of system: the reference stations, the master control center, and the user receiver.

A second challenge is that errors can be generated by different tropospheric and stratospheric models applied between the computation center and the rover. Because the initial position provided by the rover to generate the VRS data is not usually precise, especially in height, the troposphere error computed by the network will not be perfect, with every 10 meters of initial height error yielding up to 0.2 millimeters of error from the troposphere model.

Fortunately, obtaining a 10-meter height error is quite reasonable in most applications involving carrier phase data, meaning the resulting troposphere modeling errors will usually be small.

Using the VRS technique, highly improved RTK positioning can be performed inside the network area. The precision of RTK positioning using VRS reaches two centimeters in the horizontal plane and four centimeters in the vertical direction (2σ).

The VRS concept allows a less dense antenna network without accuracy degradation because the multiple reference station network better models the spatially correlated GNSS errors over longer baselines. As a result the maximum distance between the rover and the nearest reference station can be extended in comparison with the typical 10 ~15 kilometers without accuracy degradation of the single reference station case.

Another benefit of a VRS is that the reference data are free of site-specific errors such as multipath, because the VRS computation assumes that the virtual station is situated at an ideal location. On the rover side the principal gains from the VRS principle are the use of common double-difference algorithms and the simplicity of computation, because the user does not need to perform any complex error modelling because this is being done already within the network.

Additional Resources
[1] Herbert L., and U. Vollath and X. Chen, “Virtual Reference Stations versus Broadcast Solutions in Network RTK –Advantages and Limitations,” paper presented at GNSS 2003 conference, April 2003, Graz, Austria (available here last accessed May 28, 2011)
[2] Hu, G. R., and H. S. Khoo, P. C. Goh, and C. I. Law, “Development and Assessment of GPS Virtual Reference Stations for RTK Positioning,” Journal of Geodesy, Vol. 77, p.292-302, 2003
[3] Retscher, G., “Accuracy Performance of Virtual Reference Station (VRS) Networks,” Journal of Global Positioning Systems, Vol.1, No.1:40-47, 2002 (available here last accessed May 22, 2011)
[4] Van Cranenbroeck J., and V. Lui and C. Rizos, “Ultimate Advance in GNSS RTK Monitoring Accuracy,” presented at the 7th FIG (International Federation of Surveyors) Regional Conference, Spatial Data Serving People: Land Governance and the Environment – Building the Capacity, 19-22 October 2009, Hanoi, Vietnam, (available here last accessed May 28, 2011)

Editor’s Note: VRS is a trademarked term of Trimble Navigation.

By Inside GNSS
May 19, 2011

How do you compute relative position using GNSS?

Figure 1

Q: How do you compute relative positions with GNSS?

A: GNSS is well recognized as an excellent means of computing position, but many people think that GPS only provides absolute position information. However, GNSS can also provide relative position information. In this column, we will look at some of the details of how this is done.

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By Inside GNSS
March 14, 2011

GNSS Receiver Clocks

Q: Does the magnitude of the GNSS receiver clock offset matter?

A: It is well known that GNSS receiver clocks drift relative to the stable atomic time scale that ultimately defines a particular GNSS system in the first place. GNSS receiver manufacturers, however, try to limit the magnitude of the time offset to within some predefined range.

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By Inside GNSS
January 9, 2011

Differences between Signal Acquisition and Tracking

Q: Why is acquisition of GNSS signals generally more difficult than tracking and what are the limiting factors?

A: A fairly good analogy of the difference between GNSS signal acquisition and tracking can be found in the rescue of victims of a sunken ship whose location is not accurately known. The first stage of the rescue attempt typically involves an aircraft flying a search pattern, which hopefully encompasses the location where the ship went down.

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By Inside GNSS
December 2, 2010

Measuring GNSS Signal Strength

Q: What is the difference between SNR and C/N0?

A: GPS receivers built for various applications, such as handhelds, automobiles, mobile phones, and avionics, all have a method for indicating the signal strength of the different satellites they are tracking. Some receivers display the signal strength in the form of vertical bars, some in terms of normalized signal strength, and others in terms of carrier-to-noise density (C/N0) or signal-to-noise ratio (SNR).

The latter two terms are regularly used so interchangeably that their fundamental differences are often overlooked. A full understanding of the differences between SNR and C/N0 is useful both for users of GPS receivers and for GPS receiver designers and testers.

SNR and C/N0
SNR is usually expressed in terms of decibels. It refers to the ratio of the signal power and noise power in a given bandwidth.

SNR(dB) = S  – N

S is the signal power, usually the carrier power expressed in units of decibel/milliwatt (dBm) or decibel/watts (dBW);
N is the noise power in a given bandwidth in units of dBm or dBW.

C/N0, on the other hand, is usually expressed in decibel-Hertz (dB-Hz) and refers to the ratio of the carrier power and the noise power per unit bandwidth.

For the GPS L1 C/A signal, one can consider the received signal power as the power of the original unmodulated carrier power (at the point of reception in a receiver) that has been spread by the spreading (ranging) codes when transmitted from a satellite. We can express C/N0 as follows:

C/N0 (dB-Hz) = C – (N – BW) = C – N0 = SNR + BW     


C is the carrier power in dBm or dBW;
N is the noise power in dBm or dBW;
N0 is the noise power density in dBm-Hz or dBW-Hz;
BW is the bandwidth of observation, which is usually the noise equivalent bandwidth of the last filter stage in a receiver’s RF front-end.

Typical values in an L1 C/A code receiver are as follows:

C/N0: ~ 37 to 45dB-Hz

Receiver front-end bandwidth: ~ 4MHz => BW = 10*log (4,000,000) = 66dB
SNR = C/N0 – BW => SNR ~ (37 – 66) to (45 – 66) => SNR ~ -29dB to -21dB

In order to determine C/N0, then, one clearly needs to determine the carrier power and noise density at the input to the receiver.

Noise and Signal Power
The sources of white noise in a GNSS receiver are usually described by the antenna noise temperature and the receiver noise temperature. The antenna temperature models the noise entering the antenna from the sky whereas the receiver noise temperature models the thermal noise due to the motion of charges within a device such as the GPS receiver front-end. These noise sources specify the noise density.

. . .

Signal and Noise Paths from Antenna to Receiver
. . .
When considering signal and noise paths through the front-end, one needs to consider the noise figure of the various components in the front-end. The noise figure is given as

NF = SNRin / SNRout

and provides an estimate of the amount of noise added by an active component, such as a low-noise amplifier (LNA), or even a passive component, such as a filter or the cable.

. . .

Taking into consideration the noise environment and the receiver front-end components, the C/N0 of a particular tracked satellite will scale relative to the signal power. The signal power of the various satellites being tracked by the receiver will vary in relation to the satellite elevation angle due to differences in path loss and the satellite and receiver antennas’ gain patterns. So, for example, if the signal power varies ±4dB of the nominal signal power of -158.5dBW, the corresponding C/N0 will vary from 38.5dB-Hz to 46.5dB-Hz. 

Interpretation and Significance of C/N0
From our discussions thus far, the C/N0 output by a receiver clearly provides an indication of the signal power of the tracked satellite and the noise density as seen by the receiver’s front-end.

Two different GPS receivers connected to the same antenna and tracking the same GPS satellite at the same time may output different C/N0 values. If one assumes that the C/N0 values are computed accurately by both the receivers, the differences in the C/N0 values can be attributed to differences in the noise figure of the two front-ends and/or the receivers’ respective band-limiting and quantization schemes.

. . .

Receiver Acquisition, Processing Blocks, and SNR
The signal-to-noise ratio is most useful when considered within the baseband processing blocks of a GNSS receiver. In dealing with SNR, the bandwidth of interest needs to be specified. Typically the noise equivalent bandwidth is used, which is defined as the bandwidth of an ideal (i.e., brick-wall) filter whose bandwidth when multiplied by the white noise density of N0/2 will result in the total noise power at the output of the original filter. 

. . .

The improvement in SNR as the result of a longer integration occurs because of the reduction in the noise equivalent bandwidth. Note that the performance of the PLL and FLL in the presence of thermal noise is further affected by the bandwidths of the respective loops themselves. The integration time in this case establishes the input SNR and the loop update time for the respective loops.

Interpretation and Significance of SNR
As we have seen, the SNR in a GPS receiver depends on the receiver’s front-end bandwidth, acquisition, and tracking parameters. Referencing just the SNR value in a GPS receiver does not usually make sense unless one also specifies the bandwidth and processing stage within the receiver.

The SNR is very useful when evaluating the performance of the acquisition and tracking stages in a receiver. For example, when performing Monte Carlo simulations, the SNR needs to be determined at the various stages of the signal processing chain to properly simulate the receiver. In simulations the required C/N0 needs to be first converted to an SNR from which the appropriate noise variance can be readily determined.

Furthermore, the SNR is an indication of the level of noise present in the measurement, whereas C/N0 alone does not provide this information.

In conclusion, we can see that both the C/N0 and SNR are useful quantities that can be used when designing, evaluating or verifying the performance of a GPS receiver. However the use of one quantity over the other very much depends upon the context and the purpose for which the signal quality measurement is being made or is to be used for and this should be carefully considered when choosing between the two.

(For Angelo Joseph’s complete answer to this question, including formulas and tables, please download the full article using the pdf link above.)

Additional Resources
For information on how C/N0 is computed within a GNSS receiver, refer to the GNSS Solutions columns by B. Badke (InsideGNSS, September/October 2009) and E. Falletti et alia (January/February 2010).


By Inside GNSS
August 17, 2010

A Fully Digital Model for Kalman Filters

Q: Is it possible to define a fully digital state model for Kalman filtering?

A: The Kalman filter is a mathematical method, purpose of which is to process noisy measurements in order to obtain an estimate of some relevant parameters of a system. It represents a valuable tool in the GNSS area, with some of its main applications related to the computation of the user position/velocity/time (PVT) solution and to the integration of GNSS receivers with an inertial navigation system (INS) or other sensors.

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By Inside GNSS
June 22, 2010

Generating Carrier Phase Measurements

Q: What is the carrier phase measurement? How is it generated in GNSS receivers?

A: Simply put, the carrier phase measurement is a measure of the range between a satellite and receiver expressed in units of cycles of the carrier frequency. This measurement can be made with very high precision (of the order of millimeters), but the whole number of cycles between satellite and receiver is not measurable.

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By Inside GNSS
October 7, 2007

GNSS Solutions

“GNSS Solutions” is a regular column featuring questions and answers about technical aspects of GNSS.

Readers are invited to send their questions to columnist Mark Petovello, Department of Geomatics Engineering, University of Calgary in Alberta, Canada. He will find experts to answer those questions, which will be published in Inside GNSS.

Dr. Petovello is a professor at the university. He has been actively involved in many aspects of positioning and navigation since 1997.

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By Inside GNSS