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DGNSS Fundamentals
| Fundamentals | |
|---|---|
| Title | DGNSS Fundamentals |
| Author(s) | GMV |
| Level | Basic |
| Year of Publication | 2011 |
The classical DGNSS technique is an enhancement to a primary GNSS system that consists of the determination of the GNSS position for an accurately-surveyed position known as reference station. DGNSS accuracy is in the order of 1 m (1 sigma) for users in the range of few tens of km from the reference station.
The classical DGNSS technique
The standard DGNSS technique consists of the determination of the GNSS position for an accurately-surveyed position known as reference station. The basic concept of DGNSS is the use of 2 receivers, one at a known location and one at an unknown position, that see the same GNSS satellites in common. By fixing the location of one of the receivers, the other location may be found either by computing corrections to the position of the unknown receiver or by computing corrections to the pseudoranges. In the classical DGNSS technology, only corrections to C/A code pseudoranges are being transmitted, which brings rover positional errors down to values about 1m. The remaining DGNSS error source is multipath, which can be reduced by the use of special multipath mitigation methods.
The main steps of DGNSS technique are:
- Operation
A reference station calculates differential corrections for its own location and time. Users may be up to 200 nautical miles (370 km) from the station, however, and some of the compensated errors vary with space: specifically, satellite ephemeris errors and those introduced by ionospheric and tropospheric distortions. For this reason, the accuracy of DGNSS decreases with distance from the reference station. The problem can be aggravated if the user and the station lack "inter visibility"—when they are unable to see the same satellites.
- Post processing
Post-processing is used in Differential GNSS to obtain precise positions of unknown points by relating them to known points such as survey markers. The GPS measurements are usually stored in computer memory in the GNSS receivers, and are subsequently transferred to a computer running the GNSS post-processing software. The software computes baselines using simultaneous measurement data from two or more GNSS receivers.
The baselines represent a three-dimensional line drawn between the two points occupied by each pair of GNSS antennas. The post-processed measurements allow more precise positioning, because most GNSS errors affect each receiver nearly equally, and therefore can be cancelled out in the calculations.
The improvement of GNSS positioning doesn't require simultaneous measurements of two or more receivers in any case, but can also be done by special use of a single device. In the 1990s when even handheld receivers were quite expensive, some methods of quasi-differential GPS were developed, using the receiver by quick turns of positions or loops of 3-10 survey points.
- Accuracy
DGNSS accuracy is in the order of 1 m (1 sigma) for users in the range of few tens of kilometers from the reference station, growing at the rate of 1 m per 150 km of separation The United States Federal Radionavigation Plan and the IALA Recommendation on the Performance and Monitoring of DGNSS Services in the Band 283.5–325 kHz cite the United States Department of Transportation's 1993 estimated error growth of 0.67 m per 100 km from the broadcast site but measurements of accuracy across the Atlantic, in Portugal suggest a degradation of just 0.22 m per 100 km.[1]
DGNSS Algorithm
The classical DGNSS algorithm is based on single differences of pseudorange observables. At a given epoch, and for a given satellite, the simplified pseudorange observation equation is the following:
[math]\displaystyle{ \qquad P =\rho+I+Tr+c(b_{Rx}-b_{Sat} )+\varepsilon_P \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{ \varepsilon_P }[/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].
The next step is using a reference station at an accurately calibrated location [math]\displaystyle{ (x_o, y_o,z_o) }[/math], the reference-to-satellite range can be calculated as:
[math]\displaystyle{ \qquad R_o=\sqrt{〖(x_{Sat}-x_o)〗^2+〖(y_{Sat}-y_o)〗^2+〖(z_{Sat}-z_0)〗^2 } \qquad \mbox{(3)} }[/math].
When single differencing of both pseudoranges, [math]\displaystyle{ \Delta P = P_o - P }[/math], the ionospheric and tropospheric delays cancell and also the satellite bias. The basic equation per satellite to solve: range space differential correction per satellite is determined by differencing the calculated and measured reference-to-satellite ranges:
[math]\displaystyle{ \qquad \Delta P= '''u'''_o^sat Delta x +c Delta b_{Rx} +Delta \varepsilon \qquad \mbox{(4)} }[/math].
As there are not only one satellite in view, the estimation process is a linear equation system.
Based on the RTCM specification list[2], the broadcast corrections should be corrected to remove the reference receiver and satellite clock offset errors,
[math]\displaystyle{ \qquad \Delta_{DGPS}= R_o +c(\Delta b_o +\Delta b_{Sat})- P \qquad \mbox{(5)} }[/math].
Removal of clock errors prior to broadcasting the corrections greatly decreases the magnitude of the broadcast corrections without sacrificing any accuracy. Note that [math]\displaystyle{ \Delta_{DGPS} }[/math] signal contains the common mode error sources, which will cancel the corresponding errors in the user's position calculation. Since it also contains the multipath and noise terms (errors of several meters in worst cases), the [math]\displaystyle{ \Delta_{DGPS} }[/math] signal is recommended to be filtered before broadcasting.
Notes