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Table 1. Preprocessing combinations 3.2 KALMAN FORMULATION The general formulation of the Kalman filter is of the P =UDU form, with U an upper triangular matrix and D a squared diagonal matrix. The update of the solution matrix follows the Bierman algorithm [6], while the propagation of the solution uses the Thornton algorithm [5].

Table 1 Preprocessing combinations 3.2 KALMAN FORMULATION The general formulation of the Kalman filter is of the P =UDU form, with U an upper triangular matrix and D a squared diagonal matrix. The update of the solution matrix follows the Bierman algorithm [6], while the propagation of the solution uses the Thornton algorithm [5].

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Fig. 1: Orbit error incidence on measurements The useful part of these orbits, i.e. the real-time part, corresponds to the extrapolated part. Figure 1 represents the impact of real-time orbit error on GNSS measurements (computed as 4 of horizontal orbits errors). In order to correctly fix the N1 ambiguity, this error should be less than a quarter of the N1 wavelength (2.5 cm). It is easy to see that for some satellites (in general eclipsing satellites), this condition is not met.
Fig. 1: Orbit error incidence on measurements The useful part of these orbits, i.e. the real-time part, corresponds to the extrapolated part. Figure 1 represents the impact of real-time orbit error on GNSS measurements (computed as 4 of horizontal orbits errors). In order to correctly fix the N1 ambiguity, this error should be less than a quarter of the N1 wavelength (2.5 cm). It is easy to see that for some satellites (in general eclipsing satellites), this condition is not met.
The following figure represents the general architecture of the software:
The following figure represents the general architecture of the software:
Table 2. Dynamic model Table 2 presents in detail the different forces used by the dynamical model:
Table 2. Dynamic model Table 2 presents in detail the different forces used by the dynamical model:
3.5 TIME SCALE Table 3. Measurement model The time scale is given by the clock information contained in the broadcast messages in input. These clocks are processed in the filter as measurements with a loose constraint (noise measurement equals 1 km), which allows to align the clock solution to the GPS broadcast time scale. The correction step of the Kalman filter involves a modeled measurement set at the current epoch. The measurement combinations used are the ionosphere-free pseudo-range and ionosphere-free phase. The targeted accuracy for the measurement models has been set to 5 mm. To do so, the following terms and models are computed:
3.5 TIME SCALE Table 3. Measurement model The time scale is given by the clock information contained in the broadcast messages in input. These clocks are processed in the filter as measurements with a loose constraint (noise measurement equals 1 km), which allows to align the clock solution to the GPS broadcast time scale. The correction step of the Kalman filter involves a modeled measurement set at the current epoch. The measurement combinations used are the ionosphere-free pseudo-range and ionosphere-free phase. The targeted accuracy for the measurement models has been set to 5 mm. To do so, the following terms and models are computed:
ION GNSS 2013, September 16-20, 2013 - Nashville, Tennessee
ION GNSS 2013, September 16-20, 2013 - Nashville, Tennessee
Table 4. Filter parameterization 4 REAL-TIME RESULTS Measurements were pulled from the different casters using the BNC tool [13]. The sampling rate was set to 5 sec. The Kalman filter step was set to 60 sec. The number of measurements processed for this experiment was about 200 millions.
Table 4. Filter parameterization 4 REAL-TIME RESULTS Measurements were pulled from the different casters using the BNC tool [13]. The sampling rate was set to 5 sec. The Kalman filter step was set to 60 sec. The number of measurements processed for this experiment was about 200 millions.
The data used for real-time tests span 10 days from 01/14/3013 to 01/23/2013. They are representative of real- time conditions that can be met in the RTIGS project. The network is composed of around 65. stations, whose measurements can be accessed in real-time using several casters (IGS-IP, GFZ, NrCan, IGN, UNAVCO). ION GNSS 2013, September 16-20, 2013 - Nashville, Tennessee
The data used for real-time tests span 10 days from 01/14/3013 to 01/23/2013. They are representative of real- time conditions that can be met in the RTIGS project. The network is composed of around 65. stations, whose measurements can be accessed in real-time using several casters (IGS-IP, GFZ, NrCan, IGN, UNAVCO). ION GNSS 2013, September 16-20, 2013 - Nashville, Tennessee
The RMS are below 5 cm on each axis. The cross-track component is the most accurate without many outliers. The tangential component shows the most erroneous data. After investigation, it appears that these outliers are due to old block IIA satellites in eclipse, which are very difficult to model. The error on the radial component is not significant since it can be absorbed in the clocks.
The RMS are below 5 cm on each axis. The cross-track component is the most accurate without many outliers. The tangential component shows the most erroneous data. After investigation, it appears that these outliers are due to old block IIA satellites in eclipse, which are very difficult to model. The error on the radial component is not significant since it can be absorbed in the clocks.
The following figure represents the 3D orbit error. The RMS is quite stable at 3.7 cm. However, eclipsing block IT A satellites can locally be erroneous by more than 20 cm.
The following figure represents the 3D orbit error. The RMS is quite stable at 3.7 cm. However, eclipsing block IT A satellites can locally be erroneous by more than 20 cm.
Vel) Leyes Fig. 7: 3D orbit error without ambiguity resolution The following figure corresponds to the 3D orbit error, when ambiguity resolution is deactivated. RMS is twice the previous RMS. This is more or less the same result as for batch resolutions [3]. 4.4, CLOCK ACCURACY
Vel) Leyes Fig. 7: 3D orbit error without ambiguity resolution The following figure corresponds to the 3D orbit error, when ambiguity resolution is deactivated. RMS is twice the previous RMS. This is more or less the same result as for batch resolutions [3]. 4.4, CLOCK ACCURACY
The following figure represents the clock solution compared to an IGS reference (a constant by satellite and a common value by epoch have been removed). This is equivalent to the combined orbit/clock error, projected on the radial component of the orbit which impacts directly the user error budget. The overall statistic is very good, with an RMS of less than | cm. This precision is sufficient to allow ambiguity resolution on an isolated receiver, even though some small errors remain. These errors are directly related to the along-track orbit error (primarily due to eclipsing block IIA satellites).
The following figure represents the clock solution compared to an IGS reference (a constant by satellite and a common value by epoch have been removed). This is equivalent to the combined orbit/clock error, projected on the radial component of the orbit which impacts directly the user error budget. The overall statistic is very good, with an RMS of less than | cm. This precision is sufficient to allow ambiguity resolution on an isolated receiver, even though some small errors remain. These errors are directly related to the along-track orbit error (primarily due to eclipsing block IIA satellites).
6. CONCLUSION Figure 9 shows the network of Galileo stations used in this experiment (the GPS network is the standard one described on figure 4): The constellation filter was modified to compute Galileo orbits in addition to GPS orbits. Thanks to the MGEX initiative [10], and using new generation multi-constellation networks like the CNES network REGINA (REseau Gnss pour I'Tgs et la NAvigation) and CONGO [11], and new real-time protocols [10], it is possible to collect real-time Galileo measurements.
6. CONCLUSION Figure 9 shows the network of Galileo stations used in this experiment (the GPS network is the standard one described on figure 4): The constellation filter was modified to compute Galileo orbits in addition to GPS orbits. Thanks to the MGEX initiative [10], and using new generation multi-constellation networks like the CNES network REGINA (REseau Gnss pour I'Tgs et la NAvigation) and CONGO [11], and new real-time protocols [10], it is possible to collect real-time Galileo measurements.
We have shown that precise real-time GPS orbit estimation using IGS data, networks and tools as well as a suitable Kalman filter is possible. Results show an accuracy of approximately 3.5 cm 3D RMS. Ambiguity resolution improves the overall accuracy by a factor 2. The filter can be easily extended to introduce other constellations (for example Galileo). Preliminary results, using current MGEX streams, show an accuracy of 15 cm for PFM and FM2 satellites. The new filter will be introduced in the CNES real-time analysis center operational chain.
We have shown that precise real-time GPS orbit estimation using IGS data, networks and tools as well as a suitable Kalman filter is possible. Results show an accuracy of approximately 3.5 cm 3D RMS. Ambiguity resolution improves the overall accuracy by a factor 2. The filter can be easily extended to introduce other constellations (for example Galileo). Preliminary results, using current MGEX streams, show an accuracy of 15 cm for PFM and FM2 satellites. The new filter will be introduced in the CNES real-time analysis center operational chain.
Related topics:
GeographyGeodesyComputer ScienceRemote SensingOrbit DeterminationGNSS applications
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