Estimating the GNSS Broadcast Ephemeris Error - Presentation
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Transcript of Estimating the GNSS Broadcast Ephemeris Error - Presentation
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ESTIMATING THE GNSS BROADCAST
EPHEMERIS ERROR
Student Ciuban Sebastian
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OBJECTIVES
• Comparing the orbit of a certain GNSS satellite with respect to WGS84 reference system (ECEF coordinates), obtained from broadcast ephemeris and precise post-processed orbits.
• Highlight the fact that the errors between them are small enough for obtaining the right solution for navigation and positioning problems.
• Implementing a 10th order polynomial interpolation (Lagrange method) for the SV 12 orbit.
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DATA FILES USED
For this study, the orbit of GNSS SV 12 was computed using:• Broadcast ephemerides data
contained in the RINEX (Receiver Independent Exchange Format) navigation file.
• Precise ephemerides from SP3 (Standard Product Version 3) file.
• Both were downloaded from International GNSS Service ( igs.bkg.bund.de) corresponding to the same day (11.03.2013).
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INTRODUCTION
• Global Navigation Satellite Systems (GNSS) positioning and navigation is based on a process called “trilateration”.
• For a better understanding, imagine that you don’t know your location but you do know your distance from three or four known points. With that information you can trilaterate your position.
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RINEX
• Is a format for raw GNSS data
• Used to post-process the received data producing more accurate results.
• Keplerian and perturbation parameters are contained in these data blocks for every satellite in the constellation.
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KEPLERIAN PARAMETERS
The RINEX file contains the required parameters that define an orbit:• semi-major axis• orbit eccentricity• orbit inclination• true anomaly• longitude of the ascending
node• argument of perigee © www.satelliteorbitdetermination.com
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SP3
• Is a geospatial format that stores information about GNSS satellites
• Satellite position (X, Y, Z) at each 15 minutes
• Clock correction• GPS week and seconds of
week.
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COMPUTING THE SATELLITE ORBIT
To obtain the GNSS satellite coordinates from the navigation message specific algorithms must be respected for computation of:• time tk from the ephemerides reference epoch toe
• mean anomaly at tk
• eccentric anomaly (iteratively) Ek
• true anomaly vk
• argument of latitude uk
• radial distance rk
• longitude of the ascending node λk
• coordinates of the satellite in the ECEF frame (WGS84 reference system)
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MATLAB
In order to accomplish the purpose of this study, several functions, were developed under MATLAB environment, with the aim of:• importing data• computing the SV orbits• comparing the orbits• plotting the results.
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ROUTINES DEVELOPED UNDER MATLAB I
• Opens the selecting menu
• Reads the blocks of data
• Arranges the data in a matrix
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ROUTINES DEVELOPED UNDER MATLAB II
• Computes the GNSS SV orbital elements
• The algorithm is described in GNSS Data Processing Book: Volume I
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ROUTINES DEVELOPED UNDER MATLAB III
• Computes the orbit every 5 seconds at a given time
• Uses the data from SP3 file• Plots the interpolated orbit
along the precise orbit
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ROUTINES DEVELOPED UNDER MATLAB IV
A general script was made:• involving all the functions
created• computes and plots the orbit
from the RINEX navigation file and from the SP3 file
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PRECISE FULL ORBIT OF SV 12
• Results plotted from SP3 file• The precise full orbit of
SV12• Date of orbit is 11.03.2013• Will be used as reference for
the current study
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ERRORS BETWEEN BROADCASTED AND PRECISE ORBIT OF SV12
Broadcasted partial orbit
from toe=252000 to toe=258300
(seconds of GPS week)
Precise partial orbit
from toe=252000 to toe=258300
(seconds of GPS week)
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ERRORS BETWEEN RINEX-SP3
No. toe(sec) ∆x [m] ∆y [m] ∆z [m]
1 252000 0,5190 -0,7292 0,5721
2 252900 0,4597 -0,5377 0,5169
3 253800 0,4168 -0,4159 0,4562
4 254700 0,3620 -0,3355 0,3818
5 255600 0,2644 -0,2653 0,2736
6 256500 0,1003 -0,1867 0,1086
7 254700 -0,1434 -0,0985 -0,1374
8 258300 -0,4617 -0,0276 -0,4804
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THE LINEAR ERROR OVER TIME
toe(sec) Spatial dist. [m]
252000 1,0623
252900 0,8762
253800 0,7449
254700 0,6240
255600 0,4638
256500 0,2382
254700 0,2217
258300 0,6668
Mean [m] σ [m]
0,6122 ± 0,2946
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INTERPOLATION
As the SP3 file provides satellite positions at a 15 minutes rate, for other epochs, an interpolation process is necessary. A 10th order polynomial interpolation (Lagrange method) was used as this is sufficient to provide centimeter accuracy.
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INTERPOLATED AND PRECISE ORBIT
• Both orbits belong to the same period of time
• The interpolated orbit was computed every 5 seconds along the precise orbit which is every 15 minutes.
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CONCLUSIONS
• Satellite based positioning and navigation are affected by various errors that occur during these processes.
• The differences between broadcasted and post-processed orbits are small enough for real time navigation and positioning. This represents the basic concept for GNSS measurements in real time.
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Thank you for your attention!