ESTIMATING THE GNSS BROADCAST

EPHEMERIS ERROR

Student Ciuban Sebastian

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.

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).

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.

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

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.

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)

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.

ROUTINES DEVELOPED UNDER MATLAB I

• Opens the selecting menu

• Reads the blocks of data

• Arranges the data in a matrix

ROUTINES DEVELOPED UNDER MATLAB II

• Computes the GNSS SV orbital elements

• The algorithm is described in GNSS Data Processing Book: Volume I

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

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

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

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)

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

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

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.

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.

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.

Thank you for your attention!