1. TEST OF GOCE EGG DATA FOR SPACECRAFT POSITIONING
Xiucong Sun (1), Pei Chen (1), Christophe Macabiau (2), Chao Han (1)
(1)Beihang University, 37 Xueyuan Road, Beijing, , China
(2) ENAC, 7 Avenue Edouard BELIN, Toulouse, 31055, France
23/11/2018

2. Gradiometry & INS: A Brief Review
1960s: Early Investigations
Geodetic error evaluation in INS, vs. instrument errors (gyro, accelerometer)
Conceptual design and performance assessments
INS aiding by real-time determination of gravity disturbances

3. Gradiometry & INS: A Brief Review
1970s: Mechanization Studies & Optimal Design
Gradiometer as an External Navigation Aid (GAEA)

4. Gradiometry & INS: A Brief Review
1970s: Mechanization Studies & Optimal Design
Reference Ellipsoid Formula as an External Navigation Aid (REFAEA)

5. Gradiometry & INS: A Brief Review
1970s: Mechanization Studies & Optimal Design
Two-pass correlation system: a prototype of map-matching

6. Gradiometry & INS: A Brief Review
1990s: Development of Gravity Gradient Map-Matching
Designed by Affleck & Jircitano, 1991

7. Gradiometry & INS: A Brief Review
2000s: Two Branches of Gradiometer-Aided INS
Without a map:
Free-inertial navigation with gravity compensation by an onboard gradiometer
Researchers: Christopher Jekeli, Troy C. Welker, et al.
With a map:
Update an INS with gravity gradient measurements by a Kalman filter arrangement
Researchers: Justin A. Richeson, Marshall Rogers, et al.

8. Gradiometry & INS: A Brief Review
Applications
Passive
Nonemanating
No-spoofing
Serve as back up or a main system where GNSS is unavailable

9. Gradiometry & Space Navigation
1, ideal measurement platform
2, ignore terrain effects
3, high-precision attitudes
A purely graiometer & star sensor navigation system

10. Research Objective
To investigate the feasibility of gravity gradient map-matching for spacecraft navigation
To develop a position estimation method in the framework of map-matching
To evaluate the state-of-art positioning accuracy using GOCE EGG real data

11. Observation Equation
GGT in ECEF
Computation

12. Observation Equation GGT in GRF Rewriting GGT in Column Vector

13. Observation Equation
Transformation Matrix for the Column Form

14. Observation Equation Explanation of the Observation Equation Attitude
information
Position information
Star trackers
To resolve?

15. Least-Square Searching
Nonlinear Least-Square Iteration
Jacobian Matrix：
Involving the partial derivatives of gradients

16. Least-Square Searching
Covariance Equation
Observability Gramian
it is nonsingular if and only if the system is observable

17. Initial Position Estimation
In a central gravitational force field
Eigen-Decomposition of VE

18. Initial Position Estimation
Denote
Initial position estimation

19. Initial Position Estimation
Denote
Initial position estimation
Sign ambiguity

20. Initial Position Estimation
Statistical tool to kick out the incorrect solutions
The observation residuals
Expectations !

21. Data Preprocessing Signal vs. Error in GOCE EGG data
Removing the 1/f error using model:

22. Test Results
The Error of the Recovered Gravity Gradients (unit, E)

23. Test Results
Errors of the Three Components of Initial Positions (correct ones）in the ECEF Frame

24. Test Results
800/8 m
mean 3D position error 620 m
800/8 m
109 m
The Errors (black points) and Standard Deviations (±, red lines) of the Final Searched Positions (correct ones）

25. Mean ± Standard Deviation (E)
Test Results
Statistical Means and Standard Deviations of the Observation Residuals
Component
Mean ± Standard Deviation (E)
Correct solutions
Incorrect solutions xx
8.9×10-5 ± 0.010
-1.6×10-3 ± 0.11 yy
-2.3×10-4 ± 0.015
1.4×10-3 ± 0.11 zz
-7.5×10-5 ± 7.6×10-3 xy
2.8×10-3 ± 0.33
2.1×10-3 ± 0.35 xz
1.2×10-6 ± 8.9×10-5
-4.9×10-5 ± 9.4×10-4 yz
-6.4×10-3 ± 0.24
-0.11 ± 2.2

26. Test Results
15.4 m
mean 3D position error 33.4 m
15.4 m
13.0 m
The Errors (black points) and Standard Deviations (±, redlines) of Position Estimates (correct ones）for the Semi-Simulation Case

27. Conclusions
Gravity gradiometry can provide navigation service for space users.
The GOCE gradiometer could provide 800 m positioning accuracy, and the z-axis error is constant at 100 m
With a better gradiometer, (all with E accuracy), tens of meters of position accuracy could be achieved.
Position estimates would have better accuracies if the dynamic model are used to reduce the measurement noise (a further work).

28. Thanks to ESA for providing GOCE data. Thank you for your attention.
Acknowledgement
Thanks to ESA for providing GOCE data.
Thank you for your attention.