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, 100191, China (2) ENAC, 7 Avenue Edouard BELIN, Toulouse, 31055, France 23/11/2018

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

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

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

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

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

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.

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

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

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

Observation Equation GGT in ECEF Computation

Observation Equation GGT in GRF Rewriting GGT in Column Vector

Observation Equation Transformation Matrix for the Column Form

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

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

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

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

Initial Position Estimation Denote Initial position estimation

Initial Position Estimation Denote Initial position estimation Sign ambiguity

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

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

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

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

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）

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

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

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 0.011 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).

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.