1. Terrain Reconstruction Method Based on Weighted Robust Linear Estimation Theory for Small Body Exploration
Zhengshi Yu, Pingyuan Cui, and Shengying Zhu
Institute of Deep Space Exploration, Beijing Institute of Technology, Beijing, People’s Republic of China;
Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, Beijing, People’s Republic of China.

2. Contents Introduction
Terrain Reconstruction Method Based on Least Square Method
Terrain Reconstruction Method Based on Weighted Robust Linear Estimation
Numerical Simulation and results
Conclusions
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3. Introduction
Humans have never stop the steps to exploring the universe.
1996 NEAR
1998 Deep Space 1
1999 Stardust
2005 Deep Impact
2003 Hayabusa
2004 Rosetta
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4. Small body Asteroid Comet Significance
Exploring the orbital evolution, reducing potential danger of collision,
Investigating the genesis and evolution of solar system,
Exploiting natural resource,
Testing and developing new aerospace technology.
Significance
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5. Terrain Reconstruction
DEM generation,
Physical parameter estimation,
Autonomous navigation.
Terrain Reconstruction
Challenge Requirement
VS.
Long distance
Severe time delay
Large uncertainty
Limited prior knowledge
Autonomy
Robustness and adaptivity
Accuracy
Algorithm simplicity
Cost and power
No terrain reconstruction algorithm is adapted in actual mission.
Navigation camera &
Optical information
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6. Terrain Reconstruction Method Based on Least Square Method
Application of Least Square Method in Terrain Reconstruction
How to determine the position vector V ?
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7. Nonlinear observation model
Linearization
The use of prior information V0
Linear observation model
H is integrated weighting matrix
Real position of landmark can be determined by nominal position V0.and correction
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8. Robustness of Traditional Least Square Method
The robustness of algorithm can be described as Influence Function and Collapse Point.
Influence Function determines the influence of estimation by single observation
Collapse Point describes how much bias of the model the estimated states can be tolerated
Collapse Point of LSM is 0
Influence Function of LSM is infinite
Robustness of least square method is very weak,
algorithm based on least square method is not stable
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9. Equivalent weighting matrix
Terrain Reconstruction Method Based on
Weighted Robust Linear Estimation
The basic theory of robust linear estimation is M estimation
Estimation criterion
Differentiate
Equivalent weighting matrix
How to calculate?
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10. Construction of Integrated Weighting Matrix
Error Propagation Weighting Matrix
Observability Weight
Data Depth Weight
Error Propagation Weighting Matrix
Influence of different error sources to the observation model error
Singular value of error propagation matrix represent the influence degree of different error sources.
pl=[p l f]T
Error propagation matrix
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11. Integrated weighting matrix
Observability Weight
Observability of observation model
The observability can be described by the condition number of matrix Ai .
Data Depth Weight
Data depth of different observation conditions
Data depth describes the position of each data point in the data set.
Integrated weighting matrix
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12. Numerical Simulation and results
3-Demensional model of Eros 433 asteroid including 64,800 data points
Simulation parameters
Parameter
Value
Unit
Position sensor accuracy 10 m
Attitude sensor accuracy
0.1
deg
Navigation camera imaging size
4×3 mm
Navigation camera focus
0.5
Imaging error
Nominal landmark position error
200
Spacecraft flies in a 36 km round orbit around the asteroid. On orbit, the navigation camera takes photos of the asteroid every 6 degrees.
Scenario
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13. Reconstruction errors in three axes
(landmark miss match and navigation sensor fault are not considered).
Weighted robust linear estimation method
can improve the reconstruction accuracy.
Reconstruction errors in 3 axes decrease
with the increase of measurement times.
When more than 6 measurements have been
conducted, the reconstruction accuracy can
not be improved much.
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14. Reconstruction errors in three axes
(landmark miss match and navigation sensor fault are considered)
landmark miss match
Position sensor fault
Attitude sensor fault
Reconstruction errors in three axes all increase due to landmark miss match and
navigation sensor fault.
Proposed terrain reconstruction method can improve the accuracy efficiently.
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15. Conclusions A novel terrain reconstruction method is proposed based on
robust linear estimation.
Integrated weighting matrix is constructed with the consideration
of the influence of different error sources, the observability of
landmarks, and data depth of different observation conditions.
The accuracy is increased compared with least square method
and robust linear estimation.
The robustness and adaptation of the method can be efficiently
improved.
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16. Thank You! Thursday, April 19, 2018
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