Skip to main content

The J 2 invariant relative configuration of spaceborne SAR interferometer for digital elevation measurement

Abstract

A 3-craft formation configuration is proposed to perform the digital elevation model (DEM) for the distributed spaceborne interferometric synthetic aperture radar (InSAR), and it is optimized by the modified ant colony algorithm to have the best compatibility with J 2 invariant orbits created by differential correction algorithm. The configuration has succeeded in assigning the across-track baseline to vary periodically and with its mean value equal to the optimal baseline determined by the relative height measurement accuracy. The required relationship between crafts’ magnitudes and phases is formulated for the general case of interferometry measure from non-orthographic and non-lateral view. The J 2 invariant configurations created by differential correction algorithm are employed to investigate their compatibility with the required configuration. The colony algorithm is applied to search the optimal configuration holding the near-constant across-track baseline under the J 2 perturbation, and the absolute height measurement accuracy is preferable as expected.

This is a preview of subscription content, access via your institution.

References

  1. 1

    Massonnet D.: Capabilities and limitations of the interferometric cartwheel. IEEE Trans. Geosci. Remote Sens. 39(3), 506–520 (2001)

    Article  MATH  Google Scholar 

  2. 2

    Moreira, A., Krieger, G.: Spaceborne synthetic aperture radar (SAR) systems: state of the art and future developments. In: 11th GAAS Symposium, pp. 385–388. Munich, Germany (2003)

  3. 3

    Fiedler, H., Krieger, G.: Analysis of bistatic configurations for spaceborne SAR interfermetry. In: Proc. 4th European Conference on Synthetic Aperture Radar (EUSAR’02), pp. 29–32. Cologne, Germany (2002)

  4. 4

    Schaub H., Alfriend K.: J 2 invariant relative orbits for spacecraft formations. Celestial Mech. Dyn. Astron. 79, 77–95 (2001)

    MATH  Article  Google Scholar 

  5. 5

    Mrstik V., VanBlaricum G.: Terrain height measurement accuracy of interferometric synthetic aperture radars. IEEE Trans. Geosci. Remote Sens. 34(1), 219–228 (1996)

    Article  Google Scholar 

  6. 6

    He F., Liang D.: Analysis on the height measurement error of spaceborne bistatic SAR interferometry. Syst. Eng. Electron. 27(9), 1519–1523 (2005)

    Google Scholar 

  7. 7

    Rodriguez E., Martin J.M.: Theory and design of interferometric synthetic aperture radars. Proc. Inst. Electron. Eng. 139(2), 147–159 (1992)

    Google Scholar 

  8. 8

    Duan, X., Bainum, P.: Design of spacecraft formation flying orbits. In: AIAA/AAS Astrodynamics Specialist Conference, pp. 03-588. AAS, Big Sky (2003)

  9. 9

    Breger, L., How, P.: Partial J 2-invariance for spacecraft formations. In: AIAA/AAS Astrodynamics Conference, pp. 2006–6585. AIAA, Keystone (2006)

  10. 10

    Yan, H., Alfriend, K.: Numerical searches and optimal control of J 2 invariant orbits. In: the 16th Annual AAS/AIAA Spaceflight Mechanics Meeting, pp. 06–163. AAS, Tampa (2006)

  11. 11

    Yan, H., Alfriend, K.: Optimal formation flying design. In: AAS/AIAA Space Flight Mechanics Conference, pp. 07–199. AAS, Sedona (2007)

  12. 12

    Xu M., Xu S.: J 2 invariant relative orbits via differential correction algorithm. Acta Mech. Sin. 23(5), 585–595 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. 13

    Dorigo M., Gambardella L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol Comput. 1(1), 53–66 (1997)

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ming Xu.

Additional information

The project was supported by the National Natural Science Foundation of China (10702003).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Xu, M., Jia, YH. & Xu, SJ. The J 2 invariant relative configuration of spaceborne SAR interferometer for digital elevation measurement. Acta Mech Sin 26, 643–651 (2010). https://doi.org/10.1007/s10409-010-0361-4

Download citation

Keywords

  • InSAR
  • Digital elevation model (DEM)
  • J2 invariant orbit
  • Differential correction algorithm
  • Formation flying