Skip to main content

Extensive Representations and Algorithms for Nonlinear Filtering and Estimation

  • Chapter
Book cover Algorithmic Foundation of Robotics VII

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 47))

Abstract

Most estimation problems in robotics are difficult because of (a) the nonlinearity in observation models; and (b) the lack of suitable probabilistic models for the process and observation noise. In this paper we develop a set-valued approach to estimation that overcomes both these limitations and illustrates the application to localization of multiple, mobile sensor platforms with range sensors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boyd, S., Vandenberghe, L.: Convex optimization. University Press, Cambridge (2004)

    MATH  Google Scholar 

  2. Ros, L., Sabater, A., Thomas, F.: An ellipsoidal calculus based on propagation and fusion. IEEE Transactions on Systems, Man., and Cybernetics 32(4) (August 2002)

    Google Scholar 

  3. Schweppe, F.C.: Recursive state estimation: unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control AC-13(1), 22–28 (1968)

    Article  Google Scholar 

  4. Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. The MIT Press, Cambridge (2005)

    MATH  Google Scholar 

  5. Djugash, J., Singh, S., Corke, P.: Further results with localization and mapping using range from radio. In: Proceedings, Fifth Int’l Conf. on Field and Service Robotics, Pt. Douglas, Australia (July 2005)

    Google Scholar 

  6. Hanebeck, U.D.: Recursive nonlinear set- theoretic estimation based on pseudo-ellipsoids. In: Int’l Conf. on Multisensor Fusion and Integration for Intelligent Systems, pp. 159–164 (2001)

    Google Scholar 

  7. Briechle, K., Hanebeck, U.D.: Localization of a mobile robot using relative bearing measurements. IEEE Transactions on Robotics and Automation 20(1), 36–44 (2004)

    Article  Google Scholar 

  8. Horn, J., Hanebeck, U.D., Riegel, K., Heesche, K., Hauptmann, W.: Nonlinear set-theoretic position estimation of cellular phones. In: Proceedings of SPIE. AeroSense Symposium, vol. 5084, pp. 51–58 (2003)

    Google Scholar 

  9. Fox, D., Burgard, W., Dellaert, F., Thrun, S.: Monte Carlo localization: Efficient position estimation for mobile robots. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), Orlando (1999)

    Google Scholar 

  10. Murphy, K.: Bayesian map learning in dynamic environments. In: Advances in Neural Information Processing Systems (NIPS), MIT Press, Cambridge (2000)

    Google Scholar 

  11. Folkesson, J., Christensen, H.I.: Graphical SLAM: A self-correcting map. In: Proceedings of the International Symposium on Autonomous Vehicles, Lisboa, PT (2004)

    Google Scholar 

  12. Konolige, K.: Large-scale map-making. In: Proceedings of the AAAI National Conference on Artificial Intelligence, San Jose, CA, pp. 457–463 (2004)

    Google Scholar 

  13. Yildirim, E.A.: On the Minimum Volume Covering Ellipsoid of Ellipsoids. Technical Report, Dept. of Applied Mathematics and Statistics, Stony Brook University (2005)

    Google Scholar 

  14. Atiya, S., Hager, G.D.: Real-time vision-based robot localization. IEEE Trans. on Robotics and Automation 9(6), 785–800 (1993)

    Article  Google Scholar 

  15. Hanebeck, U.D., Schmidt, G.: Set theoretical localization of fast mobile robots using an angle measurement technique. In: Proc. IEEE Int. Conf. on Robotics and Automation, pp. 1387–1394 (1996)

    Google Scholar 

  16. Di Marco, M., Garulli, A., Giannitrapani, A., Vicino, A.: A set theoretic aproach to dynamic robot localization and mapping. Autonomous Robots 16, 23–47 (2004)

    Article  Google Scholar 

  17. Spletzer, J., Taylor, C.: A bounded uncertainty approach to multi-robot localization. In: Proc. IROS, pp. 1258–1265 (2003)

    Google Scholar 

  18. Grocholsky, B., Stump, E., Shiroma, P., Kumar, V.: Control for Localization of Targets Using Range-Only Sensors. In: Proceedings of the International Symposium on Experimental Robotics, Rio de Janeiro, Brazil (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Srinivas Akella Nancy M. Amato Wesley H. Huang Bud Mishra

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Stump, E., Grocholsky, B., Kumar, V. (2008). Extensive Representations and Algorithms for Nonlinear Filtering and Estimation. In: Akella, S., Amato, N.M., Huang, W.H., Mishra, B. (eds) Algorithmic Foundation of Robotics VII. Springer Tracts in Advanced Robotics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68405-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-68405-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68404-6

  • Online ISBN: 978-3-540-68405-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics