Skip to main content

Part of the book series: International Association of Geodesy Symposia ((IAG SYMPOSIA,volume 132))

  • 2156 Accesses

Abstract

An adaptive sequential adjustment and an adaptive robust sequential adjustment are presented on basis of the adaptive filtering and the robust estimation principles. The corresponding estimation formulae of the parameters in both the adaptive sequential adjustment and the adaptive robust sequential adjustment are also derived. The calculation results based on a numerical example show that the adaptive sequential adjustment can efficiently resist the abnormal influence from the prior model information and well balance the prior model information and the posterior observation information as well, and the adaptive robust sequential adjustment is not only simple in calculation but also can efficiently resist the bad influences from the abnormal disturbance in the prior information model parameters and the measurement outliers in the estimated parameters.

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

  • Andrews, D.F. (1974) A Robust Method for multiple Linear Regression, Technometrics, 16: 523–531.

    Google Scholar 

  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A. (1986) Robust Statistics: the Approach Based on Influence Functions, Wiley, New York.

    Google Scholar 

  • He H, Yang Y (1998) Robust Estimation for Sequential Adjustment (in Chinese), Engineering of Surveying and Mapping, Vol.7, No.1, 36–40.

    Google Scholar 

  • Huber, P.J. (1964) Robust Estimation of a Location Parameter, Annals of Mathematical Statistics, 35: 73–101.

    Article  Google Scholar 

  • Huber, P.J. (1981), Robust Statistics, Wiley, New York.

    Google Scholar 

  • Jazwinski, A.H. (1970) Stochastic Processes and Filtering Theory. New York: Academic press.

    Google Scholar 

  • Koch, K.R., Yang Y (1998) Robust Kalman Filter for Rank Deficient Observation Model. Journal of Geodesy, 72(8): 436–441.

    Article  Google Scholar 

  • Masreliez, C.J., Martin, R.D. (1977) Robust Bayesian Estimation for the Linear Model and Robustifying the Kalman Filter. IEEE Trans, Automat, Contr, Vol. AC-22.

    Google Scholar 

  • Mikhail, E.M. (1976), Observations and Least Squares, New York.

    Google Scholar 

  • Ou J, Chai Y, Yuan Y (2004) Adaptive Filtering for Kinematic Positioning by Selection of the Parameter Weights (in Chinese). Progress in Geodesy and Geodynamics[C]: 816–823.

    Google Scholar 

  • Yang Y (1991) Robust Bayesian Estimation, Bulletin Geodesique, 65(3): 145–150.

    Article  Google Scholar 

  • Yang Y (1993) The Theory and Application of Robust Estimation (in Chinese). Beijing: Bayi Publication House.

    Google Scholar 

  • Yang Y, He H, Xu G (2001) Adaptively Robust Filtering for Kinematic Geodetic Positioning. Journal of Geodesy, 75(2): 109–116.

    Article  Google Scholar 

  • Yang Y, Song L, Xu T (2002) Robust estimator for correlated observations based on bifactor equivalent weights, Journal of Geodesy, 76(6–7): 353–358.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sui, L., Liu, Y., Wang, W., Fan, P. (2008). Adaptive Robust Sequential Adjustment. In: Xu, P., Liu, J., Dermanis, A. (eds) VI Hotine-Marussi Symposium on Theoretical and Computational Geodesy. International Association of Geodesy Symposia, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74584-6_40

Download citation

Publish with us

Policies and ethics