Skip to main content

Adjustment and Filtering Methods

  • Chapter
  • First Online:
GPS
  • 3365 Accesses

Abstract

In this chapter, we outline the most useful and necessary adjustment and filtering algorithms for statistical and kinematic as well as dynamic GPS data processing. We derive the necessary estimators, and provide a detailed discussion of the relationships between the methods presented.

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 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
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

References

  • Cui X, Yang Y (2006) Adaptively Robust Filtering with Classified Adaptive Factors. Progress in Natural Science 16(8):846–851

    Google Scholar 

  • Cui X, Yang Y, Gao W (2006) Comparison of Adaptive Filter Arithmetics in Controlling Influence of Colored Noises. Geomatics and Information Science of Wuhan University 31(8):731-735

    Google Scholar 

  • Cui X, Yu Z, Tao B, Liu D (1982) Adjustment in surveying. Surveying Press, Peking, (in Chinese)

    Google Scholar 

  • Gao W, Feng X, Zhu D (2007a) GPS/INS Adaptively Integrated Navigation Algorithm Based on Neural Network. Journal of Geodesy and Geodynamics 27(2):64-67

    Google Scholar 

  • Gao W, Yang Y, Cui X, Zhang S (2006a) Application of Adaptive Kalman Filtering Algorithm in IMU/GPS Integrated Navigation System. Geomatics and Information Science of Wuhan University 31(5):466-469

    Google Scholar 

  • Gao W, Yang Y, Zhang S (2006b) Adaptive Robust Kalman Filter Based on the Current Statistical Model. Acta Geodaetica et Cartographica Sinica 35(1):15-18

    Google Scholar 

  • Gao W, Yang Y, Zhang T (2007b) Neural Network Aided Adaptive Filtering for GPS/INS Integrated Navigation. Acta Geodaetica et Cartographica Sinica 36(1):26-30

    Google Scholar 

  • Gao W, Yang Y, Zhang T (2008) An Adaptive UKF Algorithms for Improving the Generalizaiton of Neural Network. Geomatics and Information Science of Wuhan University 33(5):500-503

    Google Scholar 

  • Gotthardt E (1978) Einführung in die Ausgleichungsrechnung. Herbert Wichmann Verlag, Karlsruhe

    Google Scholar 

  • Huang G, Yang Y, Zhang Q (2011) Estimate and Predict Satellite Clock Error Using Adaptively Robust Sequential Adjustment with Classified Adaptive Factors Based on Opening Windows. Acta Geodaetica et Cartographica Sinica 40(1):15-21

    Google Scholar 

  • Huang G, Zhang Q (2012) Real-time estimation of satellite clock offset using adaptively robust Kalman filter with classified adaptive factors. GPS Solutions 16(4):531-539

    Article  Google Scholar 

  • Huber PJ (1964) Robust estimation of a location parameter. Ann Math Stat 35:73–101

    Article  Google Scholar 

  • Jazwinski AH (1970) Stochastic processes and filtering theory. In: Mathematics in science and engineering, Vol. 64. Academic Press, New York and London

    Google Scholar 

  • Koch KR (1986) Maximum likelihood estimate of variance components. Bulletin Géodésique, 60:329–338

    Google Scholar 

  • Koch KR (1988) Parameter estimation and hypothesis testing in linear models. Springer-Verlag, Berlin

    Book  Google Scholar 

  • Koch KR, Yang Y (1998a) Konfidenzbereiche und Hypothesentests für robuste Parameterschätzungen. ZfV 123(1):20–26

    Google Scholar 

  • Koch KR, Yang Y (1998b) Robust Kalman filter for rank deficient observation model. J Geodesy 72: 436–441

    Article  Google Scholar 

  • Masreliez CJ, Martin RD (1977) Robust Bayesian estimation for the linear model and robustifying the Kalman filter. IEEE T Automat Contr AC-22:361–371

    Google Scholar 

  • Mohamed AH, Schwarz KP (1999) Adaptive Kalman filtering for INS/GPS. J Geodesy 73:193–203

    Article  Google Scholar 

  • Ou J, Chai Y, Yuan Y (2004) Adaptive filtering for kinematic positioning by selection of the parameter weights. In: Zhu, Y. and Sun, H. (eds) Progress in Geodesy and Geodynamics. Hubei Science & Technology Press, Hubei, 816–823 (in Chinese)

    Google Scholar 

  • Ou JK (2004) Private communication

    Google Scholar 

  • Ren C, Ou J, Yuan Y (2005) Application of adaptive filtering by selecting the parameter weight factor in precise kinematic GPS positioning. Prog. Nat. Sci., 15(1), 41–46

    Article  Google Scholar 

  • Salzmann M (1995) Real-time adaptation for model errors in dynamic systems. B Geod 69:81–91

    Article  Google Scholar 

  • Schaffrin B (1991) Generating robustified Kalman filters for the integration of GPS and INS. Techni-cal Report, No. 15, Institute of Geodesy, University of Stuttgart

    Google Scholar 

  • Schwarz K-P, Cannon ME, Wong RVC (1989) A Comparison of GPS kinematic models for the determination of position and velocity along a trajectory. Manuscr Geodaet 14:345–353

    Google Scholar 

  • Sui L, Liu Y, Wang W (2007) Adaptive Sequential Adjustment and Its Application. Geomatics and Information Science of Wuhan University 32(1):51-54

    Google Scholar 

  • Teunissen P (1990) An integrity and quality control procedure for use in multi sensor integration. In: Proceedings ION GPS90, pp. 513–522

    Google Scholar 

  • Wang G, Chen Z, Chen W, Xu G (1988) The principle of GPS precise positioning system. Surveying Press, Peking, ISBN 7-5030-0141-0/P.58, 345 p, (in Chinese)

    Google Scholar 

  • Wu F, Yang Y (2010) A New Two-Step Adaptive Robust Kalman Filtering in GPS/INS Integrated Navigation System. Acta Geodaetica et Cartographica Sinica 39(5):522-533

    Google Scholar 

  • Xu G (2002) GPS data processing with equivalent observation equations, GPS Solutions, Vol. 6, No. 1-2, 6:28-33

    Google Scholar 

  • Xu G (2003) GPS – Theory, Algorithms and Applications, Springer Heidelberg, ISBN 3-540-67812-3, 315 pages, in English

    Google Scholar 

  • Xu G (2007) GPS – Theory, Algorithms and Applications, 2nd Ed. Springer Heidelberg, ISBN 978-3-540-72714-9, 350 pages

    Google Scholar 

  • Xu G, Qian Z (1986) The application of block elimination adjustment method for processing of the VLBI Data. Crustal Deformation and Earthquake, Vol. 6, No. 4, (in Chinese)

    Google Scholar 

  • Xu T, Yang Y (2000) The Improved Method of Sage Adaptive Filtering. Science of Surveying and Mapping 25(3):22-24

    Google Scholar 

  • Yang M, Tang CH, Yu TT (2000) Development and assessment of a medium-range real-time kinematic GPS algorithm using an ionospheric information filter. Earth Planets Space 52(10):783–788

    Article  Google Scholar 

  • Yang Y (1991) Robust Bayesian estimation. B Geod 65:145–150

    Google Scholar 

  • Yang Y (1997a) Estimators of covariance matrix at robust estimation based on influence functions. ZfV 122(4):166–174

    Google Scholar 

  • Yang Y (1997b) Robust Kalman filter for dynamic systems. Journal of Zhengzhou Institute of Surveying and Mapping 14:79–84

    Google Scholar 

  • Yang Y (1999) Robust estimation of geodetic datum transformation. J Geodesy 73:268–274

    Article  Google Scholar 

  • Yang Y, Chai H, Song L (1999) Approximation for Contaminated Distribution and Its Applications. Acta Geodaetica et Cartographic Sinica 28(3):209–214

    Google Scholar 

  • Yang Y, Cui X (2006) Adaptively Robust Filter with Multi Adaptive Factors. J. Surv. Eng.

    Google Scholar 

  • Yang Y, Cui X (2008) Adaptively Robust Filter with Multi Adaptive Factors. Survey Review 40(309):260-270

    Article  Google Scholar 

  • Yang Y, Gao W (2006a) A New Learning Statistic for Adaptive Filter Based on Predicted Residuals. Progress in Natural Science 16(8):833-837

    Article  Google Scholar 

  • Yang Y, Gao W (2006b) An Optimal Adaptive Kalman Filter. Journal of Geodesy 80(4):177-183

    Article  Google Scholar 

  • Yang Y, Gao W (2005) Comparison of Adaptive Factors on Navigation Results. The J. Navigation, 2005, 58: 471-478.

    Article  Google Scholar 

  • Yang Y, Gao W (2005) Influence comparison of adaptive factors on navigation results. Journal of Navigation 58, 471–478

    Article  Google Scholar 

  • Yang Y, Gao W (2006c) Optimal Adaptive Kalman Filter with Applications in Navigation. J Geodesy

    Google Scholar 

  • Yang Y, He H, Xu G (2001a) Adaptively robust filtering for kinematic geodetic positioning. J Geodesy 75:109–116

    Article  Google Scholar 

  • Yang Y, Ren X, Xu Y (2013) Main Progress of Adaptively Robust Filter with Application in Navigation. Journal of Navigation and Positioning 1(1):9-15

    Google Scholar 

  • Yang Y, Tang Y, Li Q and Zou Y (2006) Experiments of Adaptive Filters for Kinemetic GPS Positioning Applied in Road Information Updating in GIS. J. Surv. Eng. (in press)

    Google Scholar 

  • Yang Y, Wen Y (2004) Synthetically adaptive robust filtering for satellite orbit determination. Science in China Series D Earth Sciences 47(7):585-592

    Article  Google Scholar 

  • Yang Y, Xu T (2003) An Adaptive Kalman Filter Based on Sage Windowing Weights and Variance Components. Journal of Navigation 56(2):231-240

    Article  Google Scholar 

  • Yang Y, Xu T (2004) An Adaptively Regularization Method with Combination of Priori and Posterior Information. In: Zhu, Y. and Sun, H. (eds) Progress in Geodesy and Geodynamics. Hubei Science & Technology Press, Hubei

    Google Scholar 

  • Yang Y, Xu T, He H (2001b) On adaptively kinematic filtering. Selected Papers for English of Acta Geodetica et Cartographica Sinica, pp. 25–32

    Google Scholar 

  • Yang Y, Zeng A (2009) Adaptive Filtering for Deformation Parameter Estimation in Consideration of Geometrical Measurements and Geopgysical Models. Science in China Series D Earth Sciences 52(8):1216-1222

    Article  Google Scholar 

  • Yang Y, Zhang X, Xu J (2011) Adaptively Constrained Kalman Filtering for Navigation Applications. Survey Review 43(322):370-381

    Article  Google Scholar 

  • Zhang S, Yang Y, Zhang Q (2007) An Adaptively Robust Filter Based on Bancroft Algorithm in GPS Navigation. Geomatics and Information Science of Wuhan University 32(4):309-311

    Google Scholar 

  • Zhou J (1985) On the Jie factor. Acta Geodaetica et Geophysica 5 (in Chinese)

    Google Scholar 

  • Zhou J, Huang Y, Yang Y, Ou J (1997) Robust least squares method. Publishing House of Huazhong University of Science and Technology, Wuhan

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guochang Xu .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Xu, G., Xu, Y. (2016). Adjustment and Filtering Methods. In: GPS. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-50367-6_7

Download citation

Publish with us

Policies and ethics