Skip to main content
Log in

The treatment of bias in the square-root information filter/smoother

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The Dyer-McReynolds square-root information filter (SRIF) is rederived, using recursive least-square arguments. The result is applied to a system composed partly of biases. The filtersensitivity matrix,computed covariance, andconsider covariance for this augmented system are reviewed. A new computationally attractive representation for the smoothed estimates, in terms of a smoothedsensitivity matrix and a smoothedcomputed covariance is presented.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Dyer, P., andMcReynolds, S.,Extension of Square Root Filtering to Include Process Noise, Journal of Optimization Theory and Applications, Vol. 3, pp. 444–459, 1969.

    Google Scholar 

  2. Jazwinski, J. H.,Stochastic Processes and Filtering Theory, Academic Press, New York, New York, 1970.

    Google Scholar 

  3. Deutch, R.,Estimation Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1965.

    Google Scholar 

  4. Magness, T. A., andMcGuire, J. B.,Statistics of Orbit Determination—Weighted Least Squares, Space Technology Laboratories, Report Prepared for Jet Propulsion Laboratory, Contract No. 950045, 1962.

  5. Curkendall, D. W.,Problems in Estimation Theory with Applications to Orbit Determination, UCLA, School of Engineering and Applied Science, Report No. UCLA-ENG-7275, 1972.

  6. Griffin, R. E., andSage, A. P.,Sensitivity Analysis of Discrete Filtering and Smoothing Algorithms, AIAA Journal, Vol. 7, No. 10, 1969.

  7. Friedland, B.,Treatment of Bias in Recursive Filtering, IEEE Transactions on Automatic Control, Vol. AC-14, pp. 359–367, 1967.

    Google Scholar 

  8. Hanson, R. J., andLawson, C. L.,Extensions and Applications of the Householder Algorithm for Solving Linear Least-Square Problems, Mathematics of Computation, Vol. 23, pp. 787–812, 1969.

    Google Scholar 

  9. Kaminski, P. G., andBryson, A. E.,Discrete Square-Root Smoothing, Proceedings of the 1972 AIAA Guidance and Control Conference, AIAA Paper No. 72–877, 1972.

  10. McReynolds, S. R.,The Sensitivity Matrix Method for Orbit Determination, with Application to a Mars Orbiter, Jet Propulsion Laboratory, Space Programs Summary 37–56, Vol. 11, 1969.

  11. Dyer, P.,Formulae for the Implementation of the Householder Algorithm into the Double-Precision Orbit Determination Program, Jet Propulsion Laboratory, Space Programs Summary 37–58, Vol. 11, 1969.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by R. E. Kalaba

This work represents the results of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, under NASA Contract No. NAS 7-100.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bierman, G.J. The treatment of bias in the square-root information filter/smoother. J Optim Theory Appl 16, 165–178 (1975). https://doi.org/10.1007/BF00935630

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00935630

Key Words

Navigation