Skip to main content
SpringerLink
Log in

Systolic square root covariance Kalman filtering

  • Published:
Journal of VLSI signal processing systems for signal, image and video technology Aims and scope Submit manuscript

Abstract

The square root covariance Kalman filter (SRCF) and the square root covariance Kalman predictor (SRCP) are derived from a least squares viewpoint. A new systolic array architecture is presented which is suitable for implementing both forms of the filter. The systolic SRCF is found to be comparable with other architectures in the literature in terms of size, speed and processor utilization. The SRCP is faster than any comparable architecture withO(2n) timesteps between measurements.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H.T. Kung, “Why Systolic Architectures,”IEEE Computer, Vol. 15, pp. 37–46, 1982.

    Article  Google Scholar 

  2. S.Y. Kung and J.N. Hwang, “An Efficient Triarray Systolic Design for Real-Time Kalman Filtering”,Proc. IEEE ICASSP '88, New York, pp. 2045–2048, 1988.

  3. M.J. Chen and K. Yao, “On Realizations of Least-Squares Estimation and Kalman Filtering,”Proc. 1st Int. Workshop on Systolic Arrays, Oxford, pp. 161–170, 1986.

  4. F.M.F. Gaston and G.W. Irwin, “The Systolic Approach to Square Root Information Kalman Filtering”,Int. J. of Control., Vol. 15, pp. 225–248, 1989.

    Article  MathSciNet  Google Scholar 

  5. G.J. Bierman, “Factorisation Methods for Discrete Sequential Estimation,” New York: Academic Press, 1977.

    Google Scholar 

  6. D.B. Duncan and S.D. Horn, “Linear Dynamic Recursive Estimation from the Viewpoint of Regression Analysis,”J. Amer. Stat. Ass., Vol. 67, No. 340, pp. 815–821, 1972.

    MathSciNet  MATH  Google Scholar 

  7. C.C. Paige and M.A. Saunders, “Least Squares Estimation of Discrete Linear Dynamic Systems Using Orthogonal Transformations,”SIAM J. Numer. Anal., Vol. 14, No. 2, pp. 180–193, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  8. J.M. Jover and T. Kailath, “A Parallel Architecture for Kalman Filter Measurement Update and Parameter Estimation”,Automatica, Vol. 22, pp. 43–57, 1986.

    Article  MATH  Google Scholar 

  9. T-Y. Sung and Y-H. Hu, “VLSI Implementation of Real-Time Kalman Filter,”Proc. ICASSP, pp. 2223–2226, 1986.

  10. M. Verhaegen and P. Van Dooren, “Numerical Aspects of Different Kalman Filter Implementations”,IEEE Trans. Atuo. Contr., Vol. AC-31, No. 10, pp. 907–917, 1986.

    Article  Google Scholar 

  11. C.C. Paige, “Fast Numerically Stable Computations for Generalised Least Squares Problems”,SIAM J. Numer. Anal., Vol. 16, pp. 165–171, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  12. C.C. Paige, “Covariance Matrix Representations in Linear Filtering,” special issue ofContemporary Mathematics on linear algebra and its role in systems theory, pp. 309–321, 1985.

  13. M. Morf and T. Kailath, “Square Root Algorithms for Least Squares Estimation,”IEEE Trans. Auto. Contr., Vol. AC-20, pp. 487–497 1975.

    Article  MathSciNet  MATH  Google Scholar 

  14. H.G. Yeh, “Kalman Filtering and Systolic Processes,”Proc. ICASSP, pp. 2139–2142, 1986.

  15. D.K. Fadeev and V.N. Fadeeva,Computational Methods of Linear Algebra, New York: W. H. Freeman and Co., 1963.

    Google Scholar 

  16. G.W. Irwin and F.M.F. Gaston, “Occam Simulation of a Systolic Architecture for Parallel Kalman Filtering,”Parallel Processing in Control, P.J. Fleming, ed., Peter Peregrinus Ltd, pp. 214–232, 1988.

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, The Queen's University, BT9 5AH, Belfast, Northern Ireland

    F. M. F. Gaston & G. W. Irwin

  2. R.S.R.E., WR14 3PS, Gt. Malvern, Worcs.

    J. G. McWhirter

Authors
  1. F. M. F. Gaston
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. W. Irwin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. G. McWhirter
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaston, F.M.F., Irwin, G.W. & McWhirter, J.G. Systolic square root covariance Kalman filtering. J VLSI Sign Process Syst Sign Image Video Technol 2, 37–49 (1990). https://doi.org/10.1007/BF00931035

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00931035

Keywords

Search

Navigation