Skip to main content

Systolic Designs for State Space Models: Kalman Filtering and Neural Networks

  • Chapter

Abstract

In this paper, a systematic mapping methodology is introduced for deriving systolic and wavefront arrays from regular computational algorithms [10]. It consists of three stages of mapping design: (data) dependence graph (DG) design, signal flow graph (SFG) design, and array processor design. This methodology allows systolic design with many desirable properties, such as local communication and fastest pipelining rates, etc. Based on this methodology, we shall develop systolic array designs for two important applications of adaptive state-space models. One is for the Kalman filtering algorithm which is popular in many digital signal processing applications. The other one is the Hopfield model for artificial neural networks (ANN), which has recently received increasing attention from AI and parallel processing research community.

This paper was also presented at the 26th IEEE Conf. on Decision and Control, Los Angeles, CA, Dec. 9–11, 1987 and appeared in Proc. 26th IEEE Conf. Decision and Control pp. 1461–1467, 1987. ©1987 IEEE.

This research was supported in part by the National Science Foundation under Grant ECS82-13358, by the Semiconductor Research Corporation under USC SRC program, and by the Innovative Science and Technology Office of the Strategic Defense Initiative Organization and was administered through the Office of Naval Research under Contract No. N00014-85-K-0469 and N00014-85-K-0599.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. H. Ackley, G. E. Hinton, and T. J. Sejnowski. A learning algorithm for Boltzmann machines. Cognitive Science, Vol. 9: pp. 147–169, 1985.

    Article  Google Scholar 

  2. N. H. Farhat, D. Psaltis, A. Prata and E. Paek. Optical implementation of the Hopfield model. Applied Optics, Vol. 24: pp. 1469–1475, May 1985.

    Article  CAS  Google Scholar 

  3. G.H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins University Press, 1983.

    Google Scholar 

  4. J. J. Hopfield. Neural network and physical systems with emergent collective computational abilities. In Proc. Natl.. Acad. Sci. USA, Vol. 79, pp. 2554–2558, 1982.

    Google Scholar 

  5. J. J. Hopfield. Neurons with graded response have collective computational properties like those of two-state neurons. In Proc. Natl.. Acad. Sci. USA,Vol. 81, pp. 3088–3092, 1984.

    Google Scholar 

  6. J. J. Hopfield and D. W. Tank. Neural computation of decision in optimization problems. Biological Cybernetics, Vol. 52, pp. 141–152, 1985.

    CAS  Google Scholar 

  7. H. T. Kung and W. M. Gentleman. Matrix triangularization by systolic arrays. Proc. SPIE, Real Time Signal Processing, 1983.

    Google Scholar 

  8. R. E. Kalman. A new approach to linear filtering and prediction problems. J. Basic Engineering, 82: pp 35–45, 1960.

    Article  Google Scholar 

  9. C. Koch, J. Marroquin and A. Yuille. Analog “neuronal” networks in early vision. Proc. of National Academy Science, Vol. 83: pp. 4263–4267, 1986.

    Article  CAS  Google Scholar 

  10. S. Y. Kung. VLSI Array Processors. Prentice Hall Inc. N. J., 1987.

    Google Scholar 

  11. S.Y. Kung. On supercomputing with systolic/wavefront array processors. Proceedings of the IEEE, 72: pp. 867–884, July:1984.

    Google Scholar 

  12. S. Y. Kung, S. C. Lo, and P. S. Lewis. Timing analysis and optimization of VLSI data flow arrays. In Proc. IEEE ICPP’86, pp. 600–607, August 1986.

    Google Scholar 

  13. S. Y. Kung, J. N. Hwang, and S. C. Lo. Mapping digital signal processing algorithms onto VLSI systolic/wavefront arrays. In Proc. 12th Annual Asilomar Conf. on Signals, Systems and Computers, pp. 6–12, November 1986.

    Google Scholar 

  14. S. Y. Kung and J. N. Hwang. Systolic array designs for Kalman filtering. Submitted to IEEE Trans. on Acoustics, Speech, and Signal Processing, 1987.

    Google Scholar 

  15. H. Mada. Architecture for optical computing using holographic associative memories. Applied Optics, Vol. 24: 1985.

    Google Scholar 

  16. J.G. McWhirter. Recursive least-squares minimization using a systolic array. In SPIE, In Proc. Real Time Signal Processing VI, pp 105–110, SPIE, 1983.

    Google Scholar 

  17. M. J. Chen and K. Yao. On realization and implementation of Kalman filtering by systolic array. In Proc. 21st Conf. on Inf. Science and Systems, The John Hopkins University, pp. 375–380, 1987.

    Google Scholar 

  18. C. C. Paige and M. A. Saunders. Least squares estimation of discrete linear dynamic systems using orthogonal transformation. SIAM J. Numer. Anal., 14: pp. 180–193, 1977.

    Article  Google Scholar 

  19. M. Takeda and J.W. Goodman. Neural networks for computation: number representations and programming complexity. Applied Optics, Vol. 25: pp. 3033–3046, September 1986.

    Article  CAS  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Plenum Press, New York

About this chapter

Cite this chapter

Kung, SY., Huang, J.N. (1988). Systolic Designs for State Space Models: Kalman Filtering and Neural Networks. In: Tewksbury, S.K., Dickinson, B.W., Schwartz, S.C. (eds) Concurrent Computations. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5511-3_31

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-5511-3_31

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-5513-7

  • Online ISBN: 978-1-4684-5511-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics