A New Pipelined Systolic Array-Based Architecture for Matrix Inversion in FPGAs with Kalman Filter Case Study

  • Abbas Bigdeli
  • Morteza Biglari-Abhari
  • Zoran Salcic
  • Yat Tin Lai
Open Access
Research Article
Part of the following topical collections:
  1. Design Methods for DSP Systems

Abstract

A new pipelined systolic array-based (PSA) architecture for matrix inversion is proposed. The pipelined systolic array (PSA) architecture is suitable for FPGA implementations as it efficiently uses available resources of an FPGA. It is scalable for different matrix size and as such allows employing parameterisation that makes it suitable for customisation for application-specific needs. This new architecture has an advantage of Open image in new window processing element complexity, compared to the Open image in new window in other systolic array structures, where the size of the input matrix is given by Open image in new window . The use of the PSA architecture for Kalman filter as an implementation example, which requires different structures for different number of states, is illustrated. The resulting precision error is analysed and shown to be negligible.

Keywords

Information Technology Quantum Information Kalman Filter Processing Element Matrix Size 

References

  1. 1.
    Irwin GW: Parallel algorithms for control. Control Engineering Practice 1993, 1(4):635-643. 10.1016/0967-0661(93)91387-CCrossRefGoogle Scholar
  2. 2.
    Ceschia M, Bellato M, Paccagnella A, Kaminski A: Ion beam testing of ALTERA APEX FPGAs. Proceedings of IEEE Radiation Effects Data Workshop, July 2002, Phoenix, Ariz, USA 45-50.CrossRefGoogle Scholar
  3. 3.
    El-Amawy A: A systolic architecture for fast dense matrix inversion. IEEE Transactions on Computers 1989, 38(3):449-455. 10.1109/12.21131MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ghosh AK, Paparao P: Performance of modified Faddeev algorithm on optical processors. IEE Proceedings. J: Optoelectronics 1992, 139(5):325-330. 10.1049/ip-j.1992.0056Google Scholar
  5. 5.
    Zajc M, Sernec R, Tasic J: An efficient linear algebra SoC design: implementation considerations. Proceedings of 11th Mediterranean Electrotechnical Conference (MELECON '02), May 2002, Cairo, Egypt 322-326.Google Scholar
  6. 6.
    Gaston FMF, Irwin GW: Systolic Kalman filtering: an overview. IEE Proceedings. D: Control Theory & Applications 1990, 137(4):235-244. 10.1049/ip-d.1990.0029CrossRefMATHGoogle Scholar
  7. 7.
    Gaston FMF, Brown DW, Kadlec J: A parallel predictive controller. Proceedings of UKACC International Conference on Control, September 1996, Exeter, UK 2: 1070-1075.CrossRefGoogle Scholar
  8. 8.
    El-Amawy A, Dharmarajan KR: Parallel VLSI algorithm for stable inversion of dense matrices. IEE Proceedings. E: Computers and Digital Techniques 1989, 136(6):575-580. 10.1049/ip-e.1989.0079MATHGoogle Scholar
  9. 9.
    Faroughi N, Shanblatt MA: An improved systematic method for constructing systolic arrays from algorithms. Proceedings of 24th ACM/IEEE Design Automation Conference (DAC '87), June–July 1987, Miami Beach, Fla, USA 26-34.CrossRefGoogle Scholar
  10. 10.
    Chen S-G, Lee J-C, Li C-C: Systolic implementation of Kalman filter. Proceedings of IEEE Asia-Pacific Conference on Circuits and Systems (APCCAS '94), December 1994, Taipei, Taiwan 97-102.Google Scholar
  11. 11.
    Salcic Z, Lee C-R: Scalar-based direct algorithm mapping FPLD implementation of a Kalman filter. IEEE Transactions on Aerospace and Electronic Systems 2000, 36(3, part 1):879-888. 10.1109/7.869507CrossRefGoogle Scholar
  12. 12.
    Lawrie D, Fleming P: Fine-grain parallel processing implementations of Kalman filter algorithms. Proceedings of International Conference on Control, March 1991, Edinburgh, Scotland, UK 2: 867-870.MathSciNetGoogle Scholar
  13. 13.
    Mitra SK: Digital Signal Processing: A Computer-Based Approach. 2nd edition. McGraw-Hill/Irwin, Boston, Mass, USA; 2001.Google Scholar
  14. 14.
    Kalman RE: A new approach to linear filtering and prediction problems. Transaction of the ASME, Series D, Journal of Basic Engineering 1960, 82: 35-45. 10.1115/1.3662552CrossRefGoogle Scholar
  15. 15.
    Vaseghi SV: Advanced Digital Signal Processing and Noise Reduction. 2nd edition. John Wiley & Sons, New York, NY, USA; 2000.Google Scholar
  16. 16.
    Kamen EW, Su JK: Introduction to Optimal Estimation. Springer, London, UK; 1999.CrossRefMATHGoogle Scholar
  17. 17.
    Swanson DC: Signal Processing for Intelligent Sensor Systems. Marcel Dekker, New York, NY, USA; 2000.CrossRefGoogle Scholar
  18. 18.
    Lee C-R: FPLD implementation and customisation in multiple target tracking applications, Engineering Ph.D. thesis. the University of Auckland, Auckland, New Zealand; 1998.Google Scholar

Copyright information

© Bigdeli et al. 2006

Authors and Affiliations

  • Abbas Bigdeli
    • 1
  • Morteza Biglari-Abhari
    • 1
  • Zoran Salcic
    • 1
  • Yat Tin Lai
    • 1
  1. 1.Department of Electrical and Computer Engineeringthe University of AucklandPrivate BagNew Zealand

Personalised recommendations