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A square root covariance algorithm for constrained recursive least squares estimation

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Abstract

In this contribution, a covariance counterpart is described of the information matrix approach to constrained recursive least squares estimation. Unlike information-type algorithms, covariance algorithms are amenable to parallel implementation, e.g., on processor arrays, and this is also demonstrated. As compared to previously described combined covariance-information algorithms/arrays, the present implementation avoids a doubling of the hardware requirement, and therefore constitutes a significant improvement over these combined implementations as well.

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References

  1. G.H. Golub, “Numerical methods for solving linear least squares problems,”Numer. Math., vol. 7, 1965, pp. 206–216.

    Article  MathSciNet  MATH  Google Scholar 

  2. G.H. Golub and C.F. Van Loan,Matrix computations, North Oxford Academic Publishing Co., Johns Hopkins Press, 1983.

  3. P.E. Gill, G.H. Golub, W. Murray and M. A. Saunders, “Methods for modifying matrix factorizations,”Math. Comp., vol. 28, 1974, pp. 505–535.

    Article  MathSciNet  MATH  Google Scholar 

  4. W.M. Gentleman and H.T. Kung, “Matrix triangularization by systolic arrays,”Real-Time Signal Processing IV, Proc. SPIE, vol. 298, 1982, pp. 19–26.

    Article  Google Scholar 

  5. T.J. Shepherd, J.G. McWhirter and J.E. Hudson, “Parallel weight extraction from a systolic adaptive beamformer,” InMathematics in Signal Processing II (J.G. McWhirter, ed.), Oxford: Clarendon Press, 1990, pp. 775–790.

    Google Scholar 

  6. M. Moonen and J. Vandewalle, “Recursive least squares with stabilized inverse factorization,”Signal Processing, vol. 21, 1990, pp. 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Moonen and J. Vandewalle, “A systolic array for recursive least squares computations,” K. Univ. Leuven, Dept. El. Eng., ESAT-SISTA report 90-22 (submitted for publication).

  8. C.T. Pan and R.J. Plemmons, “Least squares modifications with inverse factorization: Parallel implications,”J. Comp. Appl. Math., vol. 27, 1989, pp. 109–127.

    Article  MathSciNet  MATH  Google Scholar 

  9. T.J. Shepherd and J.G. McWhirter, “A pipelined array for linearly constrained least squares optimization,” InMathematics in Signal Processing (T.S. Durrani, J.B. Abbiss, J.E. Hudson, R.W. Madan, J.G. McWhirter and T.A. Moore, eds.), Oxford: Clarendon Press, 1987, pp. 607–635.

    Google Scholar 

  10. G.W. Stewart, “A Jacobi-like algorithm for computing the Schur decomposition of a nonhermitian matrix,”SIAM J. Sc. Stat. Comp., vol. 6, 1985, pp. 853–863.

    Article  MATH  Google Scholar 

  11. F.T. Luk, “A triangular processor array for computing singular values,”Lin. Alg. Appl., vol. 77, 1986, pp. 259–273.

    Article  MATH  Google Scholar 

  12. D.P. O'Leary and G.W. Stewart, “Data flow algorithms for parallel matrix computations,”Comm. ACM, vol. 28, 1975, pp. 840–853.

    Article  MathSciNet  Google Scholar 

  13. M. Moonen and J. Vandewalle, “A hexagonally connected processor array for Jacobi-type matrix algorithms,”Electronics Letters, vol. 26, 1990, pp. 400–401.

    Article  Google Scholar 

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Moonen, M., Vandewalle, J. A square root covariance algorithm for constrained recursive least squares estimation. J VLSI Sign Process Syst Sign Image Video Technol 3, 163–172 (1991). https://doi.org/10.1007/BF00925827

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  • DOI: https://doi.org/10.1007/BF00925827

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