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Real-Time TLS Algorithms in Gaussian and Impulse Noise Environments

In: Total Least Squares and Errors-in-Variables Modeling

Author

Listed:
  • Da-Zheng Feng

    (Xidian University, Key Lab. for Radar Signal Processing)

  • Zheng Bao

    (Xidian University, Key Lab. for Radar Signal Processing)

  • Xian-Da Zhang

    (Xidian University, Key Lab. for Radar Signal Processing)

Abstract

On the basis of the total minimum mean square error or the minimum Raleigh quotient, we propose a modified total least mean squares (TLMS) algorithm with the computational complexity close to the well-known LMS algorithm. A new fast RTLS algorithm is developed by using the recursive computation of the TLS solution for adaptive finite impulse response (FIR) filters. Using the shift structure of the augmented data vector, a fast algorithm for computing the new gain vector is given. The new fast algorithm is numerically stable and of computational complexity O (n). A recursive total instrumental-variable (RTIV) algorithm is given for finding the TLS solution to the over-determined normal equations, and its applications to adaptive IIR filtering are presented. Its arithmetic operation complexity is O (mn) (where m is the number of instrumental variables and n the dimension of the input-vector) per iteration. We give the L p -norm distance from a point to a hyper-plane. A real-time algorithm is introduced for finding the robust TLS solution in impulse noise, and has computational complexity O (n).

Suggested Citation

  • Da-Zheng Feng & Zheng Bao & Xian-Da Zhang, 2002. "Real-Time TLS Algorithms in Gaussian and Impulse Noise Environments," Springer Books, in: Sabine Van Huffel & Philippe Lemmerling (ed.), Total Least Squares and Errors-in-Variables Modeling, pages 341-350, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-3552-0_30
    DOI: 10.1007/978-94-017-3552-0_30
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