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Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size

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4 Author(s)
Gollamudi, S. ; Lab. for Image & Signal Anal., Notre Dame Univ., IN, USA ; Nagaraj, S. ; Kapoor, S. ; Yih-Fang Huang

Set-membership identification (SMI) theory is extended to the more general problem of linear-in-parameters filtering by defining a set-membership specification, as opposed to a bounded noise assumption. This sets the framework for several important filtering problems that are not modeled by a "true" unknown system with bounded noise, such as adaptive equalization, to exploit the unique advantages of SMI algorithms. A recursive solution for set membership filtering is derived that resembles a variable step size normalized least mean squares (NLMS) algorithm. Interesting properties of the algorithm, such as asymptotic cessation of updates and monotonically non-increasing parameter error, are established. Simulations show significant performance improvement in varied environments with a greatly reduced number of updates.

Published in:

Signal Processing Letters, IEEE  (Volume:5 ,  Issue: 5 )