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

• Published in: IEEE signal processing letters Vol. 5; no. 5; pp. 111 - 114
• Main Authors: Gollamudi, S., Nagaraj, S., Kapoor, S., Yih-Fang Huang
• Format: Journal Article
• Language: English
• Published: IEEE 01.05.1998
• Subjects: Adaptive filters; Additive noise; Convergence; Filtering algorithms; Filtering theory; Least squares approximation; Resonance light scattering; Signal processing algorithms; System identification; Time sharing computer systems
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/97.668945

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.