Linear independence method for system identification/secondary path modeling for active control

Benjamin J. Kim, David C. Swanson

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


A method for noninvasive system identification/secondary path modeling has been developed for single- and multi-channel filtered-x least-mean-square (LMS)-based active noise control (ANC). The problem of on-line secondary path modeling is recognized as one of linear dependence associated with an underdetermined system, a one-equation/two-unknown problem in which the highly correlated primary source and secondary source contributions to the error signal are not readily distinguishable. The method resolves this uniqueness issue by introducing a second equation with similar unknowns. The critical linear independence of the two equations, hence the proposed designation, is achieved with a single perturbation of the control filter output, thereby rendering the system solvable. This secondary path modeling strategy was implemented using an innovative real-time DSP control architecture and tested on a "transducerless" system devised to investigate behavior of ANC algorithms. Results of narrowband, broadband, and multi-channel tests reveal response estimates that are accurate in both magnitude and phase; bias due to primary noise and other secondary sources is notably absent in the obtained secondary path models. The rapidity with which the system is identified can also contribute to the stability and performance of filtered-x LMS-based controllers.

Original languageEnglish (US)
Pages (from-to)1452-1468
Number of pages17
JournalJournal of the Acoustical Society of America
Issue number3 I
StatePublished - Sep 2005

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


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