  This paper proposes an online secondary path modelling (SPM) technique to
improve the performance of the modified filtered reference Least Mean Square
(FXLMS) algorithm. It can effectively respond to a time-varying secondary path,
which refers to the path from a secondary source to an error sensor. Unlike
traditional methods, the proposed approach switches modes between adaptive ANC
and online SPM, eliminating the use of destabilizing components such as
auxiliary white noise or additional filters, which can negatively impact the
complexity, stability, and noise reduction performance of the ANC system. The
system operates in adaptive ANC mode until divergence is detected due to
secondary path changes. At this moment, it switches to SPM mode until the path
is remodeled and then returns to ANC mode. Furthermore, numerical simulations
in the paper demonstrate that the proposed online technique effectively copes
with the secondary path variations.
