Truncated Singular Value Decomposition Method for Mitigating Unwanted Enhancement in Active Noise Control Systems

It is well-known that good noise cancellation performance can only be realized by a multiple-input active noise control system when the primary noise sources are persistently exciting, and the reference signals are uncorrelated. Otherwise, the noise reduction performance will deteriorate and, quite possibly, the noise can be enhanced. In particular, when the reference signals are correlated in a certain frequency band, enhancement can occur in that band. In the present work, singular value decomposition was applied to the auto-correlation matrix of the reference signals to analyze this enhancement issue. It was found that the level of enhancement was associated with the small singular values. Also, the enhancement frequency bands were found to be associated with large values of the frequency response of the filters that correspond to the singular vectors associated with the small singular values. According to this analysis, a method that removes the small singular values and associated singular vectors of the auto-correlation matrix was proposed and applied to mitigate the noise enhancement. The designed controllers were experimentally implemented in real time and the experimental performance agreed well with off-line simulation results, in which the noise enhancement was reduced.