Development of the filtered-U algorithm for active noise control

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Abstract
The filtered‐X algorithm developed by Widrow and Burgess is an alternate form of the least‐mean‐square (LMS) algorithm for use when there are transfer functions in the auxiliary path following the adaptive filter. To ensure convergence of the algorithm, the input to the error correlators is filtered by a copy of these auxiliary path transfer functions. More recently, the author has presented a new approach to active noise control in the presence of acoustic feedback that uses an infinite impulse response (IIR) filter structure with an alternate form of the recursive least‐mean‐square (RLMS) algorithm. This algorithm may be described as a filtered‐U algorithm since it uses a copy of the auxiliary path transfer functions to filter the generalized input vector U to the error correlators of both the direct and recursive elements of the filter to ensure convergence. The relationship of the filtered‐U to the filtered‐X algorithm and other earlier concepts is discussed.

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