New ANC algorithm cancels toughest noise from helicopters to gunshots

Conventional active noise control (ANC) filters like the normalized subband p‑norm (NSPN) algorithm degrade badly when faced with three common real‑world conditions: non‑Gaussian inputs, α‑stable noise with a stability parameter α ≤ 1 (which includes heavy‑tailed impulse noise), and sparse system identification. To overcome these limitations, a team led by Jianhong Ye and Haiquan Zhao (Southwest Jiaotong University) introduces the fractional‑order NSPN algorithm based on nearest Kronecker product (NKP) decomposition and fractional‑order stochastic gradient descent. Their central innovation is a transformation‑based NKP (TNKP) decomposition that dramatically lowers computational cost while maintaining stability. For ANC applications, they also develop filtered‑x variants — NKP‑FxFoNSPN and TNKP‑FxFoNSPN — and derive theoretical bounds for the fractional‑order parameter β.

The algorithms were tested on five very different noise sources: pink noise, helicopter rotor noise, gunshot impulses, pile driver impacts, and traction substation hum. In every case, the TNKP‑FoNSPN achieved lower steady‑state misadjustment and lower multiplication cost compared with earlier methods. Real‑world validation came from a single‑channel duct ANC experiment and a simulated multi‑channel ANC system — both showing clear noise reduction superiority. The work provides complete computational complexity analyses, making it practical for engineers designing ANC systems for industrial, automotive, and aerospace applications where noise is variable and unpredictable.