Abstract: A new P-norm based variable scale DFAIR diffusion fair cost function algorithm is proposed to further enhance the performance of diffusion based adaptive filtering algorithms in different noise environments. The absolute value of the error term is augmented with a P-norm and a scale factor that varies with the error is established using a tongue-like function to control the steepness of the algorithm. As a result, the convergence speed of the algorithm is accelerated and the steady-state error is reduced. The simulation results in Gaussian noise environments, as well as non-Gaussian noise environments with alpha stable distribution and Bernoulli Gaussian distribution, demonstrate the algorithm has stronger robustness and lower steady-state error. The performance of the proposed algorithm surpasses that of the comparison algorithm in various noise environments.

Key words: adaptive filtering, distributed, variable scale factor, P-norm