Abstract: At present,most distributed estimation algorithms minimize mean square error as a cost function,which willarise the performance deteriorates or even diverge under the impulsive noises.The diffusion affine projection sign algorithm (DAPSA) uses L₁ norm as cost function,which is robustness to impulsive noises environment,and has a fast convergence speed.However,there is a contradiction between maintaining a large initial convergence speed and a low steady-state erro under a fixed step-size.In order to reduce the steady-state adjustment of DAPSA in a non-Gaussian noise environment while maintaining a fast initial convergence speed,a diffusion maximum correntropy criterion variable step size affine projection sign algorithm (DMCCVSS-APSA) is proposed.Firstly,the algorithm uses the improved chi-square kernel instead of improved gaussian kernel as the kernel function.The adaptive step size method can effectively reduce the steady-state error while achieving the faster initial convergence speed.The adaptive dynamic range method based on a priori error estimation can further reduce the steady-state error.Then the improved chi-square kernel is compared with the improved gaussian kernel,the DMCCVSS-APSA is compared with other distributed algorithms and the DMCCVSS-APSA is compared with DAPSA under different impulsive noises.Experiments verify the performance of the proposed algorithm.Simulation results show that DMCCVSS-APSA performs better than the contrast algorithms,and the steady-state error is reduced more than 5 dB at a similar initial convergence speed.The experimental data fully demonstrates that the variable step size method and the adaptive dynamic range method based on fixed step-size DAPSA can effectively reduce the steady-state error and have strong robustness to impulsive noises.It is an optimization of the distributed affine projection algorithm.Finally,the proposed algorithm needs further research on the combination of ATC mode and the optimal sensitivity factor.

Key words: Chi-square kernel, Diffusion, Distributed adaptive estimation, Impulsive noises, Maximum correntropy criterion