A Distributed Adaptive Algorithm Based on the Asymmetric Cost of Error Functions

In this paper, a family of novel diffusion adaptive estimation algorithms is proposed from the asymmetric cost function perspective by combining diffusion strategy and the linear–linear cost, quadratic-quadratic cost, and linear-exponential cost at all distributed network nodes, and named diffusion LLCLMS (DLLCLMS), diffusion QQCLMS (DQQCLMS), and diffusion LECLMS (DLECLMS), respectively. Then, the stability of mean estimation error and computational complexity of those three diffusion algorithms are analyzed theoretically. Finally, several experiment simulation results are designed to verify the superiority of those three proposed diffusion algorithms. Results show that DLLCLMS, DQQCLMS, and DLECLMS algorithms are more robust to the input signal and impulsive noise than the diffusion sign-error LMS, diffusion robust variable step-size least mean square (DRVSSLMS), and least mean logarithmic absolute difference algorithms. In brief, theoretical analysis and experiment results show that those proposed DLLCLMS, DQQCLMS, and DLECLMS algorithms perform better when estimating the unknown linear system under the changeable impulsive noise environments and different environments types of input signals.