Distributed Estimation Over an Adaptive Diffusion Network Based on the Family of Affine Projection Algorithms

This paper utilizes the family of affine projection algorithms (APAs) for distributed estimation in the adaptive diffusion networks. The diffusion APA (DAPA), the diffusion selective partial update (SPU) APA (DSPU-APA), the diffusion selective regressor (SR) APA (DSR-APA), and the diffusion dynamic selection (DS) APA (DDS-APA) are introduced in a unified way. In DSPU-APA, the weight coefficients are partially updated at each node during the adaptation. Therefore, the DSPU-APA has lower computational complexity in comparison to the DAPA. In addition, the convergence speed of the DSPU-APA is close to the DAPA. In DSR-APA, a subset of input regressors is optimally selected at each node during the adaptation. The dynamic selection of input regressors is performed in the DDS-APA. These strategies improve the performance of the conventional DAPA in terms of the steady-state error and computational complexity features. Also, by combining these algorithms, the DSPU-SR-APA and the DSPU-DS-APA are established, which are computationally efficient. The mean-square performance of the proposed algorithms is analyzed in the nonstationary environment and the generic relations for the theoretical learning curve and the steady-state error are derived. The analysis is based on the spatial-temporal energy conservation relation. The validity of the theoretical results and the good performance of the introduced algorithms are demonstrated by several computer simulations in diffusion networks.