In this paper the aim is to solve the problem of distributed estimation in an incremental network when the measurements taken by the nodes follow a widely linear model. The proposed algorithm, which we refer to as incremental augmented affine projection algorithm (incAAPA), utilizes the full second order statistical information in the complex domain. Moreover, it exploits the spatio-temporal diversity to improve the estimation performance. We derive steady-state performance metric of the incAAPA in terms of mean-square deviation. We further derive sufficient conditions to ensure mean-square convergence. Our analysis illustrates that the proposed algorithm is able to process both second-order circular (proper) and non-circular (improper) signals. The validity of the theoretical results and the good performance of the proposed algorithm are demonstrated by several computer simulations.
