Distributed Error-Identification and Correction Using Block-Sparse Optimization

This article considers the problem of error identification and correction (EIC) in sensor networks, wherein the objective is to identify the agents that have erroneous state estimates and reconstruct their errors. We develop a general framework for reconstructing errors by processing nonlinear measurements obtained across the sensor network, based on the assumptions that the errors are sparse (i.e., only a fraction of the agents have errors) and that the sensor network is sparsely connected. It is shown that this twofold sparsity of the EIC problem can be leveraged using a combination of block-sparse optimization and the alternating direction method of multipliers, yielding a novel distributed EIC algorithm which can be interpreted as a multiagent residual testing mechanism. The effectiveness of the proposed distributed EIC approach is demonstrated by considering a numerical example of sensor network localization, in which the distances between connected agents are used to uniquely identify and correct the agents with erroneous position estimates without relying on anchors (i.e., agents that are assumed to be error-free).