Joint node localization and error correction in wireless sensor networks

In the node localization problem of wireless sensor networks (WSNs), distance measurements are often corrupted by large errors which will lead to inaccurate position estimates without correction. To address this issue, we propose a scheme of joint node localization and error correction from distance measurements of WSNs. The enabling fact is that only a small number of distance measurements are subject to large errors in general. Such sparsity motivates us to propose an l₁ regularized nonlinear least squares model, where the l₁ regularization term promotes the sparsity of large errors and the nonlinear least squares term reflects the fidelity of distance measurements. This nonconvex model is further relaxed to a second-order cone programming (SOCP) problem, which is convex and tractable. Extensive simulations demonstrate the effectiveness of the proposed approach.