DILAND: An Algorithm for Distributed Sensor Localization With Noisy Distance Measurements

We present an algorithm for distributed sensor localization with noisy distance measurements (DILAND) that extends and makes the DLRE more robust. DLRE is a distributed sensor localization algorithm in $\BBR ^{m}~(m\geq 1)$ introduced in our previous work (IEEE Trans. Signal Process., vol. 57, no. 5, pp. 2000–2016, May 2009). DILAND operates when: 1) the communication among the sensors is noisy; 2) the communication links in the network may fail with a nonzero probability; and 3) the measurements performed to compute distances among the sensors are corrupted with noise. The sensors (which do not know their locations) lie in the convex hull of at least $m+1$ anchors (nodes that know their own locations). Under minimal assumptions on the connectivity and triangulation of each sensor in the network, we show that, under the broad random phenomena described above, DILAND converges almost surely (a.s.) to the exact sensor locations.