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

In this correspondence, 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 $\mathbb{R}^m$ $(m\geq1)$ introduced in \cite{usman_loctsp:08}. DILAND operates when (i) the communication among the sensors is noisy; (ii) the communication links in the network may fail with a non-zero probability; and (iii) 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, this correspondence shows that, under the broad random phenomena described above, DILAND converges almost surely (a.s.) to the exact sensor locations.

💡 Research Summary

The paper introduces DILAND (Distributed sensor Localization with Noisy Distance measurements), a robust extension of the earlier DLRE algorithm, designed for wireless sensor networks where three major sources of randomness coexist: (i) noisy inter‑node communication, (ii) stochastic link failures, and (iii) noisy distance measurements. The authors assume that at least (m+1) anchor nodes with known positions are placed such that all unknown sensors lie inside the convex hull formed by these anchors. Each sensor must belong to at least one triangulation (or, in higher dimensions, an (m)-simplex) consisting of neighboring sensors and possibly anchors; this “partial strong connectivity” condition is far weaker than requiring a globally connected graph.

The algorithm proceeds in discrete time. At each iteration a sensor (i) receives from each currently active neighbor (j) a message containing the neighbor’s current position estimate, corrupted by additive zero‑mean i.i.d. communication noise (\eta_{ij}(t)). The communication link ((i,j)) is present with probability (p>0) independently across time, modeling random link failures. The measured Euclidean distance between (i) and (j) is also noisy; the algorithm uses a distance‑based weight
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