Distributed Sensor Localization in Random Environments using Minimal Number of Anchor Nodes

TL;DR

This paper introduces DILOC, a distributed, iterative algorithm for sensor localization that uses minimal anchor nodes and operates without centralized control, even in noisy and random environments.

Contribution

The paper presents DILOC, a novel distributed localization algorithm that minimizes anchor nodes and extends to stochastic environments with convergence guarantees.

Findings

DILOC converges almost surely in deterministic environments.

The stochastic version of DILOC converges despite noise and link failures.

Numerical results demonstrate robustness under various conditions.

Abstract

The paper develops DILOC, a \emph{distributive}, \emph{iterative} algorithm that locates M sensors in $\mathbb{R}^m, m\geq 1$, with respect to a minimal number of m+1 anchors with known locations. The sensors exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there centralized knowledge about the sensors' locations. DILOC uses the barycentric coordinates of a sensor with respect to its neighbors that are computed using the Cayley-Menger determinants. These are the determinants of matrices of inter-sensor distances. We show convergence of DILOC by associating with it an absorbing Markov chain whose absorbing states are the anchors. We introduce a stochastic approximation version extending DILOC to random environments when the knowledge about the intercommunications among sensors and the inter-sensor distances are noisy, and the communication links among neighbors fail at random times. We show a.s. convergence of the modified DILOC and characterize the error between the final estimates and the true values of the sensors' locations. Numerical studies illustrate DILOC under a variety of deterministic and random operating conditions.