# A Bayesian algorithm for distributed network localization using distance and direction data

## TL;DR

This paper introduces a hybrid Bayesian algorithm combining distance and direction data for distributed network localization, significantly improving accuracy and robustness over existing methods.

## Contribution

The novel MPHL algorithm integrates belief propagation and MCMC for cooperative localization, reducing dependency on anchor placement and using fewer anchors.

## Key findings

- Localization error reduced by about 50% in simulations
- Single neighbor can localize a node with the new method
- Network can be localized with only one anchor

## Abstract

A reliable, accurate, and affordable positioning service is highly required in wireless networks. In this paper, the novel Message Passing Hybrid Localization (MPHL) algorithm is proposed to solve the problem of cooperative distributed localization using distance and direction estimates. This hybrid approach combines two sensing modalities to reduce the uncertainty in localizing the network nodes. A statistical model is formulated for the problem, and approximate minimum mean square error (MMSE) estimates of the node locations are computed. The proposed MPHL is a distributed algorithm based on belief propagation (BP) and Markov chain Monte Carlo (MCMC) sampling. It improves the identifiability of the localization problem and reduces its sensitivity to the anchor node geometry, compared to distance-only or direction-only localization techniques. For example, the unknown location of a node can be found if it has only a single neighbor; and a whole network can be localized using only a single anchor node. Numerical results are presented showing that the average localization error is significantly reduced in almost every simulation scenario, about 50% in most cases, compared to the competing algorithms.