A Bayesian Algorithm for Distributed Network Localization Using Distance and Direction Data

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.Notice: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

A Geometric Approach for Distributed Multi-Hop Target Localization in Cooperative Networks

“…To analyze the worst-case computational complexity, a fully connected network (i.e., the total number of edges for each target is |E i | = N +(M −1), ∀i ∈ T ) is considered and merely the dominating terms are considered, expressed as a function of |E i |. The results regarding computational complexity of the considered algorithms are summarized in Table I, where S max , C max , and T max are used to denote the number of step in the bisection procedure in 1, the number of generated candidates and the number of iterations in MPHL [26], respectively.…”

“…Localization based on range (through Received Signal Strength (RSS) or time of arrival) and/or bearing (Angle Of Arrival (AOA)) measurements has received much attention in the recent society lately [4]- [26]. Nonetheless, most of these approaches are designed for non-cooperative networks in which target/target communication is not allowed or require a central unit which gathers all measurements and performs all computations.…”

“…Hence, stacking the line equations in vectors resulted in DLLS. In [26], a Message Passing Hybrid Localization (MPHL) for cooperative distributed localization using joint distance and direction measurements was proposed. The idea was to provide a method for sampling from a generic distribution.…”

“…The idea was to provide a method for sampling from a generic distribution. To this end, the authors in [26] employed Markov chain Monte Carlo sampling and Metropolis-Hastings random walk, to generate (dependent on a current state) and evaluate candidate points to compute their beliefs, and choose the best one. However, the performance of MPHL (both accuracy and complexity) is directly linked to the number of samples used.…”

“…The above RSS/AOA cooperative distributed localization algorithms are either excessively expensive computationwise [24], [26] or require knowledge about noise powers [25] and its distribution [26]; hence, they might not be convenient for practical use. Unlike these, a novel algorithm is proposed here based on a simple geometrical approach and multi-hopping, which has linear computational complexity and does not require any knowledge about noise powers nor its distribution.…”