[Paper Review] Maximum Likelihood based Multihop Localization in Wireless Sensor Networks

Camly Nguyen, Orestis Georgiou+1 more|arXiv (Cornell University)|Feb 6, 2015

Indoor and Outdoor Localization Technologies19 references4 citations

TL;DR

This paper proposes kHopLoc, a maximum-likelihood-based multihop localization algorithm for wireless sensor networks that uses Monte Carlo simulations to model multihop connection density functions during a training phase. By maximizing likelihood functions derived from hop counts to anchor nodes, kHopLoc achieves 20–40% higher accuracy than existing range-free methods in both isotropic and anisotropic network deployments, with lower computational and communication costs.

ABSTRACT

For data sets retrieved from wireless sensors to be insightful, it is often of paramount importance that the data be accurate and also location stamped. This paper describes a maximum-likelihood based multihop localization algorithm called kHopLoc for use in wireless sensor networks that is strong in both isotropic and anisotropic network deployment regions. During an initial training phase, a Monte Carlo simulation is utilized to produce multihop connection density functions. Then, sensor node locations are estimated by maximizing local likelihood functions of the hop counts to anchor nodes. Compared to other multihop localization algorithms, the proposed kHopLoc algorithm achieves higher accuracy in varying network configurations and connection link-models.

Motivation & Objective

• Address the limitations of conventional range-free localization in anisotropic and irregularly deployed wireless sensor networks.
• Overcome the poor performance of DV-hop and its variants when hop-distance proportionality assumptions fail due to obstacles, fading, or non-uniform node distributions.
• Develop a localization method that leverages full statistical distributions of multihop connections rather than relying on first-order statistics like average hop distance.
• Minimize computational and communication overhead while maintaining high localization accuracy across diverse network configurations.
• Enable robust localization in GPS-denied environments such as indoor or urban canyon scenarios where signal propagation is irregular.

Proposed method

• Conduct a Monte Carlo simulation during a training phase to generate empirical multihop connection probability density functions for varying hop counts.
• Model the multihop connection density using a generalized gamma distribution with parameters A(k) and B(k), fitted via Newton’s method to minimize error.
• Construct a likelihood function for each target node based on its observed hop counts to all reachable anchor nodes.
• Estimate the target node’s location by maximizing the likelihood function using the Newton-Raphson method, leveraging full statistical information of multihop connectivity.
• Flood the fitted parameters (A(k), B(k)) from a central node to all sensor nodes, enabling distributed localization with minimal runtime communication.
• Use all-pairs shortest path algorithms (e.g., Floyd-Warshall) in the training phase to compute k-hop paths across the simulated network topology.

Experimental results

Research questions

• RQ1 Can a maximum-likelihood approach using full multihop density distributions significantly improve localization accuracy in both isotropic and anisotropic WSN deployments?
• RQ2 How does the proposed kHopLoc algorithm compare in accuracy and efficiency to DV-hop and ASP in irregular or non-uniform network topologies?
• RQ3 What is the trade-off between communication cost, computational complexity, and localization accuracy in multihop range-free localization?
• RQ4 To what extent can Monte Carlo-based training reduce localization error compared to first-order statistical models like average hop distance?
• RQ5 Can the algorithm maintain high performance with fewer anchor nodes while avoiding the high overhead of range-based methods?

Key findings

• kHopLoc achieves 20–40% higher localization accuracy than conventional DV-hop and ASP algorithms in both isotropic and anisotropic network deployments.
• The algorithm reduces computational cost to O(I·N³ + M·ε⁻³/²), which is significantly lower than the O(M⁸ + Δ + M²·ε⁻³/²) cost of the ASP algorithm.
• Communication cost is approximately O(M(N−M)) for hop count collection and O(N) for broadcasting fitted parameters, totaling about half the cost of DV-hop and ASP.
• The use of full multihop density distributions instead of average hop distance improves robustness in non-uniform and obstructed environments.
• The training phase can be performed once at a central gateway or preloaded into nodes, eliminating recurring communication overhead during localization.
• The algorithm remains effective even in irregular-shaped regions and networks with non-uniform node distributions, where traditional methods fail due to broken hop-distance proportionality.