[Paper Review] Distributed Localization of Tree-structured Scattered Sensor Networks

Sina Khoshfetrat Pakazad, Emre Özkan+3 more|arXiv (Cornell University)|Jul 16, 2016

Indoor and Outdoor Localization Technologies24 references3 citations

TL;DR

This paper proposes a distributed localization algorithm for tree-structured scattered sensor networks using a primal-dual interior-point method applied to a semidefinite relaxation of the maximum-likelihood localization problem. By exploiting tree structure via message-passing and dynamic programming, the algorithm achieves fast convergence with minimal iterations and communications—outperforming first-order methods in accuracy, robustness to measurement bias, and scalability, especially under sparse or poor-quality range measurements.

ABSTRACT

Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or communications among computational agents. Furthermore, some of these distributed algorithms put a considerable computational demand on the agents. In this paper, we show that for tree-structured scattered sensor networks, which are networks that their inter-sensor range measurement graphs have few edges (few range measurements among sensors) and can be represented using a tree, it is possible to devise an efficient distributed localization algorithm that solely relies on second-order methods. Particularly, we apply a state-of-the-art primal-dual interior-point method to a semidefinite relaxation of the maximum-likelihood formulation of the localization problem. We then show how it is possible to exploit the tree-structure in the network and use message-passing or dynamic programming over trees, to distribute computations among different computational agents. The resulting algorithm requires far fewer iterations and communications among agents to converge to an accurate estimate. Moreover, the number of required communications among agents, seems to be less sensitive and more robust to the number of sensors in the network, the number of available measurements and the quality of the measurements. This is in stark contrast to distributed algorithms that rely on first-order methods. We illustrate the performance of our algorithm using experiments based on simulated and real data.

Motivation & Objective

• To address the limitations of first-order distributed localization algorithms, which require many iterations and are sensitive to measurement quality and network topology.
• To develop a scalable, robust, and efficient distributed localization method for sensor networks with few inter-sensor range measurements.
• To leverage the tree-structure of the inter-sensor range measurement graph to enable efficient computation distribution via message-passing and dynamic programming.
• To reduce communication overhead and improve convergence speed compared to existing first-order methods, especially under sparse or biased measurements.
• To demonstrate the superiority of second-order methods in distributed localization by applying a state-of-the-art primal-dual interior-point method to a semidefinite relaxation.

Proposed method

• The method uses a semidefinite programming (SDP) relaxation of the maximum-likelihood formulation of the sensor localization problem.
• A primal-dual interior-point method is applied to solve the SDP relaxation, enabling high-accuracy solutions with global convergence guarantees.
• The tree-structure of the sensor network’s range measurement graph is exploited via message-passing and dynamic programming to distribute the computational load across agents.
• The algorithm decomposes the problem into local subproblems using clique trees, enabling distributed computation while maintaining global consistency.
• Computational agents (sensors or anchors) exchange messages along the tree structure to iteratively refine the localization estimate.
• The method is robust to biased and low-quality measurements due to the inherent stability of semidefinite relaxation and second-order optimization.

Experimental results

Research questions

• RQ1 Can second-order optimization methods be effectively distributed in tree-structured sensor networks to achieve faster convergence than first-order methods?
• RQ2 How does the tree-structure of the inter-sensor range measurement graph enable efficient distribution of a second-order optimization algorithm?
• RQ3 To what extent does the proposed algorithm reduce communication and iteration count compared to first-order distributed methods like ADMM or gradient-based schemes?
• RQ4 How robust is the algorithm to measurement bias and poor-quality range data, especially when the intersection of measurement disks is empty?
• RQ5 Can the algorithm maintain performance across varying network connectivity and sensor counts without significant degradation?

Key findings

• The proposed distributed primal-dual interior-point algorithm (DPDRA) converges in approximately 17 iterations on average, regardless of network size or connectivity, demonstrating high robustness.
• DPDRA required only around 100 communications per agent, showing significantly reduced communication overhead compared to first-order methods.
• For networks with up to 30 sensors, DPDRA outperformed DDRA in all performance criteria, including accuracy, convergence speed, and robustness.
• On real-world data with biased range measurements (standard deviation 1.82 m), DDRA failed to converge due to empty intersection of disks, while DPDRA successfully localized all sensors.
• The algorithm maintained stable performance across varying communication ranges (4 to 6.5 m), with minimal variation in computational time and convergence steps.
• The performance of DPDRA was less sensitive to the number of sensors, measurement sparsity, and measurement quality, unlike first-order methods.