Node localization based on distributed constrained optimization using Jacobi's method

  title={Node localization based on distributed constrained optimization using Jacobi's method},
  author={Henrique Ferraz and Amr Alanwar and Mani B. Srivastava and Jo{\~a}o Pedro Hespanha},
  journal={2017 IEEE 56th Annual Conference on Decision and Control (CDC)},
We consider the spatial localization of nodes in a network, based on measurements of their relative position with respect to their neighbors. [] Key Method Under appropriate assumptions, it is shown that the maximum likelihood estimates are locally asymptotically stable equilibrium points of the proposed algorithm. As a case study, we consider a range-based localization problem and present simulation results to evaluate the algorithm.

Figures from this paper

TERSE-KF: Event-Trigger Diffusion Kalman Filter with Application to Localization and Time Synchronization
This work proposes an event-trigger diffusion Kalman filter, specifying when to communicate relative measurements between nodes based on a local signal indicative of the network error performance, which leads to an energy-aware state estimation algorithm, which is then applied to the distributed simultaneous localization and time synchronization problem.
D-SLATS: Distributed Simultaneous Localization and Time Synchronization
D-SLATS, a framework comprised of three different and independent algorithms to jointly solve time synchronization and localization problems in a distributed fashion, which achieves up to three microseconds time synchronization accuracy and 30 cm localization error.
Iterative algorithms for distributed leader-follower model predictive control
Two distributed algorithms to estimate the optimal control input sequence that solves a finite horizon quadratic optimization are proposed and it is shown that the converged estimate is the optimal solution to the original optimization problem, while the result is generally a suboptimal solution.
Event-Triggered Diffusion Kalman Filters
An energy-aware state estimation algorithm that regulates the resource consumption in wireless networks and ensures the effectiveness of every consumed resource and applies to the distributed simultaneous localization and time synchronization problem.
Localization of Cyber-Physical Systems: Privacy, Security and Efficiency
This work proposes three different algorithms to jointly solve time synchronization and localization problems in a distributed fashion, including an event-triggered diffusion Kalman filter, and a pointing approach for interacting with devices as an application for accurate localization.
SecSens: Secure State Estimation with Application to Localization and Time Synchronization
This work presents SecSens, a novel approach for secure nonlinear state estimation in the presence of modeling and measurement noise, which adopts a holistic approach to introduce security awareness among state estimation algorithms without requiring specialized hardware, or cryptographic techniques.
Privacy Guarantees for Cloud-based State Estimation using Partially Homomorphic Encryption
This work proposes two privacy-preserving protocols using Kalman filter and partially homomorphic encryption of the measurements and estimates while exposing the covariances and other model parameters and proves that the proposed protocols achieve satisfying computational privacy guarantees against various coalitions based on formal cryptographic definitions of indistinguishability.
Privacy Preserving Set-Based Estimation Using Partially Homomorphic Encryption
This paper presents the first privacy-preserving set-based estimation protocols using partially homomorphic encryption in which the privacy of the set of all possible estimates and the measurements is preserved and is shown to achieve computational privacy using formal cryptographic definitions of computational indistinguishability.


Convex position estimation in wireless sensor networks
  • L. Doherty, K. Pister, L. El Ghaoui
  • Computer Science
    Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213)
  • 2001
A method for estimating unknown node positions in a sensor network based exclusively on connectivity-induced constraints is described, and a method for placing rectangular bounds around the possible positions for all unknown nodes in the network is given.
Organizing a Global Coordinate System from Local Information on an Ad Hoc Sensor Network
An algorithm is presented for creating a reasonably accurate local coordinate system without the use of global control, globally accessible beacon signals, or accurate estimates of inter-sensor distances, which is robust and automatically adapts to the failure or addition of sensors.
Ad hoc positioning system (APS)
This work is proposing APS - a distributed, hop by hop positioning algorithm, that works as an extension of both distance vector routing and GPS positioning in order to provide approximate location for all nodes in a network where only a limited fraction of nodes have self location capability.
Revisiting trilateration for robot localization
New formulas for the variance and bias of the unknown robot location estimation, due to station location and range measurements errors, are derived and analyzed and are proved to be more tractable compared with previous ones, because all their terms have geometric meaning, allowing a simple analysis of their asymptotic behavior near singularities.
Distributed Wireless Sensor Network Localization Via Sequential Greedy Optimization Algorithm
A greedy optimization algorithm, named sequential greedy optimization (SGO) algorithm, is presented, which is more suitable for distributed optimization in networks than the classical nonlinear Gauss-Seidel algorithm, a unified optimization framework is proposed for both range-based localization and range-free localization, and two convex localization formulations are obtained based on semidefinite programming (SDP) relaxation techniques.
A Theory of Network Localization
This paper constructs grounded graphs to model network localization and applies graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks, and further study the computational complexity of network localization.
Constrained Consensus and Optimization in Multi-Agent Networks
A distributed "projected subgradient algorithm" which involves each agent performing a local averaging operation, taking a subgradient step to minimize its own objective function, and projecting on its constraint set, and it is shown that, with an appropriately selected stepsize rule, the agent estimates generated by this algorithm converge to the same optimal solution.
The bits and flops of the n-hop multilateration primitive for node localization problems
The collaborative multilateration presented here, enables ad-hoc deployed sensor nodes to accurately estimate their locations by using known beacon locations that are several hops away and distance measurements to neighboring nodes to prevent error accumulation in the network.
Locating the nodes: cooperative localization in wireless sensor networks
Using the models, the authors have shown the calculation of a Cramer-Rao bound (CRB) on the location estimation precision possible for a given set of measurements in wireless sensor networks.
Distributed optimization in sensor networks
  • M. Rabbat, R. Nowak
  • Computer Science
    Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004
  • 2004
This paper investigates a general class of distributed algorithms for "in-network" data processing, eliminating the need to transmit raw data to a central point, and shows that for a broad class of estimation problems the distributed algorithms converge to within an /spl epsi/-ball around the globally optimal value.