## Semidefinite Programming for Ad Hoc Wireless Sensor Network Localization (2004)

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Citations: | 165 - 12 self |

### BibTeX

@MISC{Biswas04semidefiniteprogramming,

author = {Pratik Biswas and Yinyue Ye},

title = {Semidefinite Programming for Ad Hoc Wireless Sensor Network Localization },

year = {2004}

}

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### Abstract

We describe an SDP relaxation based method for the position estimation problem in wireless sensor networks. The optimization problem is set up so as to minimize the error in sensor positions to fit distance measures. Observable gauges are developed to check the quality of the point estimation of sensors or to detect erroneous sensors. The performance of this technique is highly satisfactory compared to other techniques. Very few anchor nodes are required to accurately estimate the position of all the unknown nodes in a network. Also the estimation errors are minimal even when the anchor nodes are not suitably placed within the network or the distance measurements are noisy.

### Citations

759 | GPS-less Low Cost Outdoor Localization for Very Small Devices
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Citation Context ...orks ([6, 7]). Most techniques use distance or angle measurements from a fixed set of reference or anchor nodes, see [5, 9, 10, 11, 12, 13]; or employ a grid of beacon nodes with known positions, see =-=[4, 8]-=-. One closely related approach is described by Doherty et al. [5] wherein the proximity constraints between nodes which are within ’hearing distance’ of each other are modeled as convex constraints. T... |

720 | Location Systems for Ubiquitous Computing
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Citation Context ...tor x, denoted by �x�, is defined by � 〈x, x〉. A positive semidefinite matrix X is represented by X � 0. A great deal of research has been done on the topic of position estimation in ad-hoc networks (=-=[6, 7]-=-). Most techniques use distance or angle measurements from a fixed set of reference or anchor nodes, see [5, 9, 10, 11, 12, 13]; or employ a grid of beacon nodes with known positions, see [4, 8]. One ... |

622 | ÕDynamic fine-grained localization in ad-hoc networks of sensors,Õ
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- 2001
(Show Context)
Citation Context ...t deal of research has been done on the topic of position estimation in ad-hoc networks ([6, 7]). Most techniques use distance or angle measurements from a fixed set of reference or anchor nodes, see =-=[5, 9, 10, 11, 12, 13]-=-; or employ a grid of beacon nodes with known positions, see [4, 8]. One closely related approach is described by Doherty et al. [5] wherein the proximity constraints between nodes which are within ’h... |

394 | Convex position estimation in wireless sensor network
- Doherty, Pister, et al.
- 2001
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Citation Context ...t deal of research has been done on the topic of position estimation in ad-hoc networks ([6, 7]). Most techniques use distance or angle measurements from a fixed set of reference or anchor nodes, see =-=[5, 9, 10, 11, 12, 13]-=-; or employ a grid of beacon nodes with known positions, see [4, 8]. One closely related approach is described by Doherty et al. [5] wherein the proximity constraints between nodes which are within ’h... |

302 | Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks
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- 2002
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Citation Context ...t deal of research has been done on the topic of position estimation in ad-hoc networks ([6, 7]). Most techniques use distance or angle measurements from a fixed set of reference or anchor nodes, see =-=[5, 9, 10, 11, 12, 13]-=-; or employ a grid of beacon nodes with known positions, see [4, 8]. One closely related approach is described by Doherty et al. [5] wherein the proximity constraints between nodes which are within ’h... |

278 | Localization from Mere Connectivity - Shang, Ruml, et al. - 2003 |

276 | Ad hoc positioning system (aps - Niculescu, Nath |

223 | The bits and flops of the n-hop multilateration primitive for node localization problems
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181 |
Ad-Hoc Positioning System
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113 | Solving Large–Scale Sparse Semidefinite Programs for Combinatorial Optimization - Benson, Ye, et al. |

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Citation Context ...tor x, denoted by �x�, is defined by � 〈x, x〉. A positive semidefinite matrix X is represented by X � 0. A great deal of research has been done on the topic of position estimation in ad-hoc networks (=-=[6, 7]-=-). Most techniques use distance or angle measurements from a fixed set of reference or anchor nodes, see [5, 9, 10, 11, 12, 13]; or employ a grid of beacon nodes with known positions, see [4, 8]. One ... |

69 | Relaxation on a mesh: A formalism for generalized localization
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Citation Context ...orks ([6, 7]). Most techniques use distance or angle measurements from a fixed set of reference or anchor nodes, see [5, 9, 10, 11, 12, 13]; or employ a grid of beacon nodes with known positions, see =-=[4, 8]-=-. One closely related approach is described by Doherty et al. [5] wherein the proximity constraints between nodes which are within ’hearing distance’ of each other are modeled as convex constraints. T... |

69 | Global continuation for distance geometry problems - Moré, Wu - 1997 |

66 | Solving Euclidean distance matrix completion problems via semidefinite programming - Alfakih, Khandani, et al. - 1999 |

33 | A distributed method for solving semidefinite programs arising from ad hoc wireless sensor network localization - Biswas, Ye - 2006 |

29 | Semidefinite relaxations, multivariate normal distributions, and order statistics
- Bertsimas, Ye
- 1998
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Citation Context ...ntain random errors. Then the solution to the SDP problem provides the first and second moment information on ˜xj, j = 1, ..., n. Such an interpretation appears to be first stated in Bertsimas and Ye =-=[2]-=-. 6sand where Generally, we have E[˜xj] ∼ ¯xj, j = 1, ..., n E[˜x T i ˜xj] ∼ ¯ Yij, i, j = 1, ..., n. ¯Z = � I ¯ X ¯X T ¯ Y is the optimal solution of the SDP problem. Thus, ¯Y − ¯ X T ¯ X represents ... |

24 | An efficient algorithm for minimizing a sum of Euclidean norms with applications
- Xue, Ye
- 1997
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Citation Context ...ively, if the exact distance r1,2 ≤ R is known, we could set the constraint �(x1 − x2)�2 ≤ r1,2. (3) The second-order cone method for solving Euclidean metric problems can be also found in Xue and Ye =-=[15]-=- where its superior polynomial complexity efficiency is presented. However, this technique yields good results only if the anchor nodes are placed on the outer boundary. The estimated positions of the... |

16 | Matrix completion problems - Laurent - 2001 |

5 |
Let sedumi seduce you
- Sturm
- 2001
(Show Context)
Citation Context ...y accurate. Again, the erroneous estimations are reflected in their individual traces. The computational results presented here were generated using the interior-point algorithm SDP solvers SeDuMi of =-=[14]-=- and DSDP2.0 of [1] with their interfaces to Matlab. The average time to solve one of the 50 sensor problem is 8 seconds by SeDuMi (with the primal formulation) or 2 seconds by DSDP2.0 on a Pentium 1.... |