#### DMCA

## (Robust) Edge-Based Semidefinite Programming Relaxation of Sensor Network Localization

Venue: | MATH PROGRAM |

Citations: | 19 - 2 self |

### Citations

954 | Location systems for ubiquitous computing - Hightower, Borriello - 2001 |

493 | Convex position estimation in wireless sensor networks,” - Doherty, Pister, et al. - 2001 |

387 | Geographic Routing without Location Information," - Rao, Ratnasamy, et al. - 2003 |

383 | Robust positioning algorithms for distributed ad-hoc wireless sensor networks,” - Savarese, Rabaey, et al. - 2002 |

224 | Semidefinite Programming for Ad Hoc Wireless Sensor Network Localization,” - Biswas, Ye - 2004 |

219 | Particle filters for positioning, navigation, and tracking. - Gustafsson, Gunnarsson, et al. - 2002 |

120 | Theory of semidefinite programming for sensor network localization,” - So, Ye - 2007 |

113 | Semidefinite Programming Based Algorithms for Sensor Network Localization.
- Biswas, Lian, et al.
- 2006
(Show Context)
Citation Context ...me, and can handle noise and certify which sensors are accurately positioned. The positions of remaining sensors can be refined using any number of local improvement heuristics, such as those used in =-=[5, 6, 10, 18, 20, 36]-=-, though their accuracy cannot be certified. Throughout, Sn denotes the space of n × n real symmetric matrices, and T denotes transpose. For a vector x ∈ Rp , ‖x‖ and ‖x‖∞ denote the Euclidean norm of... |

94 | Semidefinite programming approaches for sensor network localization with noisy distance measurements,”
- Biswas, Liang, et al.
- 2006
(Show Context)
Citation Context ...me, and can handle noise and certify which sensors are accurately positioned. The positions of remaining sensors can be refined using any number of local improvement heuristics, such as those used in =-=[5, 6, 10, 18, 20, 36]-=-, though their accuracy cannot be certified. Throughout, Sn denotes the space of n × n real symmetric matrices, and T denotes transpose. For a vector x ∈ Rp , ‖x‖ and ‖x‖∞ denote the Euclidean norm of... |

90 | On the computational complexity of sensor network localization,” in Algorithmic Aspects of Wireless Sensor Networks,
- Aspnes, Goldenberg, et al.
- 2004
(Show Context)
Citation Context ... true i − x true j ‖ 2 | = d 2 1 ij ∣1 − (1 + ɛij · σ) 2 ∣ < d 2 ij max 1 |t|≤2 ∣1 − (1 + t · σ) 2 ∣ = d 2 ( ) 1 ij − 1 , (1 − 2σ) 2 where the last equality is obtained by dividing into two cases t ∈ =-=[0, 2]-=- and t ∈ [−2, 0] and comparing the respective maximum found (at t = 2 and t = −2). Accordingly, we set ρij = d 2 ( ) 1 ij − 1 ∀(i, j) ∈ A, (38) (1 − 2ˆσ) 2 where 0 ≤ ˆσ < 1 2 is our estimate of σ. If ... |

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

69 | Robust distributed node localization with error management,” - Liu, Zhang, et al. - 2006 |

42 | A distributed method for solving semidefinite programs arising from ad hoc wireless sensor network localization,” Multiscale optimization methods and applications, - Biswas, Ye - 2006 |

41 | Distributed localization in wireless ad hoc networks. - Simic, Sastry - 2002 |

41 | Further relaxations of the semidefinite programming approach to sensor network localization,” - Wang, Zheng, et al. - 2008 |

36 | Second-order cone programming relaxation of sensor network localization,” - Tseng - 2007 |

34 | Exploiting Sparsity in SDP Relaxation for Sensor Network Localization,” - Kim, Kojima, et al. - 2009 |

32 | SPACELOC: An adaptive subproblem algorithm for scalable wireless sensor network localization - Carter, Jin, et al. - 2006 |

28 | Explicit sensor network localization using semidefinite representations and facial reductions - Krislock, Wolkowicz - 2010 |

28 | Sum of Squares Method for Sensor Network Localization - Nie - 2009 |

27 | A Distributed SDP Approach for Large–Scale Noisy Anchor–Free Graph Realization with Applications to Molecular Conformation,”
- Biswas, Toh, et al.
- 2008
(Show Context)
Citation Context ...measurement errors, and there may be additional constraints on the unknown points [12]. This problem is closely related to distance geometry problems arising in the determination of protein structure =-=[7, 22]-=- and to graph rigidity [1, 13, 32]. The sensor network localization problem is NP-hard in general [29]; also see remark in [22]. This can be proved for d = 1 by reduction from the set partition proble... |

22 | A gradient search method to round the semidefinite programming relaxation solution for ad hoc wireless sensor network localization - LIAN, WANG, et al. - 2004 |

12 |
Semidefinite programming algorithms for sensor network localization using angle of arrival information
- BISWAS, AGHAJAN, et al.
- 2005
(Show Context)
Citation Context ... and method be extended to the sparse SOS relaxations studied in [18, 26]? Can they be extended to incorporate upper and lower bounds on the distances [10, 19], and angle of arrival (AoA) information =-=[4, 23, 25]-=-? It has been shown in [4] and [3, Chapter 5] that the SDP relaxation (2) can be extended to incorporate AoA information, but the resulting SDP appears more difficult to solve; see [4, Section 5] and ... |

8 |
Graph Rigidity via Euclidean Distance Matrices
- Alfakih
- 2000
(Show Context)
Citation Context ...may be additional constraints on the unknown points [12]. This problem is closely related to distance geometry problems arising in the determination of protein structure [7, 22] and to graph rigidity =-=[1, 13, 32]-=-. The sensor network localization problem is NP-hard in general [29]; also see remark in [22]. This can be proved for d = 1 by reduction from the set partition problem, and the proof readily extends f... |

7 | Robust semidefinite programming approaches for sensor network localization with anchors - Krislock, Piccialli, et al. - 2006 |

5 | Semidefinite programming approaches to distance geometry problems - BISWAS - 2007 |

1 | Novel decision-fusion algorithms for target tracking using ad hoc networks - Fariña, Miguez, et al. |