## Robust distributed node localization with error management (2006)

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Venue: | In Proceedings of the 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc’06). ACM |

Citations: | 47 - 4 self |

### BibTeX

@INPROCEEDINGS{Liu06robustdistributed,

author = {Juan Liu},

title = {Robust distributed node localization with error management},

booktitle = {In Proceedings of the 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc’06). ACM},

year = {2006}

}

### Years of Citing Articles

### OpenURL

### Abstract

Location knowledge of nodes in a network is essential for many tasks such as routing, cooperative sensing, or service delivery in ad hoc, mobile, or sensor networks. This paper introduces a novel iterative method ILS for node localization starting with a relatively small number of anchor nodes in a large network. At each iteration, nodes are localized using a least-squares based algorithm. The computation is lightweight, fast, and any-time. To prevent error from propagating and accumulating during the iteration, the error control mechanism of the algorithm uses an error registry to select nodes that participate in the localization, based on their relative contribution to the localization accuracy. Simulation results have shown that the active selection strategy significantly mitigates the effect of error propagation. The algorithm has been tested on a network of Berkeley Mica2 motes with ultrasound TOA ranging devices. We have compared the algorithm with more global methods such as MDS-MAP and SDP-based algorithm both in simulation and on real hardware. The iterative localization achieves comparable location accuracy in both cases, compared to the more global methods, and has the advantage of being fully decentralized.

### Citations

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(Show Context)
Citation Context ...ch to node localization, in which location information progressively propagates from anchor nodes to other nodes. The iterative approach has been studied by others, for example, as in multilateration =-=[1, 2]-=-. What is new about our approach is the introduction of an error control and a robust formulation of the localization problem so that the algorithm is less sensitive to noise and computes the location... |

394 | Convex position estimation in wireless sensor network
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Citation Context ...ing new anchors for other free nodes. This could lead to unbounded error in localization for large networks. The effect of error propagation is less prominent in global methods such as MDS [3] or SDP =-=[4, 5]-=-, since global constraints tend to balance against each other. However, global methods are less amendable to distributed implementation in an ad hoc network. This paper introduces a local error contro... |

302 | Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks
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Citation Context ...n, various distributed node localization techniques have been proposed. The basic idea is to decompose a global joint estimation problem into smaller sub-problems and to iterate over the sub-problems =-=[1, 7, 8, 9]-=-. There are three groups of techniques related to our proposed method. The first group (e.g., [1, 7]) starts from anchors and uses local computation to iteratively localize free nodes. This approach g... |

297 | Robust Distributed Network Localization with Noisy Range Measurements
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Citation Context ...from anchors to free nodes. Despite its impact, the error propagation problem has not received adequate attention in the current literature. Localization using robust quadrilaterals has been proposed =-=[10]-=-. However, this method requires high connectivity, i.e., the existence of many robust quadrilaterals. In Sec. 4, we address error propagation in details and design a control mechanism to mitigate the ... |

208 |
Optimum transmission radii for packet radio networks or why six is a magic number
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Citation Context ...n, various distributed node localization techniques have been proposed. The basic idea is to decompose a global joint estimation problem into smaller sub-problems and to iterate over the sub-problems =-=[1, 7, 8, 9]-=-. There are three groups of techniques related to our proposed method. The first group (e.g., [1, 7]) starts from anchors and uses local computation to iteratively localize free nodes. This approach g... |

181 |
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Citation Context ...n, various distributed node localization techniques have been proposed. The basic idea is to decompose a global joint estimation problem into smaller sub-problems and to iterate over the sub-problems =-=[1, 7, 8, 9]-=-. There are three groups of techniques related to our proposed method. The first group (e.g., [1, 7]) starts from anchors and uses local computation to iteratively localize free nodes. This approach g... |

165 | Semidefinite programming for ad hoc wireless sensor network localization
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Citation Context ...ing new anchors for other free nodes. This could lead to unbounded error in localization for large networks. The effect of error propagation is less prominent in global methods such as MDS [3] or SDP =-=[4, 5]-=-, since global constraints tend to balance against each other. However, global methods are less amendable to distributed implementation in an ad hoc network. This paper introduces a local error contro... |

144 | H.: Robust solution to least-squares problems with uncertain data
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Citation Context ...tion xi’s (i.e., vertex errors) and the measurement zi’s (i.e., edge errors). We denote the perturbation in A and b as ∆A and ∆b. The presence of the error motivates us to switch to a RLS formulation =-=[14, 15]-=- ˆxt = arg min x E||(A + ∆A)x − (b + ∆b)|| 2 . (6) The expectation is with respect to ∆A and ∆b. The cost function seeks a location estimate which minimizes data discrepancy in the average sense. This... |

84 | Nonparametric belief propagation for self-calibration in sensor networks
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Citation Context ... (such as in [2]) assume linear Gaussian observation model and linear dynamics, but the perturbation does not have to be independent or identically distributed. Particle filter approaches (such as in =-=[17]-=-) use non-parametric models and even eliminate the linear Gaussian assumptions. The more sophisticated probabilistic models come at a higher computational cost. For example, Kalman filter explicitly m... |

75 | Localization from Connectivity in Sensor Networks
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Citation Context ...d and becoming new anchors for other free nodes. This could lead to unbounded error in localization for large networks. The effect of error propagation is less prominent in global methods such as MDS =-=[3]-=- or SDP [4, 5], since global constraints tend to balance against each other. However, global methods are less amendable to distributed implementation in an ad hoc network. This paper introduces a loca... |

48 | The n-hop multilateration primitive for node localization problems
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(Show Context)
Citation Context ...ch to node localization, in which location information progressively propagates from anchor nodes to other nodes. The iterative approach has been studied by others, for example, as in multilateration =-=[1, 2]-=-. What is new about our approach is the introduction of an error control and a robust formulation of the localization problem so that the algorithm is less sensitive to noise and computes the location... |

41 | A kernel-based learning approach to ad hoc sensor network localization - Nguyen, Jordan, et al. - 2005 |

37 |
Localization for anisotropic sensor networks
- Lim, Hou
- 2005
(Show Context)
Citation Context ...igh connectivity, i.e., the existence of many robust quadrilaterals. In Sec. 4, we address error propagation in details and design a control mechanism to mitigate the problem. The second group (e.g., =-=[11]-=-) uses shortest path approximation to anchor nodes to approximate Euclidean distances. This approach introduces large position errors in anisotropic networks. Remedies to the shortest path approximati... |

35 | Distributed weighted-multidimensional scaling for node localization in sensor networks
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- 2006
(Show Context)
Citation Context ...n one hop distance to each other. The third group uses local refinement [12] which requires an initial solution. Many local refinement methods exist, the most recent one is a distributed weighted MDS =-=[13]-=-. Local refinements are very effective and can be applied to the result of any algorithm. Due to space limitations, we will not discuss and compare refinement methods in this paper. The computation st... |

7 |
Calamari: a localization system for sensor networks,” http://www.cs.virginia.edu/∼whitehouse/research/ localization
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- 2003
(Show Context)
Citation Context ...ust to noise and low connectivity. • SDP: localization based on semi-definite programming [5], working well for anisotropic networks. • SPA: localization using shortest-path length between node pairs =-=[16]-=-. This is equivalent to the initialization step of ILS without further iterations. Among the methods, MDS-MAP and SDP are global in nature, although heuristics have been used to distribute computation... |

6 | Robust solutions to l1, l2, and l∞ uncertain linear approximation problems using convex optimization
- Hindi, Boyd
- 1998
(Show Context)
Citation Context ...tion xi’s (i.e., vertex errors) and the measurement zi’s (i.e., edge errors). We denote the perturbation in A and b as ∆A and ∆b. The presence of the error motivates us to switch to a RLS formulation =-=[14, 15]-=- ˆxt = arg min x E||(A + ∆A)x − (b + ∆b)|| 2 . (6) The expectation is with respect to ∆A and ∆b. The cost function seeks a location estimate which minimizes data discrepancy in the average sense. This... |

5 | STAM: a system of tracking and mapping in real environments
- Zhang, Ackerson, et al.
- 2004
(Show Context)
Citation Context ...r example, the method described in [11] would fail when a small number of anchors, for instance three anchors, are located within one hop distance to each other. The third group uses local refinement =-=[12]-=- which requires an initial solution. Many local refinement methods exist, the most recent one is a distributed weighted MDS [13]. Local refinements are very effective and can be applied to the result ... |