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## Nonparametric belief propagation for self-localization of sensor networks (2005)

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Venue: | IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS |

Citations: | 93 - 3 self |

### Citations

8725 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.
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(Show Context)
Citation Context ... reformulate localization as an inference problem on a graphical model. This allows us to apply nonparametric belief propagation (NBP, [4]), a variant of the popular belief propagation (BP) algorithm =-=[5]-=-, to obtain an approximate solution. This approach has several advantages: • It exploits the local nature of the problem; a given sensor’s location estimate depends primarily on information about near... |

5031 |
Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
- Geman, Geman
- 1984
(Show Context)
Citation Context ...ionship of inter-sensor distances to sensor positions results in highly non-Gaussian uncertainty of the sensor location estimates. For sufficiently small networks it is possible to use Gibbs sampling =-=[15]-=- to obtain samples from the joint distribution of the sensor locations. In Fig. 1(a), we show an example network with five sensors. Calibration is performed relative to measurements from the three sen... |

3688 |
Density Estimation for Statistics and Data Analysis, Chapman and Hall,
- Silverman
- 1986
(Show Context)
Citation Context ...rnel density estimation) a single covariance Σtu is assigned to all samples. There are a number of possible techniques for choosing the covariance Σtu; one simple method is the rule of thumb estimate =-=[23]-=-, given by computing the (weighted) 5 For M bins per dimension, calculating each message requires O(M 4 ) operations, though there has been some work to improve this [21, 22]. 6 If pν is non-Gaussian ... |

1959 | A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
- Arulampalam, Maskell, et al.
(Show Context)
Citation Context ... providing a more robust estimate of sensor location, NBP also provides a measure of the reliability of each estimate. VII. PARSIMONIOUS SAMPLING We may also apply techniques from importance sampling =-=[26, 27]-=- in order to improve the small-sample performance of NBP, which may play an important part of reducingSUBMITTED TO IEEE JOURNAL ON SEL. AREAS IN COMM., SPECIAL ISSUE ON COLLABORATIVE SENSOR NETWORKS ... |

785 | Graphical models, exponential families, and variational inference
- Wainwright, Jordan
- 2003
(Show Context)
Citation Context ...ical models are a popular means of encapsulating the factorization of a probability distribution, enabling the application of a number of simple, general algorithms for exact or approximate inference =-=[5, 16, 17]-=-. Interpreting the distribution (2) as a graphical model allows one in principle to apply any of a number of inference algorithms [16, 17], of which belief propagation (BP) is perhaps the best-known. ... |

573 | Constructing free-energy approximations and generalized belief propagation algorithms
- Yedidia, Freeman, et al.
(Show Context)
Citation Context ...ical models are a popular means of encapsulating the factorization of a probability distribution, enabling the application of a number of simple, general algorithms for exact or approximate inference =-=[5, 16, 17]-=-. Interpreting the distribution (2) as a graphical model allows one in principle to apply any of a number of inference algorithms [16, 17], of which belief propagation (BP) is perhaps the best-known. ... |

510 | Efficient belief propagation for early vision.
- Felzenszwalb, Huttenlocher
- 2006
(Show Context)
Citation Context ...is the rule of thumb estimate [23], given by computing the (weighted) 5 For M bins per dimension, calculating each message requires O(M 4 ) operations, though there has been some work to improve this =-=[21, 22]-=-. 6 If pν is non-Gaussian and dtu = dut, we may draw some samples according to each of p(xu|xt, dtu) and p(xu|xt, dut) and weight by the influence of the other observation. is covariance of the sampl... |

477 | Convex position estimation in wireless sensor networks
- Doherty, Pister, et al.
(Show Context)
Citation Context ...observed distances and applying classical multidimensional scaling [8], multi-lateration [12], or other techniques [9]. Other approaches search for locations which satisfy convex distance constraints =-=[11]-=-. Yet another method heuristically minimizes the rank of the distance matrix [14].SUBMITTED TO IEEE JOURNAL ON SEL. AREAS IN COMM., SPECIAL ISSUE ON COLLABORATIVE SENSOR NETWORKS 3 Fig. 1. Example se... |

298 | Relative location estimation in wireless sensor networks
- Patwari, Perkins, et al.
(Show Context)
Citation Context ...orithms often lack a direct statistical interpretation, and as one consequence rarely provide an estimate of the remaining uncertainty in each sensor location. Iterative least-squares methods such as =-=[6, 10, 12, 13]-=- do have a statistical interpretation, but assume a Gaussian model for all uncertainty, which may be questionable in practice. As we discuss in Section III, non-Gaussian uncertainty is a common occurr... |

296 | Distributed localization in wireless sensor networks: a quantitative comparison
- Langendoen, Reijers
- 2003
(Show Context)
Citation Context ...tion in favor of computational simplicity. Some examples include approximating the unobserved distances and applying classical multidimensional scaling [8], multi-lateration [12], or other techniques =-=[9]-=-. Other approaches search for locations which satisfy convex distance constraints [11]. Yet another method heuristically minimizes the rank of the distance matrix [14].SUBMITTED TO IEEE JOURNAL ON SE... |

278 | Particle belief propagation - Ihler, McAllester - 2009 |

275 | The bits and flops of the N-hop multilateration primitive for node localization problems
- SAVVIDES, PARK, et al.
(Show Context)
Citation Context ...w a statistical interpretation in favor of computational simplicity. Some examples include approximating the unobserved distances and applying classical multidimensional scaling [8], multi-lateration =-=[12]-=-, or other techniques [9]. Other approaches search for locations which satisfy convex distance constraints [11]. Yet another method heuristically minimizes the rank of the distance matrix [14].SUBMIT... |

123 | Anchor-free Distributed Localization in Sensor Networks. [Online]. Available: http://nms. lcs.mit.edu/cricket [13
- Priyantha, Balakrishnan, et al.
- 2003
(Show Context)
Citation Context ...orithms often lack a direct statistical interpretation, and as one consequence rarely provide an estimate of the remaining uncertainty in each sensor location. Iterative least-squares methods such as =-=[6, 10, 12, 13]-=- do have a statistical interpretation, but assume a Gaussian model for all uncertainty, which may be questionable in practice. As we discuss in Section III, non-Gaussian uncertainty is a common occurr... |

120 |
Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices
- Fazel, Hindi, et al.
- 2003
(Show Context)
Citation Context ...eration [12], or other techniques [9]. Other approaches search for locations which satisfy convex distance constraints [11]. Yet another method heuristically minimizes the rank of the distance matrix =-=[14]-=-.SUBMITTED TO IEEE JOURNAL ON SEL. AREAS IN COMM., SPECIAL ISSUE ON COLLABORATIVE SENSOR NETWORKS 3 Fig. 1. Example sensor network. (a) Sensor locations are indicated by symbols and distance measurem... |

120 | PAMPAS: Real-valued graphical models for computer vision
- Isard
- 2003
(Show Context)
Citation Context ...tu ] = ∑ (where ¯m = ∑ i,j w (i) tu w (j) tu (m (i) tu − ¯m)(m (j) tu − ¯m) T (11) i w(i) tu m (i) tu ) and dividing by M 1 3 . A simple and computationally efficient alternative has been proposed by =-=[24]-=-; if the uncertainty added by ψtu is Gaussian, we may simply use the mean (ν(i) = 0) and apply the covariance of the Gaussian uncertainty to each sample (Σtu = σ2 νI). This method may also be extended... |

107 | Finding Deformable Shapes using Loopy Belief Propoagation
- Coughlan, Ferreira
- 2002
(Show Context)
Citation Context ...is the rule of thumb estimate [23], given by computing the (weighted) 5 For M bins per dimension, calculating each message requires O(M 4 ) operations, though there has been some work to improve this =-=[21, 22]-=-. 6 If pν is non-Gaussian and dtu = dut, we may draw some samples according to each of p(xu|xt, dtu) and p(xu|xt, dut) and weight by the influence of the other observation. is covariance of the sampl... |

98 | Nonparametric belief propagation for self-calibration in sensor networks
- Ihler, Moses, et al.
- 2004
(Show Context)
Citation Context ...may still not observe each other. 3 Unfortunately, fully connected graphs are very difficult for most inference algorithms, and thus it behooves us to approximate the exact model. Experimentally (see =-=[18]-=-) it appears that there is little loss in information by discarding the interactions between nodes which are far apart, in the following sense. Let the “1-step” graph be the graph in which we join two... |

86 | A general algorithm for approximate inference and its application to hybrid Bayes nets
- Koller, Lerner, et al.
- 1999
(Show Context)
Citation Context ...scribed in Alg. 1. This process is repeated until some convergence criterion is met, after which each sensor is left with an estimate of its location and uncertainty. Alg. 1 also uses a suggestion of =-=[20]-=-, in which a reweighted marginal distribution ˆp n (xt) is used as an estimate of the product of messages (9). In addition to the advantages discussed in [20], this has a hidden communication benefit—... |

76 | The design of calamari: an ad-hoc localization system for sensor networks
- Whitehouse
- 2002
(Show Context)
Citation Context ...c transceiver and distance is estimated by received signal strength or time delay of arrival between sensor locations. Typically this involves a broadcast from each source as all other sensors listen =-=[6, 7]-=-. While the framework we describe is not the most general possible, it is sufficiently flexible to be extended to more complex scenarios. For instance, our method may be easily modified to fit cases i... |

46 | Efficient multiscale sampling from products of Gaussian mixtures
- Ihler, Sudderth, et al.
- 2003
(Show Context)
Citation Context ...ures, computing ˆp n exactly is exponential in the number of incoming messages. However, efficient methods of drawing samples from the product of several Gaussian mixture densities is investigated in =-=[25]-=-; in this work we primarily use a technique called mixture importance sampling. Denote the set of neighbors of t having observed edges to t by Γo t . In order to draw M samples, we create a collection... |

37 |
Loopy-belief propagation for approximate inference: An empirical study
- Murphy, Weiss, et al.
- 2000
(Show Context)
Citation Context ...aphical model is a problem which has received considerable attention. Although exact inference in general graphs can be NP-hard, approximate inference algorithms such as loopy belief propagation (BP) =-=[5, 19]-=- produce excellent empirical results in many cases. BP can be formulated as an iterative, local message passing algorithm, in which each node vt computes its “belief” about its associated variable xt,... |

34 | Self-calibration of sensor networks
- Moses, Patterson
- 2002
(Show Context)
Citation Context ...g sensors. In the special case that the noise on distance observations is well modeled by a Gaussian distribution, localization may be formulated as a nonlinear least-squares optimization problem. In =-=[3]-=- it was shown that a relative calibration solution which approached the Cramer-Rao bound could be obtained using an iterative optimization approach. In contrast, we reformulate localization as an infe... |

30 |
BSpecial issue on sensor networks and applications
- Gharavi, Kumar
- 2003
(Show Context)
Citation Context ...o performance impact. I. INTRODUCTION Improvements in sensing technology and wireless communications are rapidly increasing the importance of sensor networks for a wide variety of application domains =-=[1, 2]-=-. Collaborative networks are created by deploying a large number of low-cost, self-powered sensor nodes of varying modalities (e.g. acoustic, seismic, magnetic, imaging, etc.). Sensor localization, i.... |

21 | Data Association Based on Optimization in Graphical Models with Application to Sensor Networks," invited paper
- Chen, Wainwright, et al.
- 2006
(Show Context)
Citation Context ... avoid quantization artifacts; for example, taking β = 16 bits is typically more than sufficient. Message censoring can be used to decrease the total number of messages and as a convergence criterion =-=[28]-=-, but its overall effect in loopy graphs is difficult to determine [29]. A. Schedule and iterations The message schedule has a strong influence on BP, affecting the number of iterations until converge... |

18 | Message errors in belief propagation - Ihler, Fisher, et al. - 2004 |

10 |
Tree–based reparameterization analysis of sum–product and its generalizations
- Wainwright, Jaakkola, et al.
- 2003
(Show Context)
Citation Context ...er of transmission by beginning with the anchor nodes, and moving outward in sequence based on the shortest observed distance to any anchor. This has similarities to schedules based on spanning trees =-=[31]-=-, though (since each sensor is transmitting to all neighbors) it is not a tree-structured message ordering. For this schedule, one iteration corresponds to one message from each sensor. Strictly speak... |

10 |
eds., Special issue on collaborative information processing
- Kumar, Zao, et al.
- 2002
(Show Context)
Citation Context ...o performance impact. I. INTRODUCTION Improvements in sensing technology and wireless communications are rapidly increasing the importance of sensor networks for a wide variety of application domains =-=[1, 2]-=-. Collaborative networks are created by deploying a large number of low-cost, self-powered sensor nodes of varying modalities (e.g. acoustic, seismic, magnetic, imaging, etc.). Sensor localization, i.... |

7 |
Self-localization for wireless networks
- Moses, Krishnamurthy, et al.
- 2003
(Show Context)
Citation Context ...estimate quality. II. SELF-LOCALIZATION OF SENSOR NETWORKS This section describes a statistical framework for the sensor network self-localization problem, similar but more general than that given in =-=[6]-=-. We restrict our attention to cases in which individual sensors obtain noisy distance measurements of a (usually nearby) subset of the other sensors in the network. This includes, for example, scenar... |

7 | Carlo Methods in Practice - Monte - 2002 |

6 |
The formulation and solution of multidimensional scaling problems
- Trosset
- 1993
(Show Context)
Citation Context ... case that we observe distance measurements between all pairs of sensors (i.e. Po(·) ≡ 1), this also corresponds to a well studied distortion criterion (“STRESS”) in multidimensional scaling problems =-=[8]-=-. However, for largescale sensor networks, it is reasonable to assume that only a subset of pairwise distances will be available, primarily between sensors which are in the same region. One model (pro... |

2 | The bits and flops of the n hop multilateration primitive for node localization problems - Savvides, Park, et al. |

1 |
Decoding low-density parity check codes with probabilistic scheduling
- Mao, Banihashemi
- 2001
(Show Context)
Citation Context ...ine [29]. A. Schedule and iterations The message schedule has a strong influence on BP, affecting the number of iterations until convergence and even potentially the quality of the converged solution =-=[30]-=-. We consider two possible BP message schedules, and analyze performance on the 10-node graph shown in Fig. 3(b). Because we are primarily concerned with the inter-sensor communications required, we e... |

1 | Ihler (S’01) received the B.S. degree from the California Institute of Technology - Syst, Technol, et al. - 1998 |

1 |
Message errors in belief propagation,” Laboratory for Information and Decision Systems
- Ihler, Fisher, et al.
- 2004
(Show Context)
Citation Context ...ally more than sufficient. Message censoring can be used to decrease the total number of messages and as a convergence criterion [28], but its overall effect in loopy graphs is difficult to determine =-=[29]-=-. A. Schedule and iterations The message schedule has a strong influence on BP, affecting the number of iterations until convergence and even potentially the quality of the converged solution [30]. We... |

1 |
Communicationconstrained inference,” Laboratory for Information and Decision
- Ihler, Fisher, et al.
- 1979
(Show Context)
Citation Context ...diagonal covariance) Gaussians before transmission (instead of sending all particles). Such approximations may be constructed in any number of ways; we use the Kullback-Liebler based approximation of =-=[32]-=- due to its computational efficiency, though more traditional methods such as Expectation-Maximization could also be employed. Note that locally, each node retains its sample-based density estimate (a... |