
ThC06 Regular Session, Jackson 
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Sensor Networks III 


Chair: Farrell, Jay  Univ. of California Riverside 
CoChair: Vidal, Rene  Johns Hopkins Univ. 

16:3016:50, Paper ThC06.1  Add to My Program 
Average Consensus on Riemannian Manifolds with Bounded Curvature 
Tron, Roberto  Johns Hopkins Univ. 
Afsari, Bijan  Center for Imaging Science, Johns Hopkins Univ. 
Vidal, Rene  Johns Hopkins Univ. 
Keywords: Sensor networks, Nonlinear systems, Optimization algorithms
Abstract: Consensus algorithms are a popular choice for computing averages and other similar quantities in adhoc wireless networks. However, existing algorithms mostly address the case where the measurements live in a Euclidean space. In this paper, we propose distributed algorithms for averaging measurements lying in a Riemannian manifold. We first propose a direct extension of the classical average consensus algorithm and derive sufficient conditions for its convergence to a consensus configuration. Such conditions depend on the network connectivity, the geometric configuration of the measurements and the curvature of the manifold. However, the consensus configuration to which the algorithm converges may not coincide with the Frechet mean of the measurements. We thus propose a second algorithm that performs consensus in the tangent space. This algorithm is guaranteed to converge to the Frechet mean of the measurements, but needs to be initialized at a consensus configuration. By combining these two methods, we obtain a distributed algorithm that converges to the Frechet mean of the measurements. We test the proposed algorithms on synthetic data sampled from manifolds such as the space of rotations, the Stiefel manifold and the Grassmann manifold.


16:5017:10, Paper ThC06.2  Add to My Program 
A Generalized Kalman Consensus Filter for WideArea Video Networks 
Kamal, Ahmed  Univ. of California, Riverside 
Ding, Chong  Univ. of California, Riverside 
Song, Bi  Univ. of California, Riverside 
Farrell, Jay  Univ. of California Riverside 
RoyChowdhury, Amit K.  Univ. of California, Riverside 
Keywords: Sensor networks, Kalman filtering
Abstract: Distributed analysis of video captured by a large network of cameras has received significant attention lately. Tracking moving targets is one of the most fundamental tasks in this regard and the wellknown Kalman Consensus Filter (KCF) has been applied to this problem. However, existing solutions do not consider the specific characteristics of video sensor networks, which are necessary for robustness across various application scenarios. Cameras are directional sensors with limited sensing range (fieldofview), and thus, targets are often not observed by many of the cameras. The network may also be spread over a wide area, preventing direct communication between all of the cameras. This limited fieldofview, combined with sparse communication and coverage topologies, motivates us to propose modifications to the traditional KCF framework. Specifically, we consider the covariance matrices of the state estimates of the neighbors and compute a weighted average consensus estimate at each node. Also, the update at each node is computed in two steps, first towards the weighted consensus estimate and then towards the final Kalman measurement update. This leads us to propose a Generalized KCF herein. Experimental results clearly show the advantage of the GKCF compared to the KCF in the considered application scenario.


17:1017:30, Paper ThC06.3  Add to My Program 
On the Performance Limit of Sensor Localization 
Huang, Baoqi  Austrailian National Univ. 
Li, Tao  Acad. of Mathematics and Systems Science, ChineseAcademyof Sci 
Anderson, Brian D.O.  Australian National Univ. 
YU, CHANGBIN (Brad)  The Australian National Univ. 
Keywords: Sensor networks, Estimation, Optimization
Abstract: In this paper, we analyze the performance limit of sensor localization from a novel perspective. We consider distancebased singlehop sensor localization with noisy distance measurements by Received Signal Strength (RSS). Differently from the existing studies, the anchors are assumed to be randomly deployed, with the result that the trace of the associated CramerRao Lower Bound (CRLB) matrix becomes a random variable. We adopt this random variable as a scalar metric for the performance limit and then focus on its statistical attributes. By the Central Limit Theorems for Ustatistics, we show that as the number of anchors goes to infinity, this scalar metric is asymptotically normal. In addition, we provide the quantitative relationship among the mean, the standard deviation, the number of anchors, parameters of communication channels and the distribution of the anchors. Extensive simulations are carried out to confirm the theoretical results. On the one hand, our study reveals some fundamental features of sensor localization; on the other hand, the conclusions we draw can in turn guide us in the design of wireless sensor networks.


17:3017:50, Paper ThC06.4  Add to My Program 
Error Probability Bounds for Balanced Binary Relay Trees 
Zhang, Zhenliang  Colorado State Univ. 
Pezeshki, Ali  Colorado State Univ. 
Moran, Bill  The Univ. of Melbourne 
Howard, Stephen David  Defence Science & Tech. Organisation 
Chong, Edwin K. P.  Colorado State Univ. 
Keywords: Sensor networks, Network analysis and control
Abstract: We study the detection error probability associated with a balanced binary relay tree, where the leaves of the tree correspond to N identical and independent detectors. The root of the tree represents a fusion center that makes the overall detection decision. Each of the other nodes in the tree are relay nodes that combine two binary messages to form a single output binary message. Only the leaves are sensors. In this way, the information from the detectors is aggregated into the fusion center via the intermediate relay nodes. In this context, we describe the evolution of Type I and Type II error probabilities of the binary data as it propagates from the leaves towards the root. Tight upper and lower bounds for the total error probability at the fusion center as functions of N are derived. These characterize how fast the total error probability converges to 0 with respect to N.


17:5018:10, Paper ThC06.5  Add to My Program 
Time Synchronization in WSNs: A Maximum Value Based Consensus Approach 
He, Jianping  Zhejiang Univ. 
Cheng, Peng  Zhengjiang Univ. 
Shi, Ling  Hong Kong Univ. of Science and Tech. 
Chen, Jiming  Zhejiang Univ. 
Keywords: Sensor networks, Estimation
Abstract: This paper proposes a novel synchronization algorithm for wireless sensor networks (WSNs), the Maximum Time Synchronization (MTS), which is based on maximum value consensus approach. The main idea is to maximize the local information to achieve a global synchronization. Compared with the existing consensusbased synchronization protocols, the main advantages of our protocol include: i) a faster convergence speed such that the synchronization can be completed in a finite time; ii) simultaneous compensation for both the skew and the offset. We provide a rigorous proof of convergence to global synchronization and also give the upper bound of the convergence time. Moreover, the protocol is completely distributed, asynchronous, and robust against packet losses, nodes failure and the addition of new nodes. Some numerical examples are presented to demonstrate the efficiency of our protocol.
