A kernel-based learning approach to ad hoc sensor network localization

Abstract

We show that the coarse-grained and fine-grained localization problems for ad hoc sensor networks can be posed and solved as a pattern recognition problem using kernel methods from statistical learning theory. This stems from an observation that the kernel function, which is a similarity measure critical to the effectiveness of a kernel-based learning algorithm, can be naturally defined in terms of the matrix of signal strengths received by the sensors. Thus we work in the natural coordinate system provided by the physical devices. This not only allows us to sidestep the difficult ranging procedure required by many existing localization algorithms in the literature, but also enables us to derive a simple and effective localization algorithm. The algorithm is particularly suitable for networks with densely distributed sensors, most of whose locations are unknown. The computations are initially performed at the base sensors and the computation cost depends only on the number of base sensors. The localization step for each sensor of unknown location is then performed locally in linear time. We present an analysis of the localization error bounds, and provide an evaluation of our algorithm on both simulated and real sensor networks.

Stochastic Cooperative Decision Approach for Studying the Symmetric Behavior of People in Wireless Indoor Location Systems

“…, where i can be from 1 to t. Several alternatives have been proposed in the literature to estimate p(l', u, h, d |l) from T: the histogram method [32,33], the Bayesian method [34], or the kernel method [32,35]. The Bayesian method is used in this paper.…”

Algorithmic Aspects of Sensor Localization

“…The off-line process of recording RSSI is not cost efficient, because location information needs to be collected together with the RSSI value at pre-determined spots in the indoor space. A kernel based learning method, aiming at relieving the system from cumbersome off-line preparation, was proposed in [49]. The idea is to formulate the localization problem as a pattern recognition problem with its kernel matrix established on the signal strength matrix, whose entries are the pairwise radio signal strength values collected at sensor nodes.…”

“…The analysis on the communication/computation costs was not extensively presented in the empirical studies due to the difficulty in measuring the cost in real implementations. [11] 10%R N/A 4 anchors at the corners DV-hop [12] 30%R for isotropic; 90%R for anisotropic 7000 messages exchanged dg=7.6 with 30% to be anchors DV-distance [12] 15%R for isotropic; 80%R for anisotropic 7200 messages exchanged dg=7.6 with 30% to be anchors Euclidean [12] 10%R for isotropic; 15%R for anisotropic 8000 messages exchanged dg=7.6 with 30% to be anchors MDS-MAP [13] 50%R computation complexity of O(n 3 ) dg 12.2 with 3 anchors at random positions Ecolocation [66] 30%D N/A 15 anchors randomly placed DV-coordinate [27] 1m for isotropic; 1.25m for anisotropic N/A dg average =9 DV-bearing [26] 1 hop distance N/A dg average =10.5 DV-radial [26] 0.8 hop distance N/A dg average =10.5 Bisector [47] 5%R 1597 packets 319 randomly deployed nodes Kernel-based Learning [49] 0.47 worst case computational time O(n 3 ) 25 anchors, 400 non-anchors EKF [67] 20%R N/A randomly deployed nodes, 1 mobile robot MCL [53] 20%R 50 samples dg=10, anchor density is 4 RSS Model [17] 5%R O(n 2 log 2 n) node density is 0.5/meter 2…”

“…Since locations of nodes are of importance to the applications' tasks, the security of the location needs to be guaranteed. Although some researches on security of localization schemes are presented [70,71], the types of attacks and the related countermeasures are restricted to a few typi- [42] 2.48m for RSS; 1.12 for TOA O(nL) 4 anchors at corners Ecolocation (outdoor) [66] 20%D N/A 11 nodes with full connectivity Ecolocation (indoor) [66] 35%D N/A 12 anchors, 5 non-anchors Robust Quad [34] 5.18cm for ultrasound ranging N/A dg=12, total 40 nodes Multilateration [21,45] 10.67m N/A range data from 1 mobile beacon Mobile Beacon [45] 1.4m N/A 12 non-anchors, 1 mobile beacon RADAR [48] 3m N/A dg=3, 3 anchors Kernel-based Learning [49] 3.5m N/A grid deployment of 25 anchors and 81 nodes LaSLAT [51] 1.9cm for ultrasound ranging N/A dg=10, total 27 nodes cal cases. Similarly, researches on privacy of nodes' locations mostly focus on preventing the locations of data sources or base stations from being exposed to adversaries [72,73].…”

Machine Learning Based Localization

“…Recently, a number of techniques that employ the concepts from machine learning have been proposed [Brunato & Battiti (2005), Nguyen et al (2005), Pan et al (2006), Tran & Nguyen (2006), , Tran & Nguyen (2008b)]. The main insight of these methods is that the topology implicit in sets of sensor readings and locations can be exploited in the construction of possibly non-Euclidean function spaces that are useful for the estimation of unknown sensor locations, as well as other extrinsic quantities of interest.…”