algorithm to locate sensors (with unknown locations) in 1, with respect to a minimal number of +1anchors with known locations. The sensors and anchors, nodes in the network, exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there a centralized fusion center to compute the sensors ’ locations. DILOC uses the barycentric coordinates of a node with respect to its neighbors; these coordinates are computed using the Cayley–Menger determinants, i.e., the determinants of matrices of internode distances. We show convergence of DILOC by associating with it an absorbing Markov chain whose absorbing states are the states of the anchors. We introduce a stochastic approximation version extending DILOC to random environments, i.e., when the communications among nodes is noisy, the communication links among neighbors may fail at random times, and the internodes distances are subject to errors. We show a.s. convergence of the modified DILOC and characterize the error between the true values of the sensors ’ locations and their final estimates given by DILOC. Numerical studies illustrate DILOC under a variety of deterministic and random operating conditions. Index Terms—Absorbing Markov chain, anchor, barycentric coordinates, Cayley–Menger determinant, distributed iterative

In this paper, we present a distributed algorithm to invert L−banded matrices that are symmetric positive definite (SPD), when the submatrices in the band are distributed among several processing nodes. We provide a distributed iterate-collapse inversion (DICI) algorithm that converges, at each node, to the corresponding submatrices in the inverse of the L−banded matrix. The computational complexity of the DICI algorithm to invert an SPD L−banded n × n matrix can be shown at each node to be independent of the size, n, of the matrix. Local information exchange is carried out after each iteration to guarantee convergence. We apply this algorithm to invert the information matrices in a computationally efficient distributed implementation of the Kalman filter and show its application towards inverting arbitrary sparse SPD matrices.

Abstract—This paper concerns the problem of estimating a spatially distributed, time-varying random field from noisy measurements collected by a wireless sensor network. When the field dynamics are described by a linear, lumped-parameter model, the classical solution is the Kalman–Bucy filter (KBF). Bandwidth and energy constraints can make it impractical to use all sensors to estimate the field at specific locations. Using graph-theoretic techniques, we show how reduced-order KBFs can be constructed that use only a subset of the sensors, thereby reducing energy consumption. This can lead to degraded performance, however, in terms of the root mean squared (RMS) estimation error. Efficient methods are presented to apply Pareto optimality to evaluate the tradeoffs between communication costs and RMS estimation error to select the best reduced-order KBF. The approach is illustrated with simulation results. Index Terms—Communication cost, estimation error, field estimation, Kalman–Bucy filter, Pareto optimality, tradeoffs, wireless sensor networks.

Abstract—Accurate clock synchronization is important in many distributed applications. Standard algorithms, such as the Network Time Protocol (NTP), essentially rely on pairwise offset estimation between adjacent nodes. Some recent work introduced more elaborate algorithms for clock offset estimation, which take into account the algebraic constraints imposed on the sum of offsets over network cycles, using a least-squares framework. These algorithms are iterative and decentralized in nature, requiring several cycles of local communication among neighbors for convergence. In this paper, we extend this approach towards a sequential estimation framework, which allows to incorporate initial time estimates along with their uncertainty, as well as multiple rounds of pairwise measurements. We propose a decentralized implementation of the estimation algorithm that employs only local broadcasts and establish its convergence to the optimal centralized solution. We also present some simulation results to illustrate the performance benefits of the suggested algorithms. Index Terms—network clock synchronization; decentralized algorithms; Kalman filtering; recursive estimation. I.

The paper develops DILOC, a distributive, iterative algorithm that locates M sensors in R m, m ≥ 1, with respect to a minimal number of m + 1 anchors with known locations. The sensors exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there centralized knowledge about the sensors’ locations. DILOC uses the barycentric coordinates of a sensor with respect to its neighbors that are computed using the Cayley-Menger determinants. These are the determinants of matrices of inter-sensor distances. We show convergence of DILOC by associating with it an absorbing Markov chain whose absorbing states are the anchors. We introduce a stochastic approximation version extending DILOC to random environments when the knowledge about the intercommunications among sensors and the inter-sensor distances are noisy, and the communication links among neighbors fail at random times. We show a.s. convergence of the modified DILOC and characterize the error between the final estimates and the true values of the sensors ’ locations. Numerical studies illustrate DILOC under a variety of deterministic and random operating conditions. Keywords: Distributed iterative sensor localization; sensor networks; Cayley-Menger determinant; barycentric coordinates; absorbing Markov chain; stochastic approximation.

Recent advances in affordable positioning hardware and software have made the availability of location data ubiquitous. Personal devices such as tablet PCs, smart phones and even sport watches are all able to collect and store a user’s location over time, providing an ever-growing supply of spatiotemporal data. Managing this plethora of data is a relatively new challenge and there has been a great deal of research in the recent years devoted to the problems that arise from spatiotemporal data. This book chapter surveys recent developments in the techniques used for the management and mining of spatiotemporal data. We focus our survey on three main areas: (i) data management, which includes indexing and querying mobile objects, (ii) tracking, making use of noisy location observations to infer an object’s actual or future position, and (iii) mining, extracting interesting patterns from spatiotemporal data. First, we cover recent advances in database systems for managing spatiotemporal data, including index structures and efficient algorithms for processing queries. Next, we review the problem of tracking for mobile objects to estimate an object’s location given a sequence of noisy observations. We discuss some of the common approaches used for tracking and examine some recent work which focuses specifically on tracking vehicles using a road network. Then we review the recent literature on mining spatiotemporal data. We conclude by discussing some interesting areas of future research.