50,189 research outputs found
The Sensing Capacity of Sensor Networks
This paper demonstrates fundamental limits of sensor networks for detection
problems where the number of hypotheses is exponentially large. Such problems
characterize many important applications including detection and classification
of targets in a geographical area using a network of sensors, and detecting
complex substances with a chemical sensor array. We refer to such applications
as largescale detection problems. Using the insight that these problems share
fundamental similarities with the problem of communicating over a noisy
channel, we define a quantity called the sensing capacity and lower bound it
for a number of sensor network models. The sensing capacity expression differs
significantly from the channel capacity due to the fact that a fixed sensor
configuration encodes all states of the environment. As a result, codewords are
dependent and non-identically distributed. The sensing capacity provides a
bound on the minimal number of sensors required to detect the state of an
environment to within a desired accuracy. The results differ significantly from
classical detection theory, and provide an ntriguing connection between sensor
networks and communications. In addition, we discuss the insight that sensing
capacity provides for the problem of sensor selection.Comment: Submitted to IEEE Transactions on Information Theory, November 200
Power Optimization for Network Localization
Reliable and accurate localization of mobile objects is essential for many
applications in wireless networks. In range-based localization, the position of
the object can be inferred using the distance measurements from wireless
signals exchanged with active objects or reflected by passive ones. Power
allocation for ranging signals is important since it affects not only network
lifetime and throughput but also localization accuracy. In this paper, we
establish a unifying optimization framework for power allocation in both active
and passive localization networks. In particular, we first determine the
functional properties of the localization accuracy metric, which enable us to
transform the power allocation problems into second-order cone programs
(SOCPs). We then propose the robust counterparts of the problems in the
presence of parameter uncertainty and develop asymptotically optimal and
efficient near-optimal SOCP-based algorithms. Our simulation results validate
the efficiency and robustness of the proposed algorithms.Comment: 15 pages, 7 figure
Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation
Sensor networks potentially feature large numbers of nodes that can sense
their environment over time, communicate with each other over a wireless
network, and process information. They differ from data networks in that the
network as a whole may be designed for a specific application. We study the
theoretical foundations of such large scale sensor networks, addressing four
fundamental issues- connectivity, capacity, clocks and function computation.
To begin with, a sensor network must be connected so that information can
indeed be exchanged between nodes. The connectivity graph of an ad-hoc network
is modeled as a random graph and the critical range for asymptotic connectivity
is determined, as well as the critical number of neighbors that a node needs to
connect to. Next, given connectivity, we address the issue of how much data can
be transported over the sensor network. We present fundamental bounds on
capacity under several models, as well as architectural implications for how
wireless communication should be organized.
Temporal information is important both for the applications of sensor
networks as well as their operation.We present fundamental bounds on the
synchronizability of clocks in networks, and also present and analyze
algorithms for clock synchronization. Finally we turn to the issue of gathering
relevant information, that sensor networks are designed to do. One needs to
study optimal strategies for in-network aggregation of data, in order to
reliably compute a composite function of sensor measurements, as well as the
complexity of doing so. We address the issue of how such computation can be
performed efficiently in a sensor network and the algorithms for doing so, for
some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE
Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals
A global network of laser interferometric gravitational wave detectors is
projected to be in operation by around the turn of the century. Here, the noisy
output of a single instrument is examined. A gravitational wave is assumed to
have been detected in the data and we deal with the subsequent problem of
parameter estimation. Specifically, we investigate theoretical lower bounds on
the minimum mean-square errors associated with measuring the parameters of the
inspiral waveform generated by an orbiting system of neutron stars/black holes.
Three theoretical lower bounds on parameter estimation accuracy are considered:
the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai
bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing
binary waveform, and compare them with published CRB and numerical Monte-Carlo
results. At large SNR, we find that the theoretical bounds are all identical
and are attained by the Monte-Carlo results. As SNR gradually drops below 10,
the WWB and ZZB are both found to provide increasingly tighter lower bounds
than the CRB. However, at these levels of moderate SNR, there is a significant
departure between all the bounds and the numerical Monte-Carlo results.Comment: 17 pages (LaTeX), 4 figures. Submitted to Physical Review
Bayesian CRLB for hybrid ToA and DoA based wireless localization with anchor uncertainty
In this paper, we derive the Bayesian Cramér-Rao lower bound for three dimensional hybrid localization using time-of-arrival (ToA) and direction-of-arrival (DoA) types of measurements. Unlike previous works, we include the practical constraint that the anchor position is not known exactly but rather up to some error. The resulting bound can be used for error analysis of such a localization system or as an optimality
criterion for the selection of suitable anchors
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