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Locating the Nodes  Cooperative localization in wireless sensor networks
, 2005
"... Accurate and lowcost sensor localization is a critical requirement for the deployment of wireless sensor networks in a wide variety of applications. Lowpower wireless sensors may be many hops away from any other sensors with a priori location information. In cooperative localization, sensors work ..."
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Cited by 145 (12 self)
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Accurate and lowcost sensor localization is a critical requirement for the deployment of wireless sensor networks in a wide variety of applications. Lowpower wireless sensors may be many hops away from any other sensors with a priori location information. In cooperative localization, sensors work together in a peertopeer manner to make measurements and then form a map of the network. Various application requirements (such as scalability, energy efficiency, and accuracy) will influence the design of sensor localization systems. In this article, we describe measurementbased statistical models useful to describe timeofarrival (TOA), angleofarrival (AOA), and receivedsignalstrength (RSS) measurements in wireless sensor networks. Wideband and ultrawideband (UWB) measurements, and RF and acoustic media are also discussed. Using the models, we show how to calculate a CramérRao bound (CRB) on the location estimation precision possible for a given set of measurements. This is a useful tool to help system designers and researchers select measurement technologies and evaluate localization algorithms. We also briefly survey a large and growing body of sensor localization algorithms. This article is intended to emphasize the basic statistical signal processing background necessary to understand the stateoftheart and to make progress in the new and largely open areas of sensor network localization research.
Propagation Delay Estimation in Asynchronous DirectSequence CodeDivision Multiple Access Systems
, 1996
"... In an asynchronous directsequence codedivision multiple access (DSCDMA) communication system the parameter estimation problem, i.e., estimating the propagation delay, attenuation and phase shift of each users' transmitted signal, may be complicated by the socalled nearfar problem. The nearfar p ..."
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Cited by 113 (20 self)
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In an asynchronous directsequence codedivision multiple access (DSCDMA) communication system the parameter estimation problem, i.e., estimating the propagation delay, attenuation and phase shift of each users' transmitted signal, may be complicated by the socalled nearfar problem. The nearfar problem occurs when the amplitudes of the users' received signals are very dissimilar, as the case might be in many important applications. In particular, the standard method for estimating the propagation delays will fail in a nearfar situation. Several new estimators, the maximum likelihood, an approximative maximum likelihood and a subspace based estimator, are therefore proposed and are shown to be robust against the nearfar problem. No knowledge of the transmitted bits is assumed and the proposed estimators can thus be used for both acquisition and tracking. In addition, the Cram'erRao bound is derived for the parameter estimation problem. I. Introduction D IRECTSEQUENCE CodeDivi...
A Performance Analysis of SubspaceBased Methods in the Presence of Model Errors  Part I: The MUSIC Algorithm
 IEEE Trans. on Signal Processing
, 1992
"... Application of subspacebased algorithms to narrowband directionofarrival (DOA) estimation requires that certain modeling assumptions be made. Most importantly, both the array response in all directions of interest and the spatial covariance of the noise must be known. In practice, however, neith ..."
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Cited by 43 (10 self)
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Application of subspacebased algorithms to narrowband directionofarrival (DOA) estimation requires that certain modeling assumptions be made. Most importantly, both the array response in all directions of interest and the spatial covariance of the noise must be known. In practice, however, neither of these quantities is known precisely. Depending on the degree...
Analysis of an Improved MUSIC Algorithm for Estimation of Time Delays in Asynchronous DSCDMA Systems
, 1997
"... This contribution treats the problem of time delay estimation in an asynchronous directsequence codedivision multiple access (DSCDMA) system in a nearfar scenario. By better exploiting the structure of the problem, estimators superior to previously known techniques [1] are obtained. An analytical ..."
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Cited by 18 (2 self)
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This contribution treats the problem of time delay estimation in an asynchronous directsequence codedivision multiple access (DSCDMA) system in a nearfar scenario. By better exploiting the structure of the problem, estimators superior to previously known techniques [1] are obtained. An analytical large sample analysis is provided, as well as numerical examples. For a typical numerical example, a gain in SNR of approximately 3 dB is obtained. 1 Introduction Lately, there has been a great interest in multiuser detection, both optimal and suboptimal, of users in a DirectSequence CodeDivision Multiple Access (DSCDMA) system [2, 3, 4, 5]. Several of these schemes assume perfect knowledge of the channel parameters in the system and are sensitive to errors in the parameter estimates, [6, 7] , especially in a nearfar situation (i.e., when there are large dissimilarities in received power between the users). Highperformance delay estimators, capable of operating in a nearfar environ...
A Bayesian Approach to AutoCalibration for Parametric Array Signal Processing
 IEEE Trans. on Sig. Proc
, 1995
"... A number of techniques for parametric (highresolution) array signal processing have been proposed in the last few decades. With few exceptions, these algorithms require an exact characterization of the array, including knowledge of the sensor positions, sensor gain/phase response, mutual coupling, ..."
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Cited by 13 (5 self)
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A number of techniques for parametric (highresolution) array signal processing have been proposed in the last few decades. With few exceptions, these algorithms require an exact characterization of the array, including knowledge of the sensor positions, sensor gain/phase response, mutual coupling, and receiver equipment effects. Unless all sensors are identical, this information must typically be obtained by experimental measurements (calibration). In practice, of course, all such information is inevitably subject to errors. Recently, several different methods have been proposed for alleviating the inherent sensitivity of parametric methods to such modeling errors. The technique proposed herein is related to the class of socalled autocalibration procedures, but it is assumed that certain prior knowledge of the array response errors is available. This is a reasonable assumption in most applications, and it allows for more general perturbation models than does pure autocalibration. T...
SubspaceBased Estimation of Time Delays and Doppler Shifts
 IEEE Trans. on Signal Processing
, 1998
"... This paper considers the problem of estimating the time delays and doppler shifts of a known waveform received via several distinct paths by an array of antennas. The general maximum likelihood estimator is presented, and is shown to require a 2ddimensional nonlinear minimization, where d is the n ..."
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Cited by 12 (2 self)
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This paper considers the problem of estimating the time delays and doppler shifts of a known waveform received via several distinct paths by an array of antennas. The general maximum likelihood estimator is presented, and is shown to require a 2ddimensional nonlinear minimization, where d is the number of received signal reflections. Two alternative solutions based on signal and noise subspace fitting are proposed, requiring only a ddimensional minimization. In particular, we show how to decouple the required search into a twostep procedure, where the delays are estimated and the dopplers solved for explicitly. Initial conditions for the time delay search can be obtained by applying generalizations of the MUSIC and ESPRIT algorithms, which are also outlined in the paper. Simulation examples are included to illustrate the algorithms' performance relative to the Cram'erRao bound. 1 Introduction The problem of using an antenna array to estimate the time delays and doppler shifts (or...
Subspace Fitting with Diversely Polarized Antenna Arrays
 IEEE Trans. on Ant. and Prop
, 1993
"... Diversely polarized antenna arrays are widely used in RF applications. The diversity of response provided by such arrays can greatly improve direction finding performance over arrays sensitive to only one polarization component. For d emitters, directly implementing a multidimensional estimation alg ..."
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Cited by 11 (6 self)
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Diversely polarized antenna arrays are widely used in RF applications. The diversity of response provided by such arrays can greatly improve direction finding performance over arrays sensitive to only one polarization component. For d emitters, directly implementing a multidimensional estimation algorithm (e.g., maximum likelihood) would require a search for 3d parameters: d directions of arrival (DOAs), and 2d polarization parameters. In this paper, we present a more efficient solution based on the socalled noise subspace fitting (NSF) algorithm. In particular, we show how to decouple the NSF search into a twostep procedure, where the DOAs are estimated separately. The polarization parameters are then obtained by solving a linear system of equations. The advantage of this approach is that the search dimension is reduced by a factor of three, and no initial polarization estimate is required. In addition, the algorithm can be shown to yield asymptotically minimum variance estimates pr...
Methods for Blind Equalization and Resolution of Overlapping Echoes of Unknown Shape
 IEEE Trans. SP
, 1997
"... This paper considers the related problems of using an uncalibrated antenna array to (1) recover an unknown signal transmitted over an unknown (but stationary) multipath channel, and (2) resolve overlapping pulse echoes with unknown shape. Unlike recently proposed multichannel blind equalization tech ..."
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Cited by 7 (1 self)
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This paper considers the related problems of using an uncalibrated antenna array to (1) recover an unknown signal transmitted over an unknown (but stationary) multipath channel, and (2) resolve overlapping pulse echoes with unknown shape. Unlike recently proposed multichannel blind equalization techniques, the methods described herein employ a model based on physical channel parameters rather than unstructured singleinput, multioutput FIR filters. The algorithms exploit similarities between a model for the data in the frequency domain and the standard directionofarrival estimation problem. This connection between the two problems suggests several different approaches based on, for example, maximum likelihood, MODE, IQML, and ESPRIT. These approaches are developed in some detail, and the results of several simulation examples are included to compare their performance. 1 Introduction Consider the situation depicted in Figure 1, where an antenna array receives a number of multipath re...
Weighted Subspace Fitting for General Array Error Models
 IEEE Transactions on Signal Processing
, 1997
"... Model error sensitivity is an issue common to all high resolution direction of arrival estimators. Much attention has been directed to the design of algorithms for minimum variance estimation taking only finite sample errors into account. Approaches to reduce the sensitivity due to array calibration ..."
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Cited by 5 (2 self)
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Model error sensitivity is an issue common to all high resolution direction of arrival estimators. Much attention has been directed to the design of algorithms for minimum variance estimation taking only finite sample errors into account. Approaches to reduce the sensitivity due to array calibration errors have also appeared in the literature. Herein, one such approach is adopted which assumes that the errors due to finite samples and model errors are of comparable size. Minimum variance estimators have previously been proposed for this case. These estimators typically lead to nonlinear optimization problems and are not in general consistent if the source signals are fully correlated. For special error models, subspace fitting methods have previously been devised. In this paper, a weighted subspace fitting method for general array perturbation models is derived. This method provides minimum variance estimates under the assumption that the prior distribution of the perturbation model i...