Search

This paper considers the problem of cooperative localization in mobile networks. In static networks, node locations can be obtained from pairwise distance measurements using the classical multidimensional scaling (MDS) approach. This paper introduces a modified MDS framework that also incorporates relative velocity measurements if available in mobile networks. The proposed cost function is minimized via a low complexity majorization algorithm. A distributed variant of the proposed algorithm is also outlined for use in large resource-constrained multi-hop networks. The proposed algorithm incurs low computational and communication cost, and handles practical constraints such as missing measurements and variable node velocities. Simulation results corroborate the performance gains obtained by the proposed algorithm over state-of-the-art localization algorithms. [ABSTRACT FROM AUTHOR]

Time-of-arrival (TOA) based localization plays a central role in current and future localization systems. Such systems, exploiting the fine delay resolution properties of wideband and ultra-wideband (UWB) signals, are particularly attractive for ranging under harsh propagation conditions in which significant multipath may be present. While multipath has been traditionally considered detrimental in the design of TOA estimators, it can be exploited to benefit ranging. This paper investigates the impact of a priori multipath information on TOA estimation. To this end, bounds on the performance of TOA estimation in dense multipath channels are provided and discussed under different operating conditions. The effects of channel dispersion and transmission bandwidth on ranging systems are investigated showing that, contrary to communication systems, diversity behavior is only exhibited in the medium signal-to-noise ratio regime. [ABSTRACT FROM AUTHOR]

In most existing localization schemes, location information leakage is inevitable, since both the locations of the target and the anchors will be revealed to the entity that conducts location estimation. A malicious entity may destroy the localization infrastructure or attack the target or anchors based on the revealed locations. Therefore, location privacy preservation in localization is of great significance. This paper investigates the privacy preservation problem in localization using time difference of arrival (TDOA) under the assumptions of safe internode communication and an honest-but-curious model. Adopting the privacy-preserving summation method, we propose two privacy-preserving localization protocols for two scenarios, where the TDOA measurements are, respectively, obtained by the target and the anchors. The proposed protocols do not utilize any encryption method, and can hide the locations of both the target and the anchors by limiting the available information to other nodes. The localization performance, sufficient conditions for privacy preservation, and computation and communication complexities of the proposed protocols are theoretically analyzed. Through simulation and numerical results, we show that the proposed protocols can implement location privacy preservation without degrading the localization performance. [ABSTRACT FROM AUTHOR]

Both localization and synchronization of mobile nodes are important for wireless networks. In this paper, we propose new methods for network localization and synchronization (NLS) using full-duplex radios through only two frames of transmission. Specifically, all nodes simultaneously transmit their signature signals in the first frame, while receiving others’ signals via full-duplex radios. In the second frame, nodes transmit either scrambled versions of their received signals in the first frame or a digital packet of the channel parameter estimates of the received signals. We develop distributed algorithms to estimate the arrival times of different components in the received signals. These arrival times are then used to determine the local network geometry and clock offsets. The Cramér-Rao lower bounds for internode distances and clock offsets are derived, and the former can be translated into error bounds of the node positions. Compared with conventional frequency division duplex or time-division duplex, we demonstrate the high efficiency of NLS using full-duplex radios, revealing its potential beyond data communications in future wireless networks. [ABSTRACT FROM AUTHOR]

This paper proposes two methods to reduce the bias of the well-known algebraic explicit solution (Chan and Ho, “A simple and efficient estimator for hyperbolic location,” IEEE Trans. Signal Process., vol. 42, pp. 1905–1915, Aug. 1994) for source localization using TDOA. Bias of a source location estimate is significant when the measurement noise is large and the geolocation geometry is poor. Bias also dominates performance when multiple times of independent measurements are available such as in UWB localization or in target tracking. The paper starts by deriving the bias of the source location estimate from Chan and Ho. The bias is found to be considerably larger than that of the Maximum Likelihood Estimator. Two methods, called BiasSub and BiasRed, are developed to reduce the bias. The BiasSub method subtracts the expected bias from the solution of Chan and Ho's work, where the expected bias is approximated by the theoretical bias using the estimated source location and noisy data measurements. The BiasRed method augments the equation error formulation and imposes a constraint to improve the source location estimate. The BiasSub method requires the exact knowledge of the noise covariance matrix and BiasRed only needs the structure of it. Analysis shows that both methods reduce the bias considerably and achieve the CRLB performance for distant source when the noise is Gaussian and small. The BiasSub method can nearly eliminate the bias and the BiasRed method is able to lower the bias to the same level as the Maximum Likelihood Estimator. The BiasRed method is extended for TDOA and FDOA positioning. Simulations corroborate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Time synchronization and localization are two important issues in wireless sensor networks. Although these two problems share many aspects in common, they are traditionally treated separately. In this paper, we present a unified framework to jointly solve time synchronization and localization problems at the same time. Furthermore, since the accuracy of synchronization and localization is very sensitive to the accuracy of anchor timings and locations, the joint time synchronization and localization problem with inaccurate anchors is also considered in this paper. For the case with accurate anchors, the joint maximum likelihood estimator and a more computationally efficient least squares (LS) estimator are proposed. When the anchor timings and locations are inaccurate, a generalized total least squares (GTLS) scheme is proposed. Cramér-Rao lower bounds (CRLBs) and the analytical mean square error (MSE) expressions of the LS based estimators are derived for both accurate and inaccurate anchor cases. Results show that the proposed joint estimators exhibit performances close to their respective CRLBs and outperform the separate time synchronization and localization approach. Furthermore, the derived analytical MSE expressions predict the performances of the proposed joint estimators very well. [ABSTRACT FROM AUTHOR]

The paper studies detection of a target buried in a rich scattering medium by time reversal. We use a multi-static configuration with receive and transmit arrays of antennas. In time reversal, the backscattered field is recorded, time reversed, and retransmitted (mathematically or physically) into the same scattering medium. We derive two array detectors: the time-reversal channel matched filter when the target channel response is known; and the time-reversal generalized-likelihood ratio test (TR-GLRT) when the target channel response is unknown. The noise added in the initial probing step to the time-reversal signal makes the analysis of the TR-GLRT detector nontrivial. The paper derives closed form expressions for the signal-to-noise ratio gain provided by this detector over the corresponding conventional clutter subtraction energy detector in the two extreme conditions of weak and strong (electronic additive) noise and shows that time reversal provides, under weak noise, the optimal waveform shape to probe the environment. We analyze the impact of the array configuration on the detection performance. Finally, experiments with electromagnetic data collected in a multipath scattering laboratory environment confirm our analytical results. Under the realistic conditions tested, time reversal provides detection gains over conventional detection that range from 2 to 4.7 dB. [ABSTRACT FROM AUTHOR]

In recent years, the sources localization has noticed an increase in research conducted on the problem of mixed far-field sources (FFSs) and near-field sources (NFSs). The main assumption of the existing researches is that the signals should be uncorrelated. Therefore, they cannot be used for multipath environments. The present paper provides a method called components separation algorithm (CSA) for the localization of multiple mixed FFSs and NFSs, including uncorrelated, lowly correlated and coherent signals. Firstly, by constructing one special cumulant matrix, and using a MUSIC-based technique, the noncoherent DOA vector (NDOAV) is extracted. By constructing another special cumulant matrix, and with respect to NDOAV, an estimate of the range, as well as a signal classification is obtained for noncoherent sources. Then, by estimating their kurtosis, the noncoherent component and consequently the coherent one of the second cumulant matrix is obtained. Finally, by introducing a novel approach based on squaring, projection, spatial smoothing, array interpolation transform and coherent component restoring, the parameters of coherent signals in each coherent group are estimated separately. The CSA prevents severe loss of the aperture. Furthermore, it does not require any pairing. The simulation results validate its satisfactory performance in terms of estimation accuracy, resolution, computational complexity, reasonable classification, and also its robustness against lowly correlated sources. [ABSTRACT FROM AUTHOR]

Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize points from a snapshot of distances. If the objects move, one expects to do better by modeling the motion. In this paper, we introduce Kinetic Euclidean Distance Matrices (KEDMs)—a new kind of time-dependent distance matrices that incorporate motion. The entries of KEDMs become functions of time, the squared time-varying distances. We study two smooth trajectory models—polynomial and bandlimited trajectories—and show that these trajectories can be reconstructed from incomplete, noisy distance observations, scattered over multiple time instants. Our main contribution is a semidefinite relaxation, inspired by similar strategies for static EDMs. Similarly to the static case, the relaxation is followed by a spectral factorization step; however, because spectral factorization of polynomial matrices is more challenging than for constant matrices, we propose a new factorization method that uses anchor measurements. Extensive numerical experiments show that KEDMs and the new semidefinite relaxation accurately reconstruct trajectories from noisy, incomplete distance data and that, in fact, motion improves rather than degrades localization if properly modeled. This makes KEDMs a promising tool for problems in geometry of dynamic points sets. [ABSTRACT FROM AUTHOR]

In this paper, we address the challenging problem of multiple source localization in wireless sensor networks (WSN). We develop an efficient statistical algorithm, based on the novel application of sequential Monte Carlo (SMC) sampler methodology, that is able to deal with an unknown number of sources given quantized data obtained at the fusion center from different sensors with imperfect wireless channels. We also derive the posterior Cramér–Rao bound (PCRB) of the source location estimate. The PCRB is used to analyze the accuracy of the proposed SMC sampler algorithm and the impact that quantization has on the accuracy of location estimates of the sources. Extensive experiments show the benefits of the proposed scheme in terms of the accuracy of the estimation method that is required for model selection (i.e., the number of sources) and the estimation of the source characteristics compared to the classical importance sampling method. [ABSTRACT FROM AUTHOR]

In the aforementioned paper the authors investigate the localization of multiple near-field narrowband sources with a symmetric uniform linear array, and develop a new linear prediction approach based on the truncated singular value decomposition. In this comment we point out several shortcomings of the model they use for the data measured by the array. The mismatch between this highly idealized mathematical model and the true array response raises concerns about the performance of the proposed method on real arrays. [ABSTRACT FROM AUTHOR]

A multistatic system uses a transmitter to illuminate the object of interest and collects the reflected signal by a number of receivers to determine its location. In some scenarios such as passive coherent localization or for gaining flexibility, the position of the transmitter is not known. This paper investigates the use of the indirect path measurements reflected off the object alone, or together with the direct path measurements from the transmitter to receivers for locating the object in the absence of the transmitter position. We show that joint estimation of the object and transmitter positions from both the indirect and direct measurements can yield a better object location estimate than using the indirect measurements only by eliminating the dependency of the transmitter position. An algebraic closed-form solution is developed for the nonlinear problem of joint estimation and is shown analytically to achieve the Cramér–Rao lower bound performance under Gaussian noise over the small error region. To complete the study and gain insight, the optimal receiver placement in the absence of transmitter position is derived by minimizing the estimation confidence region or the mean-square estimation error for the object location. The performance lost due to unknown transmitter position under the optimal geometries is quantified. Simulations confirm well with the theoretical developments. [ABSTRACT FROM AUTHOR]

Localizing a cloud of points from noisy measurements of a subset of pairwise distances has applications in various areas, such as sensor network localization and reconstruction of protein conformations from nuclear magnetic resonance measurements. Drineas et al. proposed a natural two-stage approach, named singular value decomposition (SVD)–multidimensional scaling (MDS), for this purpose at the 2006 3rd Annual IEEE Communications Society on Sensor and Ad Hoc Communications and Networks. This approach consists of a low-rank matrix completion algorithm, named SVD-reconstruct, to estimate random missing distances, and the classic MDS method to estimate the positions of nodes. In this paper, we present a detailed analysis for this method. More specifically, we first establish error bounds for Euclidean distance matrix completion in both expectation and tail forms. Utilizing these results, we then derive the error bound for the recovered positions of nodes. In order to assess the performance of SVD-reconstruct, we present the minimax lower bound of the zero-diagonal, symmetric, low-rank matrix completion problem by Fano's method. This result reveals that when the noise level is low, the SVD-reconstruct approach for Euclidean distance matrix completion is suboptimal in the minimax sense; when the noise level is high, SVD-reconstruct can achieve the optimal rate up to a constant factor. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method to localize a wireless and stationary blind node based on received signal strength measurements; the positioning scheme relies on the statistical path loss model. The operating environment is either non-homogeneous, i.e., the attenuation factors of the various links are different, or homogeneous, i.e., all links share one and the same attenuation factor. We introduce a cognitive procedure to circumvent the a priori uncertainty on the actual scenario being in force: the first stage is a properly designed hypothesis test, fed by measurements between anchors, moving along known trajectories, to decide whether or not the environment is homogeneous. Based upon the output of the test, a model-dependent maximum-likelihood localization algorithm is adopted using the measurements made by the blind node and the parameters estimated by the anchors at previous stage. The performance assessment shows that the proposed approach could be a viable means to handle localization in uncertain scenarios. [ABSTRACT FROM PUBLISHER]

For many wireless sensor networks, high accuracy and low complexity localization techniques are crucial to their successful deployment. The radio interferometric positioning system (RIPS) has been introduced for accurate localization with low complexity. In this paper, a dual-tone radio interferometric positioning system (DRIPS) is proposed to localize multiple targets simultaneously. In DRIPS, multiple asynchronous targets emit dual-tone signals, and synchronous anchor receivers (nodes with known positions) extract phase information of low-frequency differential tones created by squaring the received dual-tone signals. Multiple time-of-arrivals (TOAs) coupled with unknown offsets due to the asynchronous targets are estimated based on the phase information. Accordingly, a localization algorithm taking the integer ambiguity issue into account is developed. Moreover, considering the case without accurate knowledge of the frequencies of the differential tones, an ESPRIT-type algorithm is proposed to estimate the frequencies. The proposed DRIPS is robust to flat-fading channels, immune to uncertainties of local oscillators, and able to distinguish different targets. In order to show more insights of the performance limit of the DRIPS, Cramér-Rao bounds (CRBs) are derived. Simulation results illustrate the merits of the proposed DRIPS. [ABSTRACT FROM PUBLISHER]

In this paper, optimal power allocation strategies are investigated for jammer nodes in a wireless localization system. Building upon the concept of the restricted Bayesian approach, a generalized optimization strategy, called the restricted scheme, is proposed for power allocation of jammer nodes, and its theoretical properties are characterized. In the restricted scheme, the aim is to maximize the average Cramer-Rao lower bound (CRLB) of target nodes while keeping their minimum CRLB above a predefined level in the presence of average (total) and peak power constraints. It is proved that the average CRLB achieved by the restricted scheme is a strictly decreasing and concave function of the constraint on the minimum CRLB level. A closed-form solution is obtained for the restricted scheme when the tradeoff parameter and the total power limit are below certain thresholds. In addition, it is shown that the optimal solution of the restricted scheme corresponds to the use of at most NT jammer nodes, where NT is the number of target nodes, and that the optimal solution of the minimum CRLB maximization scheme is determined by at most NJ target nodes, where NJ is the number of jammer nodes. Extensions of the restricted scheme and an alternative scheme that aims to maximize the number of disabled target nodes (whose CRLBs are above a preset level) are considered, and the corresponding optimal strategies for jammer power allocation are identified. Numerical examples are provided to verify the theoretical derivations for various network configurations. [ABSTRACT FROM AUTHOR]

This paper establishes a tensor model for wideband coherent array processing including multiple physical diversities. A separable coherent focusing operation is proposed as a preprocessing step in order to ensure the multilinearity of the interpolated data. We propose an alternating least squares algorithm to process tensor data, taking into account the noise correlation structure introduced by the focusing operation. We show through computer simulations that the estimation of direction of arrival and polarization parameters improves compared to existing narrowband tensor processing and wideband MUltiple SIgnal Classification. The performance is also compared to the Cramér-Rao bounds of the wideband tensor model. [ABSTRACT FROM PUBLISHER]

In this paper, a novel source/target localization approach is proposed using a number of sensors (surrounding or not surrounding one or more sources) to form a sparse large aperture array of known geometry. Under a large array aperture, the array response (manifold vector) obeys a spherical wave rather than a plane wave propagation model. By rotating the array reference point to be at each of the array sensors, a number of covariance matrices are constructed. It is shown that the eigenvalues of these covariance matrices are related to the source location with respect to the array reference point. The proposed approach is robust to channel fading and considers both wideband and narrowband assumptions. The performance of the proposed approach is evaluated via simulations as a function of array geometry, number of snapshots (L) and signal to noise ratio (SNR) and is shown to exceed existing techniques. [ABSTRACT FROM PUBLISHER]

In the present paper, we focus on the design of adaptive decision schemes for point-like targets; the proposed algorithms can take advantage of the possible spillover of target energy between consecutive matched filter samples. To this end, we assume that the received useful signal is known up to a complex factor modeled as a deterministic parameter; moreover, it is embedded in correlated Gaussian noise with unknown covariance matrix. Finally, for estimation purposes we assume that a set of secondary data, free of signal components, but sharing the same covariance matrix of the noise in the cells containing signal returns, up to a possibly different scale factor, is available. Remarkably, the proposed decision schemes can provide accurate estimates of the target position within the cell under test and ensure the desirable constant false alarm rate property with respect to the unknown noise parameters. [ABSTRACT FROM AUTHOR]

A previous study shows that the use of a calibration emitter whose position is known exactly can significantly reduce the loss in time differences of arrival (TDOA) based source localization accuracy when the available sensor positions have random errors. This paper extends the previous work to a more practical scenario where the exact position of a calibration emitter is not known. By modeling the calibration position error as additive Gaussian noise, the amount of reduction in localization accuracy due to calibration position error is derived through Cramér-Rao lower bound (CRLB) analysis. In addition, the analysis also affirms the previous studies on Bayesian sensor network localization that it remains possible to improve the localization accuracy even if the calibration position is completely unknown. Next, a performance analysis illustrates that the penalty could be very high if one simply pretends the calibration position is accurate and ignores its error. A closed-form solution is then developed by accounting for the calibration position error and it is proved analytically to reach the CRLB accuracy when the sensor and calibration position errors are small relative to the distance between the calibration emitter and the sensor. Finally, the results are generalized to the case where multiple calibration emitters are available. When deploying multiple calibration emitters, although their positions may not be known exactly, we show that it is possible to completely eliminate the sensor position error and recover the best localization accuracy that is limited by the measurement noise in TDOAs only. All the theoretical developments are corroborated by simulations. [ABSTRACT FROM AUTHOR]

This paper considers the problem of time difference-of-arrival (TDOA) source localization when the TDOA measurements from multiple disjoint sources are subject to the same sensor position displacements from the available sensor positions. This is a challenging problem and closed-form solution with good localization accuracy has yet to be found. This paper proposes an estimator that can achieve this purpose. The pro- posed algorithm jointly estimates the unknown source and sensor positions to take the advantage that the TDOAs from different sources have the same sensor position displacements. The joint estimation is a highly nonlinear problem due to the coupling of source and sensor positions in the measurement equations. We introduce the novel idea of hypothesized source locations in the algorithm development to enable the formulation of psuedolinear equations, thereby leading to the establishment of closed-form solution for source location estimates. Besides the advantage of closed-form, the newly developed algorithm is shown analytically, under the condition that the TDOA measurement noise and the sensor position errors are sufficiently small, to reach the CRLB accuracy. For clarity, the localization of two disjoint sources is used in the algorithm development. The developed algorithm is then examined under the special case of a single source and extended to the more general case of more than two unknown sources. The theoretical developments are supported by simulations. [ABSTRACT FROM AUTHOR]

This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). The centroid transformation subspace-which includes representations of rotation, translation, and scaling-is characterized for a number of measurement models including distance, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and angle-difference-of-arrival (ADOA) measurements. The error decomposition may be applied to any localization algorithm in order to better understand its performance characteristics, and it may be applied to the Cramér-Rao bound (CRB) to determine performance limits in the relative and transformation domains. A geometric interpretation of the constrained CRB is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples are presented to illustrate the utility of the proposed error decomposition into relative and transformation components. [ABSTRACT FROM AUTHOR]

This paper presents a source localization algorithm based on the source signal's time-of-arrival (TOA) at sensors that are not synchronized with one another or the source. The proposed algorithm estimates source positions using a window of TOA measurements which, in effect, creates a virtual sensor array. Based on a Gaussian noise model, maximum likelihood estimates (MLE) for the source position and displacement are obtained. Performance issues are addressed by evaluating the Cramér-Rao lower bound and considering the virtual sensor array's geometric properties. To track the source trajectory from the TOA measurement, which is a nonlinear function of source position and displacement, this localization algorithm is combined with the extended Kalman filter (EKF) and the unscented Kalman filter, resulting in good tracking performance. [ABSTRACT FROM AUTHOR]

Network cooperation among agents can significantly increase their position accuracy at the cost of power consumption. Current power management techniques aim at minimizing the total position estimation errors over all the agents subject to the power budgets. There are two main drawbacks for these approaches. First, the performance of a single agent may be sacrificed for the benefit of the whole network, and second, full power budget may be used for only marginal performance improvement on the position accuracy. This paper proposes a new type of power management strategies where each agent individually minimizes its square position error bound penalized by its power cost. The strategies are obtained as solutions to two power management games that are formulated under the knowledge of local information and global information, respectively. We show that agents are more likely to cooperate when global information is available or the channel quality is good. Analytical and numerical results show that the proposed strategies significantly reduce the energy consumption with only marginal performance loss in position accuracy. [ABSTRACT FROM PUBLISHER]

Distributed radar systems are capable of enhancing the detection performance by using multiple widely spaced distributed antennas. With prior statistic information of targets, resource allocation is of critical importance for further improving the system's achievable performance. In this paper, the total transmitted power is minimized at a given mean-square target-estimation error. We derive two iterative decomposition algorithms for solving this nonconvex constrained optimization problem, namely, the optimality condition decomposition (OCD)-based and the alternating direction method of multipliers (ADMM)-based algorithms. Both the convergence performance and the computational complexity of our algorithms are analyzed theoretically, which are then confirmed by our simulation results. The OCD method imposes a much lower computational burden per iteration, while the ADMM method exhibits a higher per-iteration complexity, but as a benefit of its significantly faster convergence speed, it requires less iterations. Therefore, the ADMM imposes a lower total complexity than the OCD. The results also show that both of our schemes outperform the state-of-the-art benchmark scheme for the multiple-target case, in terms of the total power allocated, at the cost of some degradation in localization accuracy. For the single-target case, all the three algorithms achieve similar performance. Our ADMM algorithm has similar total computational complexity per iteration and convergence speed to those of the benchmark. [ABSTRACT FROM PUBLISHER]

In sparse target inference problems, it has been shown that significant gains can be achieved by adaptive sensing using convex criteria. We generalize this previous work on adaptive sensing to: a) include multiple classes of targets with different levels of importance and b) accommodate multiple sensor models. Optimization policies are developed to allocate a limited resource budget to simultaneously locate, classify and estimate a sparse number of targets embedded in a large space. Bounds on the performance of the proposed policies are derived by analyzing a baseline policy, which allocates resources uniformly across the scene, and an oracle policy which has a priori knowledge of the target locations/classes. These bounds quantify the potential benefit of adaptive sensing as a function of target frequency and importance. Numerical results indicate that the proposed policies perform close to the oracle bound when signal quality is sufficiently high. Moreover, the proposed policies improve on previous policies in terms of reducing estimation error, reducing misclassification probability, and increasing expected return. To account for sensors with different levels of agility, three sensor models are considered: global adaptive (GA), which can allocate different amounts of resource to each location in the space? global uniform (GU), which can allocate resources uniformly across the scene? and local adaptive (LA), which can allocate fixed units to a subset of locations. Policies that use a mixture of GU and LA sensors are shown to perform similarly to those that use GA sensors while being more easily implementable. [ABSTRACT FROM AUTHOR]

The estimation of a source location using directly the range or range difference measurements is difficult and requires numerical solution, which is caused by the highly non-linear relationship between the measurements and the unknown. We can obtain a computationally efficient and non-iterative algebraic solution by squaring the measurements first before solving for the unknown. However, a recent study has shown that such a solution is suboptimum in reaching the CRLB performance and the localization accuracy could be significantly worse in some localization geometries. This paper demonstrates that when range weighting factors are introduced to the squared measurements, the resulting solution will be able to reach the CRLB accuracy. Both the squared range and squared range difference cases are considered, and the mean-square error (MSE) and the bias of the resulting solutions are derived. The asymptotic efficiency of the proposed cost functions are proven theoretically and validated by simulations. The effects of range weighting factors on the localization performance under different sensor number, noise correlation, and localization geometry are examined. Introducing range weightings to the squared range measurements increases the bias but it is negligible in the MSE. Having range weightings in the squared range difference measurements improves both the MSE and bias. [ABSTRACT FROM PUBLISHER]

Time-based localization approaches attract a lot of interest due to their high accuracy and potentially low cost for wireless sensor networks (WSNs). However, time-based localization is tightly coupled with clock synchronization. Thus, the reliability of timestamps in time-based localization becomes an important yet challenging task to deal with. In this paper, we propose robust time-based localization strategies to locate a target node with the help of anchors (nodes with known positions) in asynchronous networks. Two kinds of asynchronous networks are considered: one only with clock offsets, labeled quasi-synchronous networks, whereas the other with not only clock offsets but also clock skews, labeled fully asynchronous networks. A novel ranging protocol is developed for both networks, namely asymmetric trip ranging (ATR), to reduce the communication load and explore the broadcast property of WSNs. Regardless of the reliability of the timestamp report from the target node, closed-form least-squares (LS) estimators are derived to accurately estimate the target node position. As a result, we counter the uncertainties caused by the target node by ignoring the timestamps from this node. Furthermore, in order to simplify the estimator in fully asynchronous networks, localization and synchronization are decoupled. A simple yet efficient method is proposed to first Calibrate the Clock Skews of the anchors, and then Estimate the Node Position (CCS-ENP). Finally, Cramér-Rao bounds (CRBs) and simulation results corroborate the efficiency of our localization schemes. [ABSTRACT FROM AUTHOR]

In this paper, we consider the positioning problem in wireless sensor networks from a systems perspective, including aspects of the physical layer, channel, ranging algorithm and positioning algorithm. We argue that gains in positioning accuracy and robustness, can be achieved by extending the interface between the physical layer ranging algorithm and the higher layer positioning algorithm to include more information than just a single distance estimate per link. Towards this end, we propose and analyze a "soft" distance estimator. This estimator, differently from traditional distance estimators, outputs a list of likely distances for each link together with a list of weights similar to likelihoods. Hence, we broaden the interface between ranging and positioning algorithm, and provide additional information that the positioning algorithm can exploit. The soft distance estimator we propose is of comparably low complexity, and offers competitive performance while making no assumptions on a priori channel information or network synchronization. The analysis and simulations in this work are based on the channel models adopted by the IEEE 802.15.4a working group, and highlight the benefits and drawbacks of the proposed approach. [ABSTRACT FROM AUTHOR]

The problem of multiple target tracking using a passive direction-finding system is addressed when the number of targets is not known apriori. A new method is proposed that is suitable for systems operating in low signal-to-noise ratio and high clutter. Such conditions cause unpredictable variations of stochastic characteristics of noise and signals (especially for wideband frequency ones) and create ambiguity in the output of direction-finding algorithms. In this paper, we use the predictive description length (PDL) technique, which is an information theoretic approach, and by suitable modeling, we minimize the predictive codelength for statistical data description of position measurements. The PDL-dynamic programming (DP) method is also presented, which employs the DP algorithm to reduce the computational load of the PDL technique. The concept of tracking time-varying number of targets makes PDL-DP a suitable technique for target tracking in practical systems. [ABSTRACT FROM AUTHOR]

It takes a great deal of care to accurately align direction of arrival (DOA) sensors to a reference direction. Any error in alignment degrades the localization accuracy of the entire system. We propose a method that enables the alignment using DOA measurements of arbitrary sources. This saves the efforts to set and maintain the alignment by external means. To simplify the exhibition, it is assumed that the sensors and the sources are confined to a plane. The method is based on the maximum-likelihood estimator. The main challenge is the discontinuities in the cost function due to the circular nature of angle measurements. The proposed method is verified by simulations, and the performance is compared to lower bounds and also to systems with perfect alignment. [ABSTRACT FROM PUBLISHER]

In this correspondence, we focus on the design and the analysis of schemes aimed at estimating the position of multiple point-like targets that fall among three adjacent samples of the matched filter output (typically present in the processing chain of a radar). To this end, we exploit spillover of targets' energy to adjacent range cells. The number of targets (and the corresponding Doppler frequency shifts) is assumed to be known. Moreover, we suppose that received useful signals can be modeled in terms of vectors known up to deterministic parameters and that they are embedded in correlated Gaussian noise with unknown covariance matrix. For estimation purposes we assume that a set of secondary data, free of signal components, but sharing the same covariance matrix of the noise in the cells containing signal returns, is available. The analysis, also in comparison to a possible competitor, proves the superiority of multitarget schemes with respect to single target ones, even under reasonably mismatched scenarios. [ABSTRACT FROM PUBLISHER]

Detection and estimation problems in multiple-input multiple-output (MIMO) radar have recently drawn considerable interest in the signal processing community. Radar has long been a staple of signal processing, and MIMO radar presents challenges and opportunities in adapting classical radar imaging tools and developing new ones. Our aim in this article is to showcase the potential of tensor algebra and multidimensional harmonic retrieval (HR) in signal processing for MIMO radar. Tensor algebra and multidimensional HR are relatively mature topics, albeit still on the fringes of signal processing research. We show they are in fact central for target localization in a variety of pertinent MIMO radar scenarios. Tensor algebra naturally comes into play when the coherent processing interval comprises multiple pulses, or multiple transmit and receive subarrays are used (multistatic configuration). Multidimensional harmonic structure emerges for far-field uniform linear transmit/receive array configurations, also taking into account Doppler shift; and hybrid models arise in-between. This viewpoint opens the door for the application and further development of powerful algorithms and identifiability results for MIMO radar. Compared to the classical radar-imaging-based methods such as Capon or MUSIC, these algebraic techniques yield improved performance, especially for closely spaced targets, at modest complexity. [ABSTRACT FROM PUBLISHER]

In the case of multicomponent signals with amplitude and frequency modulations, the idealized representation which consists of weighted trajectories on the time-frequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the Wigner-Ville distribution neighboring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum ℓ1-norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical experiments, its performance is assessed in various configurations and the results are compared with standard techniques. It is shown that improved representations can be obtained, though at a computational cost which is significantly increased. [ABSTRACT FROM AUTHOR]

We consider a wireless source localization network in which a target node emits localization signals that are used by anchor nodes to estimate the target node position. In addition to target and anchor nodes, there can also exist eavesdropper nodes and jammer nodes which aim to estimate the position of the target node and to degrade the accuracy of localization, respectively. We first propose the problem of eavesdropper selection with the goal of optimally placing a given number of eavesdropper nodes to a subset of possible positions to estimate the target node position as accurately as possible. As the performance metric, the Cramér-Rao lower bound (CRLB) related to the estimation of the target node position by eavesdropper nodes is derived, and its convexity and monotonicity properties are investigated. By relaxing the integer constraints, the eavesdropper selection problem is approximated by a convex optimization problem and algorithms are proposed for eavesdropper selection. Then, the problem of jammer selection is proposed where the aim is to optimally place a given number of jammer nodes to a subset of possible positions for degrading the localization accuracy of the network as much as possible. A CRLB expression from the literature is used as the performance metric, and its concavity and monotonicity properties are derived. Also, a convex optimization problem is derived after relaxation. Finally, the joint eavesdropper and jammer selection problem is proposed with the goal of placing certain numbers of eavesdropper and jammer nodes to a subset of possible positions. [ABSTRACT FROM AUTHOR]

Slepian functions provide a solution to the optimization problem of joint time-frequency localization. Here, this concept is extended by using a generalized optimization criterion that favors energy concentration in one interval while penalizing energy in another interval, leading to the “augmented” Slepian functions. Mathematical foundations together with examples are presented in order to illustrate the most interesting properties that these generalized Slepian functions show. Also the relevance of this novel energy-concentration criterion is discussed along with some of its applications. [ABSTRACT FROM AUTHOR]

We consider a registration-based approach for localizing sensor networks from range measurements. This is based on the assumption that one can find overlapping cliques spanning the network. That is, for each sensor, one can identify geometric neighbors for which all inter-sensor ranges are known. Such cliques can be efficiently localized using multidimensional scaling. However, since each clique is localized in some local coordinate system, we are required to register them in a global coordinate system. In other words, our approach is based on transforming the localization problem into a problem of registration. In this context, the main contributions are as follows. First, we describe an efficient method for partitioning the network into overlapping cliques. Second, we study the problem of registering the localized cliques, and formulate a necessary rigidity condition for uniquely recovering the global sensor coordinates. In particular, we present a method for efficiently testing rigidity, and a proposal for augmenting the partitioned network to enforce rigidity. A recently proposed semidefinite relaxation of global registration is used for registering the cliques. We present simulation results on random and structured sensor networks to demonstrate that the proposed method compares favourably with state-of-the-art methods in terms of run time, accuracy, and scalability. [ABSTRACT FROM PUBLISHER]

This correspondence studies the received signal strength-based localization problem when the transmit power or path-loss exponent is unknown. The corresponding maximum-likelihood estimator (MLE) poses a difficult nonconvex optimization problem. To avoid the difficulty in solving the MLE, we use suitable approximations and formulate the localization problem as a general trust region subproblem, which can be solved exactly under mild conditions. Simulation results show a promising performance for the proposed methods, which also have reasonable complexities compared to existing approaches. [ABSTRACT FROM PUBLISHER]

We consider problems of localization, disambiguation, and mapping in a domain filled with signals-of-opportunity generated by transmitters. One or more (static or mobile) receivers utilize these signals and from them characterize the domain, localize, disambiguate, etc. The tools we develop are topological in nature, and rely on interpreting the problem as one of embedding the domain into a sufficiently high-dimensional space of signals via a signal profile function. Varying kinds of signal processing (TOA, TDOA, DOA, etc.) and discretization are addressed. Finally, we describe experiments that demonstrate the feasibility of these ideas in practice. [ABSTRACT FROM AUTHOR]

Precise localization have attracted considerable interest in the engineering literature. Most publications consider small measurement errors. In this work we discuss localization in the presence of outliers, where several measurements are severely corrupted while sufficient other measurements are reasonably precise. It is known that maximum likelihood or least squares provide poor results under these conditions. On the other hand, robust regression can successfully handle up to 50% outliers but is associated with high complexity. Using the ℓ1 norm as the penalty function provides some immunity from outliers and can be solved efficiently with linear programming methods. We use linear equations to describe the localization problem and then we apply the ℓ1 norm and linear programming to detect the outliers and avoid the wild measurements in the final solution. Our main contribution is an exploitation of recent results in the field of sparse representation to obtain bounds on the number of detectable outliers. The theory is corroborated by simulations and by real data. [ABSTRACT FROM AUTHOR]

Sensor positioning is an important task of location-aware wireless sensor networks. In most sensor positioning systems, sensors and beacons need to emit ranging signals to each other. Sensor ranging energy should be low to prolong system lifetime, but sufficiently high to fulfill prescribed accuracy requirements. This motivates us to investigate ranging energy optimization problems. We address ranging energy optimization for an unsynchronized positioning system, which features robust sensor positioning (RSP) in the sense that a specific accuracy requirement is fulfilled within a prescribed service area. We assume a line-of-sight (LOS) channel exists between the sensor and each beacon. The positioning is implemented by time-of-arrival (TOA) based two-way ranging between a sensor and beacons, followed. by a location estimation at a central processing unit. To establish a dependency between positioning accuracy and ranging energy, we assume the adopted TOA and location estimators are unbiased and attain the associated Cramér-Rao bound. The accuracy requirement has the same form as the one defined by the Federal Communication Commission (FCC), and we present two constraints with linear-matrix-inequality form for the RSP. Ranging energy optimization problems, as well as a practical algorithm based on semidefinite programming are proposed. The effectiveness of the algorithm is illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

Underwater acoustic localization usually relies on time-of-arrival (ToA) measurements, which are then converted into range estimates. However, the water medium is inhomogeneous and the sound speed varies depending on several parameters, e.g., the temperature, pressure and salinity. As a result, sound waves do not necessarily travel in straight lines. Ignoring this stratification effect could lead to considerable bias in the range estimates. We propose a depth-based approach to compensate the stratification effect for improved underwater ranging. We assume that the sound velocity profile (SVP) is only vertically stratified, the position of the sender is known, and the receiver has a noisy depth estimate via a depth sensor. We find a numerically simple range estimator, based on reconstructing the slanted path using Fermat's Principle and calculus of variations. This estimator removes the bias and is asymptotically efficient. We compare our solution to the simplistic linear estimator that assumes straight-line propagation in a shallow-water example where the sound speed decreases monotonically with depth. We find that the bias of the linear estimator increases with range and is non-negligible when the ToA measurements have a small variance, while our solution is bias-free and meets the Cramér-Rao lower bound (CRLB). [ABSTRACT FROM AUTHOR]

We propose a massively scalable ‘imaging’ architecture for sensor networks, in which sensor nodes act as ‘pixels’ that electronically reflect (and possibly modulate data on top of) a beacon transmitted by a collector node. The collector employs sophisticated radar and image processing techniques to localize the responding sensor nodes, and (if data modulation is present) multiuser data demodulation techniques to extract the data sent by multiple sensors. The sensors do not need to know their own locations, do not need to communicate with each other, and can be randomly deployed. In this initial exposition, we develop basic insight into the localization capabilities of this approach, ignoring sensor data modulation. This reduces to an idealized one-bit, on-off keyed, communication model in which the the sensors are either ߢactive’ or ‘inactive’, with the active sensors responding to the collector's beacon without superimposing data modulation. We consider a moving collector, with the sensor reflections creating a synthetic aperture radar (SAR)-like geometry. However, the collector must employ significant modifications to SAR signal processing for estimation of the location of the active sensors: noncoherent techniques similar to those in noncoherent radar tomography to account for the lack of carrier synchronization between sensor and collector nodes, and decision feedback mechanisms for estimation of the locations of multiple closely spaced active sensors. Measures for localization performance are defined, and the effect of system parameters such as bandwidth, beamwidth and signal-to-noise-ratio (SNR) on performance is investigated. [ABSTRACT FROM AUTHOR]

We consider a multiple-input multiple-output (MIMO) radar system where both the transmitter and receiver have multiple well-separated subarrays with each subarray containing closely spaced antennas. Because of this general antenna configuration, both the coherent processing gain and the spatial diversity gain can be simultaneously achieved. We compare several spatial spectral estimators, including Capon and APES, for target detection and parameter estimation. We introduce a generalized-likelihood ratio test (GLRT) and a conditional generalized-likelihood ratio test (cGLRT) for the general antenna configuration. Based on GLRT and cGLRT, we then propose an iterative GLRT (iGLRT) procedure for target detection and parameter estimation. Via several numerical examples, we show that iGLRT can provide excellent detection and estimation performance at a low computational cost [ABSTRACT FROM PUBLISHER]

We consider the problem of detecting and localizing a material release utilizing sparse sensor measurements and formulate the problem as one of abrupt change detection. Methods which rely on single-sensor detection require dense deployment to achieve adequate coverage; costly sensors preclude such approaches. Furthermore, localization requires the fusion of multiple sensor measurements. Fusion in sparse sensor configurations is dependent on the knowledge of the dynamics of particle dispersion, which is, itself, problematic due to the inherent randomness on the wind field. We consider the efficacy of using an approximate dynamic model with coarse parameter estimates for the detection and localization of material releases. Specifically, we consider propagation models consisting of diffusion plus transport according to a Gaussian dispersion model. Assuming a known wind field, unconstrained intersensor communication, and a centralized processor, we derive optimal inference algorithms and provide a hybrid detection-localization hypothesis-testing framework with linear growth in the hypothesis space. We then analyze the probability of detection, time-to-detection, and localization performance as a function of the number of sensors. Furthermore, we examine the impact on performance when the underlying dynamical model deviates from the assumed model. This detailed analysis provides the basis for the design of more sophisticated algorithms for 1) performing robust detection followed by refined nonlinear parameter-estimation which provides enhanced localization, and 2) distributed architectures aimed at conserving communication resources in which detections within local clusters are used to trigger more intensive intercluster communication to improve detection and localization. [ABSTRACT FROM AUTHOR]