ccurate and low-cost sensor localization is a critical requirement for the deployment of wireless sensor networks in a wide variety of applications. Low-power wireless sensors may be many hops away from any other sensors with a priori location information.In cooperative localization, sensors work together in a peer-to-peer 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 measurement-based statistical models useful to describe time-of-arrival (TOA), angle-of-arrival (AOA), and received-signal-strength (RSS) measurements in wireless sensor networks. Wideband and ultra-wideband (UWB) measurements, and RF and acoustic media are also discussed. Using the models, we show how to calculate a Cramér-Rao 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 state-of-the-art and to make progress in the new and largely open areas of sensor network localization research. INTRODUCTIONDramatic advances in RF and MEMS IC design have made possible the use of large networks of wireless sensors for a variety of new monitoring and control applications [1]- [5]. For example, smart structures will actively respond to earthquakes and make buildings safer; precision agriculture will reduce costs and environmental impact by watering and fertilizing only where necessary and will improve quality by monitoring storage conditions after harvesting; condition-basedA maintenance will direct equipment servicing exactly when and where it is needed based on data from wireless sensors; traffic monitoring systems will better control stoplights and inform motorists of alternate routes in the case of traffic jams; and environmental monitoring networks will sense air, water, and soil quality and identify the source of pollutants in real time.Automatic localization of the sensors in these wireless networks is a key enabling technology. The overwhelming reason is that a sensor's location must be known for its data to be meaningful. As an additional motivation, sensor location information (if it is accurate enough) can be extremely useful for scalable, "geographic" routing algorithms. Note also that location itself is often the data that needs to be sensed; localization can be the driving force for wireless sensor networks in applications such as warehousing and manufacturing logistics.To make these applications viable with possibly vast numbers of sensors, device costs will need to be low (from a few dollars to a few cents depending on the application), sensors will need to last for years or even decades ...

In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared-error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accurateness of the proposed MSEAs and the tightness of the derived approximate bounds 1 are validated by considering the example of time-of-arrival estimation.

Abstract-Radio Tomographic Imaging (RTI) is an emerging technology for imaging the attenuation caused by physical objects in wireless networks. This paper presents a linear model for using received signal strength (RSS) measurements to obtain images of moving objects. Noise models are investigated based on real measurements of a deployed RTI system. Mean-squared error (MSE) bounds on image accuracy are derived, which are used to calculate the accuracy of an RTI system for a given node geometry. The ill-posedness of RTI is discussed, and Tikhonov regularization is used to derive an image estimator. Experimental results of an RTI experiment with 28 nodes deployed around a 441 square foot area are presented.

Accurate, distributed localization algorithms are needed for a wide variety of wireless sensor network applications. This article introduces a scalable, distributed weighted-multidimensional scaling (dwMDS) algorithm that adaptively emphasizes the most accurate range measurements and naturally accounts for communication constraints within the sensor network. Each node adaptively chooses a neighborhood of sensors, updates its position estimate by minimizing a local cost function and then passes this update to neighboring sensors. Derived bounds on communication requirements provide insight on the energy efficiency of the proposed distributed method versus a centralized approach. For received signal-strength (RSS) based range measurements, we demonstrate via simulation that location estimates are nearly unbiased with variance close to the Cramér-Rao lower bound. Further, RSS and time-of-arrival (TOA) channel measurements are used to demonstrate performance as good as the centralized maximum-likelihood estimator (MLE) in a real-world sensor network.

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This paper presents a new method for imaging, localizing, and tracking motion behind walls in real-time. The method takes advantage of the motion-induced variance of received signal strength measurements made in a wireless peerto-peer network. Using a multipath channel model, we show that the signal strength on a wireless link is largely dependent on the power contained in multipath components that travel through space containing moving objects. A statistical model relating variance to spatial locations of movement is presented and used as a framework for the estimation of a motion image. From the motion image, the Kalman filter is applied to recursively track the coordinates of a moving target. Experimental results for a 34-node through-wall imaging and tracking system over a 780 square foot area are presented.

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Accurate representation of the physical layer is required for analysis and simulation of multi-hop networking in sensor, ad hoc, and mesh networks. This paper investigates, models, and analyzes the correlations that exist in shadow fading between links in multi-hop networks. Radio links that are geographically proximate often experience similar environmental shadowing effects and thus have correlated fading. We describe a measurement procedure and campaign to measure a large number of multi-hop networks in an ensemble of environments. The measurements show statistically significant correlations among shadowing experienced on different links in the network, with correlation coefficients up to 0.33. We propose a statistical model for the shadowing correlation between link pairs which shows strong agreement with the measurements, and we compare the new model with an existing shadowing correlation model of Gudmundson (1991). Finally, we analyze multi-hop paths in three and four node networks using both correlated and independent shadowing models and show that independent shadowing models can underestimate the probability of route failure by a factor of two or greater.