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 ...

Abstract-Automatic self-localization is a critical need for the effective use of ad-hoc sensor networks in military or civilian applications. In general, self-localization involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. distance measurements between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational burden across the network and minimize the amount of inter-sensor communication. We demonstrate that the information used for sensor localization is fundamentally local with regard to the network topology and use this observation to reformulate the problem within a graphical model framework. We then present and demonstrate the utility of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical models, and can represent multi-modal uncertainty. Using simulations of small-to moderately-sized sensor networks, we show that NBP may be made robust to outlier measurement errors by a simple model augmentation, and that judicious message construction can result in better estimates. Furthermore, we provide an analysis of NBP's communications requirements, showing that typically only a few messages per sensor are required, and that even low bit-rate approximations of these messages can have little or no performance impact.

Abstract-High-frequency radar measurements of man-made targets are dominated by returns from isolated scattering centers, such as corners and flat plates. Characterizing the features of these scattering centers provides a parsimonious, physically relevant signal representation for use in automatic target recognition (ATR). In this paper, we present a framework for feature extraction predicated on parametric models for the radar returns. The models are motivated by the scattering behavior predicted by the geometrical theory of diffraction. For each scattering center, statistically robust estimation of model parameters provides highresolution attributes including location, geometry, and polarization response. We present statistical analysis of the scattering model to describe feature uncertainty, and we provide a leastsquares algorithm for feature estimation. We survey existing algorithms for simplified models, and derive bounds for the error incurred in adopting the simplified models. A model order selection algorithm is given, and an M-ary generalized likelihood ratio test is given for classifying polarimetric responses in spherically invariant random clutter.

We consider the problem of locating and orienting a network of unattended sensor nodes that have been deployed in a scene at unknown locations and orientation angles. This self-calibration problem is solved by placing a number of source signals, also with unknown locations, in the scene. Each source in turn emits a calibration signal, and a subset of sensor nodes in the network measures the time of arrival and direction of arrival (with respect to the sensor node's local orientation coordinates) of the signal emitted from that source. From these measurements we compute the sensor node locations and orientations, along with any unknown source locations and emission times. We develop necessary conditions for solving the self-calibration problem and provide a maximum likelihood solution and corresponding location error estimate. We also compute the Cramér-Rao bound of the sensor node location and orientation estimates, which provides a lower bound on calibration accuracy. Results using both synthetic data and field measurements are presented.

The problem of estimating the frequencies, phases, and amplitudes of sinusoidal signals is considered. A simplified maximumlikelihood Gauss-Newton algorithm which provides asymptotically efficient estimates of these parameters is proposed. Initial estimates for this algorithm are obtained by a variation of the overdetermined Yule-Walker method and a periodogram-based procedure. Use of the maximum-likelihood Gauss-Newton algorithm is not, however, limited to this particular initialization method. Some other possibilities to get suitable initial estimates are briefly discussed. An analytical and numerical study of the shape of the likelihood function associated with the sinusoids-in-noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure. Some numerical examples are presented to illustrate the performance of the proposed estimation procedure. Comparison to the performance corresponding to the Cramer-Rao lower bound is also presented, using a simple expression for the asymptotic Cramer-Rao bound covariance matrix derived in the paper.