A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> We develop four maximum likelihood (ML) methods to localize a moving target using a network of acoustical sensor arrays. Each array transmits a direction-of-arrival (DOA) estimate to a central processor, which employs one of the localization techniques. The four ML approaches use different target signal models where the time retardation factor for the target position and the degradation of the target signal through the air may or may not be included in the model. We compare these methods along with a linear least squares approach through a number of simulations at various signal to noise levels. <s> BIB001 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> A novel sensor network source localization method based on acoustic energy measurements is presented. This method makes use of the characteristics that the acoustic energy decays exponentially with respect to the distance from an omni-directional acoustic source. By comparing energy readings measured at surrounding acoustic sensors during the same time interval can be accurately estimated. We show that the potential target location is restricted to a hyper-sphere in the sensor field given the acoustic energy reading at a pair of sensors. Given multiple sensor acoustic energy readings, the target location is solved as the location that is closest (in the least square sense) to all the corresponding hyper-spheres. We further simplified this nonlinear least square problem to an unconstrained linear least square problem that yields a closed form solution. Experiment results using military vehicle acoustic data show great promise of this novel approach. <s> BIB002 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> We present a new approach to localizing an isotropic energy source using measurements from distributed sensors based on kernel averaging techniques. The location estimate is easily and efficiently calculated in a decentralized fashion. Statistical properties are derived for a very general measurement model. Experiments suggest that the proposed estimator is much more robust and exhibits better performance characteristics than the popular least squares estimator under a variety of conditions. <s> BIB003 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> This correspondence addresses the problem of locating an acoustic source using a sensor network in a distributed manner, i.e., without transmitting the full data set to a central point for processing. This problem has been traditionally addressed through the maximum-likelihood framework or nonlinear least squares. These methods, even though asymptotically optimal under certain conditions, pose a difficult global optimization problem. It is shown that the associated objective function may have multiple local optima and saddle points, and hence any local search method might stagnate at a suboptimal solution. In this correspondence, we formulate the problem as a convex feasibility problem and apply a distributed version of the projection-onto-convex-sets (POCS) method. We give a closed-form expression for the projection phase, which usually constitutes the heaviest computational aspect of POCS. Conditions are given under which, when the number of samples increases to infinity or in the absence of measurement noise, the convex feasibility problem has a unique solution at the true source location. In general, the method converges to a limit point or a limit cycle in the neighborhood of the true location. Simulation results show convergence to the global optimum with extremely fast convergence rates compared to the previous methods <s> BIB004 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> A new incremental optimization algorithm called normalized incremental subgradient (NIS) algorithm is proposed in this letter, which can be used for distributed maximum likelihood estimation (MLE). Its convergence with a diminishing stepsize has been proved and analyzed theoretically. We then apply the NIS algorithm to the energy-based sensor network source localization problem where the decay factor of the energy decay model is unknown. Simulation results show it can achieve very high estimation performance, which is only somewhat lower than that of the centralized localization method based on global optimization techniques, but with hundreds of times lower computational complexity than the centralized method. <s> BIB005 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> In this paper, energy-based localization methods for source localization in sensor networks are examined. The focus is on least-squares-based approaches due to a good tradeoff between performance and complexity. A suite of methods are developed and compared. First, two previously proposed methods (quadratic elimination and one step) are shown to yield the same location estimate for a source. Next, it is shown that, as the errors which perturb the least-squares equations are nonidentically distributed, it is more appropriate to consider weighted least-squares methods, which are observed to yield significant performance gains over the unweighted methods. Finally, a new weighted direct least-squares formulation is presented and shown to outperform the previous methods with much less computational complexity. Unlike the quadratic elimination method, the weighted direct least-squares method is amenable to a correction technique which incorporates the dependence of unknown parameters leading to further performance gains. For a sufficiently large number of samples, simulations show that the weighted direct solution with correction (WDC) can be more accurate with significantly less computational complexity than the maximum-likelihood estimator and approaches Cramer-Rao bound (CRB). Furthermore, it is shown that WDC attains CRB for the case of a white source. <s> BIB006 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> Localization of an isotropic source using energy measurements from distributed sensors is considered. Usually, such localization techniques require that the distances between the sensor nodes and the source of interest have been previously estimated. This, in turn, requires that sufficient information about the energy decay model as well as the transmit power of the source is available. In this work, making the assumption that the locations of nodes near the source can be well described by a uniform distribution, we derive distance estimates that are independent of both the energy decay model and the transmit power of the source. Numerical results show that these estimates lead to improved localization accuracy as compared to other model-independent approaches. <s> BIB007 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> In this paper, the source localization problem in wireless sensor networks is investigated where the location of the source is estimated based on the quantized measurements received from sensors in the field. An energy efficient iterative source localization scheme is proposed where the algorithm begins with a coarse location estimate obtained from measurement data from a set of anchor sensors. Based on the available data at each iteration, the posterior probability density function (pdf) of the source location is approximated using an importance sampling based Monte Carlo method and this information is utilized to activate a number of non-anchor sensors. Two sensor selection metrics namely the mutual information and the posterior Cramer-Rao lower bound (PCRLB) are employed and their performance compared. Further, the approximate posterior pdf of the source location is used to compress the quantized data of each activated sensor using distributed data compression techniques. Simulation results show that with significantly less computation, the PCRLB based iterative sensor selection method achieves similar mean squared error (MSE) performance as compared to the state-of-the-art mutual information based sensor selection method. By selecting only the most informative sensors and compressing their data prior to transmission to the fusion center, the iterative source localization method reduces the communication requirements significantly and thereby results in energy savings. <s> BIB008 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> The TDOA-based source localization problem in sensor networks is considered with sensor node location uncertainty. A total least squares (TLSs) algorithm is developed by a linear closed-form solution for this problem, and the uncertainty of the sensor location is formulated as a perturbation. The sensitivity of the TLS solution is also analyzed. Simulation results show its improved performance against the classic least squares approaches. <s> BIB009 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> This paper presents a study on source localization using time difference of arrival (TDOA) measurements from static sensors in the presence of random errors in sensor positions. We develop a constrained weighted least squares (CWLS) source localization method which incorporates the relationship between the source position and an auxiliary variable as a constraint. The CWLS source localization is formulated as an indefinite quadratically constrained quadratic optimization problem, which is a nonconvex problem. By employing the hidden convexity of the original optimization problem, the global optimal source location estimate can be efficiently obtained. Simulations are used to corroborate the good performance of the proposed method. <s> BIB010 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> For the purpose of source localization, we have proposed a constrained weighted least squares (CWLS) source localization method in our companion paper, which uses static sensors by accounting for random uncertainties in sensor positions. This paper is devoted to developing two recursive algorithms to deal with the source localization problem by using time difference of arrival (TDOA) measurements received by mobile sensors. More specifically, the first one uses the current TDOA measurements to estimate the unknown source position and then treats the estimate as a measurement to update the source localization. For the second approach, we estimate an auxiliary variable with the current TDOA measurements and then rearrange the nonlinear TDOA equations into a set of linear measurement equations to update the source localization. An illustrative example is given to demonstrate that the second algorithm outperforms the first one. <s> BIB011 </s> A Survey of Localization in Wireless Sensor Network <s> Single-Target/Source Localization in Wireless Sensor <s> 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. <s> BIB012
Network. The source localization methods have a wide range of possible applications. The outdoor application includes vehicle or aircraft localization. In an indoor environment, this method could track the human speakers. In underwater environment, it can be used to locate the large sea animals and ships. There are several ways to estimate the source location: energy-based, angle of arrival (AOA) BIB001 , time difference of arrival (TDOA) BIB009 BIB010 BIB011 BIB012 . As an inexpensive approach, energy-based method is an attractive method because it requires low hardware configuration. In this survey, we focus on the energy-based source localization. Single-source localization can be further divided into: energy decay model-based localization algorithm and modelindependent localization algorithms. (1) Decay Model-Based Localization Algorithm. Equation (1) shows the decay model in BIB004  BIB005 . The received signal strength at ith sensor during time interval t can be written as where g i represents the gain factor of the ith sensor. We assume that g i = 1. S(t) is the signal energy at 1 meter away. And d ik is the Euclidean distance between the ith sensor and the source. In addition n i is the measurement noise modeled as zero mean white Gaussian with variance σ 2 i , namely, n i ∼ N (0, σ 2 i ). Although this energy decay model appears quite simplistic, it is the one commonly used in the literature. Since the objective function of single-source localization method has multiple local optima and saddle points BIB004 , the authors formulated the problem as a convex feasibility problem and proposed a distributed version of the projection onto convex sets method. A weighted nonlinear least squares and weighted linear least squares methods  were proposed to estimate the location of the target. In BIB005 , the authors proposed normalized incremental subgradient algorithm to solve the energy-based sensor network source localization problem where the decay factor of the energy decay method is unknown. Unlike the signal models in BIB004  BIB005 , the authors derived a more generalized statistical model BIB006 for energy observation. And a weighted direct/one-step least-squares-based algorithm was investigated to reduce the computational complexity. And in comparison with quadratic elimination method, these methods were amenable to a correction technique which incorporates the dependence of unknown parameters leading to further performance gains. This method offered a good balance between the localization performance and computational complexity. Energy ratio formulation BIB002 was an alternative approach that is independent of the source energy S(t). This was accomplished by taking ratios of the energy reading of a pair of sensors in the noise-free case. In BIB008 , the authors proposed an energy aware source localization method to reduce the energy consumption in localization. (2) Model-Independent Methods. A kernel averaging approach BIB003 which needs not information about energy decay model was proposed. In BIB007 , a novel model-independent localization method was proposed. Since the nodes with higher received signal strength measurement were closer to the source, a distributed sorting algorithm is employed. If the sensor nodes know their rank, the required distance estimates are obtained as the expected value of the respective probability density functions. Finally, the projection onto convex sets (POCS) method was used to estimate the location of the source.