Energy-Based Acoustic Source Localization Methods: A Survey <s> Centralized Algorithms <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> BIB001 </s> Energy-Based Acoustic Source Localization Methods: A Survey <s> Centralized Algorithms <s> The localization of an acoustic source can be based on the energy measurements at a number of spatially separated microphones. This is because the amount of source energy attenuation at a microphone is proportional to the square of the distance between the source and the microphone. This paper develops an algebraic closed-form solution for the acoustic source localization problem using energy measurements, under the condition of direct line-of-sight and free space propagation. First-order analysis is applied to the proposed solution to study its performance, where only the linear noise terms are kept in obtaining the mean-square localization error. The first-order analytical results show that the proposed solution reaches the Cramer-Rao lower bound (CRLB) accuracy for Gaussian noise as the signal-to-noise ratio tends to infinity. In addition, the proposed solution provides much better accuracy than other closed-form solutions available in literature. Improvement on the proposed solution that extends its operating range beyond the threshold noise level was made by imposing nonnegative constraints. Simulations are included to corroborate the performance of the proposed method. <s> BIB002 </s> Energy-Based Acoustic Source Localization Methods: A Survey <s> Centralized Algorithms <s> We propose a novel approach to the source localization and tracking problem in wireless sensor networks. By applying minimax approximation and semidefinite relaxation, we transform the traditionally nonlinear and nonconvex problem into convex optimization problems for two different source localization models involving measured distance and received signal strength. Based on the problem transformation, we develop a fast low-complexity semidefinite programming (SDP) algorithm for two different source localization models. Our algorithm can either be used to estimate the source location or be used to initialize the original nonconvex maximum likelihood algorithm. <s> BIB003 </s> Energy-Based Acoustic Source Localization Methods: A Survey <s> Centralized Algorithms <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> BIB004
In this part, we give a brief introduction about the existing methods for centralized source localization. For the energy-based source localization using weighted least-squares method, we mainly introduce algebraic closed-form solutions proposed in  BIB001 BIB002 . The interested readers are referred to BIB003 BIB004 for the alternative methods therein. Let the source be located at an unknown coordinate pair θ = [x, y] T . We assume that there are N sensor nodes performing sensing based on energy detection. The location of the i-th sensor is denoted Here, we reproduce the energy-based sensing model for convenience. where d i = θ − r i is the Euclidean distance between the i-th sensor and the source. For simplicity, let us assume the mean ζ 2 has been subtracted from Equation (5) so that ε i follows a zero mean Gaussian distribution with variance σ 2 i = 2ζ 4 /M.