Energy-Based Acoustic Source Localization Methods: A Survey <s> Theorem 2. <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> BIB001 </s> Energy-Based Acoustic Source Localization Methods: A Survey <s> Theorem 2. <s> In this paper, we investigate source localization for wireless sensor networks based on received signal strength. We first formulate the localization problem as the intersection computation of a group of sensing rings, and then convert this non-convex problem into two weighted convex optimization problems. We next propose a unified distributed alternating projection algorithm to solve the resulting weighted optimization problems, where sensor nodes can communicate only locally with their neighbors over a time-varying jointly-connected topology. We also show that sensor nodes' estimates can achieve consensus on a possible minimizer. Both theoretical analysis and some comparative simulations reveal that the proposed approach has good estimation performance in both the consistent and inconsistent cases. <s> BIB002
If Assumptions 2 to 4 hold, then by using the proposed fully-distributed protocol Equation (30), the location estimates of all sensors will converge to the optimal minimizer of Equation (23)  . Ring-based problem formulation: In BIB002 , similar to the problem formulation shown in Figure 2 , the authors formulate the localization problem as the intersection computation of a group of sensing rings as shown in Figure 3 . In this work, the non-convex problem is converted into two weighted convex optimization problems. Similarly, the authors also consider two cases: the consistent case and the inconsistent case. For the consistent case, the problem can be formulated as finding a point in the intersection set of the sensing rings. However, due to the existence of noises, there is still some possibility for the source to be located outside of the rings. In BIB002 , the authors propose to use a distributed protocol (refer to Equation (8) in BIB002 ), which is the same as Equation BIB001 . In this work, with alternating the computing of the projection on the inner and outer disks of each sensor, by using Protocol Equation BIB001 , the estimates of all sensors converge to the optimal solution of the designed ring intersection optimization problem. The projection-based method stated above is a good choice for real implementation in a centralized or distributed manner. However, it is hard to claim its accuracy theoretically, since it only considers bounded noise cases. 