## 1 Introduction  
Target localization in underwater acoustic wireless sensor network (UWSN) has attracted much attention in recent years due to its wide applications in such fields as data collection, pollution monitoring, offshore exploration, disaster prevention, target tracking, assisted navigation, and military surveillance [1; 2; 3]. In UWSN, target localization is often performed by using such measurement information as time-of-arrival (ToA), time-different-of-arrival (TDoA), angle-of-arrival (AoA), and received-signal-strength (RSS). However, localization based on ToA and TDoA requires careful timing and synchronization, and the costs are high, especially in underwater acoustic environmental conditions [4; 5; 6]. Additionally, as AoA relies on a direct line-of-sight path from the target node to anchor nodes, it will cause large errors in AoA measurements in multi-path underwater acoustic (UWA) transmission environments [7; 8]. Therefore, RSS-based target localization is preferred by researchers due to its low complexity and easy implementation [9; 10; 11; 12]. Based on the received signal strength measurements, the maximum likelihood (ML) method is used to estimate the target position [13], and this method is robust in underwater environments. Although the ML estimator has asymptotically optimal performance, it is non-convex and has multiple local optimal solutions. Moreover, its performance depends highly on the initial solution and obtains bad results if a poor initialization is provided. In [9], the authors propose a fast iteration algorithm by using a triangulation method based on RSS measurements. In [11], the authors discuss the convex optimization method for target localization in UWSN, while the propagation model is still the terrestrial acoustic wave model. Two convex methods based respectively on RSS-based and frequency-dependent differential approaches in UWSN have been proposed [12]. A hybrid localization method was investigated by combining ToAand RSS measurements [10]. This method provides better performance by exploiting the benefits of combined measurements of the radio signal in the assumption that the RSS measurements are known in advance.  
In this paper, target localization methods for the cases of both known and unknown target transmit power are proposed. Firstly, the general target localization problems based on the ML criterion are formed, and the new weighted least square (WLS) problems are then derived using approximation techniques. These non-convex estimators are then transformed into a generalized trust region subproblem (GTRS) framework [14], which are solved in an efficient way. Furthermore, a three-step procedure is used to enhance the estimation accuracy of the target localization in the unknown target transmit power case. Finally, the closed-form expressions of the Cramer-Rao lower bounds (CRLBs) in both known and unknown target transmit power cases are derived.  
The remainder of this paper is organized as follows. In Section 2, the RSS measurement model for locating a single target node is briefly introduced, and the non-convex target localization problem is formulated. Section 3 derives the proposed methods in both the known and unknown transmit power cases. In Section 4, complexity analysis is carried out. Computer simulation comparisons of the discussed methods are presented in Section 5. The CRLBs in both known and unknown transmit power cases are derived in Section 6. In Section 7, the main conclusions are drawn. Finally, Section 8 points out the idea of further research.