## 2 Background and Related Work  
Finding a passive target has gained interest in recent years due to its wide applications, especially in indoor positioning and defensive systems where GPS signals are unavailable [3]. In general, solutions for indoor localization fall into two categories: range-based and range-free. Lateration, such as trilateration and multilateration, is the most widely employed range-based localization approach. Here, the range is defined as the distance between the target and the receivers. It can be derived from multiple signal parameters, including time of arrival (TOA) [49], TODA, received signal strength (RSS) [50], angle of arrival (AOA) [51], or a combination of these parameters [52]. It has been demonstrated that the TDOA parameter delivers more accurate and straightforward localization compared to localization techniques based on other parameters [13]. As an alternative to range-based localization techniques for indoor environments, range-free localization techniques such as the Distance Vector Hop (DV-Hop) [53], centroid or weighted centroid approach [54], and approximation point-in-triangulation test (APIT) [55] are extensively utilised. These technologies are both affordable and easy to apply since they do not necessitate complicated equipment structure. However, the range-based localization methods for indoor positioning are more accurate compared to range-free methods [56]. The formulated passive target localization problem using TDOA measurements is a nontrivial task due to its high nonlinearity and nonconvexity. In order to solve such complex localization problems, in the literature, the most widely used methods include the NLS [10] and ML [11] estimators. The NLS estimator is based on finding the extremum of the objective function, which is formulated as the sum of the squared measurement errors. However, when solving the NLS estimator with conventional gradient based methods, it can be shown to have some convergence issues, and there is a need for a promising intial solution. LLS methods are often used to linearize the NLS estimation problem so that it can be solved in closed form [12]. However, it has been shown that the CRLB can only be reached with LLS methods when the measurement errors are small enough. To improve the accuracy and provide a closed-form solution to the localization problem, a two-step weighted least-squares (2 WLS) method is put forward to approximate the NLS function [12]. The two-step WLS method rearranges the nonlinear TDOA equations into a set of linear equations by introducing an auxiliary variable [57]. In the first step, it estimates the source position and auxiliary variable independently, and then in the second step it refines the estimate by considering their connection. To further improve the accuracy and avoid ill-matrix problems, the CWLS method is proposed, which explicitly incorporates the relationship between the source position and the auxiliary variable as a constraint [58]. In this way, the CWLS method formulates the quadratically constrained quadratic problem (QCQP), which is a non-convex problem. However, it can be converted to a convex problem by exploiting the hidden convexity in the constraint. Another widely applied estimator is the ML estimator, which has been regarded as an optimal method for target estimation [11]. However, the formulation of the ML target localization problem using TDOA measurements is a non-convex optimization problem. To address this issue, a SDP method is proposed, which relaxes the non-convex ML optimization to a convex SDP problem [59]. However, as shown in the literature, the performance of the SDP method is not satisfactory in the presence of a large measurement error. In the literature, evolutionary algorithms (EAs) are used to deal with the fact that the ML estimation problem is not convex. This is because EAs can find the best global solution to such problems.