## 1 Introduction  
The explosive growth of fifth-generation (5G) wireless communications will introduce a large number of new technological scenarios with higher requirements for location-based services [1], precise target localization techniques are becoming increasingly important in the application of radar [2], sonar [3], and wireless sensor networks [4] in 5G. At the same time, in order to improve the utility of mobile navigation scenarios, there is a need not only to provide continuous and comprehensive area coverage for users and seamless and stable indoor and outdoor LBS, but also to provide new ideas by organically synchronizing multiple technologies through public mobile communication systems using convergent positioning [4]. Methods of localization based on communication infrastructure are classified into two types: direct and indirect localization. The essential premise of the direct localization technique is to establish the maximum likelihood (ML) function of the user's location with relevant information and to provide an iterative location estimation of the user [5, 6]. The direct method is more accurate, but it relies on the processing of a large amount of data, leading to a higher computational complexity [7, 8, 9]. The majority of indirect localization techniques are based on distance measuring. The server at the ground station determinesthe position of the mobile user by calculating the distance measurement results [10]. In this procedure, direct LOS paths in space are typically employed to measure relevant physical parameters, such as TOA (time of arrival), TDOA (time difference of arrival), AOA (angle of arrival), FDOA (frequency difference of arrival), RSS (received signal strength), etc. Due to their greater accuracy, TOA and TDOA approaches have garnered the most attention, and the corresponding location calculation and performance analysis methods have been intensively investigated [11; 12; 13; 14; 15; 16]. For instance, to simplify the TDOA equations, [11] utilized elliptical coordinates and asymptotes to determine the target's position in far-field situations. By linearizing the approximate ML estimation, [12] suggested a closed-form solution form for the TOA and TDOA localization methods. In [13], the authors examined closed-form solution algorithms and iterative algorithms for four localization methods, as well as a hybrid source localization algorithm based on TOA and AOA. Methods for TDOA localization based on multidimensional scaling and convex optimization have been proposed in [14; 15]. Ref. [16] developed a ML approximation for the closed-form solution of AOA under low noise conditions. Maximum Likelihood Estimators utilizing Gauss-Newton or quasi-Newton iterations were developed in [17] to localize a moving target by time delay and Doppler frequency shift using sensors in motion, a structured total least squares method with hybrid TDOA-AOA measurements was developed in [18] to reduce estimation bias, and an algebraic solution using TDOA and FDOA measurements to determine the location and velocity of moving sources was developed in [19] and the method suffers from no initialization and local convergence problems. In addition to the measurement precision of physical quantities and algorithm performance, the geometric position of the measurement sensor in relation to the target is a significant factor influencing localization accuracy. For two-dimensional TOA and TDOA measurement and localization methods, the minimum value of the target localization error CRLB can be derived theoretically when the receiving station is arranged at an identical angle around the target [20; 21]. Ref. [22] uses polar coordinates to decouple the influence of distance and angle, and then developed the optimal deployment scheme for TOA, TDOA, and AOA sensors in remote localization scenarios based on the minimal value of CRLB. TDOA and TOA both have the same optimal deployment form, which is a ring array with the same number of nodes on each ring.