# AOA-Based Three-Dimensional Multi-Target Localization in Industrial WSNs for LOS Conditions
## 2 Related Work  
[PERSON] et al. [7] has made a comprehensive summary of node positioning algorithms that can be distinguished into two main categories: range-based scheme and range-free scheme. Extensive analysis and comparison have been reported in the literature. The range-based schemes usually use the trilateration and triangulation positioning methods by accurately measuring the distance or angle information between nodes. These kinds of schemes commonly measure the received signal strength indicator (RSSI) [8; 9], AOA [10; 11; 12], time of arrival (TOA) [13], and time difference of arrival (TDOA) [14]. Although the RSSI methods are most easily realized by using only the signal strength information, they have greater instability and larger errors in complex propagation environments. [PERSON] et al. [13] used two generalized geometrical positioning algorithms based on TOA measurements without time synchronization. The TDOA technology usually uses ultrasound for measurement. [PERSON] et al. [14] formulated the localization problem as a nonconvex optimization problem and adopted semi-definite relaxation to obtain a convex optimization problem. The scheme could minimize the worst-case position estimation error. The AOA-based localization does not need synchronization among nodes and also has relatively high precision. [PERSON] et al. [10] proposed a localization and navigation system using radio interferometric AOA estimation implemented for wireless sensor nodes. However, the scheme is limited to a single dimension and susceptible to multipath effect. [PERSON] et al. [11] presented an angle of arrival (ACF) positioning scheme that utilized the tag signal AOA and the distance estimated by the power control method to locate active tags. [PERSON] et al. [12] proposed a new AOA-based approach that applied the spatial smoothing in pre-processing and computed the reference vectors. This approach was experimentally evaluated in LOS and non-LOS (NLOS) conditions. The hybrid approaches combining various range estimations together to improve localization accuracy have also been studied. [PERSON] et al. [8] proposed to track a signal-emitting mobile target with RSSI and AOA measurements. In [9], [PERSON] et al. proposed another scheme based on RSSI and AOA measurements for localization in WSNs. Obviously, AOA estimation is critical in these range-based methods. The traditional AOA estimation methods include MUSIC [15], ESPRIT [16], CLEAN [17], SAGE [18], and SPASE [19]. [PERSON] et al. [20] presented a new method with significantly reduced complexity by avoiding constructing the covariance matrix and computing the matrix inverse or applying eigenvalue decomposition. The range-based schemes are usually affected significantly by the multipath propagation effect and the NLOS problem, which cause significant measurement errors. [PERSON] et al. [21] analyzed the influence of environment transmission properties on the signal reception angular spread based on measurement results. It was shown that spatial averaging could provide a better estimation of the reception angle. They also studied the limitations in the direction-finding process of radio sources with directional antennas in an urbanized environment [22]. The results could help to correct the bearing error to improve the localization efficiency. For the NLOS scenario, [PERSON] et al. [23] proposed a maximum likelihood estimator (MLE) that utilized all the available measurements and explicitly took the probabilities of occurrences of LOS and NLOS propagations into account. The range-free methods are based on the number of hops between two communicating nodes as the distance metric. The classical range-free methods include the centroid-based, amorphous, and distance vector hop (DV-Hop) based algorithms [24; 25]. Among these, the DV-Hop scheme is most widely used due to high positioning accuracy in isotropic networks. However, it has a lower accuracy in asymmetric and sparse networks.