# AOA-Based Three-Dimensional Multi-Target Localization in Industrial WSNs for LOS Conditions
## 1 Introduction  
The wireless sensor network (WSN) is a highly integrated discipline and has been well developed in the last decade [1]. WSNs have enabled smart industry by exploiting the significant advantages such as extremely low power consumption [2], self-organization, and on-site sensing. In typical smart industrial WSNs (SIWSNs), plenty of sensor nodes are deployed in industrial facilities to monitor manufacturing processes, compute simple tasks, collect and deliver information [3]. SIWSNs can support a broad range of applications, such as factory automation, equipment management, fault diagnosis, surveillance, etc. However, SIWSNs also pose challenges due to the stringent requirements on reliability, latency, and security [4; 5], and their susceptibility to the highly complicated environments with serious electromagnetic interference and jamming [6]. Hence, we need to enhance the functionality and reliability of conventional WSNs to satisfy the requirements of industrial-grade applications. One important issue for SIWSNs is the node localization. Wireless sensors/actuators are usually placed at specified moving points in industrial environments. For example, mobile sensor nodes(MSNs) may be mounted on the carrying facilities in wharves, freight terminals, and mines. It is critical to locate the MSNs quickly and accurately for target tracking and process monitoring. The global positioning system (GPS) is not applicable because SIWSNs usually operate in indoor or underground environments without the GPS signals. Therefore, the efficient, precise, and fast determination of relative positions of multiple MSNs is an important and challenging issue for SIWSNs. Although wireless positioning methods have been studied extensively (as reviewed in Section 2), the current schemes most focus on positioning in two-dimensional (2D) planes. The positioning in three-dimensional (3D) space has been less explored. Another key limitation is that the current methods usually locate a single node/target in one measurement trial and cannot perform multi-target positioning simultaneously. As mentioned earlier, to locate a number of MSNs quickly is an essential feature for industrial applications. Motivated by the characteristics of SIWSNs and the deficiencies of current positioning algorithms, this paper proposes a new scheme, called Angle-of-arrival (AOA) based three-dimensional Multi-target Localization (ATML). This algorithm can provide fast simultaneous localization of multiple MSNs with small operational latency. The main contributions of this paper are as follows. First, the ATML algorithm based on the iterative maximum-likelihood (ML) method is proposed. We design the sensor network architecture that has two anchor nodes (ANs) with fixed positions and a number of MSNs whose positions relative to the ANs are to be determined. We propose a multi-target single-input-multiple-output (MT-SIMO) signal transmission scheme that combines the code division multiplexing access (CDMA) and ML estimation. Each MSN is assigned a pre-defined orthogonal spread spectrum sequence and broadcasts the spreading sequence using an omnidirectional antenna. The ANs capture the signals from all the MSNs simultaneously using antenna arrays. Then, we adopt the interactive ML method to estimate the 2D AOAs of the line-of-sight (LOS) paths from each MSN to the ANs in the joint time-space domain. Finally, the relative positions of the MSNs in the 3D space are deduced according to the 3D geometric theory of skew lines. Second, we conduct extensive simulations to evaluate and compare the performance of ATML with other methods in the literature. The simulations of AOA estimation and localization errors for varying the signal-to-noise ratio (SNR), number of MSNs, and AN antenna array size are presented. The results show that ATML can locate multiple MSNs simultaneously with high accuracy. Third, we have developed a testbed of ATML and performed field experiments to validate the scheme.