# Joint Azimuth, Elevation and Delay Estimation for Single Base Station Localization in 3D IIoT +
###### Abstract
Localization techniques have expanded their capabilities by leveraging additional measurements on angle of arrival (AoA)- and time of arrival (ToA)-related information. This evolution has resulted in enhanced performance and better localization outcomes. Traditional wireless localization techniques often rely on triangulation or trilateration methods, which require three or more anchor points to perform the algorithm. However, in complex industrial environments, ensuring stable connections between multiple BS inherently introduces uncertainty. Moreover, unstable links, such as non-line-of sight (NLOS) transmissions between anchor points and the target, pose challenging obstacles to localization accuracy that are difficult to overcome [10; 11] (see Figure 1). Therefore, in environments like factories and warehouses, single BS-assisted localization can be considered as an effective solution. In particular, joint angle and delay estimation (JADE) stands out as a promising solution, as it reduces the involvement of base stations and minimizes localization overhead, making it an excellent fit for various smart industry applications [12; 13]. There have been a number of mature studies that utilize JADE for localization in 2D environments, such as MUSIC and estimation of single parameters via rotational invariance techniques (ESPRIT), which offer their unique advantages [12; 14; 15]. For instance, the ESPRIT-based method in [12] achieves a low computational cost by using the Hadamard product, but it requires parameter pairing after the estimation, which introduces extra errors to the performance. The MUSIC-based algorithm in [14] estimates AoA and ToA components with relatively low complexity, but low signal-to-noise ratio (SNR) and sampling rate are still challenging. Another MUSIC-inspired approach presented in [15] achieves satisfactory accuracy using a two-step coarse and fine grid search. However, the fine search significantly increases the computational overhead. All of the aforementioned works consider only 2D scenarios, while for 3D contexts, the addition of an extra dimension in 3D localization introduces an additional parameter that needs to be estimated, increasing the complexity of the localization process. This, in turn, leads to higher computational complexity and resource requirements. Another major challenge arises from the design of the antenna array. In 2D scenarios, a linear array configuration may suffice. However, in 3D environments, the array geometry must be more elaborate to capture the necessary spatial diversity for accurate AoA estimation. In [16; 17],the UCA has already been utilized to estimate azimuth and elevation angle of arrival (AoA) jointly. They investigated the AoA estimation by MUSIC utilizing a uniform circular array (UCA), but they did not consider the ToA estimation at the same time. In our previous publication [18], we have also proposed a single portable BS-assisted localization technique based on MUSIC for smart security scenarios. Our focus was on mitigating the computational burden associated with grid searching of the MUSIC algorithm and addressing the subsequent grid bias issues. However, there are several significant distinctions between our previous work and the current study. Firstly, our prior work primarily concentrated on 2D scenarios, limiting its ability to accurately estimate the vertical dimension or height of the target. Consequently, this limitation rendered it unsuitable for applications requiring localization in multiple vertical layers, such as warehouses. In contrast, the present study represents a notable advancement as we have expanded our methodology from 2D to 3D, together with a comprehensive evaluation of the performance of single BS-assisted localization techniques from various perspectives. This expansion sheds light on the unique challenges and potential solutions associated with 3D localization.