# Joint Azimuth, Elevation and Delay Estimation for Single Base Station Localization in 3D IIoT +
###### Abstract
Secondly, to accommodate the additional spatial dimension and the consequent performance challenges, we have upgraded our antenna model from a uniform linear array (ULA) to a UCA. This enhancement is a considerable improvement that addresses the new complexities introduced by the inclusion of the third dimension. By undertaking these enhancements and modifications, our current work substantially surpasses the limitations of our previous research, offering a more comprehensive and robust approach to 3D single BS-assisted localization techniques. Table 1 summarizes all the aforementioned related works. Generally, the majority of current JADE algorithms encounter the issue of grid constraints. This means that during the search process, the estimated results are restricted to grid points. As a result, if the true values are off-grid, bias will persist regardless of the grid resolution. Unfortunately, the refinement process cannot be pushed to the extreme due to the resulting high computational complexity. Furthermore, studies concerning 3D environments are considerably fewer compared to those focusing on 2D scenarios, but the disparity between JAEDE and JADE  
Figure 1: Illustration of the single BS-assisted JAEDE, compared with other outdoor (**upper**) and indoor (**lower**) localization techniques. cannot be ignored, since it is capable of providing accurate representation, enhancing spatial awareness, enabling safety and risk assessment, and optimizing performance. Motivated by the aforementioned issues, we present a novel and computationally efficient localization technique for 3D IIoT scenarios. Our approach relies on a single BS and utilizes the MUSIC algorithm to estimate AoAz, AoAe, and ToA jointly. The key contributions of our work are as follows:  
* We propose a localization algorithm that addresses the challenges of stable connectivity to multiple access points (AP) in IIoT scenarios, offering flexibility, easy implementation, and reduced computational cost compared to conventional multi-BS [19; 20; 21] and MUSIC-based single-BS [15] algorithms. * To enhance performance without extensive grid searching, our algorithm incorporates Taylor-series in the iterative process, achieving a significant 99% reduction in computational complexity with slight improvements in localization accuracy compared to a two-step MUSIC-based algorithm [15]. * Through numerical simulations, we compare our algorithm with three others, including MUSIC-based joint or separate angle and delay estimation. The results demonstrate that our algorithm consistently outperforms the alternatives in terms of AoAz, AoAe, ToA, and the overall location estimation accuracy across various SNR conditions. Throughout the paper, capital boldface letters denote matrices; lowercase boldface letters denote vectors, e.g., \(\mathbf{M}\in\mathbb{C}^{x\times b}\) stands for a complex matrix of the dimension \(a\times b\); \(\mathbf{I}\) is the identity matrix; \(\{\cdot\}^{\rm H}\) stands for transposition; \(\mathbb{E}\{\cdot\}\) is the expectation; and \(\mathbb{R}\{\cdot\}\) represents the real part of a complex number.