Novel methods for ned angle estimation using only azimuth measurements in electronic warfare systems

Abstract

This study presents two different methods developed to estimate the North East Down (NED) azimuth and elevation angles of radar targets using only body azimuth measurements. The motivation for this research stems from the limitations of modern airborne Electronic Warfare (EW) systems, which commonly lack the ability to directly measure body elevation angles. As a result, target detection and direction finding accuracy are constrained, and the platform's movement and maneuvers can negatively impact the accuracy of direction estimation and tracking. The proposed methods aim to overcome these limitations through indirect signal processing approaches. Modern EW systems are capable of measuring various parameters of incoming radar pulses such as frequency, pulse width, pulse repetition interval, and direction of arrival. While azimuth measurement can be performed with high accuracy using antenna arrays arranged in the horizontal plane of the platform, elevation measurements are typically neglected or obtained with low precision due to the limited vertical aperture in that direction. Consequently, EW systems are often limited to one dimensional tracking. The approach proposed in this study evaluates the capability of estimating both azimuth and elevation in the NED coordinate system using only azimuth measurements. While platform maneuvers distort the azimuth measurements obtained from horizontally placed antennas, this distortion can in turn enable the estimation of the target's elevation angle in the NED system. As explained in detail in the study, accurate estimation of elevation is necessary to correctly transform the azimuth measurements to the NED system under maneuvering conditions. To estimate the azimuth and elevation angles discussed above, two main methods have been developed. These methods are based on optimization and deep learning-based image segmentation approaches. The first approach uses rotation matrices to transform body azimuth measurements into the NED coordinate system. These transformations rely on the platform's instantaneous Euler angles (roll, pitch, and yaw). However, as mentioned before, the elevation angle in the body axis cannot be measured directly. Therefore, elevation angles are sampled within certain bounds, and by applying the rotation matrices, different potential NED azimuth and elevation values are obtained. These values form several curves, where each NED elevation value corresponds to a NED azimuth value. As the number of measurements increases, more such curves are formed, and the intersection point of these curves enables accurate estimation of the true angles of the target. Similarly, as the platform's maneuver magnitude increases, the curves intersect more sharply and separate more distinctly, allowing for more precise estimation of the target's NED angles. Among the proposed methods, two distinct cost functions are defined under the optimization approach and are minimized using Particle Swarm Optimization (PSO). PSO is a metaheuristic algorithm that aims to find the best solution by initializing multiple solution points randomly in the search space and using both individual and collective knowledge. The first cost function (NEDL-Opt) minimizes the distance between the optimization variables (NED azimuth and elevation) and the generated rotation curves. The goal here is to scan in two dimensions and estimate the true NED azimuth and elevation angles of the target based on the intersection of all curve points. The second cost function (BAL-Opt) minimizes the squared differences between measured and estimated body azimuth values. Here too, the optimization variables are the NED azimuth and elevation angles of the target. Each NED coordinate obtained during the optimization iteration is converted to body coordinates using the rotation matrix, and the resulting body azimuth is compared with the measured one. The squared differences are then minimized. The second approach is based on image segmentation. In this approach, two-dimensional visualizations of the rotation curves resulting from body azimuth measurements and platform maneuvers are generated. In these images, the intersection of the curves corresponds to the target's NED azimuth and elevation angles. The raw images cover a wide area, so a specific area is zoomed. Measurements taken when the platform is not maneuvering are used as reference points, and zooming is applied around these measurements. After zooming, irrelevant axes are removed from the images to create clean visualizations and pure images. These processed images are then analyzed using deep neural networks with U-Net, U-Net++, and SegFormer architectures for segmentation. The segmentation aims to identify regions where the rotation curves concentrate. By extracting the centers of these segmented areas, the estimated NED azimuth and elevation angles of the target are obtained. The U-Net architecture is widely used in biomedical image processing and assigns a label to each pixel in the input image. Its U-shaped structure allows the generation of high-resolution segmentation maps from low-resolution inputs. U-Net++ is an improved version of U-Net, featuring denser skip connections for more effective multi-scale feature transfer, leading to enhanced segmentation accuracy. SegFormer is a transformer based segmentation model which captures local features in detail with respect to the whole image. The dataset used in the study was generated through simulation and includes scenarios with varying numbers of measurements and different noise levels. Both stationary and moving platform scenarios were analyzed independently, with a total of 3150 test cases in each. In each scenario, the target's NED angles were randomly generated, and measurement noise was added. Deep learning models were trained using custom-labeled images and optimized over 20 epochs using the Adam optimizer, each with approximately 12600 input sample images. The study's results are evaluated both qualitatively and quantitatively. Qualitative evaluations focus on visual inspections of the segmentation outputs. Test cases with different measurement counts and noise levels are analyzed in detail. For fair assessment, instances where segmentation failed or produced inaccurate results were also examined and explained. Quantitative evaluations are based on the Root Mean Square Error (RMSE) metric. The results demonstrate that image segmentation methods, particularly SegFormer, produce more accurate results with lower error compared to optimization-based methods. Deep learning approaches showed significantly better performance in scenarios with fewer measurements or higher noise levels. The magnitude of the platform's maneuvers has a direct effect on the accuracy of angular estimation. Increases in roll and yaw angles cause the rotation curves to diverge more, making their intersection points more distinct. This improves the performance of both optimization and image segmentation methods. Furthermore, in scenarios involving platform motion, despite the added positional and in return angular error, segmentation methods prove more robust and continue to show strong performance consistent with previous cases. In conclusion, the study shows that both NED azimuth and elevation angles can be successfully estimated using only body azimuth measurements under specific scenarios. This implies that existing systems can achieve 3D angle estimation under certain scenarios without requiring additional hardware. Among the deep learning methods, SegFormer demonstrated the greatest potential. This research aims to contribute to enhancing the capabilities of modern electronic warfare systems through software-based advancements even in the presence of hardware limitations.