# Angle of Arrival for the Beam Detection Method of Spatially Distributed Sensor Array
## 4 Experiment Results
light source and the spatially distributed sensor array is relatively short, it is necessary to correct the sensor output based on the intensity distribution of the Gaussian beam. The normalized output of each sensor is shown in Figure 9a, with the elevation angle set to \(0^{\circ}\) and the azimuth angle moving from \(-60^{\circ}\) to \(60^{\circ}\) in \(1^{\circ}\) intervals, and Figure 9b demonstrates the normalized output of five sensors after calibration, which significantly improves the measurement accuracy of the sensors. Figure 9: (**a**) Normalized output of five sensors. (**b**) Normalized output of five sensors after error calibration. After correcting the systematic errors of the spatially distributed sensor array, the multi-sensor data fusion algorithm was used to calculate the azimuth and elevation angles within a 110\({}^{\circ}\) field of view. Figure 10 shows the calculated AOA results of five measurements at 5\({}^{\circ}\) intervals of azimuth angle from \(-55^{\circ}\) to 55\({}^{\circ}\) at elevation angles of 0\({}^{\circ}\), 25\({}^{\circ}\), and 50\({}^{\circ}\). The results show that they are close to the actual values, with mean angle errors of 0.44\({}^{\circ}\), 0.58\({}^{\circ}\), and 2.15\({}^{\circ}\) for azimuth and 0.4\({}^{\circ}\), 0.85\({}^{\circ}\), and 2.14\({}^{\circ}\) for elevation. In the fields of view A and B, higher measurement accuracy is achieved by fusing the outputs of multiple sensors. Repeatability results with the elevation angle set to 0\({}^{\circ}\) and the azimuth angle moving from \(-50^{\circ}\) to 50\({}^{\circ}\) in 5\({}^{\circ}\) intervals are shown in Figure 11, which is better than 0.15\({}^{\circ}\). Figure 11: Repeatability results with the elevation angle set to 0\({}^{\circ}\) and the azimuth angle moving from \(-50^{\circ}\) to 50\({}^{\circ}\) in 5\({}^{\circ}\) intervals. (**a**) Repeatability results for azimuth. (**b**) Repeatability results for elevation. Figure 10: AOA detection results at different elevation angles after error correction. (**a**) The calculated azimuth coordinate curves when \(\gamma=0^{\circ}\). (**b**) The calculated azimuth coordinate curves when \(\gamma=25^{\circ}\). (**c**) The calculated azimuth coordinate curves when \(\gamma=50^{\circ}\). (**d**) The calculated elevation coordinate curves when \(\gamma=0^{\circ}\). (**e**) The calculated elevation coordinate curves when \(\gamma=25^{\circ}\). (**f**) The calculated elevation coordinate curves when \(\gamma=50^{\circ}\). The 2D AOA detection performance of the system is measured, simultaneously verifying the effectiveness of the multi-sensor data fusion algorithm. The test results are shown in Figure 12. After using the data fusion algorithm, the maximum errors of azimuth and elevation angle in field of view A are 1.59\({}^{\circ}\) and 1.7\({}^{\circ}\), respectively, and the RMSE is 0.6\({}^{\circ}\) and 0.67\({}^{\circ}\). The maximum measurements of azimuth and elevation angle in the 110\({}^{\circ}\) field of view are 4.3\({}^{\circ}\) and 6.7\({}^{\circ}\), respectively, with RMSE of 1.1\({}^{\circ}\) and 1.7\({}^{\circ}\). In the fields of view A and B, higher measurement accuracy is achieved by fusing the outputs of multiple sensors. The 2D experimental results demonstrate that the spatially distributed sensor array exhibits high accuracy within a large field of view. However, conventional spot position detection systems often require complex optical components, such as fisheye lenses, high-resolution CCDs, and multi-unit sensor arrays, to achieve a wide field of view [9,10]. The fisheye lens, composed of multiple optical elements, contributes significantly to the system's overall volume and weight. Furthermore, the associated processing circuitry tends to be more complex, resulting in higher power consumption.