Optimal Placement and Selection of Camera-Based Target Localization System Using Relative Bearing Measurements

As passive optical sensors, cameras provide low cost, low power consumption, and rich texture information, providing a more advanced positioning method than wireless sensor networks. However, in recent works, the direct influence of geometric placement (extrinsics) and camera selection (intrinsics) on target localization accuracy has received limited attention. This work investigates the optimal placement and selection problem for localizing a single target, using a multi-robot system with cameras as relative bearing sensors. We initiate our analysis by examining the mechanisms underlying measurement errors in camera-based relative bearing measurements. Specifically, we model two primary sources of these errors: geometric errors resulting from camera optical center offsets and imaging plane distortions, and random errors that occur during the measurement process. We then apply the Fisher Information Matrix (FIM) and the D-optimal criterion to characterize the localization accuracy of the target, which uniformly incorporates all the extrinsic and intrinsic parameters of cameras, including the positions, focal length, resolution, etc. Two typical scenarios of target localization are analyzed to show its potential in practical deployment by maximizing the D-optimality criterion of the FIM. Finally, numerical simulations validated the correctness and effectiveness of the proposed methods.