Depth estimation is critical for autonomous vehicles (AVs) to perceive their surrounding environment. However, the majority of current approaches rely on costly sensors, making wide-scale deployment or integration with present-day transportation difficult. This issue highlights the camera as the most affordable and readily available sensor for AVs. To overcome this limitation, this paper uses monocular depth estimation as a low-cost, data-driven strategy for approximating depth from an RGB image. To achieve low complexity, we approximate the distance of vehicles within the frontal view in two stages: firstly, the YOLOv7 algorithm is utilized to detect vehicles and their front and rear lights; secondly, a nonlinear model maps this detection to the corresponding radial depth information. It is also demonstrated how the attention mechanism can be used to enhance detection precision. Our simulation results show an excellent blend of accuracy and speed, with the mean squared error converging to 0.1. The results of defined distance metrics on the KITTI dataset show that our approach is highly competitive with existing models and outperforms current state-of-the-art approaches that only use the detected vehicle’s height to determine depth.