## 1 Introduction  
Determining the accurate pose of the camera is a fundamental problem in robot manipulations, as it provides the spatial transformation needed to map 3D world points to 2D image coordinates. The task involving camera pose estimation is essential for various applications, such as augmented reality [1], 3D reconstruction [2], SLAM [3], and autonomous navigation [4]. This becomes especially critical when robots operate in unstructured, fast-strenging, and dynamic environments, performing tasks such as human-robot interaction, accident recognition and avoidance, and eye-in-hand visual servoing. In such scenarios, accurate camera pose estimation ensures that visual data are readily available for effective robotic control [5]. A classic approach to estimating the pose of a calibrated camera is solving the Perspective-n-Point (PnP) problem [6], which establishes a mathematical relationship between a set of 3D points in the world and their corresponding 2D projections in an image. To uniquely determine the pose of a monocular camera in space, there exists the Perspective-4-Point (P4P) problem, where exactly four known 3D points and their corresponding 2D image projections are used. [PERSON] et al. [7] generalize four solutions for the P3P problem while giving a single unique solution for the P4P problem in a fully calibrated camera scenario. To increase accuracy, modern PnP approaches consider more than three 2D-3D correspondences. Among PnP solutions, the Efficient PnP method (EPnP) finds the optimal estimation of pose from a linear system that expresses each reference point as a weighted sum of four virtual control points [8]. Another advanced approach, Sparse Quadratic PnP (SQPnP), formulates the problem as a sparse quadratic optimization, achieving enhanced accuracy by minimizing a sparse cost function [9]. In recent years, many other methods have been developed to show improved accuracy over PnP-based methods. For instance, [PERSON] et al. [10] utilize Structure from Motion (SfM) to estimate a camera's pose by extracting and matching key features across various images taken from different viewpoints to establish correspondences. Moreover, [PERSON] et al. [11] introduce visual odometry into the camera's pose estimations based on the movement between consecutive frames. In addition, recent advancements in deep learning have led to the development of models, such as Convolutional Neural Networks (CNNs), specifically tailored for camera pose estimation [12; 13; 14]. However, these advanced methods often come with significant computational costs, requiring multiple images from different perspectives for accurate estimation. In contrast, PnP-based approaches offer a balance between accuracy and efficiency, as they can estimate camera pose from a single image, making them highly suitable for real-time applications such as navigation and scene understanding. In image-based visual servoing (IBVS) [15], the primary goal is to control a robot's motion using visual feedback. Accurate real-time camera pose estimation is crucial for making informed control decisions, particularly in eye-in-hand (EIH) configurations [16; 17], where a camera is mounted directly on a robot manipulator. In this setup, robot motion directly induces camera motion, making precise pose estimation essential. Due to its computational efficiency, PnP-based approaches remain widely applied in real-world IBVS tasks [18; 19; 20]. The PnP process begins by establishing correspondences between 3D feature points and their 2D projections in the camera image. The PnP algorithm then computes the camera pose from these correspondences, translating the geometric relationship into a format that the IBVS controller can use. By detecting spatial discrepancies between the current and desired camera poses, the robot can adjust its movements accordingly. However, PnP-based IBVS presents challenges for visual control in robotics.