Camera parameter estimation is a key research content in the field of visual measurement, with wide applications in robotics, augmented reality, autonomous driving, and other areas, holding significant academic and practical value. However, traditional PnP methods often heavily rely on the complete intrinsic parameters of the camera, particularly the focal length, which leads to a significant decrease in estimation accuracy in situations where the focal length is unstable or unknown. While traditional PnPf methods can handle cases with unknown focal length, they involve more unknown parameters, making the equation solving process more complex and less efficient. Moreover, most of these traditional methods are based on idealized geometric models, lacking in-depth analysis of the statistical properties of the estimators and failing to fully account for the impact of projection noise on estimation accuracy, making unbiased estimation difficult to achieve. In situations where the focal length is unknown, how to quickly, accurately, and robustly estimate both the camera pose and focal length remains an important problem that needs to be addressed and improved.

This paper revisits the PnPf problem from a statistical perspective and proposes a globally consistent PnPf solver. First, both the camera pose and focal length are treated as unknowns to be solved. A linear equation is constructed based on the original projection model to simplify the solving process, and a least squares solution is obtained that includes both the camera pose and focal length. Then, the asymptotic bias in the solution is eliminated through consistent estimation of the noise variance, resulting in a consistent and unbiased estimate of the camera pose and focal length. Finally, the solution is further optimized using the Gauss?Newton iterative method.

The experimental results obtained using synthetic data and real data are as follows. 1) In synthetic data experiments, the method proposed in this paper demonstrates significant advantages in camera pose and focal length estimation. Compared to other existing methods, its estimation error is noticeably smaller, regardless of the noise intensity (Fig. 2). 2) Four images are selected from the ETH3D Benchmark dataset as experimental data, with each image containing thousands of feature points, indicating that designing a consistent solver is feasible (Fig. 3). 3) In real data experiments, the proposed method shows higher accuracy in camera pose and focal length estimation, and its running time is the shortest, and the solution efficiency is better than that of the current mainstream methods (Fig. 4).

In response to the high computational complexity and bias issues in traditional algorithms for camera pose estimation, we propose a new CPnPf solver aimed at reducing computational complexity while achieving more accurate camera pose and focal length estimation. The algorithm simplifies the solving process through linearization, enabling rapid estimation of camera pose and focal length. Additionally, from a statistical perspective, we revisit the PnPf problem and introduce a bias elimination method that effectively removes the impact of projection noise on the estimation results, thereby enhancing the overall solution accuracy. To validate the effectiveness of this method, we compare it with other state-of-the-art PnP and PnPf algorithms. Extensive experiments on both synthetic and real-world data demonstrate that the proposed algorithm outperforms existing algorithms in terms of both accuracy and efficiency.