## 1 Introduction  
The perspective-n-point (PnP) problem [1; 2; 3; 4; 5; 6; 7] originates from the intrinsic and extrinsic parameter estimation, which are two of key steps in computer vision [8; 9] and photometry [10]. Its purpose is to retrieve the intrinsic or extrinsic parameters of a camera by using \(n\) known 2D-3D point correspondences from a single image. There are many PnP solvers for \(n=3\), known as P3P solvers [11; 12; 13; 14; 15; 16] and was first investigated in 1841 by [PERSON] [17]. These P3P solvers can estimate six extrinsic parameters (three position parameters and three orientation parameters) with a fully calibrated camera. The P3P is the minimal subset of 2D-3D point correspondences that yields a finite number of solutions and solves the multi-solution problem using a fourth 3D point. Hence, the existing P3P solvers all need a fully calibrated camera and obtain up to four possible solutions [18]. The strict requirement and multi-solution problem prevent its application from scenarios where some intrinsic parameters of a camera might change online or be unknown, such as using a zoom lens. To solve the problem, many methods were developed to estimate the extrinsic parameters and some intrinsic parameters of a partially calibrated camera [19; 20]. Some methods focus on the partially calibrated case with unknown focal length, namely the PnPf problem [2; 21; 22; 23; 24]. All the PnPf solvers need four or more points [25] and for the minimal P4 Pf, some solvers work well in planar case [26], while some work well in the nonplanar case [25]. P4 Pf solvers can obtain only one intrinsic parameter, hence there have been some methods working with unknown focal length and radial distortion [2; 27; 28], unknown focal length and aspect ratio [29], and unknown focal length and principal point [25]. When \(n\geq 6\), the PnP problem can be linearly determined [8; 25; 30], and we can obtain all the intrinsic and extrinsic parameters of a camera [31]. We can see that using more 3D control points can obtain more parameters. However, user convenience dictates the use of as few reference 3D points as possible. In some cases, such as missile range testing and aerial photogrammetry, the world frame is the space rectangular coordinate frame in general and therefore, the 3D points must be measured in this frame with professional mapping person. This will take a lot of time. In addition, the position of the 3D point is hard to remain unchanged under the influence of the wind and the 3D point is easy to be corroded by sun and rain in the open air. Because of these reasons, accurate 3D control points are troublesome and expensive to acquire and maintain in these cases. Moreover, for most digital cameras, the skew is zero and the aspect ratio of the pixels is very close to one [25; 27], hence we assume these parameters are prior knowledge, which can reduce parameters to be estimated and means fewer 3D points are needed. In some cases where the camera is fixed, the camera position can be obtained as prior knowledge. In a missile testing range, for example, the attitude measurement based on fixed cameras with the zoom lens is an important test. These cameras are fixed and the positions can be measured as the known parameters. In addition, with the growing prominence of the social security problem, visual monitoring cameras (VMCs) are used widely. In general, the position of the VMC is fixed and the lens orientation can be changed. Hence, in this paper, we focus on the case with unknown focal length, principal point and known camera position. In this case, we want to obtain the intrinsic and extrinsic parameters with a minimal (\(n=3\)) subset of 2D-3D point correspondences. In this paper, we assume that the unknown intrinsic parameters are the focal length, principal point and we will propose a novel method for intrinsic and extrinsic parameter estimation based on three 2D-3D point correspondences with known camera position, which is different from the existing P3P solvers.