This thesis considers the Perspective-N-Point (PNP) problem with orthogonal target geometry, as seen in the problem of cubesat relative navigation. Cubesats are small spacecraft often developed for research purposes and to perform missions in space at low cost. Sensor systems for cubesats have been designed that, by providing vector (equivalently line-of-sight, angle, and image plane) measurements, equate relative navigation to a PNP problem. Much study has been done on this problem, but little of it has considered the case where target geometry is known in advance, as is the case with cooperating cubesats. A typical constraint for cubesats, as well as other PNP applications, is processing resources. Therefore, we considered the ability to reduce processing burden of the PNP solution by taking advantage of the known target geometry. We did this by considering a specific P3P solver and a specific point-cloud correspondence (PCC) solver for disambiguating/improving the estimate, and modifying them both to take into account a known orthogonal geometry. The P3P solver was the Kneip solver, and the point-cloud-correspondence solver was the Optimal Linear Attitude Estimator (OLAE). We were able to achieve over 40% reduction in the computational time of the P3P solver, and around 10% for the PCC solver, vs. the unmodified solvers acting on the same problems. It is possible that the Kneip P3P solver was particularly well suited to this approach. Nevertheless, these findings suggest similar investigation may be worthwhile for other PNP solvers, if (1) processing resources are scarce, and (2) target geometry can be known in advance.