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Optical cameras are gaining popularity as the suitable sensor for relative navigation in space due to their attractive sizing, power and cost properties when compared to conventional flight hardware or costly laser-based systems. However, a camera cannot infer depth information on its own, which is often solved by introducing complementary sensors or a second camera. In this paper, an innovative model-based approach is instead demonstrated to estimate the six-dimensional pose of a target object relative to the chaser spacecraft using solely a monocular setup. The observed facet of the target is tackled as a classification problem, where the three-dimensional shape is learned offline using Gaussian mixture modeling. The estimate is refined by minimizing two different robust loss functions based on local feature correspondences. The resulting pseudo-measurements are then processed and fused with an extended Kalman filter. The entire optimization framework is designed to operate directly on the $SE\text{(3)}$ manifold, uncoupling the process and measurement models from the global attitude state representation. It is validated on realistic synthetic and laboratory datasets of a rendezvous trajectory with the complex spacecraft Envisat. It is demonstrated how it achieves an estimate of the relative pose with high accuracy over its full tumbling motion.