This paper introduces an adaptive Convolutional Neural Network (CNN)-based Unscented Kalman Filter for the pose estimation of uncooperative spacecraft. The validation is carried out at Stanford's robotic Testbed for Rendezvous and Optical Navigation on the Satellite Hardware-In-the-loop Rendezvous Trajectories (SHIRT) dataset, which simulates vision-based rendezvous trajectories of a servicer spacecraft to PRISMA's Tango spacecraft. The proposed navigation system is stress-tested on synthetic as well as realistic lab imagery by simulating space-like illumination conditions on-ground. The validation is performed at different levels of the navigation system by first training and testing the adopted CNN on SPEED+, Stanford's spacecraft pose estimation dataset with specific emphasis on domain shift between a synthetic domain and an Hardware-In-the-Loop domain. A novel data augmentation scheme based on light randomization is proposed to improve the CNN robustness under adverse viewing conditions, reaching centimeter-level and 10 degree-level pose errors in 80% of the SPEED+ lab images. Next, the entire navigation system is tested on the SHIRT dataset. Results indicate that the inclusion of a new scheme to adaptively scale the heatmaps-based measurement error covariance based on filter innovations improves filter robustness by returning centimeter-level position errors and moderate attitude accuracies, suggesting that a proper representation of the measurements uncertainty combined with an adaptive measurement error covariance is key in improving the navigation robustness.