The rapid development of deep learning has profoundly transformed image analysis, particularly through convolutional neural networks (CNNs) that allow images to be encoded into latent variables capturing hierarchical spatial and semantic features. Despite their success in object recognition and scene understanding, deep learning models share a critical limitation: they typically provide only a point estimate without reliable measures of predictive uncertainty. This shortcoming is particularly critical in the domain of spacecraft proximity operations, a safety-critical scenario in an operational environment that cannot be faithfully reproduced on the ground for training. In such settings, quantifying the epistemic uncertainty of the model is essential to detect when it encounters input outside its training distribution, enabling a more reliable deployment. Moreover, estimating the uncertainty of computer vision measurements is fundamental when such estimates are later fused into a navigation filter, allowing the measurement noise covariance matrix to transition from being arbitrarily set to becoming adaptive for more reliable state estimation.
To address this problem, this paper presents a study developed within the Astra scientific laboratory exploring the use of Deep Kernel Learning (DKL) [1], a hybrid architecture that combines the feature extraction power of a deep neural network with the non-parametric probabilistic framework of a Gaussian Process (GP). By utilizing the neural network as a deep kernel, raw high-dimensional data is transformed into a compact representation where a GP can effectively operate. This Bayesian framework allows the network to provide a principled uncertainty estimate for every inference, ensuring that predictive variance increases appropriately when the system faces conditions unseen in the training distribution. The algorithm is tested on a relative navigation scenario considering single-frame line-of-sight and range estimation of a known artificial target from synthetic images, simulating optical anomalies such as specular reflections to assess the network's reaction to out-of-distribution events.
Crucially, this work investigates solutions to a known pathology of DKL algorithms: feature collapse [2]. This phenomenon arises when the deep feature extractor converges to a degenerate mapping, projecting semantically distinct inputs into a confined region of the latent space, thus rendering the kernel distance metric ineffective for uncertainty quantification. To mitigate this, as proposed in [3], pretraining strategies and auxiliary training heads are introduced, specifically utilizing autoencoder reconstruction and contrastive learning objectives, that run in parallel to the primary regression task. These mechanisms act as regularizer, forcing the latent space to preserve representative structure and information content of the input images. Furthermore, to enhance robustness against outliers, the modelling of the observation likelihood is explored not only with standard Gaussian distributions, which can be overly sensitive to extreme values, but also with heavy-tailed distributions such as the Student's t-distribution.
Finally, to demonstrate operational relevance, the results are coupled with an Extended Kalman Filter (EKF) for relative position estimation given line-of-sight and range measurements. Rather than relying on static, manually tuned parameters, the covariance associated with visual measurements is linked directly to the network’s estimated uncertainty. This coupling allows the filter to effectively de-emphasize highly uncertain measurements in the update step. The study provides a detailed breakdown of the filter's performance, comparing the uncertainty-aware approach against a manually tuned architecture across different simulated conditions. These results provide evidence on the impact of deep-learning-based uncertainty on navigation stability.
 
[1] Wilson, A. G., Hu, Z., Salakhutdinov, R., & Xing, E. P. (2016, May). Deep kernel learning. In Artificial intelligence and statistics (pp. 370-378). PMLR.
[2] Ober, S. W., Rasmussen, C. E., & van der Wilk, M. (2021, December). The promises and pitfalls of deep kernel learning. In Uncertainty in Artificial Intelligence (pp. 1206-1216). PMLR.
[3] Wu, Z., Yang, Y., Gu, J., & Tresp, V. (2021, August). Quantifying predictive uncertainty in medical image analysis with deep kernel learning. In 2021 IEEE 9th international conference on healthcare informatics (ICHI) (pp. 63-72). IEEE.