Autonomous proximity operations, such as active debris removal and on-orbit servicing, require high-fidelity relative navigation solutions that remain robust in the presence of parametric uncertainty. Standard estimation frameworks typically assume that the target spacecraft's mass properties are known a priori; however, for non-cooperative or tumbling targets, these parameters are often unknown or uncertain, leading to rapid divergence in model-based propagators. This paper presents an augmented Unscented Kalman Filter (UKF) framework designed to jointly estimate the relative 6-DOF pose and the full inertia tensor of a non-cooperative target spacecraft. The proposed architecture fuses visual measurements from monocular vision-based Convolutional Neural Networks (CNN) with depth information from LiDAR to constrain the coupled rigid-body dynamics. By augmenting the state vector to include the six independent elements of the inertia tensor, the filter dynamically recovers the target's normalized mass distribution in real-time without requiring ground-based pre-calibration. To ensure numerical stability and physical consistency during the estimation of constant parameters, the filter employs an adaptive process noise formulation that prevents covariance collapse while allowing for the gradual convergence of the inertial parameters. Numerical validation is performed via Monte Carlo simulations, demonstrating that the proposed Augmented UKF enables the simultaneous convergence of kinematic states and inertial parameters, thereby facilitating accurate long-term trajectory prediction and robust guidance in non-cooperative deep-space environments.
Figures & tables
Parameter
Value
FoV (Field of view)
45 °
fx (Focal length in x-direction)
1920 (pxs)
fy (Focal length in y-direction)
1280 (pxs)
cx (Principal point x-coordinate)
960 (pxs)
cy (Principal point y-coordinate)
640 (pxs)
Affine translation (std. dev.)
3 pixels (in both x and y )
Table 1: Camera intrinsic properties and simulation parameters
Figure 1: Monte Carlo convergence of the trace-normalized inertia states ( N=100 )
Figure 2: Monte Carlo convergence ( N=100 ) under uninformative isotropic initialization
Spacecraft pose estimation recovers a spacecraft’s position and orientation from images and other sensor data for navigation, rendezvous, and servicing.
This work presents a novel learning-based pipeline for pose estimation of unknown spacecraft using only monocular images from a single servicer. The approach combines a transformer-based neural network with a Multi-State Constraint Kalman Filter (MSCKF) to estimate the pose (i.e., position and orientation of the target spacecraft relative to the camera) throughout rendezvous and proximity operations. Unlike existing vision-based methods that require prior knowledge of the target shape or inertia properties, rely on additional sensing modalities such as depth, lidar, or stereo, or only recover translation up to scale, the proposed pipeline generalizes to previously unseen spacecraft using a single monocular camera. The transformer network estimates the odometry, the change in pose between images up to scale, from SuperPoint features matched by LightGlue. The MSCKF uses these pseudo-measurements along with an orbit and attitude kinematics model to estimate the pose of the target. In particular, the relative orbit elements, the target's attitude with respect to the servicer's camera, and the associated angular velocity are estimated directly by the filter. Given the monocular approach and short distance to the target, the full observability of the range to the target is recovered via attitude maneuvers by the servicer. The method is trained and evaluated on a re-rendered high-resolution version of the SPE3R dataset, which includes synthetic images of 103 spacecraft. Eleven of these spacecraft are held out during training to evaluate the generalization to unseen targets. Monte Carlo simulations are then used to evaluate the navigation pipeline on rendered trajectories of the held out spacecraft. The results demonstrate that learned vision pipelines as a front-end for Kalman filters provide median errors of 3.7° in attitude and 2.2% of range in ROE when navigating about unknown targets.
Pol Francesch Huc, Simone D'Amico
Department of Aeronautics and Astronautics Stanford University Stanford, CA 94305
This work introduces a hybrid deep learning approach integrated with an Unscented Kalman Filter (UKF) to enhance pose estimation accuracy in Visual-Inertial Odometry (VIO) for autonomous navigation. The proposed model employs a Vision Transformer (ViT) network to effectively capture temporal dependencies from inertial measurement unit (IMU) data and utilizes a Multiscale Convolutional Neural Network (MCNN) to learn optical flow-based motion cues from visual data. An adaptive sensor fusion module dynamically weights IMU and visual features by leveraging estimated uncertainty, thus improving robustness in diverse and challenging environmental conditions. Additionally, a novel uncertainty-aware loss function is proposed to explicitly incorporate prediction uncertainty into the learning process, enabling robust and accurate navigation under noisy, incomplete, or unreliable sensor inputs. Comprehensive evaluations of the KITTI dataset demonstrate that the proposed method significantly outperforms baseline approaches, achieving superior performance in terms of Absolute Trajectory Error (ATE) and Relative Pose Error (RPE). The lightweight and computationally efficient model processes data at 155 FPS on an NVIDIA A100 GPU, making it highly suitable for deployment in resource-constrained autonomous systems.
Simegnew Yihunie Alaba, Yuichi Motai
Department of Electrical and Computer Engineering, College of Engineering, Virginia Commonwealth University, Richmond, VA 23220, USA
Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are applied. To cope with real-world scenarios, adaptive noise estimation methods have been developed primarily for classical Euclidean formulations. However, these methods remain largely unexplored in the tangent Lie space, despite it provides a principled geometric framework with favorable error dynamics on Lie groups. To fill this gap, we combine invariant filtering theory with neural-aided adaptive noise estimation in real-world settings. To this end, we derive a novel theoretical extension of classical innovation-based process noise adaptation formulated directly within the Lie-group framework. We further propose a lightweight neural network that estimates the process noise covariance parameters directly from raw inertial data. Trained entirely in a sim2real framework via domain adaptation, the network captures motion-dependent and sensor-dependent noise characteristics without requiring labeled real-world data. To examine our proposed neural-aided adaptive invariant Kalman filter, we focus on the challenging real-world scenario of autonomous underwater navigation. Experimental results demonstrate superior performance compared to existing methods in terms of position root mean square error. These results validate our sim2real pipeline and further confirm that geometric invariance significantly enhances learning-based adaptation and that adaptive noise estimation in the tangent Lie space offers a powerful mechanism for improving navigation accuracy in nonlinear autonomous platforms.