Physics-informed Conditional Normalizing Flows for Angles-only Cislunar Orbit Determination

Walther Litteri; Massimiliano Vasile

cs.LGJun 29, 2026

Physics-informed Conditional Normalizing Flows for Angles-only Cislunar Orbit Determination

Authors: Walther Litteri, Massimiliano Vasile

Organizations: Aerospace Centre of Excellence, University of Strathclyde, G11XQ Glasgow, UK · Aerospace Centre of Excellence, University of Strathclyde, G1 1XQ Glasgow, UK

Abstract

Generative Astrodynamics is advanced in this work by extending generative modelling to an orbit determination problem in the cislunar environment. The task is formulated as conditional density estimation, aiming to infer the probability distribution of the initial state from angles-only measurements over short observation arcs. A normalising flow is trained on perturbed topocentric observations from Near Rectilinear Halo Orbits, enabling a flexible and potentially multimodal posterior representation. Given new measurements, the learned density is sampled to generate statistically consistent and physics-informed state hypotheses. These estimates are refined via nonlinear least-squares minimisation, providing a competitive warm start for classical algorithms.

Explore similar work

ANGLE: Angular Neural Generative Learning via Engression
Jul 14, 2026Rajdeep Pathak, Archi Roy, Tanujit ChakrabortyNonparametric Urban Wind
Transformer-Informed Trajectory Optimization for Relative Motion in Cislunar Orbits
Sep 21, 2026Walter J. Manuel, Yuji Takubo, Simone D'AmicoSpacecraft Trajectory Optimization
Star-Fusion: A Multi-modal Transformer Architecture for Discrete Celestial Orientation via Spherical Topology
Apr 29, 2026May Hammad, Menatallh HammadSatellite Spatio-Temporal Transformers

Jul 14, 2026 · stat.MLJ/K move · Enter open · S save

ANGLE: Angular Neural Generative Learning via Engression

Rajdeep Pathak, Archi Roy, Tanujit Chakraborty

Circular data, representing angles or directions, are frequently encountered in computer vision, biology, geology, and meteorology. Traditional regression targets the conditional mean, which is often geometrically misleading for circular responses under multimodal, skewed, or asymmetric data structures. To address these limitations, a lightweight deep generative framework, namely ANGLE, is introduced for non-parametric distributional regression on the circle. The full conditional distribution of an angular response, given Euclidean and circular covariates, is learned through a generative map optimized via a generalized circular energy score (GCES) loss. Desirable theoretical properties, including the strict propriety of the loss and the rotational equivariance of the estimators, are established. Furthermore, both pre- and post-additive noise models are accommodated. A unified toolbox is provided for advancing previously underexplored challenges in circular statistics: extrapolation, sufficient dimension reduction, and conditional distribution equality testing. The framework's efficacy is demonstrated through extensive simulations and real-world applications. Specifically, the proposal is utilized for object pose estimation from imagery and wind direction prediction, which are integral to surveillance, autonomous vehicles, and energy systems, respectively. Superior predictive performance and robust uncertainty quantification of the proposed method in these tasks are revealed.

Nonparametric Urban Wind Exact Equivariance Generative Adversarial Network Covariate Shift Computer Vision Ear

Open paper Ask about it PDF

Abstract

Explore similar work

ANGLE: Angular Neural Generative Learning via Engression

Transformer-Informed Trajectory Optimization for Relative Motion in Cislunar Orbits

Star-Fusion: A Multi-modal Transformer Architecture for Discrete Celestial Orientation via Spherical Topology