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Initial orbit determination (IOD) from line-of-sight (i.e., bearing) measurements is a classical problem in astrodynamics. Indeed, there are many well-established methods for performing the IOD task when given three line-of-sight…

Earth and Planetary Astrophysics · Physics 2023-04-06 Michela Mancini , Timothy Duff , Anton Leykin , John A. Christian

Initial Orbit Determination (IOD) is the classical problem of estimating the orbit of a body in space without any presumed information about the orbit. The geometric formulation of the ''angles-only'' IOD in three-dimensional space: find a…

Algebraic Geometry · Mathematics 2025-09-19 Ruiqi Huang , Anton Leykin , Michela Mancini

As space traffic continues to increase in the cislunar region, accurately determining the trajectories of objects operating within this domain becomes critical. However, due to the combined gravitational influences of the Earth and Moon,…

Earth and Planetary Astrophysics · Physics 2025-07-31 Seur Gi Jo , Brian Baker-McEvilly , David Canales

Initial orbit determination (IOD) is an important early step in the processing chain that makes sense of and reconciles the multiple optical observations of a resident space object. IOD methods generally operate on line-of-sight (LOS)…

Computer Vision and Pattern Recognition · Computer Science 2023-08-29 Chee-Kheng Chng , Trent Jansen-Sturgeon , Timothy Payne , Tat-Jun Chin

An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to…

Earth and Planetary Astrophysics · Physics 2025-05-27 Alberto Fossà , Matteo Losacco , Roberto Armellin

In orbital mechanics, Gauss's method for orbit determination (OD) is a popular, minimal assumption solution for obtaining the initial state estimate of a passing resident space object (RSO). Since much of the cislunar domain relies on…

Earth and Planetary Astrophysics · Physics 2026-02-23 Ishan Paranjape , Tarun Hejmadi , Suman Chakravorty

In celestial mechanics, proper orbits related to missions are obtained by solving two-point boundary value problems. Since a selection method of initial value affects the convergence of the solution, developing an effective method to find…

Optimization and Control · Mathematics 2025-06-18 Daegyun Choi , Sungwook Yang , Henzeh Leeghim , Donghoon Kim

Accurate relative orbit determination is a significant challenge in modern space operations, particularly when relying only on angular measurements. The inherent observability limitations of this approach make initial state estimation…

Systems and Control · Electrical Eng. & Systems 2026-03-11 Kui Xie , Giovanni Romagnoli , Giordana Bucchioni , Alberto Bemporad

With debris larger than 1 cm in size estimated to be over one million, precise cataloging efforts are essential to ensure space operations' safety. Compounding this challenge is the oversubscribed problem, where the sheer volume of space…

Numerical Analysis · Mathematics 2025-03-13 Cristina Parigini , Laura Pirovano , Roberto Armellin , Darren McKnight , Adam Marsh , Tom Reddell

The computation of the Minimum Orbital Intersection Distance (MOID) is an old, but increasingly relevant problem. Fast and precise methods for MOID computation are needed to select potentially hazardous asteroids from a large catalogue. The…

Earth and Planetary Astrophysics · Physics 2018-06-22 Jose M. Hedo , Manuel Ruiz , Jesus Pelaez

In the domain of Space Situational Awareness (SSA), the challenges pertaining to orbit determination and catalog correlation are notably pronounced, partly attributable to the escalating presence of non-cooperative satellites engaging in…

Space Physics · Physics 2024-04-02 Jose M. Montilla , Jan A. Siminski , Rafael Vazquez

Given a set of astrometric observations of the same object, the problem of orbit determination is to compute the orbit and to assess its uncertainty and reliability. For the next generation surveys, with much larger number density of…

In this paper, we propose an interoceptive-only odometry system for ground robots with neural network processing and soft constraints based on the assumption of a globally continuous ground manifold. Exteroceptive sensors such as cameras,…

Robotics · Computer Science 2024-07-24 Chenxing Jiang , Kunyi Zhang , Sheng Yang , Shaojie Shen , Chao Xu , Fei Gao

The hand-eye measurements have recently been proven to be very efficient for spacecraft attitude determination relative to an ellipsoidal asteroid. However, recent method does not guarantee full attitude observability for all conditions.…

Systems and Control · Electrical Eng. & Systems 2020-03-26 Jin Wu

This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework,…

Instrumentation and Methods for Astrophysics · Physics 2026-04-28 Xingyu Zhou , Malcolm Macdonald , Roberto Armellin , Dong Qiao , Xiangyu Li

With the increase in the number of active satellites and space debris in orbit, the problem of initial orbit determination (IOD) becomes increasingly important, demanding a high accuracy. Over the years, different approaches have been…

Optimization and Control · Mathematics 2024-08-07 Ricardo Ferreira , Filipa Valdeira , Marta Guimarães , Cláudia Soares

Inertial odometry is an attractive solution to the problem of state estimation for agile quadrotor flight. It is inexpensive, lightweight, and it is not affected by perceptual degradation. However, only relying on the integration of the…

Robotics · Computer Science 2023-03-01 Giovanni Cioffi , Leonard Bauersfeld , Elia Kaufmann , Davide Scaramuzza

We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in (Gronchi et al 2015), which uses a…

Space Physics · Physics 2018-10-24 Helene Ma , Giovanni F. Gronchi , Davide Bracali Cioci

Due to the importance of satellites for society and the exponential increase in the number of objects in orbit, it is important to accurately determine the state (e.g., position and velocity) of these Resident Space Objects (RSOs) at any…

Systems and Control · Electrical Eng. & Systems 2023-12-22 Ricardo Ferreira , Marta Guimarães , Filipa Valdeira , Cláudia Soares

In this paper we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector and a very short arc (VSA) of optical observations. Using the conservation laws of the two-body dynamics, we…

Mathematical Physics · Physics 2023-12-25 Erica Scantamburlo , Giovanni F. Gronchi , Giulio Baù
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