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This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem…

Numerical Analysis · Mathematics 2023-11-07 Alberto Fossà , Roberto Armellin , Emmanuel Delande , Matteo Losacco , Francesco Sanfedino

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

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

This paper presents a novel algorithm to incorporate orbital parameters into radar ambiguity function expressions by extending the standard ambiguity function to match Keplerian two-body orbits. A coherent orbital matched-filter will…

Signal Processing · Electrical Eng. & Systems 2020-03-10 Brendan Hennessy , Mark Rutten , Steven Tingay , Robert Young

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

Doppler orbitography uses the Doppler shift in a transmitted signal to determine the orbital parameters of satellites including range and range-rate (or radial velocity). We describe two techniques for atmospheric-limited optical Doppler…

Instrumentation and Methods for Astrophysics · Physics 2020-06-09 Benjamin P. Dix-Matthews , Sascha W. Schediwy , David R. Gozzard , Simon Driver , Karl Ulrich Schreibe , Randall Carman , Michael Tobar

Simultaneous localization and mapping (SLAM) is a critical capability for autonomous systems. Traditional SLAM approaches, which often rely on visual or LiDAR sensors, face significant challenges in adverse conditions such as low light or…

Robotics · Computer Science 2026-02-06 Dong Wang , Hannes Haag , Daniel Casado Herraez , Stefan May , Cyrill Stachniss , Andreas Nüchter

The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…

Mathematical Physics · Physics 2015-05-27 Giovanni F. Gronchi , Davide Farnocchia , Linda Dimare

In passive radar, a network of distributed sensors exploit signals from so-called Illuminators-of-Opportunity to detect and localize targets. We consider the case where the IO signal is available at each receiver node through a reference…

Signal Processing · Electrical Eng. & Systems 2026-05-19 Mats Viberg , Daniele Gerosa , Tomas McKelvey , Patrik Dammert , Thomas Eriksson

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

Short-arc orbit determination is crucial when an asteroid is first discovered. In these cases usually the observations are so few that the differential correction procedure may not converge. We have developed an initial orbit computation…

Earth and Planetary Astrophysics · Physics 2018-06-13 F. Spoto , A. Del Vigna , A. Milani , G. Tommei , P. Tanga , F. Mignard , B. Carry , W. Thuillot , P. David

State estimation is a crucial component for the successful implementation of robotic systems, relying on sensors such as cameras, LiDAR, and IMUs. However, in real-world scenarios, the performance of these sensors is degraded by challenging…

Robotics · Computer Science 2024-03-18 Jui-Te Huang , Ruoyang Xu , Akshay Hinduja , Michael Kaess

We review two initial orbit determination methods for too short arcs (TSAs) of optical observations of a solar system body. These methods employ the conservation laws of Kepler's problem, and allow to attempt the linkage of TSAs referring…

Earth and Planetary Astrophysics · Physics 2021-11-05 Giovanni Federico Gronchi

We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…

Mathematical Physics · Physics 2010-04-01 Giovanni Federico Gronchi , Linda Dimare , Andrea Milani

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

We introduce a new method to perform preliminary orbit determination for space debris on low Earth orbits (LEO). This method works with tracks of radar observations: each track is composed by $n\ge 4$ topocentric position vectors per pass…

Mathematical Physics · Physics 2015-01-30 Giovanni F. Gronchi , Linda Dimare , Davide Bracali Cioci , Helene Ma

We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…

Numerical Analysis · Mathematics 2015-06-23 Michele V. Bartuccelli , Jonathan H. B. Deane , Guido Gentile

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

We study the target parameter estimation for sub-Nyquist pulse-Doppler radar. Several past works have addressed this problem but either have low estimation accuracy for off-grid targets, take large computation load, or lack versatility for…

Information Theory · Computer Science 2017-07-27 Shengyao Chen , Feng Xi , Zhong Liu

Correcting gradual position drift is a challenge in long-term subsea navigation. Though highly accurate, modern inertial navigation system (INS) estimates will drift over time due to the accumulated effects of sensor noise and biases, even…

Robotics · Computer Science 2023-07-12 Amro Al-Baali , Thomas Hitchcox , James Richard Forbes
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