Related papers: Kernel Embedding Approaches to Orbit Determination…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
This paper presents a novel methodology to control spacecraft swarms about singleasteroids with arbitrary gravitational potential coefficients. This approach enablesthe use of small, autonomous swarm spacecraft in conjunction with a…
Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…
We present a Bayesian algorithm to combine optical imaging of unresolved objects from distinct epochs and observation platforms for orbit determination and tracking. By propagating the non-Gaussian uncertainties we are able to optimally…
Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…
An innovative orbit determination method which makes use of gravity gradients for Low-Earth-Orbiting satellites is proposed. The measurement principle of gravity gradiometry is briefly reviewed and the sources of measurement error are…
Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of…
This paper proposes a distributed on-orbit spacecraft assembly algorithm, where future spacecraft can assemble modules with different functions on orbit to form a spacecraft structure with specific functions. This form of spacecraft…
We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihedral group. We show that if the group elements are drawn from…
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…
Satellite constellation missions, consisting of a large number of spacecraft, are increasingly being launched or planned. Such missions require novel control approaches, in particular for what concerns orbital phasing maneuvers. In this…
If an orbit is fitted from combined RV and astrometric data, the orbit should be physically consistent with both data sets. The Keplerian orbit of a planet is a highly nonlinear function of seven parameters. The astrometric orbit problem…
We develop a unified framework for nonparametric functional estimation based on kernel transport along orbits of discrete group actions, which we term \emph{Twin Spaces}. Given a base kernel $K$ and a group $G = \langle\varphi\rangle$…
Spaceborne gravity gradients are proposed in this paper to provide autonomous orbit determination capabilities for near Earth satellites. The gravity gradients contain useful position information which can be extracted by matching the…
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…
In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…
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…
A new Doppler radar initial orbit determination algorithm with embedded uncertainty quantification capabilities is presented. The method is based on a combination of Gauss' and Lambert's solvers. The whole process is carried out in the…
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…