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**1 - 4**of**4**### Probabilistic Admissible Region for Short-Arc Angles-Only Observations

"... The admissible region is defined as the set of physically acceptable orbits (i.e., orbits with negative energies). Given additional constraints on orbital semi-major axis, eccentricity, etc, the admissible region is further constrained, result-ing in the constrained admissible region (CAR). Based on ..."

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The admissible region is defined as the set of physically acceptable orbits (i.e., orbits with negative energies). Given additional constraints on orbital semi-major axis, eccentricity, etc, the admissible region is further constrained, result-ing in the constrained admissible region (CAR). Based on known statistics of the measurement process, in this paper we replace hard constraints with a probabilistic representation of the admissible region. This results in the probabilis-tic admissible region (PAR) that can be used for orbit initiation in Bayesian tracking. While this is a general concept that is applicable to any measurement scenario, we will illustrate the idea using a short-arc, angles-only observation scenario. 1.

### Innovative observing strategy and orbit determination for Low Earth Orbit Space Debris

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### Orbit Determination of Space Debris: Admissible Regions

"... The main problem in the orbit determination of the space debris po-pulation orbiting our planet is identifying which separate sets of data belong to the same physical object. The observations of a given object during a passage above an observing station are collectively called a Too Short Arc (TSA): ..."

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The main problem in the orbit determination of the space debris po-pulation orbiting our planet is identifying which separate sets of data belong to the same physical object. The observations of a given object during a passage above an observing station are collectively called a Too Short Arc (TSA): data from a TSA cannot allow for a complete determination of an orbit. Therefore we have to solve first the iden-tification problem, finding two or more TSAs belonging to the same physical object and an orbit fitting all the observations. This problem is well known for the determination of orbits of asteroids: we shall show how to apply the methods developed for preliminary orbit determina-tion of heliocentric objects to geocentric objects. We shall focus on the definition of an admissible region for space debris, both in the case of optical observations and radar observations; then we shall outline a strategy to perform a full orbit determination.

### Orbit determination with very short arcs. II Identications

, 2005

"... When the observational data are not enough to compute a meaningful orbit for an asteroid/comet we can represent the data with an attributable, i.e., two angles and their time derivatives. The undetermined variables range and range rate span an admissible region of solar system orbits, which can be s ..."

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When the observational data are not enough to compute a meaningful orbit for an asteroid/comet we can represent the data with an attributable, i.e., two angles and their time derivatives. The undetermined variables range and range rate span an admissible region of solar system orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by means of an optimal triangulation [Milani et al. 2004]. The attributable 4 coordinates are the result of a t and they have an uncertainty, represented by a covariance matrix. Two short arcs of observations, represented by two attributables, can be linked by considering for each VA (in the admissible region of the rst arc) the covariance matrix for the prediction at the time of the second arc, and by comparing it with the attributable of the second arc with its own covariance. By dening an identi cation penalty we can select the VAs allowing to t together both arcs and compute a preliminary orbit. Two attributables may not be enough to compute an orbit with convergent dierential corrections. Thus the preliminary orbit is used in a constrained dierential correction, providing solutions along the Line Of Variation which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identication with a third arc will ensure a well determined orbit, to which additional sets of observations can be at-