Daniel Brack

Daniel Brack



Pini Gurfil
Optimal in-orbit Tracking of High Area-to-Mass Ratio


In recent years, a population of High Area-to-Mass Ratio (HAMR) space objects has been observed at high altitude orbits [1]. Together with the observations, numerical and analytical studies of objects in Geosynchronous Earth Orbits (GEO), Geosynchronous Transfer Orbits (GTO) and in the Global Positioning System (GPS) orbits have been performed, suggesting that each orbit’s HAMR objects have originated from artifacts such as defunct satellites and launcher upper stages [2, 3, 4]. These studies also concluded that the HAMR objects are highly aected by the Solar Radiation Pressure (SRP) perturbation, some to such an extent that the SRP is the dominant perturbation.

The observations and studies have shown that HAMR orbits undergo large variations in the mean values of eccentricity and inclination in yearly and larger timescales, while keeping the mean motion relatively steady [2]. It has also been shown that the HAMR objects vary in Area-to-Mass Ratio (AMR) of between 100 to 4000 the AMR of typical operational space objects. Lower AMRs do not posses HAMR proprieties e.g. high susceptibility to the SRP, and higher AMRs lead to a rapid decay of the orbits due to atmospheric drag.

HAMR objects within the mentioned range are characterized by lifetime of decades and more. The HAMR space objects are usually flat, so that even a specic HAMR object might have a large variation of its Cross Sectional Area (CSA) facing the Sun, which leads to a strong coupling between a HAMR object’s attitude and orbit [5], as well as signicant SRP torques.

Due to their physical properties and high altitude orbits, the HAMR objects are difficult to detect and monitor from the Earth’s surface. The large eccentricity variations lead to orbits that cross the highly populated orbits (mainly GEO, but also GPS, GTO and the graveyard orbit). The combination of HAMR object properties render these objects a genuine risk for collision with operational satellites and even for a cascade eect that might render GEO unusable [6, 7].

The risk of collision requires a HAMR object capture mission for active removal. Such a mission would require a spacecraft with the ability to track and follow a HAMR object prior to performing rendezvous with and capture of the object.

Research Objectives

The main purpose of this research is to develop algorithms for HAMR object in-orbit tracking by a nearby spacecraft.

Relative motion dynamics for elliptical orbits with the SRP perturbation and a consideration of attitude-orbit coupling will be developed and used for HAMR object state estimation.

The research will investigate several types of sensing systems: monocular, stereo cameras, an omnidirectional camera and LIDAR for the HAMR object tracking process.

With the intent to develop an operational estimation algorithm, an optimization process will be performed in order to design an algorithm which uses the minimal required sensor inputs for HAMR object state estimation, required for rendezvous and capture.

As mentioned, since the discovery of HAMR objects at high altitude orbits several numerical and analytical studies have been done developing the orbital dynamics of such objects; however, relative motion dynamics between a non-HAMR spacecraft and a HAMR object have yet to be developed. The development of estimation algorithms based on these dynamics will offer progress towards HAMR space debris removal.

Technical Description

The relative motion dynamics between a non-HAMR spacecraft and a HAMR object can be developed using the relative translational motion equation for a general orbit and the relative rotational motion equation [8]. The SRP perturbation for a given space object [9] will be used as a dominant perturbation.

A complete relative 15-dimensional state vector will then be dened using the relative motion dynamics developed.

Visual sensors require a line of sight between the optical system and the target object. A possible control law for the chaser attitude [10] requires that the line of sight vector and the optical axis are aligned. As mentioned, several vision based systems will be examined as a possible relative state sensor, a leading candidate is the stereo camera, which can allow for a passive full state estimation. The observations acquired by a camera are the projections of the feature points from a 3D space onto a 2D image plane, the use of two or more cameras provides the additional dimensions required for a full state estimation.


[1] Schildknecht, T., Musci, R., and Flohrer, T., Properties of the high area-to-mass ratio space debris population at high altitudes, Advances in Space Research, Vol. 41, No. 7, 2008, pp. 10391045.

[2] Anselmo, L. and Pardini, C., Orbital Evolution of Geosynchronous Objects with High Area-To Ratios, 4th European Conference on Space Debris, Vol. 587, 2005, p. 279.

[3] Anselmo, L. and Pardini, C., Dynamical evolution of high area-to-mass ratio debris released into GPS orbits, Advances in Space Research, Vol. 43, No. 10, 2009, pp. 14911508.

[4] Musci, R., Schildknecht, T., Flohrer, T., and Beutler, G., Evolution of the orbital elements for objects with high area-to-mass ratios in geostationary transfer orbits, Advances in Space Research, Vol. 41, No. 7, 2008, pp. 10711076.

[5] Früh, C. and Schildknecht, T., Variation of the area-to-mass ratio of high area-to-mass ratio space debris objects, Monthly Notices of the Royal Astronomical Society, Vol. 419, No. 4, 2012, pp. 35213528.

[6] Flury, W., Collision probability and spacecraft disposition in the geostationary orbit, Advances in Space Research, Vol. 11, No. 12, 1991, pp. 6779.

[7] Klinkrad, H., Space debris: models and risk analysis, Springer, 2006.

[8] Segal, S. and Gurl, P., Eect of kinematic rotation-translation coupling on relative spacecraft translational dynamics, Journal of Guidance, Control, and Dynamics, Vol. 32, No. 3, 2009, pp. 10451050.

[9] Vallado, D. A., Fundamental of Astrodynamics and Applications, Microcosm Press, 4th ed., 2013.

[10] Segal, S., Gurl, P., and Shahid, K., In-orbit tracking of resident space objects: a comparison of monocular and stereoscopic vision, IEEE Transactions on Aerospace and Electronic