In order to introduce some key ideas in state-variable system modeling, we need to use signal-flow graphs. These graphs allow for only three types of operations: • Addition of incoming signals at a node: Here the node is a small circle. Any signal flowing out of a node is the sum of all the signals flowing in. • Amplification by a fixed factor, positive or negative: the gain is just written above the signal path. • Integration: This is denoted by a box containing the integral sign, or 1/s.

State space analysis of control systems

Over the past 60 years, satellite technology has demonstrated its usefulness successfully. However, this usefulness is at stake from a future point of view, due to the well-admitted orbital/space debris threat. This article thoroughly reviews all aspects of space debris issue including causes, amount and sizes of orbital debris, potential threats, counter-strategies with their latest status and related legal issues to highlight the criticality and urgency of the problem. This review elaborates the fact that despite all the worries and threats, the efforts to confront this challenge are considerably insufficient until today. This bitter reality demands for at-least curtailing the number of future launches to ensure the long-term sustainability of space, until the improvement in debris situation. However, contradictory to this necessity, large satellite constellations have been proposed that can drastically increase the existing orbital population in coming years. This approach will certainly not help in improving the space environment in the future; instead, it can worsen the space environment situation as recent studies shows. Also, space resources (i.e. orbital slots and frequencies) are limited to accommodate many more satellite projects from commercial and government organization in the future. So, there is a serious question of how the space industry can move forward to maintain a balance in controlling the future number of the satellite while accommodating many commercial or government space entities. This article also identifies two optimized approaches as a way forward for future satellite projects that can also enhance the effectiveness of space technology in the future.

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Orbital Debris Threat for Space Sustainability and Way Forward (Review Article)

Satellite laser ranging allows to measure distances to satellites equipped with retroreflectors in orbits up to 36000 km. Utilizing a higher powered laser, space debris laser ranging detects diffuse reflections from defunct satellites or rocket bodies up to a distance of 3000 km. So far space debris laser ranging was only possible within a few hours around twilight while it is dark at the satellite laser ranging station and space debris is illuminated by the sun. Here we present space debris laser ranging results during daylight. Space debris objects are visualized against the blue sky background and biases corrected in real-time. The results are a starting point for all space debris laser ranging stations to drastically increase their output in the near future. A network of a few stations worldwide will be able to improve orbital predictions significantly as necessary for removal missions, conjunction warnings, avoidance maneuvers or attitude determination. Space debris laser ranging is a technique to measure distances to defunct satellites or rocket bodies in orbits around Earth which was only possible within a few hours around twilight. Here, the authors show the first space debris laser ranging results during daylight while correcting inaccurate predictions using a real-time target detection software.

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Daylight space debris laser ranging

Analysis of the attitude and geometry of space targets with the inverse synthetic aperture radar (ISAR) technique is a significant and difficult task. Most of the existing methods hardly consider the radar observation geometry in the determination of target attitude. This paper proposes a novel approach to estimating the three-dimensional attitude and reconstructing typical component geometry of space targets from an ISAR image sequence. The approach bridges range-Doppler images and target attitude parameters with the accommodation of target trajectory information and the ISAR geometric projection model. By exploring the shape feature within the ISAR sequence, the target attitude and the rectangular component size are estimated through solving an optimization with prior shape constraints. Comparative experiments illustrate the advantages of the proposed method in both feature association and reconstruction feasibility. Moreover, considering practical circumstances, a further analysis is made of the robustness of the proposed algorithm after the attitude estimation experiment.

Attitude Estimation and Geometry Reconstruction of Satellite Targets Based on ISAR Image Sequence Interpretation

As more and more satellites are launched into the space, dynamic estimation of spin satellites has become a critical component of the space situation awareness application. Some explored studies using exterior measurements from different sensors such as optical device and inverse synthetic aperture radar (ISAR) to estimate dynamic parameters of spin satellites. As a single sensor normally provides two-dimensional observation, three-dimensional estimations resulting from these algorithms are strictly related to the prior knowledge of targets characteristics. As a result, it is difficult to expand these methods to other satellites. In order to support the dynamic estimation of most spin satellites, this paper presents a novel dynamic estimation approach which employs synchronized optical-and-radar images. The optical-and-radar fusion strategy has demonstrated its superiority in image analysis field, and breaks down the dynamic estimation of spin satellites into two sub-problems: target attitude estimation and spin parameters estimation. In this work, the proposed algorithm deduces two explicit expressions of target dynamic parameters under the imaging projection model of the joint optical-and-radar observation. Through the particle swarm optimization (PSO), target dynamic parameters are determined in two stages. This paper presents some experiments illustrating the feasibility of the proposed method and subsequent conclusions, which reflect advantages of the joint optical-and-radar observation mode in image interpretation.

Optical-and-Radar Image Fusion for Dynamic Estimation of Spin Satellites

Apparent rotation properties of space debris extracted from photometric measurements

Spin motion determination of the Envisat satellite through laser ranging measurements from a single pass measured by a single station

Slovakia became the 9th ESA European Cooperative State in 2015 and the first calls to action for the Plan for European Cooperating State (PECS) were announced shortly after. The Department of Astronomy and Astrophysics, a part of the Faculty of Mathematics, Physics and Informatics of Comenius University in Bratislava, Slovakia (FMPI CU), won the call and an activity with a main goal to transform a 0.7-m Newton telescope (AGO70) dedicated to amateur astronomical observations to a professional optical system for regular support of the space debris tracking and research has started. The transformation includes the necessary hardware and software modifications to the existing solution. The presented activity has been performed in cooperation with the Astronomical Institute of University of Bern (AIUB). The AGO70 has been installed at the FMPI's Astronomical and Geophysical Observatory in Modra, Slovakia (AGO) in fall 2016. There are several predefined objectives to be accomplished within the activity. First, it was imperative to adapt the low-level telescope control for the needs of space debris tracking. Second, the image processing software must have been developed in a modular way. The observation planning has been formulated according to the AGO70 system's hardware limitations with focus on GEO, GTO and GNSS like orbits. To verify the system's capabilities, the whole activity is concluded with an observation campaign measuring AIUB's HAMR (High-Area-to-Mass-Ratio) objects and public TLE objects. The quality of the system's output is monitored by the AIUB via its state-of-the-art epoch bias and astrometric accuracy analysis routines.

Slovakian Optical Sensor for HAMR Objects Cataloguing and Research

The precise knowledge of the trajectories of space debris objects and in particular of defunct satellites is fundamental for satellite operations. Several studies showed that it is possible to improve the accuracy of the orbit determination results by fusing different typesof observables, i.e. classical astrometric positions and range measurements. Particularly promising in the space debris field are the ranges provided by a satellite laser ranging system. The factors which limit the applicability of the SLR techniques are the accuracy of the predicted ephemeris of the target, the energy of the laser pulse, and the laser field of view. In this paper, we will show how the use of a night-tracking camera can overcome the challenges related to the quality of the predicted ephemerides providing both, real time correction to the pointing of the SLR system (active tracking), and simultaneously astrometric measurements which can be used to improve the orbits which will finally also allow studying the attitude of the target. After presenting the basic functionalities, the performance of the night-tracking camera, and the procedure to acquire the measurements, we will analyse the results of an orbit determination procedure when fusing the different observables. This study is carried out for defunct or recently decommissioned satellites. Only real angular/laser measurements provided by the sensors of the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald (SwissOGS) owned by the Astronomical Institute of the University of Bern (AIUB) are used to determine improved orbits in near real time.

Real time improvement of orbits of space debris by fusing SLR and astrometric data acquired by a night-tracking camera

Two major fragmentation events in GEO and HEO were observed in 2018. Based on measurements of the International Scientific Optical Network (ISON) and the Roscosmos Automated Warning System on Hazardous Situations in Outer Space (ASPOS OKP) a fragmentation of the Titan 3C Transtage 1969-013B, SSN #3692 on February 28, 2018 was identified. More than 100 objects detected by optical instruments operated by ASPOS OKP, the Astronomical Scientific Center, ISON, ISTP RAS and other Russian scientific and re
search organizations could be clearly identified as fragmentation debris related to this event. Another massive fragmentation event in HEO related to the Atlas Centaur upper stage 2014-055B, SSN #40209, which occurred on August 30, was identified based on the same data sources. Many of the fragment of this event are crossing the operational GEO region. In March and April 2019 two additional breakup events of Atlas Centaur upper stages took place. Since October 2018 ESA is performing a coordinated survey campaign using its 1-m telescope at the OGS, Tenerife, complemented by sensors of the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald, Switzerland. The paper will describe the development of the survey strategy to search for additional fragments of the two mentioned events, the execution of the actual observation campaign including the handover of newly discovered objects to other 
sensors and the subsequent follow-up observations, and the main results of and lessons learned from this campaign.

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Thomas Schildknecht

Papers

Apparent rotation properties of space debris extracted from photometric measurements

Spin motion determination of the Envisat satellite through laser ranging measurements from a single pass measured by a single station

Slovakian Optical Sensor for HAMR Objects Cataloguing and Research

Real time improvement of orbits of space debris by fusing SLR and astrometric data acquired by a night-tracking camera

ESA Optical Surveys to Characterize Recent Fragmentation Events in GEO and HEO