A covariance analysis to optimize the optical follow-up strategies

The Astronomical Institute of the University of Bern (AIUB) is conducting several search campaigns for space debris using optical sensors. The debris objects are discovered during systematic survey observations. In general, the result of a discovery consists in only a short observation arc, or tracklet, which is used to perform a first orbit determination in order to be able to observe t he object again in subsequent follow-up observations. The additional observations are used in the orbit improvement process to obtain accurate orbits to be included in a catalogue. In order to obtain the most accurate orbit within the time available it is necessary to optimize the follow-up observations strategy. In this paper an in‐depth study, using simulations and covariance analysis, is performed to identify the optimal sequence of follow-up observations to obtain the most accurate orbit propagation to be used for the space debris catalogue maintenance. The main factors that determine the accuracy of the results of an orbit determination/improvement process are: tracklet length, number of observations, type of orbit, astrometric error of the measurements, time interval between tracklets, and the relative position of the object along its orbit with respect to the observing station. The main aim of the covariance analysis is to optimize the follow-up strategy as a function of the object-observer geometry, the interval between follow-up observations and the shape of the orbit. This an alysis can be applied to every orbital regime but particular attention was dedicated to geostationary, Molniya, and geostationary transfer orbits. Finally the case with more than two follow-up observations and the influence of a second observing station are also analyzed.

Integrating optical fiber force sensors into microforceps for ORL microsurgery

The delicate anatomy of the ear require surgeons to use great care when operating on its internal structures. One example for such an intervention is the stapedectomy, where a small crook shaped piston is placed in the oval window of the cochlea and connected to the incus through crimping thus bypassing the diseased stapes. Performing the crimp process with the correct force is necessary since loose crimps poorly transmit sound whereas tight crimps will eventually result in necrosis of the incus. Clinically, demand is high to reproducibly conduct the crimp process through a precise force measurement. For this reason, we have developed a fiber Bragg grating (FBG) integrated microforceps for use in such interventions. This device was calibrated, and tested in cadaver preparations. With this instrument we were able to measure for the first time forces involved in crimping a stapes prosthesis to the incus. We also discuss a method of attaching and actuating such forceps in conjunction with a robot currently under development in our group. Each component of this system can be used separately or combined to improve surgical accuracy, confidence and outcome.

PM(10) remote sensing from geostationary SEVIRI and polar-orbiting MODIS sensors over the complex terrain of the European Alpine region

The subject of this study is to investigate the capability of spaceborne remote sensing data to predict ground concentrations of PM10 over the European Alpine region using satellite derived Aerosol Optical Depth (AOD) from the geostationary Spinning Enhanced Visible and InfraRed Imager (SEVIRI) and the polar-orbiting MODerate resolution Imaging Spectroradiometer (MODIS). The spatial and temporal resolutions of these aerosol products (10 km and 2 measurements per day for MODIS, ∼ 25 km and observation intervals of 15 min for SEVIRI) permit an evaluation of PM estimation from space at different spatial and temporal scales. Different empirical linear relationships between coincident AOD and PM10 observations are evaluated at 13 ground-based PM measurement sites, with the assumption that aerosols are vertically homogeneously distributed below the planetary Boundary Layer Height (BLH). The BLH and Relative Humidity (RH) variability are assessed, as well as their impact on the parameterization. The BLH has a strong influence on the correlation of daily and hourly time series, whilst RH effects are less clear and smaller in magnitude. Despite its lower spatial resolution and AOD accuracy, SEVIRI shows higher correlations than MODIS (rSEV∼ 0.7, rMOD∼ 0.6) with regard to daily averaged PM10. Advantages from MODIS arise only at hourly time scales in mountainous locations but lower correlations were found for both sensors at this time scale (r∼ 0.45). Moreover, the fraction of days in 2008 with at least one satellite observation was 27% for SEVIRI and 17% for MODIS. These results suggest that the frequency of observations plays an important role in PM monitoring, while higher spatial resolution does not generally improve the PM estimation. Ground-based Sun Photometer (SP) measurements are used to validate the satellite-based AOD in the study region and to discuss the impact of aerosols' micro-physical properties in the empirical models. A lower error limit of 30 to 60% in the PM10 assessment from space is estimated in the study area as a result of AOD uncertainties, variability of aerosols properties and the heterogeneity of ground measurement sites. It is concluded that SEVIRI has a similar capacity to map PM as sensors on board polar-orbiting platforms, with the advantage of a higher number of observations. However, the accuracy represents a serious limitation to the applicability of satellites for ground PM mapping, especially in mountainous areas.

Validation of a modified AVHRR aerosol optical depth retrieval algorithm over Central Europe

The Advanced Very High Resolution Radiometer (AVHRR) carried on board the National Oceanic and Atmospheric Administration (NOAA) and the Meteorological Operational Satellite (MetOp) polar orbiting satellites is the only instrument offering more than 25 years of satellite data to analyse aerosols on a daily basis. The present study assessed a modified AVHRR aerosol optical depth τa retrieval over land for Europe. The algorithm might also be applied to other parts of the world with similar surface characteristics like Europe, only the aerosol properties would have to be adapted to a new region. The initial approach used a relationship between Sun photometer measurements from the Aerosol Robotic Network (AERONET) and the satellite data to post-process the retrieved τa. Herein a quasi-stand-alone procedure, which is more suitable for the pre-AERONET era, is presented. In addition, the estimation of surface reflectance, the aerosol model, and other processing steps have been adapted. The method's cross-platform applicability was tested by validating τa from NOAA-17 and NOAA-18 AVHRR at 15 AERONET sites in Central Europe (40.5° N–50° N, 0° E–17° E) from August 2005 to December 2007. Furthermore, the accuracy of the AVHRR retrieval was related to products from two newer instruments, the Medium Resolution Imaging Spectrometer (MERIS) on board the Environmental Satellite (ENVISAT) and the Moderate Resolution Imaging Spectroradiometer (MODIS) on board Aqua/Terra. Considering the linear correlation coefficient R, the AVHRR results were similar to those of MERIS with even lower root mean square error RMSE. Not surprisingly, MODIS, with its high spectral coverage, gave the highest R and lowest RMSE. Regarding monthly averaged τa, the results were ambiguous. Focusing on small-scale structures, R was reduced for all sensors, whereas the RMSE solely for MERIS substantially increased. Regarding larger areas like Central Europe, the error statistics were similar to the individual match-ups. This was mainly explained with sampling issues. With the successful validation of AVHRR we are now able to concentrate on our large data archive dating back to 1985. This is a unique opportunity for both climate and air pollution studies over land surfaces.

An Instrument Design for Space-Based Optical Observation of Space Debris

Currently, observations of space debris are primarily performed with ground-based sensors. These sensors have a detection limit at some centimetres diameter for objects in Low Earth Orbit (LEO) and at about two decimetres diameter for objects in Geostationary Orbit (GEO). The few space-based debris observations stem mainly from in-situ measurements and from the analysis of returned spacecraft surfaces. Both provide information about mostly sub-millimetre-sized debris particles. As a consequence the population of centimetre- and millimetre-sized debris objects remains poorly understood. The development, validation and improvement of debris reference models drive the need for measurements covering the whole diameter range. In 2003 the European Space Agency (ESA) initiated a study entitled “Space-Based Optical Observation of Space Debris”. The first tasks of the study were to define user requirements and to develop an observation strategy for a space-based instrument capable of observing uncatalogued millimetre-sized debris objects. Only passive optical observations were considered, focussing on mission concepts for the LEO, and GEO regions respectively. Starting from the requirements and the observation strategy, an instrument system architecture and an associated operations concept have been elaborated. The instrument system architecture covers the telescope, camera and onboard processing electronics. The proposed telescope is a folded Schmidt design, characterised by a 20 cm aperture and a large field of view of 6°. The camera design is based on the use of either a frame-transfer charge coupled device (CCD), or on a cooled hybrid sensor with fast read-out. A four megapixel sensor is foreseen. For the onboard processing, a scalable architecture has been selected. Performance simulations have been executed for the system as designed, focussing on the orbit determination of observed debris particles, and on the analysis of the object detection algorithms. In this paper we present some of the main results of the study. A short overview of the user requirements and observation strategy is given. The architectural design of the instrument is discussed, and the main tradeoffs are outlined. An insight into the results of the performance simulations is provided.

Associating optical measurements and estimating orbits of geocentric objects through population-based meta-heuristic methods

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both, the correct associations among the observations and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. The number S corresponds to the number of fences involved in the problem. Each fence consists of a set of observations where each observation belongs to a different object. The S ≥ 3 MTT problem is an NP-hard combinatorial optimization problem. There are two general ways to solve this. One way is to seek the optimum solution, this can be achieved by applying a branch-and- bound algorithm. When using these algorithms the problem has to be greatly simplified to keep the computational cost at a reasonable level. Another option is to approximate the solution by using meta-heuristic methods. These methods aim to efficiently explore the different possible combinations so that a reasonable result can be obtained with a reasonable computational effort. To this end several population-based meta-heuristic methods are implemented and tested on simulated optical measurements. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to efficiently process large data sets with minimal manual intervention.

A study of the time complexity of an Elitist Genetic Algorithm used for associating optical observations of MEO and GEO Space Debris

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both the correct associations among the observations, and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. Where S stands for the number of ’fences’ used in the problem, each fence consists of a set of observations that all originate from dierent targets. For a dimension of S ˃ the MTT problem becomes NP-hard. As of now no algorithm exists that can solve an NP-hard problem in an optimal manner within a reasonable (polynomial) computation time. However, there are algorithms that can approximate the solution with a realistic computational e ort. To this end an Elitist Genetic Algorithm is implemented to approximately solve the S ˃ MTT problem in an e cient manner. Its complexity is studied and it is found that an approximate solution can be obtained in a polynomial time. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to e ciently process large data sets with minimal manual intervention.