Innovative methods of correlation and orbit determination for space debris

We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the $J_2$ effect.Comment: 18 page

A conjugate gradient algorithm for the astrometric core solution of Gaia

The ESA space astrometry mission Gaia, planned to be launched in 2013, has been designed to make angular measurements on a global scale with micro-arcsecond accuracy. A key component of the data processing for Gaia is the astrometric core solution, which must implement an efficient and accurate numerical algorithm to solve the resulting, extremely large least-squares problem. The Astrometric Global Iterative Solution (AGIS) is a framework that allows to implement a range of different iterative solution schemes suitable for a scanning astrometric satellite. In order to find a computationally efficient and numerically accurate iteration scheme for the astrometric solution, compatible with the AGIS framework, we study an adaptation of the classical conjugate gradient (CG) algorithm, and compare it to the so-called simple iteration (SI) scheme that was previously known to converge for this problem, although very slowly. The different schemes are implemented within a software test bed for AGIS known as AGISLab, which allows to define, simulate and study scaled astrometric core solutions. After successful testing in AGISLab, the CG scheme has been implemented also in AGIS. The two algorithms CG and SI eventually converge to identical solutions, to within the numerical noise (of the order of 0.00001 micro-arcsec). These solutions are independent of the starting values (initial star catalogue), and we conclude that they are equivalent to a rigorous least-squares estimation of the astrometric parameters. The CG scheme converges up to a factor four faster than SI in the tested cases, and in particular spatially correlated truncation errors are much more efficiently damped out with the CG scheme.Comment: 24 pages, 16 figures. Accepted for publication in Astronomy & Astrophysic

Correlated and zonal errors of global astrometric missions: a spherical harmonic solution

We propose a computer-efficient and accurate method of estimation of spatially correlated errors in astrometric positions, parallaxes and proper motions obtained by space and ground-based astrometry missions. In our method, the simulated observational equations are set up and solved for the coefficients of scalar and vector spherical harmonics representing the output errors, rather than for individual objects in the output catalog. Both accidental and systematic correlated errors of astrometric parameters can be accurately estimated. The method is demonstrated on the example of the JMAPS mission, but can be used for other projects of space astrometry, such as SIM or JASMINE.Comment: Accepted by AJ, to be published in 201

Efficient satellite orbit modelling using pseudo-stochastic parameters

If the force field acting on an artificial Earth satellite is not known a priori with sufficient accuracy to represent its observations on their accuracy level, one may introduce so-called pseudo-stochastic parameters into an orbit determination process, e.g. instantaneous velocity changes at user-defined epochs or piecewise constant accelerations in user-defined adjacent time subintervals or piecewise linear and continuous accelerations in adjacent time subintervals. The procedures, based on standard least-squares, associated with such parameterizations are well established, but they become inefficient (slow) if the number of pseudo-stochastic parameters becomes large. We develop two efficient methods to solve the orbit determination problem in the presence of pseudo-stochastic parameters. The results of the methods are identical to those obtained with conventional least-squares algorithms. The first efficient algorithm also provides the full variance-covariance matrix; the second, even more efficient algorithm, only parts of i

Cloud cover determination in polar regions from satellite imagery

A definition is undertaken of the spectral and spatial characteristics of clouds and surface conditions in the polar regions, and to the creation of calibrated, geometrically correct data sets suitable for quantitative analysis. Ways are explored in which this information can be applied to cloud classifications as new methods or as extensions to existing classification schemes. A methodology is developed that uses automated techniques to merge Advanced Very High Resolution Radiometer (AVHRR) and Scanning Multichannel Microwave Radiometer (SMMR) data, and to apply first-order calibration and zenith angle corrections to the AVHRR imagery. Cloud cover and surface types are manually interpreted, and manual methods are used to define relatively pure training areas to describe the textural and multispectral characteristics of clouds over several surface conditions. The effects of viewing angle and bidirectional reflectance differences are studied for several classes, and the effectiveness of some key components of existing classification schemes is tested

Orbit determination of space objects based on sparse optical data

While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained at different times. This correlation step is the most computationally intensive, and becomes more and more difficult as the number of objects to be discovered increases. In this paper we tested two different algorithms (and the related prototype software) recently developed to solve the correlation problem for objects in geostationary orbit (GEO), including the accurate orbit determination by full least squares solutions with all six orbital elements. Because of the presence in the GEO region of a significant subpopulation of high area to mass objects, strongly affected by non-gravitational perturbations, it was actually necessary to solve also for dynamical parameters describing these effects, that is to fit between 6 and 8 free parameters for each orbit. The validation was based upon a set of real data, acquired from the ESA Space Debris Telescope (ESASDT) at the Teide observatory (Canary Islands). We proved that it is possible to assemble a set of sparse observations into a set of objects with orbits, starting from a sparse time distribution of observations, which would be compatible with a survey capable of covering the region of interest in the sky just once per night. This could result in a significant reduction of the requirements for a future telescope network, with respect to what would have been required with the previously known algorithm for correlation and orbit determination.Comment: 20 pages, 8 figure

VAS Demonstration Sounding Workshop: The Proceedings of a satellite sounding workshop

Retrieval techniques that yield satellite derived temperature and moisture profiles are considered, with emphasis on TIROS-N and VISSR atmospheric sounder measurements. Topics covered include operational sounding, colocation concepts, correcting cloud errors, and the First GARP Global Experiment

Estimation of soil and vegetation temperatures with multiangular thermal infrared observations: IMGRASS, HEIFE, and SGP 1997 experiments

The potential of directional observations in the thermal infrared region for land surface studies is a largely uncharted area of research. The availability of the dual-view Along Track Scanning Radiometer (ATSR) observations led to explore new opportunities in this direction. In the context of studies on heat transfer at heterogeneous land surfaces, multiangular thermal infrared (TIR) observations offer the opportunity of overcoming fundamental difficulties in modeling sparse canopies. Three case studies were performed on the estimation of the component temperatures of foliage and soil. The first one included the use of multi-temporal field measurements at view angles of 0°, 23° and 52°. The second and third one were done with directional ATSR observations at view angles of 0° and 53° only. The first one was a contribution to the Inner-Mongolia Grassland Atmosphere Surface Study (IMGRASS) experiment in China, the second to the Hei He International Field Experiment (HEIFE) in China and the third one to the Southern Great Plains 1997 (SGP 1997) experiment in Oklahoma, United States. The IMGRASS experiment provided useful insights on the applicability of a simple linear mixture model to the analysis of observed radiance. The HEIFE case study was focused on the large oasis of Zhang-Ye and led to useful estimates of soil and vegetation temperatures. The SGP 1997 contributed a better understanding of the impact of spatial heterogeneity on the accuracy of retrieved foliage and soil temperatures. Limitations in the approach due to varying radiative and boundary layer forcing and to the difference in spatial resolution between the forward and the nadir view are evaluated through a combination of modeling studies and analysis of field data

Carrier-phase GNSS attitude determination and control for small UAV applications

As part of our recent research to assess the potential of low-cost navigation sensors for Unmanned Aerial Vehicle (UAV) applications, we investigated the potential of carrier-phase Global Navigation Satellite System (GNSS) for attitude determination and control of small size UAVs. Recursive optimal estimation algorithms were developed for combining multiple attitude measurements obtained from different observation points (i.e., antenna locations), and their efficiencies were tested in various dynamic conditions. The proposed algorithms converged rapidly and produced the required output even during high dynamics manoeuvres. Results of theoretical performance analysis and simulation activities are presented in this paper, with emphasis on the advantages of the GNSS interferometric approach in UAV applications (i.e., low cost, high data-rate, low volume/weight, low signal processing requirements, etc.). The simulation activities focussed on the AEROSONDE UAV platform and considered the possible augmentation provided by interferometric GNSS techniques to a low-cost and low-weight/volume integrated navigation system (presented in the first part of this series) which employed a Vision-Based Navigation (VBN) system, a MicroElectro-Mechanical Sensor (MEMS) based Inertial Measurement Unit (IMU) and code-range GNSS (i.e., GPS and GALILEO) for position and velocity computations. The integrated VBN-IMU-GNSS (VIG) system was augmented using the inteferometric GNSS Attitude Determination (GAD)sensor data and a comparison of the performance achieved with the VIG and VIG/GAD integrated Navigation and Guidance Systems (NGS) is presented in this paper. Finally, the data provided by these NGS are used to optimise the design of a hybrid controller employing Fuzzy Logic and Proportional-Integral-Derivative (PID) techniques for the AEROSONDE UAV

Three-D multilateration: A precision geodetic measurement system

A technique of satellite geodesy for determining the relative three dimensional coordinates of ground stations within one centimeter over baselines of 20 to 10,000 kilometers is discussed. The system is referred to as 3-D Multilateration and has applications in earthquake hazard assessment, precision surveying, plate tectonics, and orbital mechanics. The accuracy is obtained by using pulsed lasers to obtain simultaneous slant ranges between several ground stations and a moving retroreflector with known trajectory for aiming the lasers