Orbit determination and prediction for Beidou GEO satellites at the time of the spring/autumn equinox

Geostationary(GEO) satellites form an indispensable component of the constellation of Beidou navigation system(BDS). The ephemerides, or predicted orbits of these GEO satellites(GEOs), are broadcast to positioning, navigation, and timing users. User equivalent ranging error(UERE) based on broadcast message is better than 1.5 m(root formal errors: RMS) for GEO satellites. However, monitoring of UERE indicates that the orbital prediction precision is significantly degraded when the Sun is close to the Earth's equatorial plane(or near spring or autumn Equinox). Error source analysis shows that the complicated solar radiation pressure on satellite buses and the simple box-wing model maybe the major contributor to the deterioration of orbital precision. With the aid of BDS' two-way frequency and time transfer between the GEOs and Beidou time(BDT, that is maintained at the master control station), we propose a new orbit determination strategy, namely three-step approach of the multi-satellite precise orbit determination(MPOD). Pseudo-range(carrier phase) data are transformed to geometric range(biased geometric range) data without clock offsets; and reasonable empirical acceleration parameters are estimated along with orbital elements to account for the error in solar radiation pressure modeling. Experiments with Beidou data show that using the proposed approach, the GEOs' UERE when near the autumn Equinox of 2012 can be improved to 1.3 m from 2.5 m(RMS), and the probability of user equivalent range error(UERE)2.0 m can be improved from 50% to above 85%.     

Methods of rapid orbit forecasting after maneuvers for geostationary satellites

A geostationary (GEO) satellite may serve as a navigation satellite, but there is a problem that maneuvers frequently occur and the forces are difficult to model. Based on the technique of determining satellite orbits by transfer, a predicted orbit with high accuracy may be achieved by the method of statistical orbit determination in case of no maneuver force. The predicted orbit will soon be invalid after the maneuver starts, and it takes a long time to get a valid orbit after the maneuver ends. In order to improve ephemeris usability, the method of rapid orbit forecasting after maneuvers is studied. First, GEO satellite movement is analyzed in case of maneuvers based on the observation from the orbit measurement system by transfer. Then when a GEO satellite is in the free status just after maneuvers, the short arc observation is used to forecast the orbit. It is assumed that the common system bias and biases of each station are constant, which can be obtained from orbit determination with long arc observations. In this way, only 6 orbit elements would be solved by the method of statistical orbit determination, and the ephemeris with high accuracy may be soon obtained. Actual orbit forecasting with short arc observation for SINOSAT-1 satellite shows that, with the tracking network available, the precision of the predicted orbit (RMS of O-C) can reach about 5 m with 15 min arc observation, and about 3 m with 30 min arc observation. Supported by the National High Technology Research and Development Program of China (Grant No. 2006AA12Z322), the National Basic Research Program of China (Grant No. 2007CB815503), and the West Light Program of Chinese Academy of Sciences (Grant No. 2007LH01)     

An analysis of the wide area differential method of geostationary orbit satellites

This work aims to obtain a wide area differential method for geostationary orbit (GEO) constellation. A comparison between the dilution of precision (DOP) of four-dimensional (4D) calculation including satellite clock errors and ephemeris errors and that of three-dimensional (3D) calculation only including ephemeris errors with the inverse positioning theory of GPS shows the conclusion that all the 3D PDOPs are greatly reduced. Based on this, a basic idea of correcting satellite clock errors and ephemeris errors apart is put forward, and moreover, a specific method of separation is proposed. Satellite clock errors are separated in a master station with time synchronization, and all the remaining pseudo-range errors after the satellite clock errors have been deducted are used to work out ephemeris corrections of all GEO satellites. By a comparative analysis of user positioning accuracy before and after differential, the wide area differential method is verified to be quite valid for GEO constellation. Supported by the National Natural Science Foundation of China (Grant No. 10778715), the National Key Basic Research Development Program of China (Grant No. 2007CB815502), and the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 08B039)     

Precise orbit determination of a maneuvered GEO satellite using CAPS ranging data

Wheel-off-loadings and orbital maneuvers of the GEO satellite result in additional accelerations to the satellite itself. Complex and difficult to model, these time varying accelerations are an important error source of precise orbit determination (POD). In most POD practices, only non-maneuver orbital arcs are treated. However, for some applications such as satellite navigation RDSS services, uninterrupted orbital ephemeris is demanded, requiring the development of POD strategies to be processed both during and after an orbital maneuver. We in this paper study the POD for a maneuvered GEO satellite, using high precision and high sampling rate ranging data obtained with Chinese Area Positioning System (CAPS). The strategy of long arc POD including maneuver arcs is studied by using telemetry data to model the maneuver thrust process. Combining the thrust and other orbital perturbations, a long arc of 6 days’ CAPS ranging data is analyzed. If the telemetry data are not available or contain significant errors, attempts are made to estimate thrusting parameters using CAPS ranging data in the POD as an alternative to properly account for the maneuver. Two strategies achieve reasonably good data fitting level in the tested arc with the maximal position difference being about 20 m. Supported by the National Natural Science Foundation of China (Grant No. 10703011) and the Science & Technology Commission of Shanghai Municipality of China (Grant No. 06DZ22101)     

A simplex method for the orbit determination of maneuvering satellites

A simplex method of orbit determination (SMOD) is presented to solve the problem of orbit determination for maneuvering satellites subject to small and continuous thrust. The objective function is established as the sum of the nth powers of the observation errors based on global positioning satellite (GPS) data. The convergence behavior of the proposed method is analyzed using a range of initial orbital parameter errors and n values to ensure the rapid and accurate convergence of the SMOD. For an uncontrolled satellite, the orbit obtained by the SMOD provides a position error compared with GPS data that is commensurate with that obtained by the least squares technique. For low Earth orbit satellite control, the precision of the acceleration produced by a small pulse thrust is less than 0.1% compared with the calibrated value. The orbit obtained by the SMOD is also compared with weak GPS data for a geostationary Earth orbit satellite over several days. The results show that the position accuracy is within 12.0 m. The working efficiency of the electric propulsion is about 67% compared with the designed value. The analyses provide the guidance for subsequent satellite control. The method is suitable for orbit determination of maneuvering satellites subject to small and continuous thrust.     

Orbit determination and prediction accuracy analysis for a regional tracking network

China's COMPASS satellite navigation system relies on a regional tracking network to provide navigation services. Limited by its geographic border,the regional network is able to cover only 30% of the medium-earth-orbits(MEO). Accuracy of determined and predicted orbits is not able to satisfy system requirements if the tracking data processing strategy for global tracking network processing is used for the regional network. Two major error sources for orbital prediction are accuracy of initial orbital elements and dynamical modeling. To achieve better prediction accuracy,we propose a two-step orbit determination and prediction strategy. For step 1,only solar radiation pressure(SRP) parameters are estimated along with the orbital elements and other parameters; for step 2,all parameters are estimated but the SRP parameters are tightly constrained to their step 1 estimates. Experimenting with data from a regional GPS network,we conclude for orbital prediction using the proposed two-step strategy,the average user range error(URE) for 24-h prediction arcs is better than 0.6 m.     

Experimental test of the variability ofG using Viking lander ranging data

Results are presented from the analysis of solar system astrometric data, notably the range data to the Viking landers on Mars. A least-squares fit of the parameters of the solar system model to these data limits a simple time variation in the effective Newtonian gravitational constant to (0.2 ± 0.4) × 10^–11 year^–1 and a rate of drift of atomic clocks relative to the implicit clock of relativistic dynamics to (0.1 ± 0.8) × 10^–11 year^–1. The error limits quoted are the result of uncertainties in the masses of the asteroids.This paper is reprinted with minor editorial modifications fromPhysical Review Letters,51, 1609 (1983).     

The effect of the relativistic transformation law of angles on laser ranging of satellites moving in circular orbits equipped with a single retroreflector

It is shown that due to the relativistic transformation law of angles, a laser pulse reflected from a moving retroreflector propagates not strictly back, but at a small angle to the direction of the laser station. For this reason, the ray located on the periphery of a pulse reaches the receiving telescope of the laser station instead of the central ray of a pulse. As a result, the flux of electromagnetic energy received by the laser station is certainly less than the flux of energy in the vicinity of the central ray. The energy flux attenuation coefficient is assessed on the basis of numerical analysis. It is shown that if the receiving telescope is separated from the laser station in order to be mobile and is moving along the Earth’s surface so that the center of each spot formed by a pulse of the reflected light hits the telescope, then the electromagnetic energy flux during laser probing of the satellite will be higher by more than 100 times in comparison with the energy flux received by the stationary telescope of the laser station. From our study it follows that the maximum speed of motion of the centers of spots on the Earth’s surface does not exceed 8 km/h.     

Orbit determination and time synchronization for a GEO/IGSO satellite navigation constellation with regional tracking network

Aiming at regional services,the space segment of COMPASS (Phase I) satellite navigation system is a constellation of Geostationary Earth Orbit (GEO),Inclined Geostationary Earth Orbit (IGSO) and Medium Earth Orbit (MEO) satellites.Precise orbit determination (POD) for the satellites is limited by the geographic distribution of regional tracking stations.Independent time synchronization (TS) system is developed to supplement the regional tracking network,and satellite clock errors and orbit data may be obtai...     

Line shapes (absorption coefficients) for satellites and inversion of the data to obtain interaction potentials

Line shapes for cesium broadened by xenon and neopentane have been measured in an absorption cell. The growth of the red satellites. both primary and secondary, were studied on the first five principal series doublets and on the first S - D forbidden doublet. An inversion scheme based on a nearest-neighbor density was employed to invert the measured line shapes and obtain difference potential estimates. It is apparent from the inversion scheme that minor inflections in the difference potential map into strong features in the frequency plane and that contrary to popular assumption, absolute extrema may not be necessary for satellite interpretation. Strength effects observed on the forbidden satellites also demonstrate that the radial dependence of the dipole moment must be accounted for in certain cases.     

Fluorescence tomography with simulated data based on the equation of radiative transfer

The quantification of a nonuniform quantum yield or fluorophore absorption distribution is of major interest in molecular imaging of biological tissue. We introduce what is believed to be the first fluorescence image reconstruction algorithm based on the equation of radiative transfer that recovers the spatial distribution of light-emitting fluorophores inside a highly scattering medium from measurements made on the surface of the medium. We obtain images of either the quantum yield or the fluorophore absorption.     

A new method for determination of satellite orbits by transfer

The original idea of a new method for determination of satellite orbits by transfer is from Two-Way Satellite Time and Frequency Transfer (TWSTFT). The original method is called “determination of satellite orbit by transfer”. The method is not only for determination of satellite orbit but also for the time transfer with high accuracy and precision. The advantage is that the accuracy and the precision for determination of satellite orbit are very high and the new method is favorable for various applications. The combination of various signals disseminated and received forms various modes of satellite orbit determinations. If receivers at stations receive the own station-disseminated signals via a satellite transponder, it forms an orbit determination mode called “receiving the own station-disseminated signals mode”. If receivers at all stations receive the signals disseminated from the master station via satellite transponders, it forms an orbit determination mode called “receiving the master station-disseminated signals mode”. If all of receivers at stations receive all stations-disseminated signals via satellite transponders, it forms an orbit determination mode called “receiving all stations-disseminated signals mode”. Also there are other combinations of signals for satellite orbit determination. For different orbit determination modes with different signal combinations, their rigorous formulae of processing are hereby presented in this paper. The accurate and the precise satellite orbit determination for both of the modes, “receiving the own station-disseminated signals mode” and “receiving the master station-disseminated signals mode” is attempted. It shows that the accuracy and precision for both of modes are nearly the same, the ranging accuracy is better than 1 cm, and the observation residuals of satellite orbit determination are better than 9 cm in the observation duration of 1 day. Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815503100453001)     

星载激光测距合作目标的光学设计

运行于空间轨道的角反射器由于受相对速度的影响,必须进行速差补偿。针对轨道高度为20000km的角反射器,确定了能够接受的直角面平面度;针对几何光学方法速差补偿的不准确,运用衍射原理,对速差补偿的效果按角差的不同进行搜索,得到了比较理想的结果,确定了角反射器的参数。     

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.     

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

The quality of DOSY NMR data can be improved by careful pre-processing techniques. Baseline drift, peak shift, and phase shift commonly exist in real-world DOSY NMR data. These phenomena seriously hinder the data analysis and should be removed as much as possible. In this paper, a series of preprocessing operations are proposed so that the subsequent multivariate curve resolution can yield optimal results. First, the baseline is corrected according to a method by Golotvin and Williams. Next, frequency and phase shift are removed by a new combination of reference deconvolution (FIDDLE), and a method presented by Witjes et al. that can correct several spectra simultaneously. The corrected data are analysed by the combination of multivariate curve resolution with non-linear least square regression (MCR-NLR). The MCR-NLR method turns out to be more robust and leads to better resolution of the pure components than classic MCR.     

Billiards with Pockets: A Separation Principle and Bound for the Number of Orbit Types

 We introduce and prove a Separation Principle, similar in form to the familiar Uncertainty Principle of quantum mechanics, which separates the position and direction of any two phase points on distinct unfoldings of (non-parallel) trajectories on a polygonal billiard table with pockets. Applying this principle, we demonstrate that the number of orbit types (that is, classes of trajectories, up to parallelism) on a polygonal billiard table with area A and pockets of area a is strictly bounded above by . More generally, the same bound applies to any compact polyhedral surface with pockets at its vertices. If the boundary is empty (so that billiard trajectories are just geodesics), the bound is reduced by a factor of two to . We believe the Separation Principle will also have fundamental applications to other problems in the theory of billiards and related dynamical systems. Received: 28 December 2001 / Accepted: 9 April 2002 Published online: 4 September 2002     

Comparison of wire and fiber optics data transfer systems for large military aircraft

Methods for comparing the life-cycle cost of fiber optics and wire data transfer systems on large military aircraft are established. Using the B-1 as an example, the applicability of fiber optics to avionics/electrical systems on large aircraft is identified. Conceptual fiber optics data transfer systems are described. The present wire and the conceptual fiber optics designs form a basis for computerized lifecycle cost comparisons. Sensitivity analyses and cost trade-offs to determine cost drivers in the application of fiber optics are described. Results show that significant cost benefits can be gained by the implementation of fiber optics in newly designed data transfer subsystems having data rates in excess of 2-3 Mbits/sec.