Satellite State Vector Research Articles

Periodic orbits of the perturbed relative motion

This paper presents a novel dynamical system for the perturbed relative motion of deputy satellite. The governing equations are derived in the LVLH frame under the second zonal harmonic coefficient effect of the Earth on both chief and deputy satellites. An extended numerical analysis on the deputy satellite motion is performed, where the initial state vector of deputy satellite and eccentricity of chief satellite are used as initial conditions for finding its own periodic orbits. The interior loops of periodic orbits are obtained using numerical integrator RKEOM. Such orbits are analysed for different parameters and their stability are also discussed, where these orbits have considerable importance in the resonance analysis of motion The second zonal harmonic coefficient effect on the periodicity, initial position, initial true anomaly is studied, alongside exploring these orbits with one, two and three loops. Furthermore, a single variable nonlinear regression model is developed to predict initial true anomaly using eccentricity of chief satellite’s orbit.

Geolocation accuracy improvement for NovaSAR-1 imagery acquired through TLE orbit

NovaSAR-1 is a small S-band Synthetic Aperture Radar (SAR) mission mainly for land and maritime applications. Since SAR has side-looking geometry, thus slant and ground range SAR products have geometric distortions. To correct these geometric distortions, orthorectification needs to be done using SAR Rigorous Sensor Model (RSM) algorithm and Digital Elevation Model (DEM). NovaSAR-1 provides the satellite state vectors either through a Global Positioning System (GPS) or through a Two-Line Element (TLE) orbit source. It is observed that, after orthorectification, it shows poor geolocation accuracy (200 m to 9000 m) for the TLE orbit source. In this paper, geolocation accuracy improvement has been done for NovaSAR-1 ground range imagery acquired through TLE orbit source by generating orthorectified products using SAR Rigorous Sensor Model (RSM) algorithm and Ground control point (GCP). After orthorectification, geolocation accuracy of the NovaSAR-1 imagery acquired through TLE orbit source is reduced to less than 10 m.

The orbits of Triton and Nereid and the pole orientation of Neptune from Voyager,HubbleSpace Telescope, and Earth-based astrometry in 1847–2020

Context.New observations and new planetary and satellite ephemerides provide opportunities to improve the ephemerides for Triton and Nereid as well as relevant parameters. In particular, the observations include a lot of new accurate Earth-based positions reduced withGaiaastrometic catalogs and accurate positions obtained fromHubbleSpace Telescope.Aims.We aim to reliably improve the ephemerides for Triton and Nereid along with some parameters by using all the available astrometric data from 1847 to 2020 and by updating the dynamical model. We also aim to improve the geometrical descriptions based on the improved orbits of the two satellites and the pole orientation of Neptune.Methods.The orbits of Triton and Nereid are determined by fitting dynamical and observational model parameters to observations in a weighted least-squares sense. The dynamical model makes use of the new ephemerides from Jet Propulsion Laboratory for planets, DE440, and those for the inner satellites of Neptune, NEP090. For completeness, in addition to the gravitational effects considered by NEP081, the model also includes perturbations from inner satellites and a revised model for the motion of the pole orientation of Neptune. Moreover, model simplifications are investigated to speed up the motion equation integration. Since the pole orientation angles of Neptune at epoch are possibly improvable according to the preliminary post-fit sensitivity analysis, these angles are adjusted together with the satellite state vectors at epoch. Linear mapping of the covariance matrix is a measure of formal uncertainties of our orbit and pole solutions. However, to obtain more reliable accuracy estimations, it is necessary to consider the uncertainties in the observations and the unadjusted model parameters. To accomplish this, a method (BR-RS) that performs bootstrap resampling of observations (BR) and random sampling of unadjusted model parameters (RS) is used. Analytical representations are fitted to the orbit and pole solutions to provide their geometric descriptions.Results.The model we use can be fitted to the observations with their estimated accuracies. The new ephemerides,FORCES-8-MAIN-2020, covering years 1600–2650 are available online in SPICE format. The orbits are well determined with the orbital uncertainties expected to be within 200 km (about 10 mas as seen from the Earth) for Triton and 1000 km (50 mas) for Nereid for the next 100 yr as estimated by the BR-RS method. In particular, the correction in the Nereid mean orbit motion from the NEP081 solution is +4.′′9 yr−1, and has a BR-RS uncertainty of 0.′′24 yr−1. In the fitting process, we also determine the pole orientation of Neptune. At the initial epoch 1989 September 1 TDB, the right ascension and declination of the new pole orientation referred to the International Celestial Reference System areαp= 299.°339 ± 0.°012 (formal)∕ ± 0.°014 (BR-RS) andδp= 42.°985 ± 0.°016 (formal)∕ ± 0.°045 (BR-RS), respectively. From 1800 to 2200, the motion of the pole orientation is well constrained with a BR-RS uncertainty of about 0.°01–0.°05. We also provide geometrical descriptions for the new orbits and pole orientation.

Research on the method of determining satellite state vector based on Kepler orbital parameters

to simplify the process of satellite orbit determination, can use limited conditions known to the calculation of satellite orbit dynamic state vector to determine satellite position to implement the standardization of satellite orbit, this paper introduces the satellite state vector at any time using the Kepler orbital parameters method, the calculation method of Kepler orbit parameters are mostly only for satellite without disturbing force movement. This paper is based on the three-point method which is used to calculate the orbit parameters of Kepler satellite in the case of satellite unphotographed.

Fault-tolerant estimation of satellite orbital states

This paper is devoted to global positioning system (GPS)-based fault-tolerant satellite orbital states estimation which is used for the pseudo-ranging model. GPS is widely used by many researchers to determine the orbit state vectors of satellites, but errors in GPS measurements can cause major errors in satellite location detection. Therefore, there is a need for an architecture that will resist possible measurement errors and GPS malfunctions. This study aims to present the novel approaches to tolerate the errors that may take place in GPS measurements. The satellite localisation has been detected via a pseudo-ranging model between four GPS satellites and the target satellite. The Keplerian equations and orbit elements are used for the satellite dynamic model with orbital J2 perturbation which is due to the flattened shape of the earth is taken into account via the extended Kalman filter (EKF) algorithms. The reconfigurable and the adaptive version of fault-tolerant localisation architecture eliminate the GPS measurement errors during estimating satellite position vectors. The comparison of the prediction architectures of the fault tolerant satellite state vectors originally proposed. At the same time, it is possible to use fault tolerant architectures designed to detect whether GPS satellites are malfunctioning or not.

Modeling Orbital Error in InSAR Interferogram Using Frequency and Spatial Domain Based Methods

Synthetic Aperture Radar Interferometry (SAR, InSAR) is increasingly being used for deformation monitoring. Uncertainty in satellite state vectors is considered to be one of the main sources of errors in applications such as this. In this paper, we present frequency and spatial domain based algorithms to model orbital errors in InSAR interferograms. The main advantage of this method, when applied to the spatial domain, is that the order of the polynomial coefficient is automatically determined according to the features of the orbital errors, using K-cross validation. In the frequency domain, a maximum likelihood fringe rate estimate is deployed to resolve linear orbital patterns in strong noise interferograms, where spatial-domain-based algorithms are unworkable. Both methods were tested and compared with synthetic data and applied to historical Environmental Satellite Advanced Synthetic Aperture Radar (ENVISAT ASAR) sensor and modern instruments such as Gaofen-3 (GF-3) and Sentinel-1. The validation from the simulation demonstrated that an accuracy of ~1mm can be obtained under optimal conditions. Using an independent GPS measurement that is discontinuous from the InSAR measurement over the Tohoku-Oki area, we found a 31.45% and 73.22% reduction in uncertainty after applying our method for ASAR tracks 347 and 74, respectively.

Application of Gravity Gradients in the Process of GOCE Orbit Determination

The possibility of improving the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission satellite orbit using gravity gradient observations was investigated. The orbit improvement is performed by a dedicated software package, called the Orbital Computation System (OCS), which is based on the classical least squares method. The corrections to the initial satellite state vector components are estimated in an iterative process, using dynamic models describing gravitational perturbations. An important component implemented in the OCS package is the 8th order Cowell numerical integration procedure, which directly generates the satellite orbit. Taking into account the real and simulated GOCE gravity gradients, different variants of the solution of the orbit improvement process were obtained. The improved orbits were compared to the GOCE reference orbits (Precise Science Orbits for the GOCE satellite provided by the European Space Agency) using the root mean squares (RMS) of the differences between the satellite positions in these orbits. The comparison between the improved orbits and the reference orbits was performed with respect to the inertial reference frame (IRF) at J2000.0 epoch. The RMS values for the solutions based on the real gravity gradient measurements are at a level of hundreds of kilometers and more. This means that orbit improvement using the real gravity gradients is ineffective. However, all solutions using simulated gravity gradients have RMS values below the threshold determined by the RMS values for the computed orbits (without the improvement). The most promising results were achieved when short orbital arcs with lengths up to tens of minutes were improved. For these short arcs, the RMS values reach the level of centimeters, which is close to the accuracy of the Precise Science Orbit for the GOCE satellite. Additional research has provided requirements for efficient orbit improvement in terms of the accuracy and spectral content of the measured gravity gradients.

Translation Dynamical Nonlinear Models in Perturbed Keplerian Conditions For a Geostationary Satellite

The dynamics of a GEO satellite will be studied in this work to obtain a dynamical model as accurate as possible. This model will be obtained in terms of Gauss' variation of osculating parameter (VOP) equations containing the environmental perturbing accelerations, which are traditionally used to plan the station keeping maneuvers. The idea is to implement a controller for geostationary station keeping purposes based on a model written in terms of osculating orbital elements instead of averaged elements. Such a controller plans in an automatic way the station keeping (SK) maneuvers and it could be integrated on board in view of autonomous station keeping control loop. The Geostationary Earth Orbit (GEO) satellites maintain an essentially fixed position with respect to the surface of the Earth. This is made possible by inserting the spacecraft into a circular, equatorial orbit at an altitude of roughly 36000 km. At this altitude, if the main environmental disturbing forces (the Earth's non-spherical gravity attraction, the Moon's and Sun's gravity attraction and the solar radiation pressure) are neglected except the Kepler attraction of the Earth, the geostationary motion is ideal. The satellite remains fixed with respect to the surface of the Earth. The mean motion n matches the Earth's rotation rate  of one revolution per 23 hours and 56 minutes. In presence of perturbations, it is a common practice to control a GEO satellite actively via station keeping maneuvers such that it stays confined in a box of 100-150 km width around a nominal geostationary longitude and latitude (1). Traditionally this is done with an open loop control technique based on a dynamical model of the satellite state vector subject to the only environmental perturbing forces and on a separate dynamical model taking into account the only thrust effects. Moreover, this latter model is derived supposing to use a chemical propulsion system characterized by high thrusts and very short thrust durations relative to the orbital period. These impulsive thrust hypotheses lead to assume that maneuvers induce jumps in the velocity part of the state vector but not in the position part. The GEO station keeping problem is thus dealt with in a discrete way, without considering spacecraft acceleration but only velocity and position vectors. With a view to substitute chemical propulsion systems with electrical ones, the solution approaches of the GEO station keeping problem should become continuous, in order to gain benefit from the technology change. A GEO satellite dynamics model has to be obtained taking into account all the perturbing forces (environmental or not) acting on the spacecraft. In this paper, we explain in detail the nonlinear dynamical model used to design the station keeping controller and the analytical approximations done to implement this

A New Method of Removing Unsynchronized Signal for ScanSAR Interferometry

We have analyzed most of the commonly used burst-mode focusing algorithms and chose the one that can be easily combined with unsynchronized-signal removal. In order to remove the unsynchronized signal in scanning synthetic aperture radar (ScanSAR) interferometry, we calculate the burst synchronization using satellite state vectors at first. Then, based on the focusing algorithm chosen and the synchronization calculated, we propose a method to remove the unsynchronized signal. The method rejects the unsynchronized phase and keeps all of the magnitude information. It has been tested with simulated Envisat Advanced Synthetic Aperture Radar ScanSAR data, and the result demonstrated that the method could effectively remove the unsynchronized signal for ScanSAR interferometric processing.

Terrain-flattened gamma nought Radarsat-2 backscatter

Radarsat-2 offers a variety of new modes and capabilities. We present results from rigorous application of geometric and radiometric calibration to backscatter values, enabling comparisons between different modes. First, the system's a priori geometric accuracy was tested (tiepoint free) by comparing the measured positions of corner reflectors in ultrafine images with predicted locations calculated based on the satellite state vectors and radar timing annotations. Second, the geometric accuracy of the dual-pol ScanSAR SCNB mode was tested by correlating each backscatter image to a radar image simulation calculated using the same product annotations. Third, the radar image simulation was used to normalize the backscatter values in both polarisations, generating terrain-flattened gamma nought values that were then terrain geocoded. Fourth, the available ascending and descending SCNB image pair was overlaid with and without such radiometric terrain correction applied. The advantages gained by using terrain-flattened gamma nought are discussed.

Precise orbit determination for the FORMOSAT-3/COSMIC satellite mission using GPS

The joint Taiwan–US mission FORMOSAT-3/ COSMIC (COSMIC) was launched on April 17, 2006. Each of the six satellites is equipped with two POD antennas. The orbits of the six satellites are determined from GPS data using zero-difference carrier-phase measurements by the reduced dynamic and kinematic methods. The effects of satellite center of mass (COM) variation, satellite attitude, GPS antenna phase center variation (PCV), and cable delay difference on the COSMIC orbit determination are studied. Nominal attitudes estimated from satellite state vectors deliver a better orbit accuracy when compared to observed attitude. Numerical tests show that the COSMIC COM must be precisely calibrated in order not to corrupt orbit determination. Based on the analyses of the 5 and 6-h orbit overlaps of two 30-h arcs, orbit accuracies from the reduced dynamic and kinematic solutions are nearly identical and are at the 2–3 cm level. The mean RMS difference between the orbits from this paper and those from UCAR (near real-time) and WHU (post-processed) is about 10 cm, which is largely due to different uses of GPS ephemerides, high-rate GPS clocks and force models. The kinematic orbits of COSMIC are expected to be used for recovery of temporal variations in the gravity field.

Tide model errors and GRACE gravimetry: towards a more realistic assessment

SUMMARY The manner in which errors in tide models affect monthly gravity solutions from GRACE satellite data is re-examined. We perform a complete simulation of GRACE gravity estimation, including allowance for accelerometer calibrations and satellite state-vector adjustment. Errors in monthly geoid estimates are for most regions of a order of 0.5 mm, or roughly 1 cm of equivalent water height when smoothed over radii of 600 km. In polar regions where ocean tide models are suspect, errors can grow significantly larger: over 2 mm in geoid height, although over very localized regions. Errors from diurnal tides tend to cancel, but they are not completely eliminated, inducing geoid errors of the order of 0.3 mm. The currently accepted GRACE total error budget is roughly an order of magnitude larger than the component arising from tide modelling errors.

Correction of the Satellite's State Vector and the Atmospheric Excess Path Delay in the SAR Interferometry

Correction of the Satellite's State Vector and the Atmospheric Excess Path Delay in the SAR Interferometry

Accurate Orbit Determination from Short-Arc Dense Observational Data

Requirements have existed for several decades for highly accurate satellite orbits. With increased computer power, simplified analytical techniques have lost most of their competitive edge and numerical techniques are experiencing wide-spread popularity. When coupled with increased accuracy requirements from commercial satellites owners and accurate computations for debris and close approach for the International Space Station, a reliable method must be found to form highly-accurate satellite state vectors. This paper explores one approach using dense observational data from short-arcs of geographically distributed sensor sites. In particular, dense observations (consisting of one observation per second for about two minutes) are analyzed to determine the accuracy that can be achieved via high fidelity, numerical, orbit-determination techniques.

Spectral analyses of the drag-like coefficient Cd from LAGEOS data

From the global SLR data of LAGEOS between 1983 and 1986 inclusive, two series for the drag-like coefficient C D were obtained, the first one using simultaneous estimation of the initial state vector of satellite, C D and the solar radiation pressure coefficient C R for each 15-day arc, the second using multiarc estimation with 10-day orbital state, C D, C R and 5-day ERP. The Marple algorithm for AR spectrum was applied to both series, the first series giving the periods 475.5, 365.2, 216.4, 183.4, 69.0, 39.9 and 32.25 d, the second, 173.3, 152.8, 127.6, 61.3 and 27.64 d. A comparative analysis shows that the periods 475.5, 365.5 and 183.4 d in the first series are a reflection of systematic differences between the x p components of the polar motion derived from the BIH and the SLR data.

Comparative studies of atmospheric density models used for earth satellite orbit estimation

The results of a comparative orbit determination study of four global atmospheric density models (modified Harris-Priester, Jacchia-Roberts, Mass Spectrometer/Incoherent Scatter, and Simple Exponential Model) are presented. The primary objective of this study was quantitative evaluation of the definitive orbit determination consistency and accuracy obtained using these models as measured by the maximum position differences that occur during solution overlap periods. A secondary objective was comparison of propagated ephemerides with definitive orbit solutions in order to evaluate predictive accuracies. The results indicate that, for satellites above 300 km, all four atmospheric density models produce comparable orbit determination accuracies when an atmospheric drag scaling factor and the satellite state vector are estimated during the orbit determination process.