Orbit Determination Techniques Research Articles

Observability-Aware Differential Dynamic Programming with Impulsive Maneuvers

In autonomous space systems, the reliability of navigation systems is essential. Observability in autonomous orbit determination techniques depends on the spacecraft’s orbital motion, making the design of autonomous navigation systems and orbital maneuvers a coupled process. This study develops a stable and efficient algorithm based on differential dynamic programming to design maneuver sequences that improve navigation performance. Our approach incorporates the Fisher information matrix into a cost function to quantify state observability and facilitates its convergence using a semi-analytic gradient and Hessian derived under impulsive maneuvers. Two numerical examples show the validity and effectiveness of our algorithm. The results indicate the stability and efficiency in determining maneuver sequences and the improvement of state estimation accuracy along an optimized trajectory. It is also applicable to other observability-aware optimal control problems because the algorithm is independent of specific systems.

Yere Eşlenik Uydularda Tümleşik Uzay Tabanlı Alıcılar Kullanarak Yörünge Belirleme

The use of space-born GNSS receiver onboard geosyncronous communication satellite is an effective alternative orbit determination technique compared to traditional methods, although the communication satellite operator and manufacturers need some proof. In this study, GPS-based range measurement via space-born receivers’ onboard communication satellite platforms was proposed for precise orbit determination of geostationary satellites. Thus this research investigates how proposed method can be applied to obtain reliable and sustainable results. The analysis was performed to find out the accuracy and validity of the proposed method. Moreover, the results were compared with the simulation of four satellites’ orbital parameters at different orbital slots. The sequential process (SP) Kalman filter method was chosen to process the measured data. The processing method was kept the same for all analyses to investigate the gathered measurement data effects. The results show that the average position differences between the determined and actual orbit are 17.613 m, 13.637 m and 14.998 m, for in-track, cross-track, and radial direction. The average in-track, cross-track, and radial velocity differences are 0.339 cm/s, 0.160 cm/s, and 0.066 cm/s respectively. The results show that the proposed method is approved in communication satellites orbit determination. The utilization of GPS satellites is a promising approach for geostationary satellite orbit determination. The communication satellites operators can utilize the GPS-based orbit determination with its benefits.

Analysis of Galileo five-frequency precise satellite clock estimation models and its effect on multi-frequency PPP

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) applications. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8–12% for triple-frequency models, and 19–27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi-frequency satellite clock offsets can be improved by 7–18% for dual-frequency PPP, 8–15% for triple-frequency PPP, 4–16% for five-frequency PPP. The positioning accuracy can be further improved by 11–28% for triple-frequency PPP and 7–20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.

Interferometric Orbit Determination System for Geosynchronous SAR Missions: Experimental Proof of Concept

Future Geosynchronous Synthetic Aperture Radar (GEOSAR) missions will provide permanent monitoring of continental areas of the planet with revisit times of less than 24 h. Several GEOSAR missions have been studied in the USA, Europe, and China with different applications, including water cycle monitoring and early warning of disasters. GEOSAR missions require unprecedented orbit determination precision in order to form focused Synthetic Aperture Radar (SAR) images from Geosynchronous Orbit (GEO). A precise orbit determination technique based on interferometry is proposed, including a proof of concept based on an experimental interferometer using three antennas separated 10–15 m. They provide continuous orbit observations of present communication satellites operating at GEO as illuminators of opportunity. The relative phases measured between the receivers are used to estimate the satellite position. The experimental results prove the interferometer is able to track GEOSAR satellites based on the transmitted signals. This communication demonstrates the consistency and feasibility of the technique in order to foster further research with longer interferometric baselines that provide observables delivering higher orbital precision.

On Autonomous Reconfiguration of SAR Satellite Formation Flight With Continuous Control

Satellites clusters for Earth observation purposes entail precise orbit monitoring and control to satisfy application needs efficiently. Fast technological progress in GNSS receivers, intersatellite communications/vision links, and propulsion technologies have inspired and fostered autonomous orbit determination and control techniques, allowing more efficient ground segment operations. Moreover, new distributed satellite missions have been enabled by autonomous formation flying, with unprecedented Earth observation potential. These missions may adopt varying observational modes associated with different relative orbital configurations and also transit among these modes as required by mission control. In this article, we consider a hypothetic distributed synthetic aperture radar (SAR) mission with a main SAR illuminator, as CONAE's SAOCOM 1 satellites, and one or more companions able to adopt different bistatic SAR geometries, enabling interferometry, tomography, or specular acquisition. To approach this problem, we formulate a basic task for any actively controlled companion satellite (deputy satellite) consisting of following a reference maneuver relative to the chief satellite orbit. This task is performed by means of a feedback control law based on newly introduced relative orbital elements (ROEs) and suitable to continuous actuators (e.g., electric propulsion) with bounded thrust. As a main result, we prove the asymptotic stability of the maneuver orbit tracking task for low Earth, nonequatorial, and near-circular chief orbits. This required a reformulation of the relative orbit tracking problem and the associated ROEs. A control allocation along the orbit is also proposed to reduce the propellant consumption and the transient time between SAR modes. The theoretical results are validated with simulated controlled transitions between different acquisition modes.

Updated Europa gravity field and interior structure from a reanalysis of Galileo tracking data

The Galileo radio tracking data were reanalysed exploiting the new knowledge of Jupiter obtained by the Juno mission, together with modern orbit determination techniques developed for the Cassini data analysis. Using Doppler data acquired during six encounters of Europa an updated gravity field of the moon was obtained, resulting in a value of C22 statistically different from the available literature. The new value suggests a thinner ice-water shell and a less dense interior.

Initial Orbit Determination and Event Reconstruction From Estimation of Particle Trajectories About (101955) Bennu.

The OSIRIS‐REx mission has observed multiple instances of particles being ejected from the surface of near‐Earth asteroid (101955) Bennu. The ability to quickly identify the particle trajectories and origins is necessary following a particle ejection event. Using proven initial orbit determination techniques, we can rapidly estimate particle trajectories and ejection locations. We present current results pertaining to the identification of particle tracks, an evaluation of the estimated orbits and the excess velocity necessary to induce the particle ejection from the surface, and the uncertainty quantification of the ejection location. We estimate energies per particle ranging from 0.03 to 11.03 mJ for the largest analyzed events and velocities ranging from 5 to 90 cm/s, though we exclude the highest‐velocity particles in this technique. We estimate ejection times for eight events and constrain six of the analyzed ejection events to have occurred between about 16:30 and 19:00 local solar time, with the largest events occurring between 16:30 and 18:05.

Statistical Orbit Determination Algorithm for Satellites in Indian Navigation Constellation (NavIC): Towards Extended Ephemeris Technology for NavIC Receiver

Abstract Ephemerides are essential for the satellite positioning in Global Navigation Satellite Systems (GNSS) user receivers. Acquisition of navigation data and ephemeris parameters are difficult in remote areas as well as in challenging environments. Statistical orbit determination techniques can help to predict the orbital parameters in the absence of navigation data. The present study is a first step towards the solution for generating orbital parameters and predicting the satellite positions in the absence of navigation data for satellites in NavIC constellation. The orbit determination algorithm predicted the satellite position using single station navigation data. The perturbations affecting the satellite orbits in NavIC constellation were also studied and an algorithm using perturbation force models is proposed for the satellites in NavIC constellation. Extended Kalman Filter (EKF) was used to address the non-linear dynamics model of the perturbation forces and distance of the ground station from the centre of Earth was used as measurement to solve the measurement equation. The satellite orbits were predicted up to 1 hour using the single station navigation data. The root mean square error (RMSE) of 12.59 m and 13.03 m were observed for NavIC satellites in Geosynchronous and Geostationary orbits, respectively, after 1 hour. The Kolmogorov-Smirnov test used to assess the goodness of fit of the proposed EKF algorithm for orbit prediction was found to be significant at 1% level of significance.

Improved GNSS-R Ocean Surface Altimetry With CYGNSS in the Seas of Indonesia

Ocean surface altimetry with GNSS reflectometry (GNSS-R) has the potential to improve the observation and retrieval of mesoscale ocean current flows by increasing the spatial density of ocean surface observations. The leading challenges in current GNSS-R altimetry investigations include precise delay retracking, correction of ionospheric effects, and spacecraft receiver positioning. Here, we present improved methods to account for these challenges. A reflection-model-based approach is presented for delay retracking that uses simulated delay-Doppler maps (DDMs) to retrieve the specular delay from measured DDMs. Global ionosphere maps are used to estimate the group delay effect along the direct and reflection paths. Precise orbit determination techniques are used to improve estimates of the receiving spacecraft position and reduce systematic intersatellite biases. We analyze altimetric height retrievals from two cases, strongly coherent or diffuse reflections. We study the residual systematic error signals with a focus on understanding the errors identified above. The strong coherent observations have narrow, symmetric delay waveforms and provide higher than average signal-to-noise ratio. The DDMs of diffuse observations, originate from relatively rough ocean surfaces and have the characteristic horse-shoe shape. Only measurements from the ocean and seas surrounding Indonesia are considered as this area provides a significant number of strongly coherent reflections. More than 50 000 single-point observations and week-long averaged results are presented to quantify the noise and systematic characteristics of the retrieved surface heights.

Status of Satellite Orbit Determination and Time Synchronization Technology for Global Navigation Satellite System

In the form of satellite ephemerides and clock parameters, the information of space datum and system time of one global navigation satellite system (GNSS) is transferred to users. With continuously updating of satellite payload such as high precision atomic clocks, monitoring and tracking techniques such as inter-satellite links, and data processing techniques, the accuracy and real-time performance of satellite ephemerides and clock products are steadily improved. Starting from December 27th, 2018, BeiDou Navigation System 3, or BDS-3 has been providing accurate and reliable basic positioning, navigation, and timing (PNT) services to users in the countries within the “one belt and one road”. This paper summarizes the challenges of precise orbit determination and time synchronization faced and specific solutions sought from the regional BDS-2 system to BDS-3 global system at the control segment. It is interesting to compare BDS with other GNSS systems in terms of technical characteristics. Finally, aiming at higher accuracy and more reliable PNT services, a road map of precise orbit determination and time synchronization technique for next generation navigation systems is discussed, which will lead to better and better global navigation satellite systems.

Solving Velocity Ambiguity for Pulse Doppler Radar Space Target Measurement

In order to solve the problem of severe velocity ambiguity for pulse Doppler radar high-speed space orbital targets measurement, a new velocity ambiguity resolution method based on the short arc orbit determination technique is presented in this paper. By means of a modified orbit determination model, this method can adopt the original radar measurements with the range-Doppler coupling term directly. It uses the numerical integration method to solve the differential equation of the state transition matrix and corrects the range-Doppler coupling term simultaneously, and then the optimal reference orbit is obtained by using the iterative least squares method. Finally, the velocity ambiguity is determined with the accurate reference velocity which can be calculated from the above reference orbit. The experimental results indicate that the proposed method can estimate the reference velocity accurately and satisfies the performance requirement of velocity ambiguity resolution.

Short arc orbit determination and imminent impactors in the Gaia era

Short-arc orbit determination is crucial when an asteroid is first discovered. In these cases usually the observations are so few that the differential correction procedure may not converge. We developed an initial orbit computation method, based on systematic ranging, which is an orbit determination technique that systematically explores a raster in the topocentric range and range-rate space region inside the admissible region. We obtained a fully rigorous computation of the probability for the asteroid that could impact the Earth within a few days from the discovery without any a priori assumption. We tested our method on the two past impactors, 2008 TC3 and 2014 AA, on some very well known cases, and on two particular objects observed by the European Space Agency Gaia mission.

Satellite laser ranging to low Earth orbiters: orbit and network validation

Satellite laser ranging (SLR) to low Earth orbiters (LEOs) provides optical distance measurements with mm-to-cm-level precision. SLR residuals, i.e., differences between measured and modeled ranges, serve as a common figure of merit for the quality assessment of orbits derived by radiometric tracking techniques. We discuss relevant processing standards for the modeling of SLR observations and highlight the importance of line-of-sight-dependent range corrections for the various types of laser retroreflector arrays. A 1–3 cm consistency of SLR observations and GPS-based precise orbits is demonstrated for a wide range of past and present LEO missions supported by the International Laser Ranging Service (ILRS). A parameter estimation approach is presented to investigate systematic orbit errors and it is shown that SLR validation of LEO satellites is not only able to detect radial but also along-track and cross-track offsets. SLR residual statistics clearly depend on the employed precise orbit determination technique (kinematic vs. reduced-dynamic, float vs. fixed ambiguities) but also reveal pronounced differences in the ILRS station performance. Using the residual-based parameter estimation approach, corrections to ILRS station coordinates, range biases, and timing offsets are derived. As a result, root-mean-square residuals of 5–10 mm have been achieved over a 1-year data arc in 2016 using observations from a subset of high-performance stations and ambiguity-fixed orbits of four LEO missions. As a final contribution, we demonstrate that SLR can not only validate single-satellite orbit solutions but also precise baseline solutions of formation flying missions such as GRACE, TanDEM-X, and Swarm.

Application of Semi-analytical Satellite Theory orbit propagator to orbit determination for space object catalog maintenance

Catalog maintenance for Space Situational Awareness (SSA) demands an accurate and computationally lean orbit propagation and orbit determination technique to cope with the ever increasing number of observed space objects. As an alternative to established numerical and analytical methods, we investigate the accuracy and computational load of the Draper Semi-analytical Satellite Theory (DSST). The standalone version of the DSST was enhanced with additional perturbation models to improve its recovery of short periodic motion. The accuracy of DSST is, for the first time, compared to a numerical propagator with fidelity force models for a comprehensive grid of low, medium, and high altitude orbits with varying eccentricity and different inclinations. Furthermore, the run-time of both propagators is compared as a function of propagation arc, output step size and gravity field order to assess its performance for a full range of relevant use cases. For use in orbit determination, a robust performance of DSST is demonstrated even in the case of sparse observations, which is most sensitive to mismodeled short periodic perturbations. Overall, DSST is shown to exhibit adequate accuracy at favorable computational speed for the full set of orbits that need to be considered in space surveillance. Along with the inherent benefits of a semi-analytical orbit representation, DSST provides an attractive alternative to the more common numerical orbit propagation techniques.

The global impact distribution of Near-Earth objects

Asteroids that could collide with the Earth are listed on the publicly available Near-Earth object (NEO) hazard web sites maintained by the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The impact probability distribution of 69 potentially threatening NEOs from these lists that produce 261 dynamically distinct impact instances, or Virtual Impactors (VIs), were calculated using the Asteroid Risk Mitigation and Optimization Research (ARMOR) tool in conjunction with OrbFit. ARMOR projected the impact probability of each VI onto the surface of the Earth as a spatial probability distribution. The projection considers orbit solution accuracy and the global impact probability. The method of ARMOR is introduced and the tool is validated against two asteroid-Earth collision cases with objects 2008 TC3 and 2014 AA. In the analysis, the natural distribution of impact corridors is contrasted against the impact probability distribution to evaluate the distributions’ conformity with the uniform impact distribution assumption. The distribution of impact corridors is based on the NEO population and orbital mechanics. The analysis shows that the distribution of impact corridors matches the common assumption of uniform impact distribution and the result extends the evidence base for the uniform assumption from qualitative analysis of historic impact events into the future in a quantitative way. This finding is confirmed in a parallel analysis of impact points belonging to a synthetic population of 10,006 VIs. Taking into account the impact probabilities introduced significant variation into the results and the impact probability distribution, consequently, deviates markedly from uniformity. The concept of impact probabilities is a product of the asteroid observation and orbit determination technique and, thus, represents a man-made component that is largely disconnected from natural processes. It is important to consider impact probabilities because such information represents the best estimate of where an impact might occur.

Orbital elements of the material surrounding comet 67P/Churyumov-Gerasimenko

We investigate the dust coma within the Hill sphere of comet 67P/Churyumov-Gerasimenko. Aims. We aim to determine osculating orbital elements for individual distinguishable but unresolved slow-moving grains in the vicinity of the nucleus. In addition, we perform photometry and constrain grain sizes. Methods. We performed astrometry and photometry using images acquired by the OSIRIS Wide Angle Camera on the European Space Agency spacecraft Rosetta. Based on these measurements, we employed standard orbit determination and orbit improvement techniques. Results. Orbital elements and effective diameters of four grains were constrained, but we were unable to uniquely determine them. Two of the grains have light curves that indicate grain rotation. Conclusions. The four grains have diameters nominally in the range 0.14–0.50 m. For three of the grains, we found elliptic orbits, which is consistent with a cloud of bound particles around the nucleus. However, hyperbolic escape trajectories cannot be excluded for any of the grains, and for one grain this is the only known option. One grain may have originated from the surface shortly before observation. These results have possible implications for the understanding of the dispersal of the cloud of bound debris around comet nuclei, as well as for understanding the ejection of large grains far from the Sun.

Systematic ranging and late warning asteroid impacts

We describe systematic ranging, an orbit determination technique suitable to assess the near-term Earth impact hazard posed by newly discovered asteroids. For these late warning cases, the time interval covered by the observations is generally short, perhaps a few hours or even less, which leads to severe degeneracies in the orbit estimation process. The systematic ranging approach gets around these degeneracies by performing a raster scan in the poorly-constrained space of topocentric range and range rate, while the plane of sky position and motion are directly tied to the recorded observations. This scan allows us to identify regions corresponding to collision solutions, as well as potential impact times and locations. From the probability distribution of the observation errors, we obtain a probability distribution in the orbital space and then estimate the probability of an Earth impact. We show how this technique is effective for a number of examples, including 2008 TC3 and 2014 AA, the only two asteroids to date discovered prior to impact.

Orbit Propagation and Determination of Low Earth Orbit Satellites

This paper represents orbit propagation and determination of low Earth orbit (LEO) satellites. Satellite global positioning system (GPS) configured receiver provides position and velocity measures by navigating filter to get the coordinates of the orbit propagation (OP). The main contradictions in real-time orbit which is determined by the problem are orbit positioning accuracy and the amount of calculating two indicators. This paper is dedicated to solving the problem of tradeoffs. To plan to use a nonlinear filtering method for immediate orbit tasks requires more precise satellite orbit state parameters in a short time. Although the traditional extended Kalman filter (EKF) method is widely used, its linear approximation of the drawbacks in dealing with nonlinear problems was especially evident, without compromising Kalman filter (unscented Kalman Filter, UKF). As a new nonlinear estimation method, it is measured at the estimated measurements on more and more applications. This paper will be the first study on UKF microsatellites in LEO orbit in real time, trying to explore the real-time precision orbit determination techniques. Through the preliminary simulation results, they show that, based on orbit mission requirements and conditions using UKF, they can satisfy the positioning accuracy and compute two indicators.

Association of optical tracklets from a geosynchronous belt survey via the direct Bayesian admissible region approach

The direct Bayesian admissible region approach is an a priori state free measurement association and initial orbit determination technique for optical tracks. In this paper, we test a hybrid approach that appends a least squares estimator to the direct Bayesian method on measurements taken at the Zimmerwald Observatory of the Astronomical Institute at the University of Bern. Over half of the association pairs agreed with conventional geometric track correlation and least squares techniques. The remaining pairs cast light on the fundamental limits of conducting tracklet association based solely on dynamical and geometrical information.

Formula omitted], a QB50 CubeSat mission to study rarefied-gas drag modelling

A CubeSat mission to study the impact of flow incidence angle, surface material and surface roughness on gas–surface interactions on spacecraft in low Earth orbits has been designed. To accomplish this scientific goal the CubeSat deploys a variable geometry aerofoil capable of exposing different surfaces to the flow at different incident angles. By using the on-board GPS measurements and an orbit determination technique the drag experienced by the CubeSat can be estimated. The CubeSat has been designed to be part of the QB50 mission, and hence it carries a sensor that can take in-situ measurements of the atmosphere. This is then used to estimate the atmospheric density and hence to extract information on the drag coefficient. To minimise any bias present in the measurement chain a differential approach is used. Therefore no absolute drag coefficients are estimated, instead, ratios of drag coefficients are computed. This allows direct comparisons of the drag coefficients of different materials, different surface roughness or different incident angles. Simulations indicate that this CubeSat mission will be able to obtain drag coefficient ratios with an uncertainty level of less than 5%.