Autonomous Formation Flying for the PRISMA Mission

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.

Precise relative GPS navigation is essential technology for rendezvous and formation flying of spacecraft in Low Earth Orbit. Key design issues of precise relative GPS navigation software are studied and a novel formulation is proposed for the mission which requires high accuracy when the separation distance is up to several km. The navigation filter estimates float navigation solutions by extended Kalman filter with elaborate dynamics models, and resolves ambiguities of integer carrier phase biases to achieve high accuracy fix navigation solutions. A relative navigation software with the proposed formulation is implemented and evaluated in two different ways. One is a test using spacebourne GPS receivers and a GPS signal simulator to evaluate the performance and sensitivity of the software against variation of parameters. The other is a test using actual telemetry data from Gravity Recovery and Climate Experiment (GRACE) to demonstrate the software performance. The design, implementation, and results of the evaluation are presented and discussed on this paper.

The use of Global Positioning System (GPS) measurements provides the primary technique for determining the relative position of cooperative, formation-flying satellites in low Earth orbit. Similar to terrestrial applications, the relative navigation benefits from a high level of common error cancellation. Furthermore, the integer nature of double-difference carrier phase ambiguities can be exploited in carrier phase differential GPS (CDGPS). Both aspects enable a substantially higher relative accuracy than can be achieved in single-spacecraft navigation. Following an overview of spaceborne GPS receivers, the dynamical and measurement models for relative navigation using single- or dual-frequency measurements are presented along with a discussion of estimation schemes for real-time and offline applications. Actual flight results from the TanDEM-X and PRISMA missions are presented to demonstrate the feasibility of mm-level post-facto baseline determination and cm-level real-time navigation using CDGPS.

Precise Orbit Determination (POD) is an integral part for analyzing measurements from space geodetic techniques such as Satellite Laser Ranging (SLR) and Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS). In the last two decades, POD based on GPS data has furthermore been established as one of the standard techniques to derive trajectories of satellites in the low Earth orbit (LEO) with highest accuracy. Since the launch of dedicated gravity missions, GPS sensors are not only used as a key tracking system for LEO POD, but also for extracting the long wavelength part of the Earth’s gravity field (together with SLR to spherical satellites). This chapter introduces SLR and GNSS measurements collected by the terrestrial networks of the International Laser Ranging Service (ILRS) and the International GNSS Service (IGS) as the observational basis for the realization of a terrestrial reference frame from satellite data. On this foundation, the basic equations and mathematical methods of orbit determination are introduced and extensively discussed. Pseudo-stochastic orbit modeling techniques are eventually presented as a general and efficient concept to determine satellite trajectories of highest quality even in presence of deficient force models, covering the full range between dynamic and purely kinematic solutions. Selected results from the application of the discussed orbit determination techniques are highlighted for GPS LEO data. Special emphasis is also put to present orbit determination in the context of more general orbit determination problems, where satellite trajectories are simultaneously determined with other parameters encompassing (at maximum) all pillars of geodesy, i.e., the shape, rotation, and gravity field of the Earth.

Global Positioning System (GPS) radio occultation signals received by a low Earth orbit (LEO) satellite provide information about the global distribution of electron density in the ionosphere. We examine two radio occultation inversion algorithms. The first algorithm utilizes the Abel integral transform, which assumes spherical symmetry of the electron density field. We test this algorithm with two approaches: through the computation of bending angles and through the computation of total electron content (TEC) assuming straight line propagation. We demonstrate that for GPS frequencies and for observations in LEO, the assumption of straight‐line propagation (neglecting bending) introduces small errors when monitoring the F2 layer. The second algorithm, which also assumes straight‐line propagation, is a three‐dimensional (3‐D) inversion constrained with the horizontal structure of a priori electron density fields. As a priori fields we use tomographic solutions and the parameterized real‐time ionospheric specification model (PRISM) when adjusted with ionosonde data or ground‐based GPS vertical TEC maps. For both algorithms we calibrate the occultation data by utilizing observations from the part of the LEO that is closer to the GPS satellite. For inversions we use dual‐frequency observational data (the difference of Ll and L2 phase observables) which cancel orbit errors (without applying precise orbit determination) and clock errors (without requiring synchronous ground data) and thus may allow inversions to be computed close to real time in the future. The Abel and 3‐D constrained algorithms are validated by statistically comparing 4 days of inversions with critical frequency (ƒ0F2) data from a network of 45 ionosonde stations and with vertical TEC data from the global network of GPS ground receivers. Globally, the Abel inversion approach agrees with the ƒ0F2 correlative data at the 13% rms level, with a negligible mean difference. All tested 3‐D constrained inversion approaches possess a statistically significant mean difference when compared with the ionosonde data. The vertical TEC correlative comparisons for both the Abel and 3‐D constrained inversions are significantly biased (∼30%) by the electrons above the 735‐km LEO altitude.

An ever increasing number of low Earth orbiting (LEO) satellites is, or will be, equipped with retro-reflectors for Satellite Laser Ranging (SLR) and on-board receivers to collect observations from Global Navigation Satellite Systems (GNSS) such as the Global Positioning Sys- tem (GPS) and the Russian GLONASS and the European Galileo systems in the future. At the Astronomical Insti- tute of the University of Bern (AIUB) LEO precise or- bit determination (POD) using either GPS or SLR data is performed for a wide range of applications for satellites at different altitudes. For this purpose the classical numeri- cal integration techniques, as also used for dynamic orbit determination of satellites at high altitudes, are extended by pseudo-stochastic orbit modeling techniques to effi- ciently cope with potential force model deficiencies for satellites at low altitudes. Accuracies of better than 2 cm may be achieved by pseudo-stochastic orbit modeling for satellites at very low altitudes such as for the GPS-based POD of the Gravity field and steady-state Ocean Circula- tion Explorer (GOCE).

With the ever-increasing number of satellites in Low Earth Orbit (LEO) for scientific missions, the precise determination of the position and velocity of the satellite is a necessity. GPS (Global Positioning System) based reduced-dynamic orbit determination (RPOD) method is commonly used in the post processing with high precision. This paper presents a sequential RPOD strategy for LEO satellite in the framework of Extended Kalman Filter (EKF). Precise Point Positioning (PPP) technique is used to process the GPS observations, with carrier phase ambiguity resolution using Integer Phase Clocks (IPCs) products. A set of GRACE (Gravity Recovery And Climate Experiment) mission data is used to test and validate the RPOD performance. Results indicate that orbit determination accuracy could be improved by 15% in terms of 3D RMS error in comparison with traditional RPOD method with float ambiguity solutions.

Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing precision dual spacecraft formation flying to enable a “virtual” telescope (VT). Using precision alignment of two spacecraft very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Furthermore, orders of magnitude improvement in science imaging over conventional single spacecraft instruments is possible with advances in precision formation flying. Precise astrometric alignment control is required for accurate inertial pointing of the VT. This work presents orbit design and control approaches for VT formation flying, with specific application to the recently proposed Virtual Telescope Demonstration Mission (VTDM) using cubesats. The characteristics of the mission orbit are derived from solutions to Hill’s equations for the relevant mission orbit. A relative orbit control technique pertaining to the astrometric alignment problem is developed by utilizing the Constrained Model Predictive Control (CMPC) approach. This method enables design of formation flying control laws for a thruster assembly with limited magnitude. Precision formation flying is achieved by use of separate control laws for formation maintenance and precision astrometric alignment. The proposed control scheme compensates for inertial astrometric alignment errors as well as differences in orbital perturbations between the VTDM satellites. Numerical simulations are shown to validate the performance of the proposed relative orbit and alignment control laws for the VTDM. The results satisfy mission requirements and indicate the general applicability of the control algorithm to the VT formation flying architecture. Consequently, the proposed methods of orbit design and control can be applied to inertial astrometric alignment and formation keeping for the many proposed dual spacecraft precision formation flying missions.

Abstract. Future radio occultation (RO) receivers are planned to utilize the newly implemented Global Positioning System (GPS) L5 band centered at 1176.45 MHz. Since there are currently no operational GPS L5 receivers used for space-based RO applications, the interference environment is unclear. Distance measuring equipment (DME) and tactical air navigation (TACAN) stations share the same frequency band as GPS L5. The signals from these stations have been identified as possible sources of interference for any GPS L5 receiver, including those used in RO applications. This study utilizes Systems Tools Kit (STK) simulations to gain insight into the power received by a RO satellite in low Earth orbit (LEO) from a DME–TACAN transmission as well as the amount of interfering stations. In order to confirm the validity of utilizing STK for communication purposes, a theoretical scenario was recreated as a simulation and the results were confirmed. Once the method was validated, STK was used to output a received power level aboard a RO satellite from a DME–TACAN station as well as a tool to detail the number of interfering DME–TACAN stations witnessed by a space-based RO receiver over time. The results indicated a large number of DME–TACAN stations transmitting at similar orientations as a receiving RO satellite, thereby leading to the possibility of signal degradation in an unclear interference environment.

Glacier height is determined by the range and orbit height of the satellite. The Range (R) is measured between the satellite and the surface of glacier using a space-borne altimeter. The satellite orbit height (H) is measured from the reference ellipsoid using Global Positioning System (GPS). The difference of orbital height and the altimeter range (H-R) is termed as the glacier height 'h.' Accuracy of the glacier height depends on the precise measurement of both orbital height and altimeter range. The orbital height measured using GPS is accurate compared to all the other tracking systems available. The optimal estimate of the satellite position is obtained using the ODTK tool by setting the mathematical model of the equation of Low Earth Orbit (LEO) satellite and the GPS measurements by applying Kalman filtering.

The chief objective of the PATH2Go multimodal traveler information application is to improve the accessibility and the quality of real-time traveler information and to make transit a known and viable choice for travelers. PATH2Go was developed as part of a field test on the US-101 corridor in the San Francisco Bay Area of California, with the primary hypothesis that travelers would benefit from real-time multimodal traveler information and therefore would be likely to consider using transit. PATH2Go integrates a web-based multimodal trip-planning tool that uses real-time transit, traffic, and parking information; a web-based search tool that finds real-time information about transit arrivals and schedules; and a mobile application that provides personalized en route transit trip information. PATH2Go integrates these major components of traveler information in one platform and makes real-time information easily accessible to travelers. The PATH2Go system architecture and major design considerations are described, and enabling technologies–including the Global Positioning System (GPS) fusing algorithm and a scenario-parsing algorithm based on GPS location data–are introduced.

T HE relative motion of a follower satellite with respect to the leader in a given circular orbit is described by autonomous nonlinear differential equations. The linearized equations around the null solution are known as Hill–Clohessy–Wiltshire (HCW) equations [1–3]. The HCWequations were used by many authors to study rendezvous problems (see [4] and references therein). The Tschauner–Hempel (TH) equations replace the HCW equations, when the orbit of the leader is eccentric [2,5]. Rendezvous problems along an eccentric orbit were studied in [4,5]. The HCW equations possess periodic solutions, which are useful as temporary orbits before mission and for proximity operations such as inspection and repair. The leader–follower formation and reconfiguration problems based on the periodic solutions were studied bymany authors [6–10]. The TH equations also have periodic solutions. They are characterized by Inalhan et al. [11], and the initialization procedure to periodic motion is given. Periodic solutions also follow from the transition matrix of the TH system given byYamanaka and Ankersen [12]. The effects of eccentricity on the shape and size of relative orbits are studied by Sengupta andVadali [13]. Periodic solutions of the TH equations are used for formation flying [14,15] because no control efforts are needed to maintain them. However, their period is fixed and is equal to that of the leader orbit, which would be inconvenient for a quick inspection of the leader. The shape of periodic solutions is irregular compared with that of the HCWequations, which would be undesirable for some missions. In this Note, active formation flying for the TH system is considered, in which the desired relative orbit of the follower is generated by an exosystem. This allows for flexibility of the shape and period of the reference orbit. Typical examples are elliptic relative orbits of the HCWequations with higher frequencies. Formation flying for the TH system with generated reference orbits has not been studied in the literature. To realize such a formation flying, the output regulation theory for linear periodic systems recently given by Ichikawa and Katayama [16] is employed. Output regulation covers tracking and disturbance rejection [17], but the tracking aspect of the theory is used. The regulator equation, which is necessary to achieve output regulation, is a differential equationwith periodic coefficients. The main contribution of this Note is to show that the regulator equation can be solved algebraically if the system is in the controllable canonical form and the observation matrix is of a special form. To achieve asymptotic tracking, stabilizing feedback controls are necessary. They are designed by the differential Riccati equation (DRE) of the linear quadratic regulator theory [18]. To show the effectiveness of this approach, two examples are given. In the first example, the orbit of the leader is assumed to be circular and the HCW equations are considered. The reference orbit of the follower for formation flying is circularwith arbitrary frequency. Starting from a periodic solution of the HCW equations, the follower satellite is asymptotically steered to the reference orbit. In this case, both the regulator equation and theRiccati equation become algebraic. TheL1 norm of the input ΔV and the settling time are given as functions of the weight parameter in the Riccati equation. The L1 norm of the input to maintain the reference orbit for one period is also calculated. These performance indices are further examined by varying the frequency of the reference orbit. The second example is concerned with the TH equations for the elliptic leader orbit. The reference relative orbit of the follower is circular, as in the first example. The regulator equation has periodic coefficients, but it is algebraically solved and explicitly given. The DRE is solved backward and the stabilizing periodic solution is obtained. TheL1 normof the input and the settling time are computed by varying eccentricity and frequency of the reference orbit.

Formation Flying is revolutionizing Earth and Space science and the way the space community conducts science missions. This technological transformation provides new, innovative techniques in spacecraft guidance, navigation, and control, and how the science community gathers and shares information between space vehicles and the ground. These technologies will also expedite the human exploration of space. Once fully matured, this technology will result in swarms of space vehicles flying as virtual platforms or distributed space systems and sensor webs which gather significantly more and better science data than is possible today. Formation flying will be enabled through the development and deployment of automated spaceborne guidance, navigation, and control (GN&C) systems integrated with intrasatellite communications infrastructure. Innovative spacecraft autonomy techniques, such as differential Global Positioning System (GPS) technology, optical, and vision-based navigation and celestial navigation allow autonomous navigation while other technologies provide for the autonomous control methods to maintain and optimize these formations. This paper provides a vision of the future of space exploration in the context of GN&C technology, and an overview of the current status of NASA technology development and its partnerships with the Department of Defense (DoD), Industry, and University to bring formation flying technology to the forefront as quickly as possible. We address the impediments that need to be overcome to achieve the distributive spacecraft vision and NASA GSFC's approach to transfer this technology to space. We will also describe some of the formation flying testbeds, such as the on-orbit Air Force Research Laboratory (AFRL) University Nanosats, and Orion test beds and ground based GSFC Formation Flying Test Bed, which are being developed to demonstrate and validate innovative position sensing and formation control technologies.

Combination of swarm, Jason-3, and GNSS observations to construct a new modeling of global ionospheric maps

Jena-Optronik GmbH (JOP) has a strong heritage in the development of cameras for numerous space-based applications. So far, our focus has been on cameras working in the visible & near-infrared range of the spectrum. The main application case for these cameras is the use as autonomous star trackers being part of a satellite’s Guidance, Navigation & Control System. JOP has been very successful with these cameras –for a long time and is the world market leader in providing such sensors to satellite prime manufactures. Investigating the possible applications of cameras in space, one realizes that thermal or long wave infrared (IR) cameras are necessary for specific applications. One major field for several of such applications is the field of Space Situational Awareness (SSA). SSA has been attracting more and more attention over the past years especially for space objects, natural debris as well as man-made threats & disturbances such as military conflicts. Two further application fields for IR cameras are formation flying and docking. The first rendezvous and docking with a non-cooperative satellite (Intelsat 901) in geostationary orbit by Northrop Grummans MEV-1 was a key milestone for docking capabilities. Additionally, the recent years have shown that a transition from few big and multi-purpose satellites towards small, medium or even large constellations consisting of numerous small satellites is taking place. Especially for constellations, a key aspect is formation flying which usually requires relative navigation. The relative angles between the satellites can be easily provided by IR cameras as they detect the satellites reliably and independently of local lighting conditions due to their elevated temperature against the cold space background. Based on the very successful ASTRO product range of space proven cameras, ASTROtir (tir = thermal infra-red) will extend JOPs product capabilities into the thermal / long wave infrared (LWIR) wavelength range to cover all of the applications cases listed above. Following a successful ESA co-funded first evaluation, the ASTROtir development project has been kicked-off in December 2022 in cooperation with ESA. Target of this project is to demonstrate TRL8 of ASTROtir. Future applications are formation flying (relative navigation), approach and docking with a non-cooperative space object as well as detailed image generation of near satellite objects. Currently, no European solution for an IR camera covering the application cases and mission scenarios is available as off-the-shelf product, which further increases ASTROtir’s already promising market potential. As the market demand, especially in the field of SSA, is rising further in the coming years, its development will be closely followed and its market entry is eagerly awaited. Jena-Optronik will present the preliminary design and development status of ASTROtir. As ASTROtir aims primarily at applications on small and medium satellites, its target mass budget of 300g is a driving requirement. Following our intermediate / preliminary design review scheduled for August 2023, Jena-Optronik aims at presenting first results from ASTROtir’s system analyses as well as the related plans for the EM and EQM campaigns.