Orbit Determination Strategy Research Articles

Multi-GNSS ultra-rapid orbit determination through epoch-parallel processing

High-precision Global Navigation Satellite Systems (GNSS) orbits are critical for real-time clock estimation and precise positioning service; however, the prediction error grows gradually with the increasing prediction session. In this study, we present a new efficient precise orbit determination (POD) strategy referred to as the epoch-parallel processing to reduce the orbit update latency, in which a 24-h processing job is split into several sub-sessions that are processed in parallel and then stacked to solve and recover parameters subsequently. With a delicate handling of parameters crossing different sub-sessions, such as ambiguities, the method is rigorously equivalent to the one-session batch solution, but is much more efficient, halving the time-consuming roughly. Together with paralleling other procedures such as orbit integration and using open multi-processing (openMP), the multi-GNSS POD of 120 satellites using 90 stations can be fulfilled within 30 min. The lower update latency enables users to access orbits closer to the estimation part, that is, 30–60-min prediction with a 30-min update latency, which significantly improves the orbit quality. Compared to the hourly updated orbit, the averaged 1D RMS values of predicted orbit in terms of overlap for GPS, GLONASS, Galileo, and BDS MEO are improved by 39%, 35%, 41%, and 37%, respectively, and that of BDS GEO and IGSO satellites is improved by 47%. We also demonstrate that the boundary discontinuities of half-hourly orbit are within 2 cm for the GPS, GLONASS, and Galileo satellites, and for BDS the values are 2.6, 15.5, and 9.8 cm for MEO, GEO, and IGSO satellites, respectively. This method can also be implemented for any batch-based GNSS processing to improve the efficiency.

Assessment of Swarm Kinematic Orbit Determination Using Two Different Double-Difference Methods

The Swarm mission aims to study the principle and change regularities of the Earth’s magnetic field. Precise orbit determination is essential to the successful implementation of the mission and relevant scientific research. This article focuses on using two different double-difference methods to improve the accuracy of Swarm kinematic orbit determination. The accuracy of the kinematic orbit determination relies entirely on the space-borne observation data, independent of any dynamic parameters. The article analyzes the data quality of the Swarm space-borne global positioning system (GPS) receiver and presents a detailed introduction to the data pre-processing algorithms. The double-difference observation gathering and the applied orbit determination strategy using two different double-difference methods are discussed. The results of the kinematic orbits under different solar cycle conditions are presented, along with an evaluation based on analysis of GPS carrier phase residuals, subtracting from the post-processed orbits, and assessment with satellite laser ranging (SLR) measurements. The results show that the accuracy of the kinematic orbit determination is at the centimeter level for the three Swarm satellites’ orbit solutions. The daily root mean square (RMS) values of the three satellites’ phase residuals remain at around the 6 mm level. The RMS values of the position residuals between the kinematic orbits and the reduced dynamic orbits released by the European Space Agency (ESA) are at about the 2–3 cm level. The external evaluation with SLR measurements shows a good agreement with the ESA level, with the RMS values of the SLR residuals for kinematic orbits around 2 cm.

Precise orbit determination for TH02-02 satellites based on BDS3 and GPS observations

The Tianhui-2 02 (TH02-02) satellite formation, as a supplement to the microwave mapping satellite system Tianhui-2 01 (TH02-01), is the first Interferometric Synthetic Aperture Radar (InSAR) satellite formation-flying system that supports the tracking of BeiDou global navigation Satellite system (BDS3) new B1C and B2a signals. Meanwhile, the twin TH02-02 satellites also support the tracking of Global Positioning System (GPS) L1&L2 and BDS B1I&B3I signals. As the spaceborne receiver employs two independent boards to track the Global Navigation Satellite System (GNSS) satellites, we design an orbit determination strategy by estimating independent receiver clock offsets epoch by epoch for each GNSS to realize the multi-GNSS data fusion from different boards. The performance of the spaceborne receiver is evaluated and the contribution of BDS3 to the kinematic and reduced-dynamic Precise Orbit Determination (POD) of TH02-02 satellites is investigated. The tracking data onboard shows that the average number of available BDS3 and GPS satellites are 8.7 and 9.1, respectively. The carrier-to-noise ratio and carrier phase noise of BDS3 B1C and B2a signals are comparable to those of GPS. However, strong azimuth-related systematic biases are recognized in the pseudorange multipath errors of B1C and B3I. The pseudorange noise of BDS3 signals is better than that of GPS after eliminating the multipath errors from specific signals. Taking the GPS-based reduced-dynamic orbit with single-receiver ambiguity fixing technique as a reference, the results of BDS3-only and BDS3 + GPS combined POD are assessed. The Root Mean Square (RMS) of orbit comparison of BDS3-based kinematic and reduced-dynamic POD with reference orbit are better than 7 cm and 3 cm in three-Dimensional direction (3D). The POD performance based on B1C&B2a data is comparable to that based on B1I&B3I. The precision of BDS3 + GPS combined kinematic orbit can reach up to 3 cm (3D RMS), which has a more than 25% improvement relative to the GPS-only solution. In addition, the consistency between the BDS3 + GPS combined reduced-dynamic orbit and the GPS-based ambiguity-fixed orbit is better than 1.5 cm (3D RMS).

Real-Time Multi-GNSS Precise Orbit Determination Based on the Hourly Updated Ultra-Rapid Orbit Prediction Method

Offering real-time precise point positioning (PPP) services for global and large areas based on global navigation satellite systems (GNSS) has drawn more and more attention from institutions and companies. A precise and reliable satellite orbit is a core premise for multi-GNSS real-time services, especially for the GPS and GLONASS, which are undergoing modernization, whereas the Galileo, BDS and QZSS have just fulfilled the construction stage. In this contribution, a real-time precise orbit determination (POD) strategy for the five operational constellations based on the hourly updated ultrarapid orbit prediction method is presented. After combination of 72 h arc through three adjacent 24 h arc normal equations, the predicted orbits are finally generated (hourly updated). The POD results indicate that the mean one-dimensional (1-D) root mean square (RMS) values compared with the Deutsches GeoForschungsZentrum (GFZ) final multi-GNSS orbits are approximately 3.7 cm, 10.2 cm, 5.8 cm, 5.7 cm, 4.1 cm and 25.1 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The mean 1-D RMS values of the hourly updated ultrarapid orbit boundary overlapping comparison are approximately 1.6 cm, 6.9 cm, 3.2 cm, 2.7 cm, 1.8 cm and 22.2 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The satellite laser ranging (SLR) validation illuminates that the mean RMS values are approximately 4.53 cm and 4.73 cm for the four MEOs of BDS-3 and four BDS-2 satellites, respectively.

GNSS receiver for Q-Sat and its analysis of precise orbit determination

The Earth's gravity field and upper atmosphere are very important scientific information and their mechanical models can be obtained by inversion of the satellite precision orbit. It would be ideal to develop a constellation of satellites distributed with different orbits to measure atmospheric drag and gravity. Based on this idea, Tsinghua University developed a microsatellite Q-Sat for measuring the gravity field and the density of the upper atmosphere. Low-cost, high-precision measurements can greatly improve the cost effectiveness of scientific missions. In this paper, a spatial modification method for GNSS receivers based on commercial off-the-shelf was proposed. The base module of the receiver is a ground-based general-purpose device, and this modification method allows for the space-batch modification of industrial-grade devices. The modified receiver was successfully applied to the Q-Sat and a large amount of continuous on-orbit data were obtained. Data analysis results show that the receiver can simultaneously receive GPS-L1\\L2 and BD1\\BD2 multifrequency navigation satellite signals in the highly dynamic spatial environment. To reduce the precision orbit determination error, the GNSS observations were corrected by antenna center modelling, and the long-term orbit determination accuracy is stabilized at the centimeter level. The commercial off-the-shelf based GNSS receiver modification method and precision orbit determination strategy can provide a reference for low-cost and high-precision microsatellites.

Relative Kinematic Orbit Determination for GRACE-FO Satellite by Jointing GPS and LRI

As the first in-orbit formation satellites equipped with a Laser Ranging Interferometer (LRI) instrument, Gravity Recovery and Climate Experiment Follow-on (GRACE-FO) satellites are designed to evaluate the effective ability of the new LRI ranging system applied to satellite-to-satellite tracking. To evaluate the application of LRI in GRACE-FO, a relative kinematic orbit determination scheme for formation satellites integrating Kalman filters and GPS/LRI is proposed. The observation equation is constructed by combining LRI and spaceborne GPS data, and the intersatellite baselines of GRACE-FO formation satellites are calculated with Kalman filters. The combination of GPS and LRI techniques can limit the influence of GPS observation errors and improve the stability of orbit determination of the GRACE-FO satellites formation. The linearization of the GPS/LRI observation model and the process of the GPS/LRI relative kinematic orbit determination are provided. Relative kinematic orbit determination is verified by actual GPS/LRI data of GRACE-FO-A and GRACE-FO-B satellites. The quality of relative kinematic orbit determination is evaluated by reference orbit check and K-Band Ranging (KBR) check. The result of the reference orbit check indicates that the accuracy of GRACE-FO relative kinematic orbit determination along X, Y, and Z (components of the baseline vector) directions is better than 2.9 cm. Compared with the relative kinematic orbit determination by GPS only, GPS/LRI improves the accuracy of the relative kinematic orbit determination by approximately 1cm along with X, Y and Z directions, and by about 1.8 cm in 3D directions. The overall accuracy of relative kinematic orbit determination is improved by 25.9%. The result of the KBR check indicates that the accuracy of the intersatellite baseline determination is about +/−10.7 mm.

Improved Single-Frequency Kinematic Orbit Determination Strategy of Small LEO Satellite with the Sun-Pointing Attitude Mode

Kinematic orbit determination (KOD) of low earth orbit (LEO) satellites only using single-frequency global navigation satellite system (GNSS) data is a suitable solution for space applications demanding meter-level orbit precision. For some small LEO satellites with the sun-pointing attitude mode, the rotation of the GNSS antenna radiation pattern changes the observation noise characteristics. Since the rotation angle information of the antenna plane may not be available for most low-cost missions, the true elevation cannot be computed and a general elevation-dependent weighting model remains invalid for the onboard GNSS observations. Furthermore, the low-stability GNSS receiver clock oscillator of the LEO satellite at high speeds makes single-frequency cycle slip detection ineffective and difficult since the clock steering events occur frequently. In this study, we investigated the improved KOD strategy to improve the performance of orbit solution using single-frequency GPS and BeiDou navigation satellite system (BDS) observations collected from the Luojia-1A satellite. The weighting model based on exponential function and signal strength is proposed according to the analysis of satellite attitude impact, and a joint single-frequency detection algorithm of receiver clock jump and cycle slip is investigated as well. Based on the GPS/BDS-combined KOD results, it is demonstrated that the clock jump and cycle slip can be properly detected and observations can be effectively utilized with the proposed weighting model considering satellite attitude, which significantly improves the availability and accuracy of orbit solution. The number of available epochs is increased by 12.9% benefitting from this strategy. The orbital root mean square (RMS) precision improvements in the radial, along-track, and cross-track directions are 22.1%, 16.4%, and 6.5%, respectively. Combining BDS observations also contributes to orbit precision improvement, which reaches up to 28.8%.

Inter-satellite link augmented BeiDou-3 orbit determination for precise point positioning

Precise Point Positioning (PPP) requires precise products, including high-accuracy satellite orbit and clock parameters. It is impossible to obtain an orbit solution that is sufficiently accurate for PPP services with a regional tracking network; therefore, satellite orbits are usually estimated by a global tracking network with a large number of ground stations. However, it is expensive to build globally distributed stations. Fortunately, BeiDou-3 satellites carry an Inter-Satellite Link (ISL) payload, which can track the whole arc of the BeiDou-3 satellites and enhance the orbit determination accuracy with regional ground stations. In this contribution, a novel orbit determination strategy for BeiDou-3 PPP is proposed, in which the BeiDou-3 satellite orbits are enhanced by the ISL. First, the generation of precise satellite products is demonstrated in detail. In addition, the products are assessed by Satellite Laser Ranging (SLR) residuals and overlap comparisons. Moreover, the products are used for receivers in mainland China to carry out the static and kinematic modes to research the PPP performance of BeiDou-3′s 3IGSO/24MEO constellation. The SLR validations of the satellite orbits demonstrate an accuracy better than 0.1 m in the radial component, and the orbit overlap comparisons show accuracies of 0.016 m in the radial component, 0.088 m in the along-track component and 0.087 m in the cross-track component. The Standard Deviation (STD) in the differences in overlapping arcs for the estimated satellite clocks is approximately 0.10 ns. The static PPP results demonstrate that the error in both the horizontal and vertical components is smaller than 10 cm after 30 minutes of convergence. After 24 hours of convergence, the errors are 0.70 cm, 0.63 cm and 1.99 cm for the north, east and up components, respectively. The kinematic PPP experiment illustrates that the Root Mean Square (RMS) position errors in the north, east and up components are approximately 3.23 cm, 5.27 cm and 8.64 cm, respectively, after convergence. The obtainable positioning and convergence performances are comparable to those using products generated by global tracking networks.

GPS triple-frequency undifferenced and uncombined precise orbit determination with the consideration of receiver time-variant bias

As the development of the global navigation satellite system (GNSS), the navigation satellite transmitting multi-frequency signals becomes a prevailing trend. Currently, the usual GNSS precise orbit determination (POD) strategy uses dual-frequency (DF) ionosphere-free (IF) linear combination to build up the observation equation. In the area of precise positioning, it has been validated that the third frequency can decrease the convergence time of ambiguity resolution and has a subtle improvement on the positioning accuracy. However, there is no report about the benefits of the third frequency on GNSS POD. Although the precision of dual-frequency POD can meet requirements for generating different types of products, an obvious advantage of multi-frequency observations is that more robust results can be derived. Besides, with the third frequency observations, the improvements of orbits and clocks need to be validated. Thus, a triple-frequency (TF) uncombined (UC) POD method of GNSS satellites is developed. The hardware delay of carrier phase is divided by time-invariant and -variant components. Then the UC observation model is given by re-parameterizing the unknown parameters. The datum of satellite clocks is aligned to IGS products. The step-by-step ambiguity fixing method, i.e. the extra-wide-lane, wide-lane and narrow-lane ambiguities being fixed in sequence, is deduced by using double-differenced ambiguities in a network. We select 74 ground stations and 12 GPS BLOCK IIF satellites to process POD with a length of 20 days. Results of TF-UC POD show that about 10% improvements on orbits and clocks are received compared to L1/L2 DF-IF POD. The time-variant characteristic of phase biases from satellites and stations at the third frequency is analyzed, which shows that the bias at the station has a slight influence on the derived products. These results imply that the precision of orbits and clocks can be improved with observations from the third frequency added.

Toward the 1-cm Galileo orbits: challenges in modeling of perturbing forces

Precise orbit determination demands knowledge of perturbing forces acting on the satellites of the Global Navigation Satellite Systems (GNSS). The metadata published by the European GNSS Agency for the Galileo satellites allow for the composition of the analytical box-wing model dedicated for coping with the direct solar radiation pressure (SRP), albedo, and infrared radiation (IR). Based on the box-wing model, we evaluated both the magnitude and the characteristic periods of accelerations caused by all the aforementioned forces. We assess which perturbations can be absorbed by the extended Empirical CODE Orbit Model (ECOM2) and what are the consequences of neglecting higher-order ECOM2 coefficients. In order to evaluate the impact of SRP, albedo, IR, and the navigation antenna thrust, we perform a series of precise Galileo orbit determination strategies for Galileo In-Orbit-Validation (IOV), Full Operational Capability (FOC), and two FOC satellites launched into eccentric orbits. The proposed box-wing model is capable of absorbing approximately 97% of the SRP in the Sun-satellite direction, whereas the rest can be mitigated by an additionally estimated small set of empirical parameters. The purely physical box-wing model does not fully handle satellite misorientation and re-radiation effects, such as Y-bias, solar panel rotation lag, that is the misalignment causing a constant acceleration perpendicular to the solar panel axis and the direction to the Sun. However, the box-wing model is especially crucial in terms of the absorption of the higher-order terms of SRP and stabilizes the orbit solutions during the eclipsing periods. Based on the SLR residual analysis, we found a systematic effect at the level up to 50 mm resulting from the omission of the high-order empirical orbit coefficients. We also found that the impact of the albedo, IR, and transmitter antenna thrust on the Galileo orbits reach the level of 5, 14, and 20 mm, respectively. Eventually, we obtain the overall accuracy of the Galileo-FOC orbits at the level of 22.5 mm, even for the eclipsing period for the solution which considers the box-wing model with the estimation of the constant empirical accelerations.

Analysis on the Orbit Determination of Longjiang-2 Lunar Microsatellite

The TT&C (Tracking Telemetry and Command) resources are usually limited for the deep space exploration mission of micro-nano satellites. It is necessary to analyze the orbit determination accuracy under the limited resource of TT&C. The orbit determination precision of Longjiang-2 lunar microsatellite is analyzed. Longjiang-2 microsatellite only has USB orbital measurement data, and the TT&C resources in the lunar phase are relatively tight. There are two stations are used to track the Longjiang-2 satellite every day,and a total of about 3-4 hours of orbital measurement data is available. Firstly,the Longjiang-2 mission is introduced and the factors which have effect on orbit determination are presented. Secondly, the dynamical model is given. The orbit determination precision of earth-moon transfer orbit is analyzed. Lastly,the effects of perturbative force, wheeloff loading and data arc length are studied and then the orbit determination strategy is proposed. The orbit determination precision of lunar orbit is given. The conclusions can provide useful reference for the future deep space exploration mission of micro-nano satellites.

Observational Arc-Length Effect on Orbit Determination for KPLO Using a Sequential Estimation Technique

In this study, orbit determination (OD) simulation for the Korea Pathfinder Lunar Orbiter (KPLO) was accomplished for investigation of the observational arc-length effect using a sequential estimation algorithm. A lunar polar orbit located at 100 km altitude and 90° inclination was mainly considered for the KPLO mission operation phase. For measurement simulation and OD for KPLO, the Analytical Graphics Inc. Systems Tool Kit 11 and Orbit Determination Tool Kit 6 software were utilized. Three deep-space ground stations, including two deep space network (DSN) antennas and the Korea Deep Space Antenna, were configured for the OD simulation. To investigate the arc-length effect on OD, 60-hr, 48-hr, 24-hr, and 12-hr tracking data were prepared. Position uncertainty by error covariance and orbit overlap precision were used for OD performance evaluation. Additionally, orbit prediction (OP) accuracy was also assessed by the position difference between the estimated and true orbits. Finally, we concluded that the 48-hr-based OD strategy is suitable for effective flight dynamics operation of KPLO. This work suggests a useful guideline for the OD strategy of KPLO mission planning and operation during the nominal lunar orbits phase.

Autonomous Orbit Determination for a Hybrid Constellation

A new orbit determination scheme targeting communication and remote sensing satellites in a hybrid constellation is investigated in this paper. We first design one such hybrid constellation with a two-layer configuration (LEO/MEO) by optimizing coverage and revisit cycle. The main idea of the scheme is to use a combination of imagery, altimeter data, and inter-satellite range data as measurements and determine orbits of the satellites in the hybrid constellation with the help of the extended Kalman filter (EKF). The performance of the new scheme is analyzed with Monte Carlo simulations. We first focus on an individual remote sensing satellite and compared the performance of orbit determination using only imagery with its counterpart using both imagery and altimeter measurements. Results show that the performance improves when imagery is used with altimeter data pointing to geometer calibration sites but declines when used with ocean altimeter data. We then expand the investigation to the whole constellation. When inter-satellite range data is added, orbits of all the satellites in the hybrid constellation can be autonomously determined. We find that the combination of inter-satellite range data with remote sensing observations lead to a further improvement in orbit determination precision for LEO satellites. Our results also show that the performance of the scheme would be affected when remote sensing observations on certain satellites are absent.

Relative positioning of formation-flying spacecraft using single-receiver GPS carrier phase ambiguity fixing

In recent years, differential carrier phase-based relative positioning (or “baseline determination”) with precision at the millimeter and submillimeter levels has been demonstrated for the GRACE, TanDEM-X and Swarm missions in offline processing. Specific features of such missions have included the use of spacecraft of similar shapes placed in almost identical orbits as well as the use of consistent geodetic-class GPS receivers. These elements have proven to be advantageous for the computation of baseline solutions with such precision levels. Particularly, they have allowed to fully leverage the use of differential GPS techniques, including the estimation and use of carrier phase integer ambiguities. Similarly, the aforementioned spacecraft and orbit characteristics have made it possible to tightly constrain the relative dynamics of formations in the generation of reduced-dynamic solutions. Other than the former examples, prospective formation-flying mission proposals, such as SAOCOM-CS and PICOSAR, may comprise spacecraft with very different characteristics, including dissimilar GPS/GNSS receivers. Such cases may no longer provide favorable conditions for relative orbit determination strategies. As an alternative, absolute orbit solutions may be computed individually for each spacecraft and used for the generation of precise baseline products. This study aims at the assessment of the potential of single-receiver ambiguity fixing for the generation of precise baseline solutions. Results using flight data from the GRACE, TanDEM-X and Swarm missions exhibit baseline accuracy better than 5 mm (3D RMS) for a one-month test period in June 2016. As such, the presented solutions may be considered for prospective formation-flying remote sensing missions with baseline precision requirements at the subcentimeter level. Likewise, the method is considered of particular interest for future multi-spacecraft formations and swarms that require efficient determination of a large number of individual baselines.

Improving multi-GNSS ultra-rapid orbit determination for real-time precise point positioning

Currently, with the rapid development of multi-constellation Global Navigation Satellite Systems (GNSS), the real-time positioning and navigation are undergoing dramatic changes with potential for a better performance. To provide more precise and reliable ultra-rapid orbits is critical for multi-GNSS real-time positioning, especially for the three merging constellations Beidou, Galileo and QZSS which are still under construction. In this contribution, we present a five-system precise orbit determination (POD) strategy to fully exploit the GPS $$+$$ GLONASS $$+$$ BDS $$+$$ Galileo $$+$$ QZSS observations from CDDIS $$+$$ IGN $$+$$ BKG archives for the realization of hourly five-constellation ultra-rapid orbit update. After adopting the optimized 2-day POD solution (updated every hour), the predicted orbit accuracy can be obviously improved for all the five satellite systems in comparison to the conventional 1-day POD solution (updated every 3 h). The orbit accuracy for the BDS IGSO satellites can be improved by about 80, 45 and 50% in the radial, cross and along directions, respectively, while the corresponding accuracy improvement for the BDS MEO satellites reaches about 50, 20 and 50% in the three directions, respectively. Furthermore, the multi-GNSS real-time precise point positioning (PPP) ambiguity resolution has been performed by using the improved precise satellite orbits. Numerous results indicate that combined GPS $$+$$ BDS $$+$$ GLONASS $$+$$ Galileo (GCRE) kinematic PPP ambiguity resolution (AR) solutions can achieve the shortest time to first fix (TTFF) and highest positioning accuracy in all coordinate components. With the addition of the BDS, GLONASS and Galileo observations to the GPS-only processing, the GCRE PPP AR solution achieves the shortest average TTFF of 11 min with $$7{^{\circ }}$$ cutoff elevation, while the TTFF of GPS-only, GR, GE and GC PPP AR solution is 28, 15, 20 and 17 min, respectively. As the cutoff elevation increases, the reliability and accuracy of GPS-only PPP AR solutions decrease dramatically, but there is no evident decrease for the accuracy of GCRE fixed solutions which can still achieve an accuracy of a few centimeters in the east and north components.

On-board orbit determination for low thrust LEO-MEO transfer by Consider Kalman Filtering and multi-constellation GNSS

In the framework of the novel navigation scenario offered by the next generation satellite low thrust autonomous LEO-to-MEO orbit transfer, this study proposes and tests a GNSS based navigation system aimed at providing on-board precise and robust orbit determination strategy to override rising criticalities. The analysis introduces the challenging design issues to simultaneously deal with the variable orbit regime, the electric thrust control and the high orbit GNSS visibility conditions. The Consider Kalman Filtering approach is here proposed as the filtering scheme to process the GNSS raw data provided by a multi-antenna/multi-constellation receiver in presence of uncertain parameters affecting measurements, actuation and spacecraft physical properties. Filter robustness and achievable navigation accuracy are verified using a high fidelity simulation of the low-thrust rising scenario and performance are compared with the one of a standard Extended Kalman Filtering approach to highlight the advantages of the proposed solution. Performance assessment of the developed navigation solution is accomplished for different transfer phases.

Orbit determination for remote-sensing satellites using only optical imagery

ABSTRACTThe development of high-resolution remote-sensing satellites is paving a promising path towards autonomous orbit determination using optical imagery. In this article, an image-based orbit determination strategy is investigated with a focus on the effects of lighting constraints, image resolution, and pointing accuracy on orbit determination performance. The measurement model is established based on the perspective projection and its observability is demonstrated. To investigate the influence of lighting constraints, four cases of simulations (considering no lighting constraints, either cloud-coverage constraint or night-time constraint, or both constraints) are conducted for the WorldView-3 satellite. The obtained root- mean square (RMS) errors of position and velocity in the four cases remain below 10.83 m and 1.42 cm , respectively, at an image resolution of 0.3 m and a pointing accuracy of 0.0005. By varying the values of image resolution and pointing accuracy, the effects of these two factors and their relative importance are further investigated. The final results indicate that pointing accuracy plays a dominant role in image-based orbit determination for high-resolution remote-sensing satellites.

Space Object Detection in Images Using Matched Filter Bank and Bayesian Update

Electrooptical sensors, when used to track space objects, are often used to produce detections of space objects for some orbit determination scheme. Instead, this paper proposes a series of methods to use electrooptical images directly in orbit determination. This work uses the signal-to-noise ratio optimal image filter, called a matched filter, to search for partially known space objects. By defining a metric for measuring matched filter template similarity, a bank of matched filters is efficiently defined by partitioning the prior knowledge set. Once partitioned sets are known, the matched filter bank can be localized to regions of the sky. A method for hypothesis testing the result of a matched filter for a space object is developed. Finally, a framework for orbit determination based on the matched filter result is developed. Simulation shows that the analytic results enable a better framework for implementing matched filters for low-signal-to-noise ratio object detection.

Estimating maneuvers for precise relative orbit determination using GPS

Precise relative orbit determination is an essential element for the generation of science products from distributed instrumentation of formation flying satellites in low Earth orbit. According to the mission profile, the required formation is typically maintained and/or controlled by executing maneuvers. In order to generate consistent and precise orbit products, a strategy for maneuver handling is mandatory in order to avoid discontinuities or precision degradation before, after and during maneuver execution. Precise orbit determination offers the possibility of maneuver estimation in an adjustment of single-satellite trajectories using GPS measurements. However, a consistent formulation of a precise relative orbit determination scheme requires the implementation of a maneuver estimation strategy which can be used, in addition, to improve the precision of maneuver estimates by drawing upon the use of differential GPS measurements. The present study introduces a method for precise relative orbit determination based on a reduced-dynamic batch processing of differential GPS pseudorange and carrier phase measurements, which includes maneuver estimation as part of the relative orbit adjustment. The proposed method has been validated using flight data from space missions with different rates of maneuvering activity, including the GRACE, TanDEM-X and PRISMA missions. The results show the feasibility of obtaining precise relative orbits without degradation in the vicinity of maneuvers as well as improved maneuver estimates that can be used for better maneuver planning in flight dynamics operations.

REVISITING THE ROLE OF OBSERVATION SESSION DURATION ON PRECISE POINT POSITIONING ACCURACY USING GIPSY/OASIS II SOFTWARE

The accuracy of GPS precise point positioning (PPP) was previously modelled as a function of the observing session duration T. The NASA, JPL's software GIPSY OASIS II (GOA-II) along with the legacy products was used to process the GPS data. The original accuracy model is not applicable anymore because JPL started releasing its products using new modelling and analysis strategies as of August 2007, and the legacy products are no longer available. The developments mainly comprise the new orbit and clock determination strategy, second order ionosphere modelling, and single station ambiguity resolution. Previously, the PPP accuracy was studied using v 4.0 of the GOA-II. The accuracy model showed coarser results compared to that of the relative positioning. Here, we processed the data of the International GNSS Service (IGS) stations to refine the accuracy of GOA-II PPP from version 6.3. Considering the above changes we refined the accuracy of PPP. First we modified the previous model used for the accuracy assessment. Then we tested out this model using straightforward polynomial and logarithmic models. The tests indicate the previous formulation still satisfactorily models the accuracy using refined coefficient values Sn = 7.8 mm , Se = 6.8 mm , Sv = 29.9 mm for T ≥ 2 h.