Angles-only relative orbit determination for space non-cooperative targets based on passive sensor is subject to weakly observable problem of the relative state between two spacecraft. Previously, the evidence for ang...Angles-only relative orbit determination for space non-cooperative targets based on passive sensor is subject to weakly observable problem of the relative state between two spacecraft. Previously, the evidence for angles-only observability was found by using cylindrical dynamics, however, the solution of orbit determination is still not provided. This study develops a relative orbit determination algorithm with the cylindrical dynamics based on differential evolution. Firstly, the relative motion dynamics and line-of-sight measurement model for nearcircular orbit are established in cylindrical coordinate system.Secondly, the observability is qualitatively analyzed by using the dynamics and measurement model where the unobservable geometry is found. Then, the angles-only relative orbit determination problem is modeled into an optimal searching frame and an improved differential evolution algorithm is introduced to solve the problem. Finally, the proposed algorithm is verified and tested by a set of numerical simulations in the context of highEarth and low-Earth cases. The results show that initial relative orbit determination(IROD) solution with an appropriate accuracy in a relative short span is achieved, which can be used to initialize the navigation filter.展开更多
Low-Earth-Orbit（LEO） formation-flying satellites have been widely applied in many kinds of space geodesy. Precise Relative Orbit Determination（PROD） is an essential prerequisite for the LEO formation-flying satell...Low-Earth-Orbit（LEO） formation-flying satellites have been widely applied in many kinds of space geodesy. Precise Relative Orbit Determination（PROD） is an essential prerequisite for the LEO formation-flying satellites to complete their mission in space. The contribution of the BeiDou Navigation Satellite System（BDS） to the accuracy and reliability of PROD of LEO formation-flying satellites based on a Global Positioning System（GPS） is studied using a simulation method. Firstly, when BDS is added to GPS, the mean number of visible satellites increases from9.71 to 21.58. Secondly, the results show that the 3-Dimensional（3 D） accuracy of PROD, based on BDS-only, GPS-only and BDS ＋ GPS, is 0.74 mm, 0.66 mm and 0.52 mm, respectively. When BDS co-works with GPS, the accuracy increases by 29.73%. Geostationary-Earth-Orbit（GEO） satellites and Inclined Geosynchronous-Orbit（IGSO） satellites are only distributed over the Asia-Pacific region; however, they could provide a global improvement to PROD. The difference in PROD results between the Asia-Pacific region and the non-Asia-Pacific region is not apparent. Furthermore, the value of the Ambiguity Dilution Of Precision（ADOP）, based on BDS ＋ GPS, decreases by 7.50% and 8.26%, respectively, compared with BDS-only and GPS-only. Finally, if the relative position between satellites is only a few kilometres, the effect of ephemeris errors on PROD could be ignored. However, for a several-hundred-kilometre separation of the LEO satellites, the SingleDifference（SD） ephemeris errors of GEO satellites would be on the order of centimetres. The experimental results show that when IGSO satellites and Medium-Earth-Orbit（MEO） satellites co-work with GEO satellites, the accuracy decreases by 17.02%.展开更多
When formation flying spacecrafts are used as platform to gain earth oriented observation, precise baselines between these spacecrafts are always essential. Gravity recovery and climate experiment （GRACE） mission is...When formation flying spacecrafts are used as platform to gain earth oriented observation, precise baselines between these spacecrafts are always essential. Gravity recovery and climate experiment （GRACE） mission is aimed at mapping the global gravity field and its variation. Accurate baseline of GRACE satellites is necessary for the gravity field modeling. The determination of kinematic and reduced dynamic relative orbits of twin satellites has been studied in this paper, and an accuracy of 2 mm for dynamic relative orbits and 5 mm for kinematic ones can be obtained, whereby most of the double difference onboard GPS ambiguities are resolved.展开更多
This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for non-cooperative target close-in proximity operations when the camera offset from the...This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for non-cooperative target close-in proximity operations when the camera offset from the vehicle center-of-mass allows for range observability.In previous work,the solution to this problem had been shown to be non-global optimal in the sense of least square and had only been discussed in the context of Clohessy–Wiltshire.In this paper,the emphasis is placed on developing a more compact and improved solution to the problem by using state augmentation least square method in the context of the Clohessy–Wiltshire and Tschauner–Hempel dynamics,derivation of corresponding error covariance,and performance analysis for typical rendezvous missions.A two-body Monte Carlo simulation system is used to evaluate the performance of the solution.The sensitivity of the solution accuracy to camera offset,observation period,and the number of observations are presented and discussed.展开更多
A closed-form solution to the angles-only initial relative orbit determination(IROD)problem for space rendezvous with non-cooperated target is developed,where a method of hybrid dynamics with the concept of virtual fo...A closed-form solution to the angles-only initial relative orbit determination(IROD)problem for space rendezvous with non-cooperated target is developed,where a method of hybrid dynamics with the concept of virtual formation is introduced to analytically solve the problem.Emphasis is placed on developing the solution based on hybrid dynamics(i.e.,Clohessy-Wiltshire equations and two-body dynamics),obtaining formation geometries that produce relative orbit state observability,and deriving the approximate analytic error covariance for the IROD solution.A standard Monte Carlo simulation system based on two-body dynamics is used to verify the feasibility and evaluate the performance proposed algorithms.The sensitivity of the solution accuracy to the formation geometry,observation numbers is presented and discussed.展开更多
The visibility for low earth orbit（LEO） satellites provided by the BeiDou-2 system is analyzed and compared with the global positioning system（GPS）. In addition, the spaceborne receivers＇ observations are simulat...The visibility for low earth orbit（LEO） satellites provided by the BeiDou-2 system is analyzed and compared with the global positioning system（GPS）. In addition, the spaceborne receivers＇ observations are simulated by the BeiDou satellites broadcast ephemeris and LEO satellites orbits. The precise orbit determination（POD） results show that the along-track component accuracy is much better over the service area than the non-service area, while the accuracy of the other two directions keeps at the same level over different areas. However, the 3-dimensional（3D） accuracy over the two areas shows almost no difference. Only taking into consideration the observation noise and navigation satellite ephemeris errors, the 3D accuracy of the POD is about30 cm. As for the precise relative orbit determination（PROD）, the 3D accuracy is much better over the eastern hemisphere than that of the western hemisphere. The baseline length accuracy is 3.4 mm over the service area, and it is still better than 1 cm over the non-service area. This paper demonstrates that the BeiDou regional constellation could provide global service to LEO satellites for the POD and the PROD. Finally, the benefit of geostationary earth orbit（GEO） satellites is illustrated for POD.展开更多
Relative navigation is a key enabling technology for space missions such as on-orbit servicing and space situational awareness.Given that there are several special advantages of space relative navigation using angles-...Relative navigation is a key enabling technology for space missions such as on-orbit servicing and space situational awareness.Given that there are several special advantages of space relative navigation using angles-only measurements from passive optical sensors,angles-only relative navigation is considered as one of the best potential approaches in the field of space relative navigation.However,angles-only relative navigation is well-known for its range observability problem.To overcome this observability problem,many studies have been conducted over the past decades.In this study,we present a comprehensive review of state-of-the-art space relative navigation based on angles-only measurements.The emphasis is on the observability problem and solutions to angles-only relative navigation,where the review of the solutions is categorized into four classes based on the intrinsic principle:complicated dynamics approach,multi-line of sight(multi-LOS)approach,sensor offset center-of-mass approach,and orbit maneuver approach.Then,the fight demonstration results of angles-only relative navigation in the two projects are briefly reviewed.Finally,conclusions of this study and recommendations for further research are presented.展开更多
基金supported by the National Natural Science Foundation of China (12272168)the Foundation of Science and Technology on Space Intelligent Control Laboratory (HTKJ2023KL502015)。
文摘Angles-only relative orbit determination for space non-cooperative targets based on passive sensor is subject to weakly observable problem of the relative state between two spacecraft. Previously, the evidence for angles-only observability was found by using cylindrical dynamics, however, the solution of orbit determination is still not provided. This study develops a relative orbit determination algorithm with the cylindrical dynamics based on differential evolution. Firstly, the relative motion dynamics and line-of-sight measurement model for nearcircular orbit are established in cylindrical coordinate system.Secondly, the observability is qualitatively analyzed by using the dynamics and measurement model where the unobservable geometry is found. Then, the angles-only relative orbit determination problem is modeled into an optimal searching frame and an improved differential evolution algorithm is introduced to solve the problem. Finally, the proposed algorithm is verified and tested by a set of numerical simulations in the context of highEarth and low-Earth cases. The results show that initial relative orbit determination(IROD) solution with an appropriate accuracy in a relative short span is achieved, which can be used to initialize the navigation filter.
基金supported by the National Natural Science Foundation of China (Nos. 91438202, 61370013)
文摘Low-Earth-Orbit（LEO） formation-flying satellites have been widely applied in many kinds of space geodesy. Precise Relative Orbit Determination（PROD） is an essential prerequisite for the LEO formation-flying satellites to complete their mission in space. The contribution of the BeiDou Navigation Satellite System（BDS） to the accuracy and reliability of PROD of LEO formation-flying satellites based on a Global Positioning System（GPS） is studied using a simulation method. Firstly, when BDS is added to GPS, the mean number of visible satellites increases from9.71 to 21.58. Secondly, the results show that the 3-Dimensional（3 D） accuracy of PROD, based on BDS-only, GPS-only and BDS ＋ GPS, is 0.74 mm, 0.66 mm and 0.52 mm, respectively. When BDS co-works with GPS, the accuracy increases by 29.73%. Geostationary-Earth-Orbit（GEO） satellites and Inclined Geosynchronous-Orbit（IGSO） satellites are only distributed over the Asia-Pacific region; however, they could provide a global improvement to PROD. The difference in PROD results between the Asia-Pacific region and the non-Asia-Pacific region is not apparent. Furthermore, the value of the Ambiguity Dilution Of Precision（ADOP）, based on BDS ＋ GPS, decreases by 7.50% and 8.26%, respectively, compared with BDS-only and GPS-only. Finally, if the relative position between satellites is only a few kilometres, the effect of ephemeris errors on PROD could be ignored. However, for a several-hundred-kilometre separation of the LEO satellites, the SingleDifference（SD） ephemeris errors of GEO satellites would be on the order of centimetres. The experimental results show that when IGSO satellites and Medium-Earth-Orbit（MEO） satellites co-work with GEO satellites, the accuracy decreases by 17.02%.
基金Supported by the National Natural Science Foundation of China (No. 40874004, No.40504002)the National 973 Program of China (No.2006CB701301)+1 种基金the National 863 Program of China (No. 2006AA12Z326, No. 2007AA12Z345)the 111 Project(No. B07037)
文摘When formation flying spacecrafts are used as platform to gain earth oriented observation, precise baselines between these spacecrafts are always essential. Gravity recovery and climate experiment （GRACE） mission is aimed at mapping the global gravity field and its variation. Accurate baseline of GRACE satellites is necessary for the gravity field modeling. The determination of kinematic and reduced dynamic relative orbits of twin satellites has been studied in this paper, and an accuracy of 2 mm for dynamic relative orbits and 5 mm for kinematic ones can be obtained, whereby most of the double difference onboard GPS ambiguities are resolved.
基金this work is supported in part by the National Postdoctoral Program for Innovative Talents(No.BX201700304)the Foundation of Science and Technology on Aerospace Flight Dynamics Laboratory(No.61422100306707).
文摘This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for non-cooperative target close-in proximity operations when the camera offset from the vehicle center-of-mass allows for range observability.In previous work,the solution to this problem had been shown to be non-global optimal in the sense of least square and had only been discussed in the context of Clohessy–Wiltshire.In this paper,the emphasis is placed on developing a more compact and improved solution to the problem by using state augmentation least square method in the context of the Clohessy–Wiltshire and Tschauner–Hempel dynamics,derivation of corresponding error covariance,and performance analysis for typical rendezvous missions.A two-body Monte Carlo simulation system is used to evaluate the performance of the solution.The sensitivity of the solution accuracy to camera offset,observation period,and the number of observations are presented and discussed.
基金the Natural Science Foundation of China(11802119)the National Postdoctoral Program for Innovative Talents(BX201700304)Fundamental Research Funds for Central Universities(NT2019023).
文摘A closed-form solution to the angles-only initial relative orbit determination(IROD)problem for space rendezvous with non-cooperated target is developed,where a method of hybrid dynamics with the concept of virtual formation is introduced to analytically solve the problem.Emphasis is placed on developing the solution based on hybrid dynamics(i.e.,Clohessy-Wiltshire equations and two-body dynamics),obtaining formation geometries that produce relative orbit state observability,and deriving the approximate analytic error covariance for the IROD solution.A standard Monte Carlo simulation system based on two-body dynamics is used to verify the feasibility and evaluate the performance proposed algorithms.The sensitivity of the solution accuracy to the formation geometry,observation numbers is presented and discussed.
基金co-supported by the National Natural Science Foundation of China (Nos: 61002033, 61370013)the Program for New Century Excellent Talents in University and the Scientific Research Foundation for the Returned Overseas Chinese Scholars of Ministry of Education of China
文摘The visibility for low earth orbit（LEO） satellites provided by the BeiDou-2 system is analyzed and compared with the global positioning system（GPS）. In addition, the spaceborne receivers＇ observations are simulated by the BeiDou satellites broadcast ephemeris and LEO satellites orbits. The precise orbit determination（POD） results show that the along-track component accuracy is much better over the service area than the non-service area, while the accuracy of the other two directions keeps at the same level over different areas. However, the 3-dimensional（3D） accuracy over the two areas shows almost no difference. Only taking into consideration the observation noise and navigation satellite ephemeris errors, the 3D accuracy of the POD is about30 cm. As for the precise relative orbit determination（PROD）, the 3D accuracy is much better over the eastern hemisphere than that of the western hemisphere. The baseline length accuracy is 3.4 mm over the service area, and it is still better than 1 cm over the non-service area. This paper demonstrates that the BeiDou regional constellation could provide global service to LEO satellites for the POD and the PROD. Finally, the benefit of geostationary earth orbit（GEO） satellites is illustrated for POD.
基金supported by the National Natural Science Foundation of China(12272168,11802119)Foundation of Science and Technology on Space Intelligent Control Laboratory(6142208200303,2021-JCJQ-LB-010-04).
文摘Relative navigation is a key enabling technology for space missions such as on-orbit servicing and space situational awareness.Given that there are several special advantages of space relative navigation using angles-only measurements from passive optical sensors,angles-only relative navigation is considered as one of the best potential approaches in the field of space relative navigation.However,angles-only relative navigation is well-known for its range observability problem.To overcome this observability problem,many studies have been conducted over the past decades.In this study,we present a comprehensive review of state-of-the-art space relative navigation based on angles-only measurements.The emphasis is on the observability problem and solutions to angles-only relative navigation,where the review of the solutions is categorized into four classes based on the intrinsic principle:complicated dynamics approach,multi-line of sight(multi-LOS)approach,sensor offset center-of-mass approach,and orbit maneuver approach.Then,the fight demonstration results of angles-only relative navigation in the two projects are briefly reviewed.Finally,conclusions of this study and recommendations for further research are presented.
