Orbit determination for geostationary satellites with the combination of transfer ranging and pseudorange data

Geostationary satellites(GEOs) play a significant role in the regional satellite navigation system.Simulation experiments show that the clock corrections could be mitigated through a single strategy or double differencing strategies for a navigation constellation,but for the mode of individual GEO orbit determination,high precision orbit and clock correction could not be obtained in the orbit determination based on the pseudorange data.A new GEO combined precise orbit determination(POD) strategy is studied in this paper,which combines pseudorange data and C-band transfer ranging data.This strategy overcomes the deficiency of C-band transfer ranging caused by limited stations and tracking time available.With the combination of transfer ranging and pseudorange data,clock corrections between the GEO and the stations can be estimated simultaneously along with orbital parameters,maintaining self-consistency between the satellite ephemeris and clock correction parameters.The error covariance analysis is conducted to illuminate the contributions from the transfer ranging data and the psudoranging data.Using data collected for a Chinese GEO satellite with 3 C-band transfer ranging stations and 4 L-band pseudorange tracking stations,POD experiments indicate that a meter-level accuracy is achievable.The root-mean-square(RMS) of the post-fit C-band ranging data is about 0.203 m,and the RMS of the post-fit pseudorange is 0.408 m.Radial component errors of the POD experiments are independently evaluated with the satellite laser ranging(SLR) data from a station in Beijing,with the residual RMS of 0.076 m.The SLR evaluation also suggests that for 2-h orbital predication,the predicted radial error is about 0.404 m,and the clock correction error is about 1.38 ns.Even for the combination of one C-band transfer ranging station and 4 pseudorange stations,POD is able to achieve a reasonable accuracy with the radial error of 0.280 m and the 2-h predicted radial error of 0.888 m.Clock synchronization between the GEO and tracking stations is achieved with an estimated accuracy of about 1.55 ns,meeting the navigation service requirements.     

Satellite-station time synchronization information based real-time orbit error monitoring and correction of navigation satellite in Beidou System

Satellite-station two-way time comparison is a typical design in Beidou System(BDS)which is significantly different from other satellite navigation systems.As a type of two-way time comparison method,BDS time synchronization is hardly influenced by satellite orbit error,atmosphere delay,tracking station coordinate error and measurement model error.Meanwhile,single-way time comparison can be realized through the method of Multi-satellite Precision Orbit Determination(MPOD)with pseudo-range and carrier phase of monitor receiver.It is proved in the constellation of 3GEO/2IGSO that the radial orbit error can be reflected in the difference between two-way time comparison and single-way time comparison,and that may lead to a substitute for orbit evaluation by SLR.In this article,the relation between orbit error and difference of two-way and single-way time comparison is illustrated based on the whole constellation of BDS.Considering the all-weather and real-time operation mode of two-way time comparison,the orbit error could be quantifiably monitored in a real-time mode through comparing two-way and single-way time synchronization.In addition,the orbit error can be predicted and corrected in a short time based on its periodic characteristic.It is described in the experiments of GEO and IGSO that the prediction accuracy of space signal can be obviously improved when the prediction orbit error is sent to the users through navigation message,and then the UERE including terminal error can be reduced from 0.1 m to 0.4 m while the average accuracy can be improved more than 27%.Though it is still hard to make accuracy improvement for Precision Orbit Determination(POD)and orbit prediction because of the confined tracking net and the difficulties in dynamic model optimization,in this paper,a practical method for orbit accuracy improvement is proposed based on two-way time comparison which can result in the reflection of orbit error.     

GEO and IGSO joint precise orbit determination

Experiments and analyses are carried out for GEO and joint GEO/IGSO precise orbit determination using data recorded by China's regional tracking network.Results show that joint GEO/IGSO orbit determination effectively solves the problem of poor observation geometry for GEO satellites.The laser radial evaluation thus confirms that precision is as good as less than 0.1 m.In the case of joint orbit determination,solving the empirical acceleration can reduce errors introduced by the imprecise solar radiation pr...     

SIS accuracy and service performance of the BDS-3 basic system

On December 27,2018,the basic system of the third-generation BeiDou navigation satellite system(BDS-3)completed the deployment of its constellation of 18 MEO networking satellites as well as the construction of the operation control system(OCS)and began to provide basic navigation services to users worldwide.Compared with BDS-2,BDS-3 aims to offer users better navigation signals and higher precision with a series of new technologies.For example,the spaceborne atomic clock of BDS-3 is upgraded for higher performance,the Ka-band inter-satellite link is adopted for inter-satellite ranging and communication,and new B1C and B2a signals are broadcast in addition to B1I and B3I signals(compatible with BDS-2).In addition,a 9-parameter model based on a spherical harmonic function is employed for ionospheric delay corrections.Using the observation data from 18 satellites of the basic system,this paper conducts a comprehensive evaluation of the pseudorange measurement characteristics,signal-in-space(SIS)accuracy of navigation messages and global service capability of BDS-3.The results indicate that the pseudorange measurement multipath effect and observation noise of BDS-3 satellites are better than those of BDS-2;additionally,with the support of inter-satellite links,the user range error(URE)of the BDS-3 satellite broadcast ephemeris is better than 10 cm,the precision of the broadcast clock parameter is better than 1.5 ns,and the SIS accuracy is better than 0.6 m overall.Different from the traditional Klobuchar model,the BeiDou global broadcast ionospheric delay correction model(BDGIM)can provide ionospheric delay corrections better than 70%for worldwide single-frequency users.The service capability evaluation of the basic system consists mainly of the accuracy improvement of the B1I and B3I signals according to BDS-2 as well as the global positioning accuracy of the new signals.These results prove that the BDS-3 basic system has achieved the design goal;that is,both the horizontal and the vertical global positioning accuracies are better than 10 m(95%).In the future,6 MEO satellites as well as 3 GEO satellites and 3 IGSO satellites for regional enhancement purposes will be deployed for full operation;consequently,BDS-3 will definitely provide a higher SIS accuracy and better service capability.     

The principle of the positioning system based on communication satellites

It is a long dream to realize the communication and navigation functionality in a satellite system in the world. This paper introduces how to establish the system, a positioning system based on communication satellites called Chinese Area Positioning System (CAPS). Instead of the typical navigation satellites, the communication satellites are configured firstly to transfer navigation signals from ground stations, and can be used to obtain service of the positioning, velocity and time, and to achieve the function of navigation and positioning. Some key technique issues should be first solved; they include the accuracy position determination and orbit prediction of the communication satellites, the measuring and calculation of transfer time of the signals, the carrier frequency drift in communication satellite signal transfer, how to improve the geometrical configuration of the constellation in the system, and the integration of navigation & communication. Several innovative methods are developed to make the new system have full functions of navigation and communication. Based on the development of crucial techniques and methods, the CAPS demonstration system has been designed and developed. Four communication satellites in the geosynchronous orbit (GEO) located at 87.5°E, 110.5°E, 134°E, 142°E and barometric altimetry are used in the CAPS system. The GEO satellites located at 134°E and 142°E are decommissioned GEO (DGEO) satellites. C-band is used as the navigation band. Dual frequency at C1=4143.15 MHz and C2=3826.02 MHz as well as dual codes with standard code (CA code and precision code (P code)) are adopted. The ground segment consists of five ground stations; the master station is in Lintong, Xi’an. The ground stations take a lot of responsibilities, including monitor and management of the operation of all system components, determination of the satellite position and prediction of the satellite orbit, accomplishment of the virtual atomic clock measurement, transmission and receiving navigation signals to and from each satellite. In the north, the south, the east, the west and the center of Chinese main land, the function of CAPS demonstration system is checked and measured. In cars and on board the system is also checked and measured. The results are as follow: CA-code, horizontal positioning accuracy, 15–25 m (1 σ), vertical, 1–3 m; P-code, horizontal positioning accuracy, 8–10 m (1 σ), vertical, 1–3 m; velocity accuracy, CA-code, 0.13–0.30 m/s, P-code, 0.15–0.17 m/s; time accuracy, CA-code, 160 ns, P-code, 13 ns; determination accuracy of orbit ≤2 m. About 20 million US $ and two years are spent for the development of demonstration. A complete CAPS system is now being established. Supported by the National Natural Science Foundation of China (Grant No. 10453001), the National Basic Research Program of China (Grant No. 2007CB815500), the National High Technology Research and Development Program of China (Grant No. 2004AA105030), and the Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering (Grant No. KGCXI-21)     

Multi-life cycles utilization of retired satellites

Retired geosynchronous (GEO) communication satellites affect the GEO orbit environment in outer space. According to the new concept of modern design, the authors propose creatively a method of reusing retired GEO communication satellites, through adjusting retired GEO satellites to slightly inclined orbit geosynchronous (SIGSO) satellites. After these retired satellites are applied to the navigation and communication system, integrity of navigation system and positioning accuracy of the system is improved. Meanwhile, some transponders on these retired satellites can be used to establish a new satellite communication service, and initiate the study and utilization of the multi-life cycle for retired satellites. Experimental results show that this project has significant social value and can make remarkable economic benefit. Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815501) and the National High Technology Research and Development Program of China (Grant No. 2007AA12z343)     

Selection of satellite constellation framework of CAPS

Based on the idea of transmitting the satellite navigation and positioning system, taking the distribution and variation of the Position Dilution of Precision factor (PDOP), which is closely related with the precision of navigation and positioning, within the China area as the primary criterion, we analyze and discuss the tentative plan of constellation configuration consisting of geosynchronous orbit (GEO) communication satellites and inclined geosynchronous orbit (IGSO) satellites for the transmitting Chinese Area Positioning System (CAPS). We emphatically consider the effect on the PDOP by the three major orbit parameters including the inclination, eccentricity and right ascension of the ascending node (RAAN) of IGSO satellites, to research the strategies of the constellation configuration of CAPS through software emulation. Various constellation configurations are analyzed and compared and the results show that the constellation configuration, consisting of three IGSO communication satellites in three orbits with the same inclination as 50°, the difference in RAAN as 120° and the same “8” shaped ground track centered near 115°E and four or five GEO communication satellites within 60°E to 150°E, can satisfy the requirement that Chinese domain is availably covered and the navigation and positioning with high precision could be obtained. Three relatively excellent constellation configurations are initially suggested and some concerned issues are discussed in this work. Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815501) and the Chinese National Programs for High Technology Research and Development (Grant No. 2007AA12z343)     

Analysis of RDSS positioning accuracy based on RNSS wide area differential technique

The BeiDou Navigation Satellite System(BDS) provides Radio Navigation Service System(RNSS) as well as Radio Determination Service System(RDSS).RDSS users can obtain positioning by responding the Master Control Center(MCC) inquiries to signal transmitted via GEO satellite transponder.The positioning result can be calculated with elevation constraint by MCC.The primary error sources affecting the RDSS positioning accuracy are the RDSS signal transceiver delay,atmospheric trans-mission delay and GEO satellite position error.During GEO orbit maneuver,poor orbit forecast accuracy significantly impacts RDSS services.A real-time 3-D orbital correction method based on wide-area differential technique is raised to correct the orbital error.Results from the observation shows that the method can successfully improve positioning precision during orbital maneuver,independent from the RDSS reference station.This improvement can reach 50% in maximum.Accurate calibration of the RDSS signal transceiver delay precision and digital elevation map may have a critical role in high precise RDSS positioning services.     

Functions of retired GEO communication satellites in improving the PDOP value of CAPS

This paper briefly introduces the maneuverable feature of the slightly inclined geosynchronous orbit (SIGSO) satellites under a new control model degraded from the geosynchronous orbit (GEO) communication satellites which will retire as most of the fuel in these satellites has been consumed. Basing on the transmitting Chinese Area Positioning System (CAPS), the authors, by analyses, indicate that such satellites can make an improvement to CAPS constellation configuration, especially to the PDOP value from simulation. The results show that the use of SIGSO satellites can (1) actualize three-dimensional (3D) navigation and positioning compared with the situation, which, only using GEO satellites, cannot be carried out, and improve navigation and positioning accuracy to some extent; (2) reuse the communication services of these satellites for more years, and GEO communication satellites will be retired at a later time and delay their time to become space debris and reduce their pollution of the space environment, so that valuable space resources are maximally used. As for the use of these satellites in the transmitting positioning system, the authors present some views and suggestions in this work. Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815501) and the Chinese National Programs for High Technology Research and Development (Grant No. 2007AA12z343)     

Precise orbit determination of a maneuvered GEO satellite using CAPS ranging data

Wheel-off-loadings and orbital maneuvers of the GEO satellite result in additional accelerations to the satellite itself. Complex and difficult to model, these time varying accelerations are an important error source of precise orbit determination (POD). In most POD practices, only non-maneuver orbital arcs are treated. However, for some applications such as satellite navigation RDSS services, uninterrupted orbital ephemeris is demanded, requiring the development of POD strategies to be processed both during and after an orbital maneuver. We in this paper study the POD for a maneuvered GEO satellite, using high precision and high sampling rate ranging data obtained with Chinese Area Positioning System (CAPS). The strategy of long arc POD including maneuver arcs is studied by using telemetry data to model the maneuver thrust process. Combining the thrust and other orbital perturbations, a long arc of 6 days’ CAPS ranging data is analyzed. If the telemetry data are not available or contain significant errors, attempts are made to estimate thrusting parameters using CAPS ranging data in the POD as an alternative to properly account for the maneuver. Two strategies achieve reasonably good data fitting level in the tested arc with the maximal position difference being about 20 m. Supported by the National Natural Science Foundation of China (Grant No. 10703011) and the Science & Technology Commission of Shanghai Municipality of China (Grant No. 06DZ22101)     

Orbit determination and prediction accuracy analysis for a regional tracking network

China's COMPASS satellite navigation system relies on a regional tracking network to provide navigation services. Limited by its geographic border,the regional network is able to cover only 30% of the medium-earth-orbits(MEO). Accuracy of determined and predicted orbits is not able to satisfy system requirements if the tracking data processing strategy for global tracking network processing is used for the regional network. Two major error sources for orbital prediction are accuracy of initial orbital elements and dynamical modeling. To achieve better prediction accuracy,we propose a two-step orbit determination and prediction strategy. For step 1,only solar radiation pressure(SRP) parameters are estimated along with the orbital elements and other parameters; for step 2,all parameters are estimated but the SRP parameters are tightly constrained to their step 1 estimates. Experimenting with data from a regional GPS network,we conclude for orbital prediction using the proposed two-step strategy,the average user range error(URE) for 24-h prediction arcs is better than 0.6 m.     

Methods of rapid orbit forecasting after maneuvers for geostationary satellites

A geostationary (GEO) satellite may serve as a navigation satellite, but there is a problem that maneuvers frequently occur and the forces are difficult to model. Based on the technique of determining satellite orbits by transfer, a predicted orbit with high accuracy may be achieved by the method of statistical orbit determination in case of no maneuver force. The predicted orbit will soon be invalid after the maneuver starts, and it takes a long time to get a valid orbit after the maneuver ends. In order to improve ephemeris usability, the method of rapid orbit forecasting after maneuvers is studied. First, GEO satellite movement is analyzed in case of maneuvers based on the observation from the orbit measurement system by transfer. Then when a GEO satellite is in the free status just after maneuvers, the short arc observation is used to forecast the orbit. It is assumed that the common system bias and biases of each station are constant, which can be obtained from orbit determination with long arc observations. In this way, only 6 orbit elements would be solved by the method of statistical orbit determination, and the ephemeris with high accuracy may be soon obtained. Actual orbit forecasting with short arc observation for SINOSAT-1 satellite shows that, with the tracking network available, the precision of the predicted orbit (RMS of O-C) can reach about 5 m with 15 min arc observation, and about 3 m with 30 min arc observation. Supported by the National High Technology Research and Development Program of China (Grant No. 2006AA12Z322), the National Basic Research Program of China (Grant No. 2007CB815503), and the West Light Program of Chinese Academy of Sciences (Grant No. 2007LH01)     

Orbit determination and time synchronization for a GEO/IGSO satellite navigation constellation with regional tracking network

Aiming at regional services,the space segment of COMPASS (Phase I) satellite navigation system is a constellation of Geostationary Earth Orbit (GEO),Inclined Geostationary Earth Orbit (IGSO) and Medium Earth Orbit (MEO) satellites.Precise orbit determination (POD) for the satellites is limited by the geographic distribution of regional tracking stations.Independent time synchronization (TS) system is developed to supplement the regional tracking network,and satellite clock errors and orbit data may be obtai...     

COMPASS time synchronization and dissemination—Toward centimetre positioning accuracy

In this paper we investigate methods to achieve highly accurate time synchronization among the satellites of the COMPASS global navigation satellite system (GNSS). Owing to the special design of COMPASS which implements several geo-stationary satellites (GEO), time synchronization can be highly accurate via microwave links between ground stations to the GEO satellites. Serving as space-borne relay stations, the GEO satellites can further disseminate time and frequency signals to other satellites such as the inclined geo-synchronous (IGSO) and mid-earth orbit (MEO) satellites within the system. It is shown that, because of the accuracy in clock synchronization, the theoretical accuracy of COMPASS positioning and navigation will surpass that of the GPS. In addition, the COMPASS system can function with its entire positioning, navigation, and time-dissemination services even without the ground link, thus making it much more robust and secure. We further show that time dissemination using the COMPASS-GEO satellites to earth-fixed stations can achieve very high accuracy, to reach 100 ps in time dissemination and 3 cm in positioning accuracy, respectively. In this paper, we also analyze two feasible synchronization plans. All special and general relativistic effects related to COMPASS clocks frequency and time shifts are given. We conclude that COMPASS can reach centimeter-level positioning accuracy and discuss potential applications.     

A simplex method for the orbit determination of maneuvering satellites

A simplex method of orbit determination (SMOD) is presented to solve the problem of orbit determination for maneuvering satellites subject to small and continuous thrust. The objective function is established as the sum of the nth powers of the observation errors based on global positioning satellite (GPS) data. The convergence behavior of the proposed method is analyzed using a range of initial orbital parameter errors and n values to ensure the rapid and accurate convergence of the SMOD. For an uncontrolled satellite, the orbit obtained by the SMOD provides a position error compared with GPS data that is commensurate with that obtained by the least squares technique. For low Earth orbit satellite control, the precision of the acceleration produced by a small pulse thrust is less than 0.1% compared with the calibrated value. The orbit obtained by the SMOD is also compared with weak GPS data for a geostationary Earth orbit satellite over several days. The results show that the position accuracy is within 12.0 m. The working efficiency of the electric propulsion is about 67% compared with the designed value. The analyses provide the guidance for subsequent satellite control. The method is suitable for orbit determination of maneuvering satellites subject to small and continuous thrust.     

A new method of ionospheric-free hybrid differential positioning based on a double-antenna CAPS receiver

Chinese Area Positioning System (CAPS) is a transmitted satellite navigation system moved by the Chinese Academy of Sciences. Three basic modes of navigation and positioning with CAPS are given, and then a comparative analysis is made in this paper. In terms of the principle that the ionospheric delay is at an inverse ratio to the frequency square, a new ionospheric-free positioning method based on a double-antenna CAPS receiver is put forward. Then the hybrid differential observations and the solving equations and algorithms for one epoch and multi epochs are deduced according to the basic principle of the method. The method may remove the global errors in signal emission, propagation, transmission and receiving (e.g., ionospheric delay, hardware delay, and clock error). So it is very convenient for the single-epoch solution and multi-epoch navigation and positioning, and may efficiently improve the precision of real time CAPS navigation. Furthermore, the method can be used not only for the geometric orbit determination of CAPS GEO and IGSO satellites and the navigation and positioning, but also for the estimation of the tropospheric zenith delay, which is useful for the study of water vapor changes in the atmosphere. Polynomials are used in this method to express the tropospheric zenith delay and CAPS satellite orbits within the limited time interval, which reduces the number of unknown parameters and thus speeds the computation. Supported by the Knowledge Innovation Project of the Chinese Academy of Sciences (Grant No. KGCX1-21), the National Basic Research Program of China (Grant No. 2007CB815500), the National High Technology Research and Development Program of China (Grant No. 2006AA12z303), the National Natural Science Foundation of China (Grant No. 40774009), and the Special Project of Taishan Scholars of Shandong Province of China (Grant No. TSXZ0502)     

无人机侦察多目标实时定位技术研究

目标定位是无人机侦察系统中至关重要一步。为增强无人机侦察目标定位的实时性、提高定位精度及侦察效率,提出一种多目标实时定位的方法,建立主次目标定位几何关系及坐标转换模型,结合已知数据信息求取各目标大地坐标,并用蒙特卡洛法分析目标定位误差。最后,基于即将组网成功"北斗二代"卫星导航系统对无人机空中定位,同时采用递归最小二乘算法滤波处理,提高了目标定位精度。研究及实验结果表明,北斗导航定位能够有效提高无人机空中定位精度,且有望达到厘米级精度,同时采用RLS滤波处理能使目标定位精度提高10 m左右。该方法能够有效增强无人机定位实时性,提高定位精度及侦察效率。     

三轴稳定GEO卫星漫反射光变特性

利用天文测光方法研究了地球同步轨道卫星可见光波段的反射光变特性.以三轴稳定地球同步轨道通讯卫星为研究样本,进行了可见光波段的光学非高分辨成像观测,并使用天文标准星进行定标.基于相位角序列的测光观测数据表明:在大相位角区域卫星光变曲线分布与漫反射光照数学模型计算结果有很好的一致性,以卫星主体和太阳能电池板的漫反射效应为主;而在小相位角区域与漫反射模型计算结果有明显的差异,为卫星的太阳帆板镜面反射效应影响所致.     

Applications of two-way satellite time and frequency transfer in the BeiDou navigation satellite system

A two-way satellite time and frequency transfer(TWSTFT) device equipped in the BeiDou navigation satellite system(BDS)can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination(MPOD)method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service(IGS) analysis centers(ACs) show that the reference time difference between BeiDou time(BDT) and golbal positoning system(GPS) time(GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10.12, which is similar to the GPS IIR.     

Performance evaluation method of hybrid navigation constellations with invalid satellites

The construction of a navigation system plays an important role in the development of national politics,economy and military affairs.Nowadays,the Beidou navigation system is facing a transition period from the regional navigation system to the global one.For the global constellation,the system performance will not be seriously degraded when one or two satellites are invalid,but it is out of case for the regional constellation,which usually has fewer satellites and less redundancy.This paper deals with this ...