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Author

Li Liu

Bio: Li Liu is an academic researcher from Chinese Academy of Sciences. The author has contributed to research in topics: Satellite & Satellite navigation. The author has an hindex of 13, co-authored 28 publications receiving 507 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the authors proposed a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy, where the derived clock offsets are used for time synchronization, and the derived geometry distances are used by the satellite for autonomous orbit determination.
Abstract: Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure The ranging error of the ISL measurements is less than 025 ns This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 05 ns The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination Therefore, the hardware delays are estimated simultaneously with the satellite orbits To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination The root-mean-square values of orbit determination residuals are within 100 cm, and the standard deviation of the estimated ISL hardware delays is within 02 ns The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits The results indicate that the radial overlap differences between the autonomous orbits are less than 150 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 100 cm for the MEO satellites The SLR residuals are approximately 150 cm for the IGSO satellites and approximately 100 cm for the MEO satellites, representing an improvement over the L-band orbits

77 citations

Journal ArticleDOI
TL;DR: This study estimates orbital elements and clock errors for a 3GEO+2IGSO constellation using a multi-satellite precise orbit determination (MPOD) strategy, with which clock error elimination algorithm is applied to separate orbital and clock estimates to improve numerical efficiency.
Abstract: 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 obtained by simultaneously processing both tracking data and TS data. Consequently, inconsistency between tracking system and TS system caused by remaining instrumental errors not calibrated may decrease navigation accuracy. On the other hand, POD for the mixed constellation of GEO/IGSO/MEO with the regional tracking network leads to parameter estimations that are highly correlated. Notorious example of correlation is found between GEO’s orbital elements and its clock errors. We estimate orbital elements and clock errors for a 3GEO+2IGSO constellation in this study using a multi-satellite precise orbit determination (MPOD) strategy, with which clock error elimination algorithm is applied to separate orbital and clock estimates to improve numerical efficiency. Satellite Laser Ranging (SLR) data are used to evaluate User Ranging Error (URE), which is the orbital error projected on a receiver’s line-of-sight direction. Two-way radio-wave time transfer measurements are used to evaluate clock errors. Experimenting with data from the regional tracking network, we conclude that the fitting of code data is better than 1 m in terms of Root-Mean-Square (RMS), and fitting of carrier phase is better than 1 cm. For orbital evaluation, difference between computed receiver-satellite ranging based on estimated orbits and SLR measurements is better than 1 m (RMS). For clock estimates evaluation, 2-hour linear-fitting shows that the satellite clock rates are about 1.E-10 s/s, while receiver clock rates are about 1×10−13–1×10−12 s/s. For the 72-hour POD experiment, the average differences between POD satellite clock rates estimates and clock measurements based on TS system are about 1×10−13 s/s, and for receiver clock rates, the differences are about 1×10−15 s/s.

64 citations

Journal ArticleDOI
TL;DR: In this article, the frequency stability, clock prediction accuracy and clock rate variation characteristics of the third generation of Beidou Satellite Navigation System (BDS3) experimental satellites were analyzed using the high-precision clock values obtained by satellite-ground and inter-satellite measurement and communication systems.
Abstract: Various types of onboard atomic clocks such as rubidium, cesium and hydrogen have different frequency accuracies and frequency drift rate characteristics. A passive hydrogen maser (PHM) has the advantage of low-frequency drift over a long period, which is suitable for long-term autonomous satellite time keeping. The third generation of Beidou Satellite Navigation System (BDS3) is equipped with PHMs which have been independently developed by China for their IGSO and MEO experimental satellites. Including Galileo, it is the second global satellite navigation system that uses PHM as a frequency standard for navigation signals. We briefly introduce the PHM design at the Shanghai Astronomical Observatory (SHAO) and detailed performance evaluation of in-orbit PHMs. Using the high-precision clock values obtained by satellite-ground and inter-satellite measurement and communication systems, we analyze the frequency stability, clock prediction accuracy and clock rate variation characteristics of the BDS3 experimental satellites. The results show that the in-orbit PHM frequency stability of the BDS3 is approximately 6 × 10−15 at 1-day intervals, which is better than those of other types of onboard atomic clocks. The BDS3 PHM 2-, 10-h and 7-day clock prediction precision values are 0.26, 0.4 and 2.2 ns, respectively, which are better than those of the BDS3 rubidium clock and most of the GPS Block IIF and Galileo clocks. The BDS3 PHM 15-day clock rate variation is − 1.83 × 10−14 s/s, which indicates an extremely small frequency drift. The 15-day long-term stability results show that the BDS3 PHM in-orbit stability is roughly the same as the ground performance test. The PHM is expected to provide a highly stable time and frequency standard in the autonomous navigation case.

59 citations

Journal ArticleDOI
TL;DR: In this paper, a new concept called united ambiguity decorrelation (UIC) is proposed for multidimensional ambiguity decor correlation. But the HL process performs very well in high-dimensional ambiguity-decorrelation tests.
Abstract: Ambiguity decorrelation is a useful technique for rapid integer ambiguity fixing. It plays an important role in the least-squares ambiguity decorrelation adjustment (Lambda) method. An approach to multi-dimension ambiguity decorrelation is proposed by the introduction of a new concept: united ambiguity decorrelation. It is found that united ambiguity decorrelation can provide a rapid and effective route to ambiguity decorrelation. An approach to united ambiguity decorrelation, the HL process, is described in detail. The HL process performs very well in high-dimension ambiguity decorrelation tests.

56 citations

Journal ArticleDOI
TL;DR: The results show that the inter-satellite link (ISL) contributes a lot to the accuracy improvement of orbit determination and time synchronization for the whole constellation.
Abstract: BeiDou Global Navigation Satellite System (BDS-3) not only performs the normal positioning, navigation and timing (PNT) functions, but also provides featured services, which are divided into geostationary orbit (GEO) and medium earth orbit (MEO) satellite-based featured services in this paper. The former refers to regional services consisting of the regional short message communication service (RSMCS), the radio determination satellite service (RDSS), the BDS satellite-based augmented service (BDSBAS) and the satellite-based precise point positioning service via B2b signal (B2b-PPP). The latter refers to global services consisting of the global short message communication service (GSMCS) and the MEO satellite-based search and rescue (MEOSAR) service. The focus of this paper is to describe these featured services and evaluate their performances. The results show that the inter-satellite link (ISL) contributes a lot to the accuracy improvement of orbit determination and time synchronization for the whole constellation. Compared with some other final products, the root mean squares (RMS) of the BDS-3 precise orbits and broadcast clock are 25.1 cm and 2.01 ns, respectively. The positioning accuracy of single frequency is better than 6 m, and that of the generalized RDSS is usually better than 12 m. For featured services, the success rates of RSMCS and GSMCS are better than 99.9% and 95.6%, respectively; the positioning accuracies of single and dual frequency BDSBAS are better than 3 and 2 m, respectively; the positioning accuracy of B2b-PPP is better than 0.6 m, and the convergence time is usually smaller than 30 min; the single station test shows that the success rate of MEOSAR is better than 99%. Due to the ISL realization in the BDS-3 constellation, the performance and capacities of the global featured services are improved significantly.

53 citations


Cited by
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Journal ArticleDOI
TL;DR: The relations between the LAMBDA method and some relevant methods in the information theory literature are pointed out when it is introduced and several strategies are proposed to reduce the computational complexity.
Abstract: The least-squares ambiguity Decorrelation (LAMBDA) method has been widely used in GNSS for fixing integer ambiguities. It can also solve any integer least squares (ILS) problem arising from other applications. For real time applications with high dimensions, the computational speed is crucial. A modified LAMBDA (MLAMBDA) method is presented. Several strategies are proposed to reduce the computational complexity of the LAMBDA method. Numerical simulations show that MLAMBDA is (much) faster than LAMBDA. The relations between the LAMBDA method and some relevant methods in the information theory literature are pointed out when we introduce its main procedures.

346 citations

Journal ArticleDOI
TL;DR: The basic performance of BDS-3 is described and some methods to improve the positioning, navigation and timing (PNT) service are suggested and the comprehensive and resilient PNT infrastructures are proposed for the future seamless PNT services.
Abstract: The core performance elements of global navigation satellite system include availability, continuity, integrity and accuracy, all of which are particularly important for the developing BeiDou global navigation satellite system (BDS-3). This paper describes the basic performance of BDS-3 and suggests some methods to improve the positioning, navigation and timing (PNT) service. The precision of the BDS-3 post-processing orbit can reach centimeter level, the average satellite clock offset uncertainty of 18 medium circular orbit satellites is 1.55 ns and the average signal-in-space ranging error is approximately 0.474 m. The future possible improvements for the BeiDou navigation system are also discussed. It is suggested to increase the orbital inclination of the inclined geostationary orbit (IGSO) satellites to improve the PNT service in the Arctic region. The IGSO satellite can perform part of the geostationary orbit (GEO) satellite’s functions to solve the southern occlusion problem of the GEO satellite service in the northern hemisphere (namely the “south wall effect”). The space-borne inertial navigation system could be used to realize continuous orbit determination during satellite maneuver. In addition, high-accuracy space-borne hydrogen clock or cesium clock can be used to maintain the time system in the autonomous navigation mode, and stability of spatial datum. Furthermore, the ionospheric delay correction model of BDS-3 for all signals should be unified to avoid user confusion and improve positioning accuracy. Finally, to overcome the vulnerability of satellite navigation system, the comprehensive and resilient PNT infrastructures are proposed for the future seamless PNT services.

279 citations

Journal ArticleDOI
TL;DR: To facilitate the joint analysis of GNSS observations and satellite laser ranging measurements, laser retroreflector array coordinates consistent with the IGS-specific spacecraft frame conventions are provided in addition to representative antenna offset values for all GNSS constellations.

176 citations

Journal ArticleDOI
TL;DR: An integrated indoor positioning system (IPS) combining IMU and UWB through the extended Kalman filter (EKF) and unscented Kalmanfilter (UKF) to improve the robustness and accuracy and two random motion approximation model algorithms are proposed and evaluated in the real environment.
Abstract: The emerging Internet of Things (IoT) applications, such as smart manufacturing and smart home, lead to a huge demand on the provisioning of low-cost and high-accuracy positioning and navigation solutions. Inertial measurement unit (IMU) can provide an accurate inertial navigation solution in a short time but its positioning error increases fast with time due to the cumulative error of accelerometer measurement. On the other hand, ultrawideband (UWB) positioning and navigation accuracy will be affected by the actual environment and may lead to uncertain jumps even under line-of-sight (LOS) conditions. Therefore, it is hard to use a standalone positioning and navigation system to achieve high accuracy in indoor environments. In this article, we propose an integrated indoor positioning system (IPS) combining IMU and UWB through the extended Kalman filter (EKF) and unscented Kalman filter (UKF) to improve the robustness and accuracy. We also discuss the relationship between the geometric distribution of the base stations (BSs) and the dilution of precision (DOP) to reasonably deploy the BSs. The simulation results show that the prior information provided by IMU can significantly suppress the observation error of UWB. It is also shown that the integrated positioning and navigation accuracy of IPS significantly improves that of the least squares (LSs) algorithm, which only depends on UWB measurements. Moreover, the proposed algorithm has high computational efficiency and can realize real-time computation on general embedded devices. In addition, two random motion approximation model algorithms are proposed and evaluated in the real environment. The experimental results show that the two algorithms can achieve certain robustness and continuous tracking ability in the actual IPS.

150 citations

Journal ArticleDOI
Peiliang Xu1
TL;DR: A random simulation approach is proposed and an inverse integer Cholesky decorrelation method is proposed, which will be shown to out-perform the integer Gaussian decorrelation and the Lenstra, Lenstra and Lovász (LLL) algorithm, and indicates that the integerGaussian decor correlation is not the best decorrelation technique and that further improvement is possible.
Abstract: (i) A random simulation approach is proposed, which is at the centre of a numerical comparison of the performances of different GPS decorrelation methods. The most significant advantage of the approach is that it does not depend on nor favour any particular satellite–receiver geometry and weighting system. (ii) An inverse integer Cholesky decorrelation method is proposed, which will be shown to out-perform the integer Gaussian decorrelation and the Lenstra, Lenstra and Lovasz (LLL) algorithm, and thus indicates that the integer Gaussian decorrelation is not the best decorrelation technique and that further improvement is possible. (iii) The performance study of the LLL algorithm is the first of its kind and the results have shown that the algorithm can indeed be used for decorrelation, but that it performs worse than the integer Gaussian decorrelation and the inverse integer Cholesky decorrelation. (iv) Simulations have also shown that no decorrelation techniques available to date can guarantee a smaller condition number, especially in the case of high dimension, although reducing the condition number is the goal of decorrelation.

109 citations