GPS Based Reduced-Dynamic Orbit Determination for Low Earth Orbiters with Ambiguity Fixing

The precise point positioning (PPP) is widely used as a typical representative of GNSS. But the main challenge of dual-frequency PPP is that it requires quite a long time to succeed in the ambiguity-fixed so it takes more than 30 min to obtain centimeter-level accuracy. A combination of GPS and low earth orbit (LEO) satellites can improve the diversity of available satellites' geometric distribution and reduce the correlation of observation data between epochs. Then the accuracy of float solution will be promoted and the ambiguity of GPS will take less time to get fixed. The purpose of this paper is to reduce the convergence time of PPP by the contribution of LEO satellites which have low earth orbit and move speedily. We adopt a free-ionosphere PPP model to combine GPS and LEO satellites. Numerous experimental results show that GPS/LEO PPP requires much less convergence time and gets higher positioning accuracy than that of PPP with GPS alone. In addition, an analysis is also made to compare GPS/LEO PPP and GPS/GLONASS PPP. The results indicate that GPS/LEO PPP also requires much less convergence time and gets higher positioning accuracy than that of GPS/GLONASS PPP when increasing the same number of available satellites. This proved that LEO satellites have more contribution to PPP performance than MEO.

Since Global Positioning System (GPS) has been routinely conducted in many engineering projects, it is also effectively applied to the assessment and preventing of forest and natural resources. Depending on the GPS survey method preferred in the applications performed around the forest environments, different level point positioning accuracy can be achieved. Traditionally, for many precise positioning applications, relative static positioning has been used. The data obtained have been analyzed with high-cost scientific and commercial software, which are required a good knowledge of processing procedures. However, in recent years, web based online services that use Precise Point Positioning (PPP) technique, developed as a special type of relative positioning, that enables to process and analyze the static data easily, have become a significant alternative for users. These developments on GPS based surveyings that significantly make contributions to the studies applied around the forest environment, in terms of time, cost, accuracy and labour are preferred in many engineering facilities. In this study, it is aimed to research performance of GPS PPP technique and web based online services in positioning applications especially performed around the forest environments. For this purpose, two test stations have been established in different locations around the forest area, located in Campus of Davutpasa, Yildiz Technical University, Istanbul, and stations have been observed repeatedly in static GPS surveying mode for 3 days and per day with 3-hours observation duration. The observations have been computed by commercial software as using final GPS ephemerides products so called TopconTools v8.2 and also by web based online services namely OPUS, AUSPOS, CSRS-PPP, GAPS and APPS. From the results, when 3D positioning differences have been examined, it is seen that the positional accuracy is range from 0.024 m to 0.251 m for TP01 and from 0.078 m to 1.033 m for TP02 with respect to both relative solution and PPP solution, which is used by web based online services. When the results have been examined for only CSRS-PPP, APPS and GAPS services, which are used PPP solution, it is seen that the positional accuracy for 3D positioning differences is range from 0.024 m to 0.251 m for TP01 and from 0.078 m to 0.859 m for TP02. The results show that since the static GPS data is collected for duration of 3-hours and more, PPP technique and the web based online services using this technique for precise positioning applications around the forest environment give effective solutions to the users and at the same time decrease the survey cost with respect to equipment and software.

: This paper represents orbit propagation and determination of Low Earth Orbit(LEO) satellites, which is immediate orbit satellite positioning. Beiseds, satellite global positioning system (GPS) configured satellite receiver provides position and velocity measures by navigating the filter to get the coordinates of the orbit propagation (OP), while the satellite orbit coordinates is an important basis for the task operation. The main contradictions in real time orbit which is determined by the problem are: orbit positioning accuracy and the amount of calculating two indicators; how to balance these two indicators. This article is dedicated to solving the problem of tradeoffs. To plan to use a non-linear filtering method for immediate orbit tasks requires more precise satellite orbit state parameters in a short time. Although the traditional extended Kalman filter (Extended Kalman Filter, EKF) method is widely used, its linear approximation of the drawbacks in dealing with nonlinear problems was especially evident, without compromising Kalman filter (Unsented Kalman Filter, UKF). As a new non-linear estimation method, it is measured at the estimated measurements on more and more applications. This paper will be the first study to UKF microsatellites in LEO orbit in real time, trying to explore the real-time precision orbit determination techniques.

The improvement of BDS Observation Geometry with LEO constellations in Orbit Determination

Owing to the intense tectonic activity and significant seasonal surface mass change, Southwest China is characterized by noticeable vertical land movement. We determined the vertical movement of Southwest China using 10 years of data from 41 continuous global positioning system (GPS) stations, gravity recovery and climate experiment (GRACE), and surface loading model (SLM). The annual variation in hydrological loading is the main factor causing the seasonal oscillation of surface deformation in Southwest China. Seasonal deformations captured by GPS, GRACE, and SLM are consistent to a certain extent, and the correlation coefficients between GPS/GRACE, and GPS/SLM are 0.82 and 0.81, respectively. After deducting the results yielded by GRACE and SLM from the GPS time series, the average reductions in root mean square were 41.3% and 38.0%, respectively. However, some systematic differences were observed among the annual amplitudes and phases of the seasonal deformations among the three products. For example, the average amplitudes estimated by GRACE and SLM were 7.4 mm and 6.1 mm, respectively, which were smaller than the amplitude deduced from GPS (9.7 mm). Furthermore, mean phase delays of 16, 22, and 6 days were observed between GPS/GRACE, GPS/SLM, and GRACE/SLM. The data processing errors and local geophysical signals in GPS and the underestimation of land water storage in GRACE and SLM were jointly responsible for the systemic differences. The simulated data show that the misestimating of hydrological loading can explain approximately 50%, 64%, and 83% of the phase delays between GPS/GRACE, GPS/SLM, and GRACE/SLM, respectively. In addition, we obtained long-term vertical crustal motion rates by subtracting the loading deformation rates estimated by GRACE from the linear rates of the GPS. The vertical crustal motion in this region is block-dependent. The Central Yunnan block and its eastern boundary are uplifted; meanwhile, the Southwest Yunnan block, which features stretching in the horizontal direction, appears to be subsiding. The aforementioned results can provide data support for the study of water resource utilization and geodynamics in Southwest China.

Precise Point Positioning (PPP) algorithms have been widely used in the Global Positioning System (GPS)-based applications. A PPP technique with a single receiver provides effective solutions where accurate absolute positioning is required. This paper provides the performance assessment of GPS PPP for detecting the displacements caused by an earthquake. For this purpose, the earthquake that occurred on 21 July 2017 at Kos-Bodrum with the impact of Mw 6.6 was investigated by analyzing the data of the permanent GPS stations located around the related region with the PPP technique. The location distances of these GPS stations range from 10 to 89 km to the epicenter of this earthquake. GPS data provided from seven permanent stations from the Continuously Operating Reference Stations-Turkey (CORS-TR) and local Bodrum CORS networks were processed to determine the co-seismic displacements during the earthquake. The data of these stations for days of year (DOYs) 200, 201, 202, and 203 were analyzed with post-process static PPP and kinematic PPP methods. GIPSY-OASIS II v6.4 was used for processing the data and all of the solutions were performed in the ITRF2008 reference frame. Two strategies were followed on the post-process static solutions. In the first strategy, 4-day data with 24-h observations were separately analyzed day by day. In the second strategy, the 24-h data were divided into 3-h duration, which is the minimum duration for optimum PPP solutions, and then the analyses were performed. When the displacements between DOYs 200 and 203 are considered in the 24-h data analysis, significant displacements have been observed through northwest direction in the northern stations whereas MUG1 is excluded. Moreover, there is significant displacement through the southeast direction in the station DATC located in the south of the epicenter. When the 3-h solutions are examined, displacements, especially on n and e directions, are observed starting from the solutions, which include Mw 6.6 earthquake. According to the kinematic PPP solutions, the effects of the Mw 6.6 earthquake can be seen clearly in the stations DATC, ORTA, TRKB, and YALI. Considering all outcomes, the PPP technique with both static and kinematic solutions provides effective results for detecting the displacements during the earthquake.

For real-time precise orbit determination (POD) of low earth orbit (LEO) satellites, high-accuracy global navigation satellite system (GNSS) orbit and clock products are necessary in real time. Recently, the Japanese multi-GNSS advanced demonstration of orbit and clock analysis precise point positioning (PPP) service and the new generation of the Australian/New Zealand satellite-based augmentation system (SBAS)-aided PPP service provide free and precise GNSS products that are directly broadcast through the navigation and geostationary earth orbit satellites, respectively. With the high quality of both products shown in this study, a 3D accuracy of centimeters can be achieved in the post-processing mode for the reduced-dynamic orbits of small LEO satellites having a duty cycle down to 40% and at sub-dm to dm level for the kinematic orbits. The results show a promising future for high-accuracy real-time POD onboard LEO satellites benefiting from the precise free-of-charge PPP corrections broadcast by navigation systems or SBAS.

In this study an integrated Newton-Raphson Method (NRM)/Extended Kalman Filter (EKF) Global Positioning System (GPS) based orbit determination for a Low Earth Orbit (LEO) satellite method is presented. The NRM and EKF algorithms are combined to estimate satellite's position and velocity vector components, respectively. Coarse position values computed at NRM preprocessing step are provided as measurement input to EKF algorithm. Orbital motion of LEO satellite is modelled with Keplerian and Newtonian equations taking into consideration the J2 perturbation effect caused by Earth's oblateness. Compared to traditional methods, utilizing such a preprocessing block (NRM) in filter design considerably reduces the complexity of the filter algorithm.

The precise orbit determination (POD) accuracy of the Chinese BeiDou Navigation Satellite System (BDS) is still not comparable to that of the Global Positioning System because of the unfavorable geometry of the BDS and the uneven distribution of BDS ground monitoring stations. Fortunately, low Earth orbit (LEO) satellites, serving as fast moving stations, can efficiently improve BDS geometry. Nearly all studies on Global Navigation Satellite System POD enhancement using large LEO constellations are based on simulations and their results are usually overly optimistic. The receivers mounted on a spacecraft or an LEO satellite are usually different from geodetic receivers and the observation conditions in space are more challenging than those on the ground. The noise level of spaceborne observations needs to be carefully calibrated. Moreover, spaceborne observational errors caused by space weather events, i.e., solar geomagnetic storms, are usually ignored. Accordingly, in this study, the actual spaceborne observation noises are first analyzed and then used in subsequent observation simulations. Then, the observation residuals from the actual-processed LEO POD during a solar storm on 8 September 2017 are extracted and added to the simulated spaceborne observations. The effect of the observational errors on the BDS POD augmented with different LEO constellation configurations is analyzed. The results indicate that the noise levels from the Swarm-A, GRACE-A, and Sentinel-3A satellites are different and that the carrier-phase measurement noise ranges from 2 mm to 6 mm. Such different noise levels for LEO spaceborne observations cause considerable differences in the BDS POD solutions. Experiments calculating the augmented BDS POD for different LEO constellations considering spaceborne observational errors extracted from the solar storm indicate that these errors have a significant influence on the accuracy of the BDS POD. The 3D root mean squares of the BDS GEO, IGSO, and MEO satellite orbits are 1.30 m, 1.16 m, and 1.02 m, respectively, with a Walker 2/1/0 LEO constellation, and increase to 1.57 m, 1.72 m, and 1.32 m, respectively, with a Walker 12/3/1 constellation. When the number of LEO satellites increases to 60, the precision of the BDS POD improves significantly to 0.89 m, 0.77 m, and 0.69 m for the GEO, IGSO, and MEO satellites, respectively. While 12 satellites are sufficient to enhance the BDS POD to the sub-decimeter level, up to 60 satellites can effectively reduce the influence of large spaceborne observational errors, i.e., from solar storms.

The Earth’s time-variable gravity field is of great significance to study mass change within the Earth’s system. Since 2002, the NASA-DLR Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE follow-on mission provide observations of monthly changes in the Earth gravity field with unprecedented accuracy and resolution by employing low-low satellite-to-satellite tracking (LLSST) measurements. In addition to LLSST, monthly gravity field models can be acquired from satellite laser ranging (SLR) and high-low satellite-to-satellite tracking (HLSST). The monthly gravity field solutions HLSST+SLR were derived by combining HLSST observations of low earth orbiting (LEO) satellites with SLR observations of geodetic satellites. Bandpass filtering was applied to the harmonic coefficients of HLSST+SLR solutions to reduce noise. In this study, we analyzed the performance of the monthly HLSST+SLR solutions in the spectral and spatial domains. The results show that: (1) the accuracies of HLSST+SLR solutions are comparable to those from GRACE for coefficients below degree 10, and significantly improved compared to those of SLR-only and HLSST-only solutions; (2) the effective spatial resolution could reach 1000 km, corresponding to the spherical harmonic coefficient degree 20, which is higher than that of the HLSST-only solutions. Compared with the GRACE solutions, the global mass redistribution features and magnitudes can be well identified from HLSST+SLR solutions at the spatial resolution of 1000 km, although with much noise. In the applications of regional mass recovery, the seasonal variations over the Amazon Basin and the long-term trend over Greenland derived from HLSST+SLR solutions truncated to degree 20 agree well with those from GRACE solutions without truncation, and the RMS of mass variations is 282 Gt over the Amazon Basin and 192 Gt in Greenland. We conclude that HLSST+SLR can be an alternative option to estimate temporal changes in the Earth gravity field, although with far less spatial resolution and lower accuracy than that offered by GRACE. This approach can monitor the large-scale mass transport during the data gaps between the GRACE and the GRACE follow-on missions.

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

An opportunistic navigation framework using low Earth orbit (LEO) satellites is analyzed. This framework, termed simultaneous tracking and navigation (STAN), estimates a navigating vehicle’s state along with the states of orbiting LEO satellites. STAN employs an extended Kalman filter (EKF) to fuse measurements from satellite receivers and an inertial navigation system (INS). The navigation performance is analyzed due to: (i) the vehicle being equipped with (1) different inertial measurement unit (IMU) grades: consumer, industrial, and tactical and (2) different receiver clock quality: temperature-compensated crystal oscillators (TCXO) and oven-controlled crystal oscillators (OCXO) and (ii) the LEO satellites being equipped with different transmitter clock quality: OCXO and chip-scale atomic clock (CSAC). Additionally, the effect of utilizing a large number of LEO satellites for navigation is investigated. This analysis provides insight into the achievable performance of STAN, which can serve as an alternative navigation system in global navigation satellite system (GNSS)-denied environments. The performance predictions from simulations are compared with experimental results with real signals from the Orbcomm LEO constellation. A close match between the simulation and experimental results is demonstrated for an unmanned aerial vehicle (UAV) navigating via the STAN framework with signals from two Orbcomm LEO satellites for 160 seconds, the last 35 seconds of which are without GNSS signals. The UAV’s position root-mean squared error (RMSE) from simulations was 8.6 m, while the experimental position RMSE was 10 m.

The PPP is a technique being actively researched and developed for estimating the precise position of a stationary point on the surface of the earth. Its particular features are that unlike the relative positioning method, the PPP does not require reference points and it provides the centimeter-level positioning accuracy in real-time using the precise orbit and clock information of the navigation satellites such as the GPS satellites. Lately, the application of the PPP technique to the onboard navigation of the low earth orbit (LEO) satellites is attracting attentions from aerospace researchers and engineers. Such a navigation technique is called the PPP in Space or the Space PPP. As for the existing approaches, the PPP in Space methods using precise LEO satellite dynamics [1] and kinematic PPP which does not use such dynamics [2] [3] were proposed and these results were impressive: the decimeter-level or even the centimeter-level satellite positioning accuracy was confirmed by the offline experiments using actual European LEO satellites dataset. Although these navigation methods are obviously state-of-the-art, this paper takes an another approach that focuses on improving the accuracy of satellite onboard navigation (NAV) using the PPP technique. The methodology presented in this paper is similar to the work [4] that used a reference orbit trajectory for the PPP in Space, that is, the errors of the reference trajectory were estimated using the PPP technique. However, the calculation of their reference trajectories requires the computational time and it can not be performed onboard a satellite. Therefore, we designed our method to work in realtime by using the onboard NAV as the reference trajectory. The performance of the proposed PPP NAV method was evaluated using the actual data of a Japanese earth observation satellite ALOS2 (Advanced Land Observing Satellite) [5].

Globally, the groundwater is the most favourable and demandable freshwater resource. The threat to surface water resources and subsurface aquifer systems increased with climate change as well as surplus usage of groundwater in highly populated regions. Thus, in present day, groundwater is the primary resource for the sustainability of agriculture, industries and domestic activities in arid and semi-arid areas of the world. The overexploitation of subsurface water initiates land subduction. As water is the source of life on Earth, so it is essential to monitor and predict the capability of groundwater for secure sustainable management of subsurface water with the extreme climate conditions and population growth. The traditional way of keeping a check on groundwater level change is considering in situ or point measurements using the local network of well data. But these measurements are insufficient as hydrological models depend on the spatial data referring over large areas. Global Positioning System (GPS) and Gravity Recovery and Climate Experiment (GRACE) mission are perfect tools to overcome the drawbacks of the traditional groundwater monitoring. It measures the change in ice sheets and glaciers, near-surface and subsurface GWS changes, as well as sea-level changes by GRACE 1 mission and GRACE, Follow on (FO) mission. Most of the researches are based on GRACE satellite data to monitor GWS changes over a large-scale area as continental or regional achieved successful consequences. Although the past decade GRACE studies exhibited that GRACE solution is capable of developing accurate quantitative estimations for GWS scenarios with the high temporal resolution. Still, it restricts only to continental or regional scale studies. Therefore, most of the recent studies took the step for effective downscaling of GRACE data.

Validation of enhanced orbit determination for GPS satellites with LEO GPS data considering multi ground station networks