Analysis and improvement of the Bancroft algorithm for GNSS satellite orbit determination

Satellite orbit information is crucial for ensuring that global navigation satellite systems (GNSSs) provide appropriate positioning, navigation and timing services. Typically, users can obtain access to orbit information of a specific accuracy level from navigation messages or precise ephemeris products. Without this information, a system will not be able to provide normal service. In response to this problem, initial orbit information of a certain level of precision must be obtained to support subsequent applications, such as broadcasting or precise ephemeris calculations, thereby ensuring the successful subsequent operation of the navigation system. One of two ways to calculate the initial orbit of a GNSS satellite is to utilize ground tracking stations to observe satellite vector information in the geocentric inertial system; the second way is to utilize GNSS range observations and known orbit information from other satellites. For the second approach, some researchers use the Bancroft algorithm combined with receiver clock offset to determine the initial orbit of GNSS satellites. Because this method requires an additional known receiver clock offset, we study the dependence of the Bancroft algorithm on clock offset in GNSS orbit determination. By assessing the impact of errors of different magnitude on the accuracy of the orbit results, we obtain experimental conclusions. After comprehensively analyzing various errors, we determine the accuracy level that the Bancroft algorithm can achieve for orbit determination without considering receiver clock correction. Dual-frequency and single-frequency pseudorange data from IGS stations are used in orbit determination experiments. When a small receiver clock offset is considered and no correction is made, the deviations in the calculated satellite positions in three dimensions are approximately 979.3 and 1118.1 meters (dual and single frequency); with a satellite clock offset, these values are approximately 928.8 and 1062.7 meters (dual and single frequency).

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%.

Performance evaluation of GNSS receiver clock modelling in urban navigation using geodetic and high-sensitivity receivers

In urban areas, the Global Navigation Satellite System (GNSS) can lead to position errors of tens of meters due to signal obstruction and severe multipath effects. In cases of 3D-positioning, the vertical coordinate is estimated less accurately than are the horizontal coordinates. Multisensor systems can enhance navigation performance in terms of accuracy, availability, continuity and integrity. However, the addition of multiple sensors increases the system cost, and thereby the applicability to low-cost applications is limited. By using the concept of receiver clock modelling (RCM), the position estimation can be made more robust; the use of high-sensitivity (HS) GNSS receivers can improve the system availability and continuity. This paper investigates the integration of a low-cost HS GNSS receiver with an external clock in urban conditions; subsequently, the gain in the navigation performance is evaluated. GNSS kinematic data is recorded in an urban environment with multiple geodetic-grade and HS receivers. The external clock stability information is incorporated through the process noise matrix in a Kalman filter when estimating the position, velocity and time states. Results shows that the improvement in the precision of the height component and vertical velocity with both receivers is about 70% with RCM compared with the estimates obtained without applying RCM. Pertaining accuracy, the improvement in height with RCM is found to be about 70% and 50% with geodetic and HS receivers, respectively. In terms of availability, the HS receiver delivers an 100% output compared with a geodetic receiver, which provides an output 99⋅4% of the total experiment duration.

The Benefits of Receiver Clock Modelling in Satellite Timing

Satellite timing is an effective and convenient method that has been widely accepted in the time community. The key to satellite timing is obtaining a clean receiver clock offset. In this paper, instead of regarding the receiver clock offset as white noise, a two-state stochastic clock model involving three kinds of noise was conceived and used in PPP filter estimation. The influence of clock type and sampling time on satellite timing performance was first analysed. In addition, the kinematic scheme and static scheme were both investigated for meeting the demands of multi-occasional users. The values show that the model works well for both the kinematic scheme and static scheme; in contrast to that of the white noise model, the timing stability is enhanced at all the sampling times. For the six stations, especially when the averaging time is less than 1000 s, the average stability improvement values of the kinematic scheme are 75.53, 43.24, 75.00, 69.05, 40.57, and 25.45%, and the average improvement values of the static scheme are 65.49, 77.94, 56.71, 60.78, 64.41, and 39.41%. Furthermore, the enhancement magnitude is related to clock type. For a high-stability clock, the improvement of the kinematic scheme is greater than that of the static scheme, whereas for a low-stability clock, the improvement of the kinematic scheme is less than that of the static scheme.

The Effect of BDS-3 Time Group Delay and Differential Code Bias Corrections on Positioning

The timing group delay parameter (TGD) or differential code bias parameter (DCB) is an important factor that affects the performance of GNSS basic services; therefore, TGD and DCB must be taken seriously. Moreover, the TGD parameter is modulated in the navigation message, taking into account the impact of TGD on the performance of the basic service. International GNSS Monitoring and Assessment System (iGMAS) provides the broadcast ephemeris with TGD parameter and the Chinese Academy of Science (CAS) provides DCB products. In this paper, the current available BDS-3 TGD and DCB parameters are firstly described in detail, and the relationship of TGD and DCB for BDS-3 is figured out. Then, correction models of BDS-3 TGD and DCB in standard point positioning (SPP) or precise point positioning (PPP) are given, which can be applied in various situations. For the effects of TGD and DCB in the SPP and PPP solution processes, all the signals from BDS-3 were researched, and the validity of TGD and DCB has been further verified. The experimental results show that the accuracy of B1I, B1C and B2a single-frequency SPP with TGD or DCB correction was improved by approximately 12–60%. TGD will not be considered for B3I single-frequency, because the broadcast satellite clock offset is based on the B3I as the reference signal. The positioning accuracy of B1I/B3I and B1C/B2a dual-frequency SPP showed that the improvement range for horizontal components is 60.2% to 74.4%, and the vertical components improved by about 50% after the modification of TGD and DCB. In addition, most of the uncorrected code biases are mostly absorbed into the receiver clock bias and other parameters for PPP, resulting in longer convergence time. The convergence time can be max increased by up to 50% when the DCB parameters are corrected. Consequently, the positioning accuracy can reach the centimeter level after convergence, but it is critical for PPP convergence time and receiver clock bias that the TGD and DCB correction be considered seriously.

Performance of miniaturized atomic clocks in static laboratory and dynamic flight environments

Miniaturized atomic clocks with high frequency stability as local oscillators in global navigation satellite system (GNSS) receivers promise to improve real-time kinematic applications. For a number of years, such oscillators are being investigated regarding their overall technical applicability, i.e., transportability, and performance in dynamic environments. The short-term frequency stability of these clocks is usually specified by the manufacturer, being valid for stationary applications. Since the performance of most oscillators is likely degraded in dynamic conditions, various oscillators are tested to find the limits of receiver clock modeling in dynamic cases and consequently derive adequate stochastic models to be used in navigation. We present the performance of three different oscillators (Microsemi MAC SA.35m, Spectratime LCR-900 and Stanford Research Systems SC10) for static and dynamic applications. For the static case, all three oscillators are characterized in terms of their frequency stability at Physikalisch-Technische Bundesanstalt, Germany's national metrology institute. The resulting Allan deviations agree well with the manufacturer's data. Furthermore, a flight experiment was conducted in order to evaluate the performance of the oscillators under dynamic conditions. Here, each oscillator is replacing the internal oscillator of a geodetic-grade GNSS receiver and the stability of the receiver clock biases is determined. The time and frequency offsets of the oscillators are characterized with regard to the flight dynamics recorded by a navigation-grade inertial measurement unit. The results of the experiment show that the frequency stability of each oscillator is degraded by about at least one order of magnitude compared to the static case. Also, the two quartz oscillators show a significant g-sensitivity resulting in frequency shifts of − 1.2 × 10−9 and + 1.5 × 10−9, respectively, while the rubidium clocks are less sensitive, thus enabling receiver clock modeling and strengthening of the navigation performance even in high dynamics.

Evaluation of the Effect of Higher-Order Ionospheric Delay on GPS Precise Point Positioning Time Transfer

In high-precision GPS precise point positioning (PPP) time transfer, errors caused by the effect of ionosphere delay have to be corrected. Usually the ionosphere-free combinations of the pseudo code and the carrier phase is used in GPS PPP data processing, and it effectively eliminates the effect of the first-order ionospheric delay. This study quantitatively analyzes the errors caused by higher-order ionospheric (Ion2+) delays in precise PPP time transfer. Data of two 7-day test periods, including low and moderate ionospheric conditions, from 20 stations located in middle- and low-latitude, were analyzed. The difference in clock solution with and without the Ion2+ correction, including the receiver clock solution and time-link clock solution, was deeply analyzed and discussed. The difference sequence shows a constant bias plus some variations with a diurnal variation. For the difference of the receiver clock solutions, the mean standard deviation of the variations is 3.92 ps in low-latitude, which is much larger than that of 2.59 ps in mid-latitude due to the influence of the larger ionospheric electron density on the low-latitude. The maximum constant bias reached more than 15 ps and was negative at most stations in the northern hemisphere, while it was positive at most stations located in the southern hemisphere. The difference in the time-link solutions correlates not only with time and region, but also with the length of the time-links. The largest difference in the long time-link SYDN-PTBB, BJNM-SYDN, AMC2-SYDN, etc., reaches more than 25 ps, while that of the short time-link IENG-PTBB, BRUX-PTBB, etc., is less than 3.5 ps. Therefore, the Ion2+ correction is necessary for high-precision PPP time transfer over long time-links, especially time-links made by one station located in the northern hemisphere and another located in the south hemisphere; however, it could be ignored for short time-links.

Time Synchronization Method Based on Real-Time Precise Point Positioning

<p>Precise point positioning (PPP) technique is an effective tool for time and frequency applications. Using phase/code observations and precise products, the PPP time transfer allows an accuracy of sub-nanoseconds within a latency of several days. Although the PPP time transfer is usually implemented in the post-processing mode, using the real-time PPP (RT-PPP) technique for time transfer with the shorter latency remains attractive to time community. In 2012, the IGS (International GNSS Service) launched an open-access real-time service (RTS) project, broadcasting satellite orbit and clock corrections on the Internet, which enables PPP time transfer in the real-time mode. In this contribution, we apply the RT-PPP for high-precision time transfer and synchronization. The GNSS receiver is required to be equipped with an atomic clock as the external local clock. We use the RT-PPP technique to compute the receiver clock offset with respective to the GNSS time scale. On the basis of clock offsets, we steer the local clock by frequency adjustment method. In this way, all the local clocks are synchronized to the GNSS time scale, making local clocks synchronized with each other.</p><p>The time scales of the RTS products are evaluated at first. Six kinds of the RTS products (IGS01, CLK10, CLK53, CLK80 and CLK93) on DOY220-247, 2019 are pre-saved to compute the receiver clock offsets. The clock offset with respect to the GPST (GPS Time) obtained from the IGS final product is applied as the reference. The standard deviations (STDs) of the clock offsets with respect to the reference are 0.63, 1.76, 0.28, 0.27 and 1.28 ns for IGS01, CLK10, CLK53, CLK80 and CLK93, respectively.</p><p>Finally, we set up a hardware system to examine the validity of our time synchronization method. The baseline of the time synchronization experiment is about 5 m. The synchronization error of the 1 PPS outputs is precisely measured by the frequency counter. The STD of the 4-days results is about 0.48 ns. The peak-to-peak value of the synchronization error is about 2.5 ns.</p>

COSMIC-2 Precise Orbit Determination Results

<p>We present results for GNSS orbit estimation strategies implemented for the FORMOSAT-7/COSMIC-2 (Constellation Observing System for Meteorology, Ionosphere, and Climate) constellation. The six COSMIC-2 satellites launched on June 25, 2019 into a 24 deg inclination, ~725 km circular orbit. Over time, all satellites will be lowered to an operational altitude of ~520 km. The primary COSMIC-2 science payload is the JPL designed Tri-GNSS Radio-occultation Receiver System (TGRS), which tracks GPS and GLONASS signals on two upward looking choke-ring precise orbit determination antennas facing the forward- and anti-velocity directions. We evaluate recently implemented post-processed orbit determination strategies. These include single antenna GPS-only and GPS+GLONASS solutions, as well as experimental dual-antenna GPS-only processing applying different approaches for the handling of receiver clock parameters (e.g. dual clocks, single clock plus bias). Evaluation metrics include data volume and tracking arc coverage, postfit residuals, internal orbit overlaps, and stability of the receiver clock estimates. We furthermore compare the performance of the six orbiters, and look for differences in quality metrics at the higher and lower orbit altitudes.</p>