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).

A Method for Calculating Dynamic Parameters of Intersatellite Link Signals

Aiming at the complex dynamic changes of inter-satellite link signals, this paper proposes a low-complexity method to calculate dynamic parameters of inter-satellite link signals so as to simulate inter-satellite link signals with complex dynamic characteristics. Based on the precise ephemeris, the algorithm is used to calculate the transmission delay and Doppler frequency of the signals in an inertial frame of reference by using iteration and interpolation. The calculation result is compared with the result obtained by using the simulation software of the global navigation system. It is found that the error of the transmission delay is at the nanosecond level and the error of Doppler frequency is at the Hertzian level. Therefore, the dynamic signal simulation accuracy can meet the requirements of load testing and verification of inter-satellite links. The algorithm is simple to implement.

Optical detection of the rapidly spinning white dwarf in V1460 Her

Accreting magnetic white dwarfs offer an opportunity to understand the interplay between spin-up and spin-down torques in binary systems. Monitoring of the white dwarf spin may reveal whether the white dwarf spin is currently in a state of near-equilibrium, or of uni-directional evolution towards longer or shorter periods, reflecting the recent history of the system and providing constraints for evolutionary models. This makes the monitoring of the spin history of magnetic white dwarfs of high interest. In this paper we report the results of a campaign of follow-up optical photometry to detect and track the 39 sec white dwarf spin pulses recently discovered in Hubble Space Telescope data of the cataclysmic variable V1460 Her. We find the spin pulsations to be present in g-band photometry at a typical amplitude of 0.4 per cent. Under favourable observing conditions, the spin signal is detectable using 2-meter class telescopes. We measured pulse-arrival times for all our observations, which allowed us to derive a precise ephemeris for the white dwarf spin. We have also derived an orbital modulation correction that can be applied to the measurements. With our limited baseline of just over four years, we detect no evidence yet for spin-up or spin-down of the white dwarf, obtaining a lower limit of $|P/\dot{P}| > 4\times 10^{7}$ years, which is already 4 to 8 times longer than the timescales measured in two other cataclysmic variable systems containing rapidly rotating white dwarfs, AE Aqr and AR Sco.

Prediction of High Rate GPS Satellite Orbit Using Artificial Neural Networks

Precise real-time GPS orbit at a high rate is required for a number of applications, including real-time Precise Point Positioning (PPP), long range RTK and weather forecasts. To support these applications, the International GNSS Service (IGS) has developed a precise orbital service. At present, users may take advantage of the predicted part of the IGS ultra-rapid orbit for real-time and near real-time applications. Unfortunately, however the data rate of such precise orbits is usually limited to 15 minutes. In addition, the precision of the predicted part of the IGS ultrarapid orbit is limited to about 10 cm. for the 24-hour predicted part, which may not be sufficient for the above applications, This research proposes algorithms for interpolation and prediction methods that are intended to reduce the effect of such limitations. This research examines the performance of four interpolation methods for IGS precise GPS orbits, nameley Lagrange, Newton Divided Difference, Bernese Polynomial, Cubic Spline and Trigonometric Interpolation. In addition, a comparison between this research and earlier studies were conducted. A new approach that utilizes the residuals between the broadcast and precise ephemeris to generate a high-density precise ephemeris is also introduced in this research. A three-step neural network-based model is then developed in this research to generate a 6-hour predicted orbital arc. First, an initial predicted orbit is generated by extrapolating a concentrated group of previous precise ephemeris for 5 days. GPS observations for 35 globally distributed tracking stations, corresponding to the 24-hour period preceding the predicted part, are then utilized within the Bernese software to further enhance the predicted orbit. FInally, the predicted orbit is refined by implementing a modular - three-layer feed-forward back-propagation neural network. A comparison is made between our predicted orbit and the IGS ultra-rapid orbit to verify the efficiency of the newly developed neural network-based model. It is shown that the newly developed neural network-based model improved the orbit prediction by 47%, 22% and 37% for three randomly selected satellites from Blocks IIA, IIR and IIR-M respectively.

Prediction of High Rate GPS Satellite Orbit Using Artificial Neural Networks

Precise real-time GPS orbit at a high rate is required for a number of applications, including real-time Precise Point Positioning (PPP), long range RTK and weather forecasts. To support these applications, the International GNSS Service (IGS) has developed a precise orbital service. At present, users may take advantage of the predicted part of the IGS ultra-rapid orbit for real-time and near real-time applications. Unfortunately, however the data rate of such precise orbits is usually limited to 15 minutes. In addition, the precision of the predicted part of the IGS ultrarapid orbit is limited to about 10 cm. for the 24-hour predicted part, which may not be sufficient for the above applications, This research proposes algorithms for interpolation and prediction methods that are intended to reduce the effect of such limitations. This research examines the performance of four interpolation methods for IGS precise GPS orbits, nameley Lagrange, Newton Divided Difference, Bernese Polynomial, Cubic Spline and Trigonometric Interpolation. In addition, a comparison between this research and earlier studies were conducted. A new approach that utilizes the residuals between the broadcast and precise ephemeris to generate a high-density precise ephemeris is also introduced in this research. A three-step neural network-based model is then developed in this research to generate a 6-hour predicted orbital arc. First, an initial predicted orbit is generated by extrapolating a concentrated group of previous precise ephemeris for 5 days. GPS observations for 35 globally distributed tracking stations, corresponding to the 24-hour period preceding the predicted part, are then utilized within the Bernese software to further enhance the predicted orbit. FInally, the predicted orbit is refined by implementing a modular - three-layer feed-forward back-propagation neural network. A comparison is made between our predicted orbit and the IGS ultra-rapid orbit to verify the efficiency of the newly developed neural network-based model. It is shown that the newly developed neural network-based model improved the orbit prediction by 47%, 22% and 37% for three randomly selected satellites from Blocks IIA, IIR and IIR-M respectively.

Accuracy Evaluation of Broadcast Ephemeris for BDS-2 and BDS-3

The BDS-3 system was completed in July 2020 and began to provide services to users around the world. The inspection of its operation, especially the detailed evaluation of the orbit, clock error, TGD and other indicators, plays an important role in the subsequent positioning. This study conducts an investigation of the satellite broadcast ephemeris of the BDS-2 and BDS-3. The difference between the satellite orbit position calculated by the broadcast ephemeris and the position calculated by the precise ephemeris is used for analysis. First, the ephemeris form January 2020 to February 2020 are investigated. The results show that the broadcast ephemeris accuracy of the BDS-2 MEO satellite is the highest, while the GEO satellite broadcast ephemeris accuracy is the lowest. And their three-dimensional orbit difference is 3m and 7.5m, respectively. Second, the BDS-3 MEO satellite broadcast ephemeris accuracy is higher than the BDS-2, its three-dimensional orbit accuracy is about 0.39m, while its clock error is slightly smaller than the BDS-2. The result of ephemeris calculation is basically equivalent to the clock error of satellite-to-earth observation, which is related to the addition of the clock error of the inter-satellite link in the BDS-3. Finally, the clock error of the BDS-3 MEO satellite with the H clock is basically the same as that of the MEO satellite with the Rb clock.

Impact of the precise ephemeris on accuracy of GNSS baseline in relative positioning technique

For advanced geodesy tasks that require high-accuracy, such as tectonics, surveying services usually use not only long-baselines but also the duration of tracking GNSS satellites in a long (e.g., 24/7). The accuracy of these baselines in baseline analysis is dominated by inaccuracy satellite positioning and orbit, leading to specified accuracy may not be adequate. One way to overcome this problem is to use the final precise ephemeris, provided by IGS. The objective of this study is to investigate the impact of precise ephemeris on the accuracy of GNSS baselines in relative positioning techniques in two aspects: baseline length and duration of tracking GNSS satellites. To this end, 197 baselines were generated from a total of 88 CORS stations in South Korea, and then thirteen testing cases were constructed by grouping baseline lengths from under 10 km to over 150 km. Besides, data for one day of each CORS was divided into the different duration, such as 1, 2, 3, 6, and 24 hours. The GNSS measurements have been processed by TBC software with an application of the broadcast and precise ephemerides. The precision of the baseline processing from two types of ephemeris was analyzed about baseline lengths and time of data. The obtained results showed that using precise ephemeris significantly improved the accuracy of baseline solutions when the length of the baseline larger than 50km. In addition, this accuracy is independent of the length of baselines in the case of the precise ephemeris. Finally, the result of the testing baselines was enhanced when the duration of tracking data increases.

STABILITY TESTS FOR THE NETWORK OF PERMANENT GNSS STATIONS OF THE REPUBLIC OF SRPSKA

The network of permanent GNSS stations of the Republic of Srpska is located in a fairly seismic area and belongs to different sides of regional faults. This paper provides an overview of the stability tests for fifteen permanent stations of the SRPOS network using the published precise ephemeris of the International GNSS Service (IGS) and the downloaded RINEX data from the permanent GNSS stations of the SRPOS network. The research was conducted for the data taken during the period from April 2015 to March 2016. The paper presents position vectors for permanent stations ranging from 0.71 mm (permanent station Srbac) to 22 mm (permanent station Nevesinje).