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 higher-multipole gravitational waveform model for an eccentric binary black holes based on the effective-one-body-numerical-relativity formalism

We have previously constructed a waveform model, SEOBNRE, for spinning binary black hole moving along eccentric orbit based on effective-one-body (EOB) formalism. In the current paper, we update SEOBNRE waveform model in the following three respects. Firstly, we update the EOB dynamics from SEOBNRv1 to SEOBNRv4. Secondly we properly treat the Schott term which has been ignored in previous SEOBNRE. Thirdly, we construct a new factorized waveform including (l,|m|)=(2,2),(2,1),(3,3),(4,4) modes based on effective-one-body (EOB) formalism, which is valid for spinning binary black holes (BBH) in general equatorial orbit. Following our previous SEOBNRE waveform model, we call our new waveform model SEOBNREHM. The (l,|m|)=(2,2) mode waveform of SEOBNREHM can fit the original SEOBNRv4 waveform very well in the case of a quasi-circular orbit. We have validated SEOBNREHM waveform model through comparing the waveform against the Simulating eXtreme Spacetimes (SXS) catalog. The comparison is done for BBH with total mass in (20,200)M_sun using Advanced LIGO designed sensitivity. For the quasi-circular cases we have compared our (2,2) mode waveforms to the 281 numerical relativity (NR) simulations of BBH along quasi-circular orbits. All of the matching factors are bigger than 98\%. For the elliptical cases, 24 numerical relativity simulations of BBH along an elliptic orbit are used. For each elliptical BBH system, we compare our modeled gravitational polarizations against the NR results for different combinations of the inclination angle, the initial orbit phase and the source localization in the sky. We use the minimal matching factor respect to the inclination angle, the initial orbit phase and the source localization to quantify the performance of the higher modes waveform. We found that after introducing the higher modes, the minimum of the minimal matching factor among the 24 tested elliptical BBHs increases from 90\% to 98\%. Our SEOBNREHM waveform model can match all tested 305 SXS waveforms better than 98\% including highly spinning ($\chi=0.99$) BBH, highly eccentric ($e\approx0.6$ at reference frequency $Mf_0=0.002$) BBH and large mass ratio ($q=10$) BBH.

A New Triangulation Algorithm for Positioning Space Debris

A single electro-optical (EO) sensor used in space debris observation provides angle-only information. However, space debris position can be derived using simultaneous optical measurements obtained from two EO sensors located at two separate observation sites, and this is commonly known as triangulation. In this paper, we propose a new triangulation algorithm to determine space debris position, and its analytical expression of Root-Mean-Square (RMS) position error is presented. The simulation of two-site observation is conducted to compare the RMS positioning error of the proposed triangulation algorithm with traditional triangulation algorithms. The results show that the maximum RMS position error of the proposed triangulation algorithm is not more than 200 m, the proposed triangulation algorithm has higher positioning accuracy than traditional triangulation algorithms, and the RMS position error obtained in the simulation is nearly consistent with the analytical expression of RMS position error. In addition, initial orbit determination (IOD) is carried out by using the triangulation positioning data, and the results show that the IOD accuracy of two-site observation is significantly higher than that of the single-site observation.

Generalization of a method by Mossotti for initial orbit determination

Here, we revisit an initial orbit determination method introduced by O. F. Mossotti employing four geocentric sky-plane observations and a linear equation to compute the angular momentum of the observed body. We then extend the method to topocentric observations, yielding a quadratic equation for the angular momentum. The performance of the two versions is compared through numerical tests with synthetic asteroid data using different time intervals between consecutive observations and different astrometric errors. We also show a comparison test with Gauss’s method using simulated observations with the expected cadence of the VRO–LSST telescope.

Acquisition and Tracking Strategies for Satellite to Ground Optical Communication Systems

Optical wireless communication (OWC) offers a promising alternative to radio frequency (RF) based communication because it can support the increased demand for bandwidth in modern networks. This thesis examined three strategies that could be implemented to improve or simplify the design of a ground and satellite optical communication link. The acquisition of a laser beam emitted from a space orbiting satellite was examined. Atmospheric conditions and how they affect beam refraction was modeled using beam geometry and the refractive properties of air. Simulation results indicate that a beam with a large zenith angle is refracted to a higher degree than a beam with a smaller zenith angle. Beam refraction of an emitted beam with zenith angles of 61º and 82º reached the Earth surface with a peak power of 1179 photons/bit and 305 photons/bit respectively. Initial orbit estimation methods were examined, and it was found that Gauss’ Angles Only method was able to predict the azimuth and elevation of a target satellite with an average error of 6.38e−1. Which were positive results, and indicated that the Gauss method would be useful for initial orbit determination of an emitting satellite. Finally, a Extended Kalman Filter (EKF) state estimator was designed to evaluate whether the use of a Kalman filter is suitable for orbit determination when only using the angular observations that are available at an optical groundstation. Results indicated that when measurement errors of ±0.3 degrees were introduced into the system, position error state estimates reached a maximum of 6.9 km and 0.013 km/s. When the EKF was given smaller measurement errors of ±0.1 degrees, the errors in the state estimates were found to be a maximum of 1.4 km and 0.002 km/s. The results from the simulation for the state estimator indicated that an EKF can be applied to track the motion of a target satellite

Acquisition and Tracking Strategies for Satellite to Ground Optical Communication Systems

Optical wireless communication (OWC) offers a promising alternative to radio frequency (RF) based communication because it can support the increased demand for bandwidth in modern networks. This thesis examined three strategies that could be implemented to improve or simplify the design of a ground and satellite optical communication link. The acquisition of a laser beam emitted from a space orbiting satellite was examined. Atmospheric conditions and how they affect beam refraction was modeled using beam geometry and the refractive properties of air. Simulation results indicate that a beam with a large zenith angle is refracted to a higher degree than a beam with a smaller zenith angle. Beam refraction of an emitted beam with zenith angles of 61º and 82º reached the Earth surface with a peak power of 1179 photons/bit and 305 photons/bit respectively. Initial orbit estimation methods were examined, and it was found that Gauss’ Angles Only method was able to predict the azimuth and elevation of a target satellite with an average error of 6.38e−1. Which were positive results, and indicated that the Gauss method would be useful for initial orbit determination of an emitting satellite. Finally, a Extended Kalman Filter (EKF) state estimator was designed to evaluate whether the use of a Kalman filter is suitable for orbit determination when only using the angular observations that are available at an optical groundstation. Results indicated that when measurement errors of ±0.3 degrees were introduced into the system, position error state estimates reached a maximum of 6.9 km and 0.013 km/s. When the EKF was given smaller measurement errors of ±0.1 degrees, the errors in the state estimates were found to be a maximum of 1.4 km and 0.002 km/s. The results from the simulation for the state estimator indicated that an EKF can be applied to track the motion of a target satellite