Orbit Determination For Low Earth Orbiting CubeSat Using GNSS

The goal of Global Geodetic Observing System(GGOS)in 2020 is to monitor geodetic parameters and their temporal variations,in a global reference frame with a relative accuracy of 10^-9 or better.To achieve such an ambitious goal,GGOS relies on an integrated network of current and future terrestrial,airborne and various satellite missions.Satellites observing the Earth from space will be an indispensable component of GGOS.The Low Earth Orbiter(LEO)satellite missions collect data homogeneously and consistently over large parts of the Earth surface.These satellites are nowadays equipped with a multitude of sensors and instruments,monitoring the land,ocean and ice surfaces as well as the Earth's gravity field and its temporal variations.Precise orbit determination(POD)is of central importance for many applications of geodesy and earth science,and numerous position-critical missions(e.g.altimetry,SAR,and gravity missions)are currently in orbit.Global Navigation Satellite Systems(GNSS)have been used as a key and efficient technology for satellite orbit determination since 1990s.With the increasing popularity of miniaturized satellites(e.g.,Cube Sats that are nanosatellites based on standardized 10 cm-sized units)the need for an adapted payload for orbit determination arises.We developed a small-size versatile GNSS payload board using Commercial-Off-The-Shelf(COTS)single-frequency GNSS receivers with extremely small weight(1.6 g),size(12.2 x 16.0 x 2.4 mm³)and power consumption(100 m W).Two prototypes of the GNSS positioning board have been successfully launched onboard the Astrocast-01 and-02 3-unit cube satellites with altitudes of 575 km and 500 km,respectively.In this research,the design of the POD payload and the results from the thermal and irradiation tests have been introduced and analyzed.Then,the main contributions focus on the performance evaluation of the onboard Navigation Solution(NAVSOL),the analysis of the various experiments in space,also the POD using raw code and phase data in post-processing mode and Satellite Laser Ranging(SLR)validation.Besides,the combination of GNSS precise clock products and its impact on Precise Point Positioning(PPP)and LEO POD have been investigated.The main work and contributions of the thesis are as follows:(1)The design of the POD payload for Cube Sat includes a GNSS payload board and a small array of three laser retroreflectors enabling orbit validation with SLR.As initially the receivers are not intended to be used in space applications,they have been tested for vacuum,temperature variations and irradiation.Based on extensive tests we show the general suitability of these low-cost receivers for orbit determination in space applications.(2)The Cube Sat NAVSOL orbits have been improved and evaluated in post-processing mode.The performance evaluation of the GNSS payload for navigation in space relies on the Reduced-Dynamic(RD)orbit determination using modified and well-established Bernese GNSS Software.In the orbit fitting,the along-track acceleration caused by perturbing forces has been estimated with different arc lengths.A reprocessing has been performed to estimate the weighted mean of the empirical constant acceleration in along-track using all available NAVSOL data.Gaussian perturbation equations have been used as an alternative method to compute the along-track acceleration from the variations of the semi-major axis of the satellite orbit.In addition,air drag modeling has been implemented in the POD program to correct the air drag perturbation,which is mainly in the along-track,and to validate our estimates for the constant acceleration.It would be preferable to use a constant acceleration in along-track as empirical parameter to compensate for the deficiencies of the orbit model.We improve the orbit using a full dynamic model,including a high-degree gravity field,air drag and solar radiation pressure,preserving the information content of the measurements including stochastic pulses.The overall performance evaluation shows the RMS of a daily NAVSOL orbit fitting is about 2?5 m despite errors caused by the ionosphere and the orbit model.(3)The performance of the GNSS payload in space has been tested and analyzed in different experiments.These include the analysis of receiver clock behavior in space;the orbit determination using on-board velocity observations by fitting the equation of motion of the Cube Sat orbit to the velocities only,to the positions only and to both positions and velocities;the identification and validation of the systematic errors existing in the positions and velocities of NAVSOL data;the comparison of various single-system solutions and advances in combining the different satellite navigation systems for orbit determination;the analysis of the orbit elements changes and the thrust force estimation for two satellite maneuvers.The RMS of the NAVSOL errors in orbit fitting is 4.3,2.6,and 2.2 m in RSW components respectively for Astrocast-01,and is 2.9,2.3,and 1.1 m in RSW components respectively for Astrocast-02.(4)For a few satellite arcs,the recording of the GNSS raw code and phase data was enabled,allowing orbit determination using raw data in a post-processing mode.This allows a better assessment of the raw data quality,the achievable orbit quality and the overall performance estimation.The tests performed so far include the GNSS satellite visibility and the carrier to noise density(C/N0)analysis,the improvement of the orbit quality by eliminating the ionospheric refraction based on a linear combination of phase and code observations,the optimal strategy for orbit prediction using on-board NAVSOL data,the calculation of the SLR link budget at selected stations and the successful SLR campaigns to track the nanosatellites.The SLR measurements with high accuracy were used to validate the GNSS orbit of Astrocast satellites.The dynamic orbit of GPS code-only solution shows an accuracy of about 0.9 m from the orbit validation using SLR measurements.(5)The precise clock products from different Analysis Centers(ACs)are further processed and combined for the Positioning,Navigation and Timing(PNT)users.We propose the combined robust least-squares estimation for Multi-GNSS clock products combination.Besides the different clock reference,systematic errors existing in the clock differences among ACs show a linear trend and could be removed completely.The results show that the agreement and stability of the newly combined Multi-GNSS clock products are better than those of ACs.Furthermore,the performance of the combined precise clock products used in PPP and LEO POD has been validated.