Precise Orbit Determination of CubeSats

CubeSats are faced with some limitations, mainly due to the limited onboard power and the quality of the onboard sensors. These limitations significantly reduce CubeSats' applicability in space missions requiring high orbital accuracy. This thesis first investigates the limitations in the precise orbit determination of CubeSats and next develops algorithms and remedies to reach high orbital and clock accuracies. The outputs would help in increasing CubeSats' applicability in future space missions

The impact of precise inter-satellite ranges on relative precise orbit determination in a smart CubeSats constellation

The use of CubeSats is expanding in space and earth science applications due to the low costs of building and the possibility of launching them in a large low-earth orbits (LEO) constellation. Such constellation can serve as an augmentation system for positioning, navigation and timing. However, real-time precise orbit determination (POD) is still one of the challenges for this application. Real-time reduced-dynamic POD requires more processing capability than what is available in current CubeSats, and the kinematic POD highly depends on the number and the quality of the signals from Global Navigation Satellite Systems (GNSS). In this study, an approach is proposed to increase the orbital accuracy by implementing the precise inter-satellite ranges in the Kinematic POD. The precise orbits of a set of CubeSats from the Spire Global constellation that are determined using the reduced-dynamic POD is to be used to generate the precise inter-satellite ranges. These ranges vary from hundreds to thousands of kilometres and are constrained in the relative kinematic POD between the tested CubeSats. The results, which depend on the length of the inter-satellite ranges, show the improvement of the orbital accuracy in all directions. An initial architecture for implementing such a method in a smart CubeSats constellation is proposed and the limitations and remedies are discussed

Phase centre variation of the GNSS antenna onboard the CubeSats and its impact on precise orbit determination

CubeSats as small Low Earth Orbiting (LEO) satellites are equipped with space-based receiver and antenna capable of tracking Global Navigation Satellite Systems (GNSS). These GNSS signals provide the possibility of precise orbit determinations (POD) of the CubeSats which is essential for different earth and space science applications. Examples of these applications are monitoring the movement of the Earth’s surface and oceans using Interferometric Synthetic Aperture Radar (InSAR) and GNSS reflectometry, weather forecasting using GNSS Radio Occultation, satellites rendezvous and docking in orbits, and attitude and relative motion control of the CubeSats in a formation flying. The nominal antenna phase centre variations (PCV) as direction-dependent delays in the GNSS observations are generally determined using ground calibration methods such as the anechoic chamber and robotic tests. However, these methods do not consider the actual space environment and multipath effects due to the CubeSat structure, and neighboring space vehicles in orbit. In this contribution, the empirical PCV pattern for the GNSS antenna onboard a set of CubeSats that are flying in a mega-constellation are determined using the residual approach and compared with the nominal values derived from ground calibrations. The estimated PCV values based on in-flight GNSS observations more realistically represent the near-field effects than the ground calibrated values. The new bin-wise PCV pattern is used in an iteratively POD procedure to determine the precise orbits of the CubeSats. Internal validation methods such as those analyse the overlapping orbits, the posterior variance factors, and the observation residuals confirm the benefits of the proposed PCV patterns. The estimated orbits using these patterns have shown higher accuracies compared with the derived orbits using the nominal PCV values

THE IMPACT OF ORBITAL AND CLOCK ERRORS ON POSITIONING FROM LEO CONSTELLATIONS AND PROPOSED ORBITAL SOLUTIONS

Two approaches are discussed for the estimation and prediction of the orbits of low earth orbit (LEO) satellites that can be used for navigation. The first approach relays on using a ground monitoring network of stations. The procedures to generate the LEO orbital products in this approach are proposed at two accuracy levels to facilitate different positioning applications. The first type targets producing orbits at meter-level accuracy, defined here as LEO-specific broadcast ephemeris. The second type of products would produce orbits with an accuracy of cm as polynomial corrections to the first type of orbits. Real and simulated LEO satellite data is used for testing, mimicking LEO satellites that can be used for positioning. For the first type of products, it was found that orbital prediction errors play the dominant role in the total error budget, especially in cases of mid and long-term prediction. For the second type of products, the predicted orbits within a short period of up to 60 s generate errors at a few cm, and fitting the corrections with a quadratic polynomial reduced the fitting range errors to the cm level compared to the case of applying a linear polynomial. This level of accuracy can fulfill the requirement for precise point positioning (PPP). The second approach is computing the orbits in real time applying the kinematic or reduced-dynamic mode, where the orbits are computed in the PPP mode using GNSS observations collected onboard LEO satellites and the GNSS orbits and clock products are received through inter-satellite links such as the free-access SouthPAN service in Australia, Galileo HAS, or Beidou (BDS-3, PPP-B2b service). The limitations of this approach and preliminary results are given. Furthermore, the LEO satellite clocks determined together with the orbits in the reduced-dynamic LEO satellite orbit process in near-real-time are also analysed. Finally, the impact of possible orbital and clock errors in the range of decimetres to several meters of LEO satellites on positioning performance is analysed

Absolute and relative POD of LEO satellites in formation flying: Undifferenced and uncombined approach

Absolute or relative precise orbit determination (POD) is an essential prerequisite for many low earth orbit (LEO) missions. The POD of LEO satellites typically relays on processing the onboard global navigation satellite system (GNSS) measurements. The absolute POD is usually based on an ionosphere-free (IF) combination, and currently, integer ambiguity resolution (IAR) can be achieved only when external GNSS satellite phase bias (SPB) products are used. The use of these products is not flexible in multi-frequency/multi-constellation scenarios and is difficult to achieve in real-time missions. For relative POD, the double-differenced (DD) with IAR is the most general method. However, the differencing process amplifies observation noise and loses the opportunity to impose dynamic constraints on some eliminated parameters. In this contribution, based on the use of undifferenced and uncombined (UDUC) observations, a new model for both absolute and relative POD is proposed. In this model, the ambiguities of common-view satellites are constructed into DD form, thus IAR can be achieved without any external SPB products. Working with the UDUC observations, multi-frequency scenarios can be easily applied, and residuals can be separated for each frequency. In addition, with precise GNSS satellite clock/orbit products, both the absolute and relative orbits can be derived, which supports absolute and relative LEO POD. Based on onboard GPS observations of T-A and T-B satellites in formation flying, the performance of the UDUC POD model with DD ambiguity was evaluated. With the UDUC algorithm and IAR, the proposed model presented a consistency of 2.8–3.8 cm in 3D with the reference orbits, and the orbit difference was reduced by 16.3% and 10.6% for T-A and T-B compared with the IF-based POD, respectively. In addition, the relative orbit of the two satellites derived from the proposed model showed a consistency of 1.1–1.5 mm, which proved the feasibility of the UDUC POD model with DD ambiguity for formation flying missions

Stability of CubeSat Clocks and Their Impacts on GNSS Radio Occultation

Global Navigation Satellite Systems’ radio occultation (GNSS-RO) provides the upper troposphere-lower stratosphere (UTLS) vertical atmospheric profiles that are complementing radiosonde and reanalysis data. Such data are employed in the numerical weather prediction (NWP) models used to forecast global weather as well as in climate change studies. Typically, GNSS-RO operates by remotely sensing the bending angles of an occulting GNSS signal measured by larger low Earth orbit (LEO) satellites. However, these satellites are faced with complexities in their design and costs. CubeSats, on the other hand, are emerging small and cheap satellites; the low prices of building them and the advancements in their components make them favorable for the GNSS-RO. In order to be compatible with GNSS-RO requirements, the clocks of the onboard receivers that are estimated through the precise orbit determination (POD) should have short-term stabilities. This is essential to correctly time tag the excess phase observations used in the derivation of the GNSS-RO UTLS atmospheric profiles. In this study, the stabilities of estimated clocks of a set of CubeSats launched for GNSS-RO in the Spire Global constellation are rigorously analysed and evaluated in comparison to the ultra-stable oscillators (USOs) onboard the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-2) satellites. Methods for improving their clock stabilities are proposed and tested. The results (i) show improvement of the estimated clocks at the level of several microseconds, which increases their short-term stabilities, (ii) indicate that the quality of the frequency oscillator plays a dominant role in CubeSats’ clock instabilities, and (iii) show that CubeSats’ derived UTLS (i.e., tropopause) atmospheric profiles are comparable to those of COSMIC-2 products and in situ radiosonde observations, which provided external validation products. Different comparisons confirm that CubeSats, even those with unstable onboard clocks, provide high-quality RO profiles, comparable to those of COSMIC-2. The proposed remedies in POD and the advancements of the COTS components, such as chip-scale atomic clocks and better onboard processing units, also present a brighter future for real-time applications that require precise orbits and stable clocks

Shadow Toolbox (1st release)

Shadow is a Matlab toolbox written to detect the GNSS satellite in the shadow of the earth and remove them from the RINEX observation file. The main toolbox performs the following tasks: 1- Reads Rinex observation file 2- Reads precise ephemeris file (SP3) 3- Detect the satellite in the shadow of the Earth 4- Remove the observation of the satellite and create a refined Rine