Graphical Representation of Multiple Observation Orbit Determination

Introduction

The retrieval of data from operational space assets is an essential concern of all organizations attempting to build and operate spacecraft. However, there exist limitation to this process from the perspective of secondary payloads because dedicated systems for any orbit determination let along precision orbit estimation far exceed the financial budget available. Many spacecraft in LEO are using GPS for their orbit determination needs and this has a useful price point when compared against the utility of the data provided. Still though this is not always the case.

Presented for consideration is the Drag & Atmospheric Neutral Density Explorer (DANDE). This is a full body spin stabilized satellite built at the University of Colorado Boulder, GPS was not an option during the design and build phases because of the difficulty associated with maintaining a lock on the spacecraft given a changing attitude state. Instead partnership with Air Force Space Command for High Task Tracking will be utilized to provide higher fidelity and higher frequency updates to the spacecraft ephemeris. This is so necessary to DANDE because it is studying the spatial and temporal fluctuations in atmospheric density in LEO, hence leading to mission requirement to geo-locate data products to within an agreed 10km. This agreement external to the university will certainly aid in meeting these requirements as the mission goes on, however there is still a lingering need to establish quick consistent contact with the spacecraft.

Initial contact can be one of the more nerve racking experiences since there is the stigma that initial launch insertion vectors can be fraught with error. A primary concern is that DANDE as a secondary spacecraft will be deployed from the launch vehicle along with all the other secondary spacecraft. This is launch scenario dependent, but with the advent of the widely accepted cubesat standard there can be dozens of payloads in a relatively confined vicinity and determining which spacecraft is which for the first couple months is a challenge.

To help solve this problem DANDE can in principle leverage the amateur radio observer community (HAMs) around the globe to help refine its orbit estimates. At the cost of high precision at any one measurement the larger global community can help provide a greater population of measurements useful to orbit determination. HAMs generally have UHF/VHF transceivers connected to Yagi antennae that are not in themselves narrow beamwidth (~20̊ to 3dB). With ranges to spacecraft between 200km (at zenith) and 2000-3000km (just above the horizon) the local along track width can vary between 50-1000km as the beam propogates outwards directly depending on the slant range. To that point as well operators generally do not record the inphase and quadrature channels of their transceivers, most are just commercial units from Kenwood or Yaesu which do not afford that opportunity. Without that data set it is difficult to observe the frequency shift from doppler effects to make range and range rate measurements. What is available though is a technique used in GPS called "Time Difference of Arrival" (TDOA). The locations of the ground stations in this case are known to a precision of meters, and the clock of the spacecraft and ground stations are synced to UTC within microseconds. Observation of the DANDE beacon with that high precision time value by multiple ground sites yields an observable scenario for determining a orbit.

In this course concepts of SITE-Track and Gibbs method were discussed and in particular the latter Gibbs Method can be extended with the observable data products from the situation found with DANDE to produce orbit ephermides. In principle any satellite with a time correlated beacon message on the UHF/VHF bands could benefit from this tracking method. Using the concepts of this orbital mechanics course a scenario for a satellite can be developed to show how a Gibbs Method using TDOA measurements from a minimum of three ground sites could deliver usable, and cost effective orbit solutions.