Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion

Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. By generating relationships between the vehicles that are intuitive, these approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a specific geometrical shape. Furthermore, the results obtained using geometrical approaches can be used to better constrain numerical optimization methods; allowing those methods to converge to optimal satellite configurations faster. This paper presents a set of geometrical relationships for formations in eccentric orbits, where Hill.s equations are not valid, and shows how these relationships can be used to investigate formation designs and how they evolve with time

Investigation of CSAC Driven One-Way Ranging Performance for CubeSat Navigation

Current two-way satellite tracking methods are insufficient to support the growing interest in deep space small satellite missions. To meet the low cost and minimal resource allocations that make CubeSats so appealing, navigation methods must be developed that reduce ground communication requirements. One promising approach is the use of a stable onboard timing reference to enable one-way ground uplink ranging capabilities. The Chip Scale Atomic Clock (CSAC) is a stable oscillator that meets the size, weight, and power requirements for use on CubeSats. Maxwell, a University of Colorado Boulder CubeSat mission, provides the opportunity for a flight test of CSAC-driven one-way ranging. This work presents a preliminary simulation of the mission, modeling the expected LEO orbit determination (OD) performance using CSAC-driven radiometric measurements. The effect of thermal variations on the CSAC behavior are specifically considered, and the OD performance in the presence of both stochastic clock and thermal variations is evaluated. It is shown that the use of a Dynamic Model Compensation algorithm is more effective than a State Noise Compensation algorithm in mitigating the thermal clock effects, for both one second and thirty second data rates. This LEO simulation and eventual Maxwell CSAC flight provide the first steps towards demonstrating the feasibility of CubeSat navigation using one-way ranging

Simulation of a High Stability Reference Clock for Small Satellites with Modeled GPS Timing Errors

Small satellites have become capable platforms for a wide range of commercial, scientific and defense missions. Improved onboard clocks would make small satellites a viable option for even more missions, enabling radio aperture interferometry, improved radio occultation measurements, high altitude GPS navigation, and GPS augmentation missions, among others. Previous research by the authors investigated methods for creating a high stability reference clock for small satellites by combining a heterogeneous group of oscillators including multiple CSACs, a GPS receiver and an EMXO. This work predicted that time error standard deviations of ~500 ps were possible with GPS timing errors modeled as AWGN. This paper builds on previous work by developing a high-fidelity model for the GPS receiver timing error onboard a LEO spacecraft. Signal-In-Space Ranging Errors (SISRE) are modeled using post-fit GPS orbit and clock data, and ionospheric delays are approximated using IONEX maps and ionosphere models. GPS point solutions are then calculated over several days of LEO orbits to generate realistic receiver timing errors, which were then used in simulations of the high-stability heterogeneous clock ensemble. Simulations show degraded clock system performance compared to the prior model, with standard deviations of time errors increasing to 1.3 ns 1-σ. The results provide insight into the nature of GPS receiver clock errors for LEOs, as well as practical limitations that should be expected when implementing advanced clock systems on small satellites

Application of Shaken Lattice Interferometry Based Sensors to Space Navigation

High-sensitivity shaken lattice interferometry (SLI) based sensors have the potential to provide deep space missions with the ability to precisely measure non-gravitational perturbing forces. This work considers the simulation of the OSIRIS-REx mission navigation in the vicinity of Bennu with the addition of measurements from onboard SLI-based accelerometers. The simulation is performed in the Jet Propulsion Laboratory's (JPL) Mission Analysis, Operations and Navigation Toolkit (MONTE) and incorporates OSIRIS-REx reconstructed trajectory and attitude data from the Navigation and Ancillary Information Facility (NAIF) database. The use of the reconstructed data from NAIF provides realistic true dynamical errors and JPL's MONTE software allows for a high-fidelity simulation of a nominal reference for the filter. The navigation performance and reduction of tracking and complex modeling enabled by the onboard SLI-based sensor are presented for two orbital phases of the OSIRIS-REx mission. Overall, the results show that the addition of SLI-based accelerometer measurements improves navigation performance, when compared to a radiometric tracking only configuration. In addition, results demonstrate that highly-precise accelerometer measurements can effectively replace at least one day of DSN passes over a three-day period, thereby reducing tracking requirements. Furthermore, it is shown that lower-fidelity surface force modeling and parameter estimation is required when using onboard SLI-based accelerometers.Comment: 30 pages, 8 figure

CSAC Flight Experiment to Characterize On-Orbit Performance

Precise positioning, navigation, and timing requirements are driving a need for increasingly accurate spacecraft timing systems. This paper describes an experiment being developed at the University of Colorado Boulder to quantify the stability and behavior of a chip-scale atomic clock (CSAC) onboard an Air Force Research Laboratory (AFRL) University Nanosatellite Program (UNP-9) MAXWELL CubeSat mission. The CSAC experiment will run onboard MAXWELL, enabling the GPS receiver measurements to occur using the unsteered CSAC as an external clock. The experiment will record and downlink the position, clock bias, pseudorange, phase, and temperature. These data will allow us to characterize the on-orbit performance of the CSAC

GLAS Spacecraft Pointing Study

Science requirements for the GLAS mission demand that the laser altimeter be pointed to within 50 m of the location of the previous repeat ground track. The satellite will be flown in a repeat orbit of 182 days. Operationally, the required pointing information will be determined on the ground using the nominal ground track, to which pointing is desired, and the current propagated orbit of the satellite as inputs to the roll computation algorithm developed by CCAR. The roll profile will be used to generate a set of fit coefficients which can be uploaded on a daily basis and used by the on-board attitude control system. In addition, an algorithm has been developed for computation of the associated command quaternions which will be necessary when pointing at targets of opportunity. It may be desirable in the future to perform the roll calculation in an autonomous real-time mode on-board the spacecraft. GPS can provide near real-time tracking of the satellite, and the nominal ground track can be stored in the on-board computer. It will be necessary to choose the spacing of this nominal ground track to meet storage requirements in the on-board environment. Several methods for generating the roll profile from a sparse reference ground track are presented

A Machine-Designed Optical Lattice Atom Interferometer

Performing interferometry in an optical lattice formed by standing waves of light offers potential advantages over its free-space equivalents since the atoms can be confined and manipulated by the optical potential. We demonstrate such an interferometer in a one dimensional lattice and show the ability to control the atoms by imaging and reconstructing the wavefunction at many stages during its cycle. An acceleration signal is applied and the resulting performance is seen to be close to the optimum possible for the time-space area enclosed according to quantum theory. Our methodology of machine design enables the sensor to be reconfigurable on the fly, and when scaled up, offers the potential to make state-of-the art inertial and gravitational sensors that will have a wide range of potential applications

Near Earth orbit determination and rendezvous navigation using GPS

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1986.MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO.Bibliography: leaves 144-148.by Penina Axelrad.M.S

Comparison of QuikSCAT and GPS-Derived Ocean Surface Winds

The Colorado Center for Astrodynamics has completed a study comparing ocean surface winds derived from GPS bistatic measurements with QuikSCAT wind fields. We have also compiled an extensive database of the bistatic GPS flight data collected by NASA Langley Research Center over the last several years. The GPS data are augmented with coincident data from QuikSCAT, buoys, TOPEX, and ERS

Relative Navigation In Elliptical Orbits Using An Iterative Nonlinear Filter

The two step filter is applied to process intersatellite radar measurements to determine the motion of one satellite relative to another in close elliptical orbits. This filter breaks a nonlinear estimation problem into two state vectors. The 'first step' state is chosen so as to have a linear measurement equation. This is nonlinearly related to the 'second step' state which describes the dynamics. Two different forms are used. In one, the first step state is the second step state vector augmented by the measurement equation. In the other, the first step and second step state vectors are of equal dimension. The two step filter is compared against an iterated extended Kalman filter and a Kalman filter using a change of variables. Analytical differences between the two step estimator and these conventional filters are highlighted. Special concerns for initializing the first step state covariance matrix and handling the possibility of numerically rank deficient covariance matrices are addressed. Numerical simulations are performed which show that the Two Step estimator produces a lower estimation bias under two circumstances; large apriori initial error; and small dimension observation vectors which require a longer arc of measurements to generate observability of the state