AceFDS implements two types of orbit determination: Batch Least Square and Kalman Filter. Common to either type is the high-fidelity models of the measurements (observation) of the SV range, azimuth, and elevation as obtained from a particular ground station. The modeling of these measurements account for atmospheric refraction, light-time delay, and electronic equipment delays (measurement biases). AceFDS also allows the user to specify an existing orbit state covariance to be incorporated into the OD process thus enhancing the stability of the orbit determination process. One advanced feature of the AceFDS orbit determination is the ability to perform orbit determination during periods of orbit maneuvers by the SV when telemetry is available to account for thruster firing activities.

Real-Time Orbit Determination

The real-time orbit determination implements the Kalman Filter algorithm. This capability allows for real-time tracking data to be streamed into the database allowing the application access to continually update the orbit estimation. The Kalman Filter also processes tracking data solving for a number of parameters including thrust performance parameters during periods of thruster firings. The Kalman Filter can be configured to run indefinitely without human intervention delivering true automated maneuver operations.

AceFDS offers many choices of orbit propagators each of which can be categorized in two distinct groups: 1) analytical and 2) numerical. The analytical propagators include: Two-Body (Keplerian), SGP4 (open-source library), Variation of Parameter (VOP), VOPMean – VOP using mean orbital elements, and Vinti (a future capability).

The various numerical integrators implemented in AceFDS carry out the integration of the astrodynamics equation of motion using the “Special Perturbation” theory. The accuracy of the propagated orbit depends on how well the forces acting on the satellite are being modeled. These forces have two major contributions: the force field, and the SV size and shape characteristics. For controlled thruster firings, the orbit propagation accuracy depends on the fidelity of the propulsion system models including the characteristics of the fuel mass depletion and the thruster performance parameters. AceFDS currently supports two propulsion models: liquid and ion propulsion systems. AceFDS allows for the performance parameters of these models to be calibrated during operations.

AceFDS has the capability to provide prediction for orbit covariance using the unscented transform. This particular algorithm mimics closely the non-linearity of the equation of motion and provides a result that closely matches that of the Monte-Carlo simulation of hundreds of thousands of points. It is well-known in the astrodynamics community that the Kalman Filter that implements the unscented-transform is more stable than the linearized versions. This unscented-transform feature has been incorporated into the current implementation of the AceFDS orbit covariance propagation.

The result of the AceFDS covariance propagation is more representative of the orbit uncertainties than the conventional covariance propagation in use today in many operational systems. This desirable feature has a direct application to covariance prediction of space debris where hundreds of thousands of objects are tracked and predicted.

The industry-standard of massive parallel processing is a maturing technology. Braxton is moving our robust orbit and covariance prediction onto the parallel code base to take advantage of the processing power of the Graphics Processing Unit (GPU) technology. The implementation of astrodynamics algorithms using general purpose GPU has recently taken roots in many academic institutions in the US as well as worldwide.

The combination of the covariance matrix representation for space debris application coupled with the technology for parallel processing is one of the main issues addressed in the recent study of the Air Force Space Command’s astrodynamics standards.

Performs sequential estimation of spacecraft orbit using a Kalman Filter, as well as estimation of tracking measurement biases and other miscellaneous parameters.

Since the underlying principles of the Batch Least Square do not change, the algorithm for the Batch Least Square OD was reused for implementing the Batch Least Square Attitude Determination for a spin-stabilized vehicle. The key differences are in the state vector formulation and measurement models. The recent FAT results indicated the AceFDS Attitude Determination function produced the spin vector attitude solution to within 0.25 deg of customer-provided observation data and reference solution. Additional data will be needed to further validate the AceFDS attitude determination capability.

The fidelity of the orbit propagation also depends on how well the SV attitude is being modeled. There are many attitude control modes available within AceFDS to allow the user to specify for a particular vehicle. These include spin-stabilized modes as well as three-axis modes. For passively controlled SV, high-fidelity torque environments are modeled. These include gravity gradient torque, magnetic torque, solar radiation torque, Sun-Moon torque, and drag torque.

Braxton selected the following components for integration into the AceFDS astrodynamics libraries:

LAPACK++ (Linear Algebra PACKage in C++) is a software library for numerical linear algebra that solves systems of linear equations and eigenvalue problems on high performance computer architectures. Computational support is provided for various matrix classes for vectors, non-symmetric matrices, SPD matrices, symmetric matrices, banded, triangular, and tridiagonal matrices; however, it does not include all of the capabilities of the original f77 LAPACK. Emphasis is given to routines for solving linear systems consisting of non-symmetric matrices, symmetric positive definite systems, and solving linear least-square systems. (Ref. 9)

SOFA (Standards of Fundamental Astronomy) operates under the auspices of the International Astronomical Union (IAU) to provide algorithms and software for use in astronomical computing. The initiative is managed by an international panel, the SOFA Board, appointed through IAU Division I. The Board obtains the latest IAU-approved models and theories from the fundamental-astronomy community, implements them as computer code and checks them for accuracy. SOFA also works closely with the International Earth Rotation and Reference Systems Service (IERS) and its reporting commission, IAU Commission 19 — “Rotation of the Earth”. (Ref. 5)

Jet Propulsion Lab DE405 Ephemeris: The JPL Solar System Ephemeris specifies the past and future positions of the Sun, Moon, and nine planets in three-dimensional space. Many versions of this ephemeris have been produced to include improved measurements of the positions of the Moon and planets and to conform to new and improved coordinate system definitions. The DE100-series ephemeris is in the B1950 coordinate system, the DE200 series is in the J2000 system, and the DE400 series is in the reference frame defined by the International Earth Rotation Service (IERS). DE200 has been the standard from which the Astronomical Almanac tables are computed since 1984. Updated planetary position accuracy is generally available in more than one series. For example, DE118 and DE200 are from the same data as are DE140 and DE400. As of this writing the latest data set is DE421. (Ref. 4)

NAIF JPL SPICE Libraries: NASA’s Navigation and Ancillary Information Facility (NAIF) offers NASA planetary flight projects and NASA funded planetary researchers an information system named “SPICE” to assist scientists in planning and interpreting scientific observations from space-based instruments. SPICE is also widely used in engineering tasks associated with planetary missions. SPICE is focused on solar system geometry (pdf). The SPICE system includes a large suite of software, mostly in the form of application program interfaces (APIs), that customers incorporate in their own application programs to read SPICE data files and, using those data, compute derived observation geometry, such as altitude, latitude/longitude, and lighting angles. SPICE data and software may be used within many popular computing environments. The software is offered in FORTRAN, C, IDL® and MATLAB®, with versions for Java Native Interface and Python planned for the future. (Ref. 22)

Modern Density Model from the Naval Research Lab (NRL): NRL has completed the new NRLMSISE-00 empirical model of the atmosphere for worldwide distribution to operational users and scientists. MSIS stands for Mass Spectrometer and Incoherent Scatter Radar, the two primary data sources underlying early versions of the model, and E indicates that the model extends from the ground to space, as opposed to early versions that covered only the upper atmosphere or “thermosphere” (altitude > 90 km). NRLMSISE-00 represents the culmination of an effort to preserve and radically extend NASA’s MSIS technology so that future military and scientific users could exploit the model’s advantages. The model calculates composition, temperature, and total mass density, and is the standard for international space research. Improvements have focused on the thermosphere, which offers the potential for a number of vital operational and scientific applications. (Ref. 6)

Open-source SGP4: code based on Revisiting Spacetrack Report #3: Over a quarter century ago, the United States Department of Defense (DoD) released the equations and source code used to predict satellite positions through SpaceTrack Report Number 3 (STR#3). Because the DoD’s two-line element sets (TLEs) were the only source of orbital data, widely available through NASA, this code became commonplace among users needing accurate results. However, end users made code changes to correct the implementation of the equations and to handle rare cases encountered in operations. These changes migrated into numerous new versions and compiled programs outside the DoD. Changes made to the original STR#3 code have not been released in a comprehensive form to the public, so the code available to the public no longer matches the code used by DoD to produce the TLEs. Fortunately, independent efforts, technical papers, and source code enabled the synthesization of a non-proprietary version which is believed to be up to date and accurate. The Revisiting Spacetrack Report #3 paper provides source code, test cases, results, and analysis of a version of SGP4 theory designed to be highly compatible with recent DoD versions.

The AceFDS provides the capability to plan for orbit and attitude maneuvers. These include delta-V planning, spin-axis reorientation planning, and spin rate change planning.

These maneuvers can be performed using a number of propulsion systems available within the AceFDS, including monopropellant, bi-propellant, and ion propulsion systems. The AceFDS architecture also allows for the integration of customer-provided propulsion models. The maneuver capabilities within AceFDS can link multiple maneuvers into a sequence for execution.

In addition to the maneuver planning capabilities, AceFDS provide the capability to calibrate the performance parameters of a particular thruster using operational data, including thruster firing data along with orbit determination and attitude determination solutions. The thruster firing data from telemetry may be used to calculate a high-fidelity of mass consumed during the periods of thruster firings.

Calculates individual thruster performance factors based on pre and post maneuver states.

Provides the ability to reconstruct maneuver profiles based on simulated or actual telemetry data.

Provides the ability to create sequenced plans for spacecraft maneuvers using a generic Xenon Ion Propulsion System.

The AceFDS provides the capability to plan for orbit and attitude maneuvers. These include delta-V planning, spin-axis reorientation planning, and spin rate change planning.

These maneuvers can be performed using a number of propulsion systems available within the AceFDS, including monopropellant, bi-propellant, and ion propulsion systems. The AceFDS architecture also allows for the integration of customer-provided propulsion models. The maneuver capabilities within AceFDS can link multiple maneuvers into a sequence for execution.

In addition to the maneuver planning capabilities, AceFDS provide the capability to calibrate the performance parameters of a particular thruster using operational data, including thruster firing data along with orbit determination and attitude determination solutions. The thruster firing data from telemetry may be used to calculate a high-fidelity of mass consumed during the periods of thruster firings.

Fundamental to mission planning is the ability to model the orbit propagation of the space vehicle with a high-degree of accuracy. This has been demonstrated in the operational GPS LADO system. AceFDS enhances this capability by using modern force models available in the open literature or as open-source software libraries.

As with many mission planning software products available commercially, AceFDS implements a number of orbit propagators, each with a different purpose. There are analytical propagators as well as numerical propagators. To achieve a high degree of accuracy, the numerical orbit propagator using special perturbation techniques is the propagator of choice.

There are a number of upgrades within the AceFDS software from its legacy LADO suite that allow for a high-degree of fidelity to be achieved in its physics models. These areas include: accurate coordinate transformation using the IAU open-source library, the high-fidelity solar system ephemeris, the JPL DE405 library for third body perturbation, variable-step numerical integrators, high-fidelity density model from the Naval Research Laboratory, and the detailed modeling of the propulsion systems accounting for all thruster firings during the orbital maneuver phases.

Provides for automated task scheduling and visualization.

Provides the ability to analyze the long-term behavior of orbit drifts due to perturbations and to target a maneuver to maintain the satellite within the assigned orbital box.

Provides an element set and coordinate frame conversion capability either from values entered by the user or imported from saved states.

Provides the ability to ingest and manipulate a set of data files comprising the vehicle specification. Upon completion of a vehicle ingest operation, the data is converted to a format and naming convention for used by all FDS tools.

Provides the ability to export or ingest entire saved operational databases as well as manage elements of the operational database.

Provides the ability to generate plots or tables of any data collected or simulated in FDS and the ability to modify and configure those plots and tables.

The AceFDS toolset includes a simulation capability to support tracking data generation with the ability to export results in real-time or batch to support rehearsals, testing, and integration with external systems. Increased data management capabilities, to include upgrading distributed data management capabilities.

Enables interactive collaboration, ensuring all users work with the same data; allows system administrators a common data ingestion point, and facilitates data mining capabilities to perform trend analysis and anomaly detection.

Improved graphical displays have been added including the addition of estimated state vector, tracking data, data residuals over time (with real-time updates) displays, received versus predicted data displays, and state vectors. Integration with AGI 3D visualization is an option for planning and playback analysis.

Allows users to save and reload templates of common missions which reduce User Data Entries and Increases Productivity and Performance.

TCP/IP interfaces allow interoperability with 3rd Party and Legacy Tools to accommodate integration with other systems.

Provides Data Stream Collection, Monitoring of System Status, and User Administration.

SOFA, CSpice, MSISE00, WGS-84 ensures compliance, accuracy, and acceptance.

Deployable in a Microsoft Windows or Linux environment.

To support the software maintenance at the algorithm level, the AceFDS design of the astrodynamics library features a separation of the numerical computation (pure math, e.g., numerical integrators) from the physics models (pure physics, e.g. drag models). This separation affords the developers the ease of upgrading the numerical algorithms without perturbing the physics models and vice versa. The ability of accommodating new algorithms and models is a critical feature of the AceFDS in support of future enhancements.