1. Purpose

OREKIT library is a low-level library for space mechanics projects. It is implemented in the JAVA language.

OREKIT project was initiated by CS with the following goals in mind:

• provide a common base layer for space projects
• support both quick developments with loose requirements and complex projects with rich physical modeling, fine customization, and high accuracy
• be user-extensible through clear and as simple as possible architecture
• use unified interfaces to allow models and algorithms switching with almost no effort
• provide both basic and rich models that can be plugged interchangeably to ease applications validation
• separate models configuration from models usage to hide away complexity and keep caller code simple
• support both development of standalone and embedded applications (web services, plugins, scripting frameworks ...)
• use up-to-date techniques for low cost development and maintenance
• remove platforms and system dependencies and leverage environment-hell (environment variables, dynamic libraries versions, operating system, filesystem layout ...)

2. Features

Orekit can be used for many purposes, from simple geometrical or orbital tools up to complex orbits propagators with several perturbing forces, maneuvers and discrete events. Here is a short list of the features offered by the library:

• Time
  • high accuracy absolute dates
  • time scales (TAI, UTC, UT1, GPS, TT, TCG, TDB, TCB, GMST, GST, GLONASS, QZSS, BDT, IRNSS ...)
  • transparent handling of leap seconds
  • support for CCSDS time code standards
• Geometry
  • frames hierarchy supporting fixed and time-dependent (or telemetry-dependent) frames
  • predefined frames (EME2000/J2000, ICRF, GCRF, all ITRF from 1988 to 2014 and intermediate frames, TOD, MOD, GTOD and TEME frames, Veis, topocentric, tnw and qsw local orbital frames, Moon, Sun, planets, solar system barycenter, Earth-Moon barycenter, ecliptic)
  • user extensible (used operationally in real time with a set of about 60 frames on several spacecraft)
  • transparent handling of IERS Earth Orientation Parameters (for both new CIO-based frames following IERS 2010 conventions and old equinox-based frames)
  • transparent handling of JPL DE 4xx (405, 406 and more recent) and INPOP ephemerides
  • transforms including kinematic combination effects
  • composite transforms reduction and caching for efficiency
  • extensible central body shapes models (with predefined spherical and ellipsoidic shapes)
  • Cartesian and geodesic coordinates, kinematics
  • Computation of Dilution Of Precision (DOP) with respect to GNSS constellations
• Spacecraft state
  • Cartesian, elliptical Keplerian, circular and equinoctial parameters, with non-Keplerian derivatives if available
  • Two-Line Elements
  • transparent conversion between all parameters
  • automatic binding with frames
  • attitude state and derivative
  • Jacobians
  • mass management
  • user-defined associated state (for example battery status, or higher order derivatives, or anything else)
• Maneuvers
  • analytical models for small maneuvers without propagation
  • impulse maneuvers for any propagator type
  • continuous maneuvers for numerical propagator type
• Propagation
  • analytical propagation models (Kepler, Eckstein-Heschler, SDP4/SGP4 with 2006 corrections)
  • numerical propagators
    • customizable force models
      • central attraction
      • gravity models including time-dependent like trends and pulsations (automatic reading of ICGEM (new Eigen models), SHM (old Eigen models), EGM and GRGS gravity field files formats, even compressed)
      • atmospheric drag
      • third body attraction (with data for Sun, Moon and all solar systems planets)
      • radiation pressure with eclipses
      • solid tides, with or without solid pole tide
      • ocean tides, with or without ocean pole tide
      • general relativity
      • multiple maneuvers
    • state of the art ODE integrators (adaptive stepsize with error control, continuous output, switching functions, G-stop, step normalization ...)
    • computation of Jacobians with respect to orbital parameters and selected force models parameters
    • serialization mechanism to store complete results on persistent storage for later use
  • semi-analytical propagation model (DSST) with customizable force models
  • tabulated ephemerides
    • file based
    • memory based
    • integration based
  • specialized GPS propagation, using SEM or YUMA files
  • Taylor-algebra (or any other real field) version of most of the above propagators, with all force models, events detection, orbits types, coordinates types and frames allowing allowing high order uncertainties and derivatives computation or very fast Monte-Carlo analyzes
  • unified interface above analytical/numerical/tabulated propagators for easy switch from coarse analysis to fine simulation with one line change
  • all propagators can be used in several different modes
    • slave mode: propagator is driven by calling application
    • master mode: propagator drives application callback functions
    • ephemeris generation mode: all intermediate results are stored during propagation and provided back to the application which can navigate at will through them, effectively using the propagated orbit as if it was an analytical model, even if it really is a numerically propagated one, which is ideal for search and iterative algorithms
  • handling of discrete events during integration (models changes, G-stop, simple notifications ...)
  • predefined discrete events
    • eclipse (both umbra and penumbra)
    • ascending and descending node crossing
    • anomaly, latitude argument or longitude argument crossings, with either true, eccentric or mean angles
    • apogee and perigee crossing
    • alignment with some body in the orbital plane (with customizable threshold angle)
    • angular separation thresholds crossing between spacecraft and a beacon (typically the Sun) as seen from an observer (typically a ground station)
    • raising/setting with respect to a ground location (with customizable triggering elevation and ground mask, optionally considering refraction)
    • date and on-the-fly resetting countdown
    • latitude, longitude, altitude crossing
    • latitude, longitude extremum
    • elevation extremum
    • anomaly, latitude argument, or longitude argument crossings, either true, mean or eccentric
    • moving target detection (with optional radius) in spacecraft sensor Field Of View (any shape, with special case for circular)
    • spacecraft detection in ground based Field Of View (any shape)
    • sensor Field Of View (any shape) overlapping complex geographic zone
    • complex geographic zone traversal
    • inter-satellites direct view
    • ground at night
    • impulse maneuvers occurrence
  • possibility of slightly shifting events in time (for example to switch from solar pointing mode to something else a few minutes before eclipse entry and reverting to solar pointing mode a few minutes after eclipse exit)
  • events filtering based on their direction (for example to detect only eclipse entries and not eclipse exits)
  • events filtering based on an external enabling function (for example to detect events only during selected orbits and not others)
  • events combination with boolean operators
  • ability to run several propagators in parallel and manage their states simultaneously throughout propagation
• Attitude
  • extensible attitude evolution models
  • predefined laws
    • central body related attitude (nadir pointing, center pointing, target pointing, yaw compensation, yaw-steering)
    • orbit referenced attitudes (LOF aligned, offset on all axes)
    • space referenced attitudes (inertial, celestial body-pointed, spin-stabilized)
    • tabulated attitudes, either respective to inertial frame or respective to Local Orbital Frames
    • specific law for GNSS satellites: GPS (block IIA, block IIF, block IIF), GLONASS, GALILEO, BEIDOU (GEO, IGSO, MEO)
• Orbit determination
  • batch least squares fitting
    • optimizers choice (Levenberg-Marquardt or Gauss-Newton)
    • decomposition algorithms choice (QR, LU, SVD, Cholesky)
    • choice between forming normal equations or not
  • Kalman filtering
    • customizable process noise matrices providers
    • time-dependent process nous provider
  • parameters estimation
    • orbital parameters estimation (or only a subset if desired)
    • force model parameters estimation (drag coefficients, radiation pressure coefficients, central attraction, maneuver thrust or flow rate)
    • measurements parameters estimation (biases, satellite clock offset, station clock offset, station position, pole motion and rate, prime meridian correction and rate, total zenith delay in tropospheric correction)
  • multi-satellites orbit determination
  • ground stations displacements due to solid tides
  • ground stations displacements due to ocean loading (based on Onsala Space Observatory files in BLQ format)
  • several predefined measurements
    • range
    • range rate (one way and two way)
    • turn-around range
    • azimuth/elevation
    • right ascension/declination
    • position-velocity
    • position
    • inter-satellites range (one way and two way)
    • GNSS code
    • GNSS phase with integer ambiguity resolution (not complete yet and experimental)
  • possibility to add custom measurements
  • several predefined modifiers
    • tropospheric effects
    • ionospheric effects
    • station offsets
    • biases
    • delays
    • Antenna Phase Center
    • Shapiro relativistic effect
  • possibility to add custom measurement modifiers (even for predefined events)
  • possibility to parse CCSDS Tracking Data Message files
  • measurements generation
    • with measurements feasibility triggered by regular event detectors (ground visibility, ground at night, sunlit satellite, inter satellites direct view, boolean combination...)
    • with measurement scheduling as fixed step streams (optionally aligned with round UTC time)
    • with measurement scheduling as high rate bursts rest periods (optionally aligned with round UTC time)
    • possibility to customize measurement scheduling
• GNSS
  • computation of Dilution Of Precision
  • loading of ANTEX antenna models file
  • loading of RINEX observation files (version 2 and version 3)
• Orbit file handling
  • loading of SP3 orbit files (from versions a to d)
  • loading of CCSDS Orbit Data Messages (both OPM, OEM, and OMM types are supported)
  • loading of SEM and YUMA files for GPS constellation
  • exporting of ephemeris in CCSDS OEM file format
• Earth models
  • atmospheric models (DTM2000, Jacchia-Bowman 2008, NRL MSISE 2000, Harris-Priester and simple exponential models), and Marshall solar Activity Future Estimation, optionally with lift component
  • tropospheric delay (modified Saastamoinen, Mendes-Pavlis, Vienna 1, Vienna 3, estimated, fixed)
  • tropospheric refraction correction angle (Recommendation ITU-R P.834-7 and Saemundssen's formula quoted by Meeus)
  • tropospheric model for laser ranging (Marini-Murray)
  • Klobuchar ionospheric model (including parsing α and β coefficients from University of Bern Astronomical Institute files)
  • Global Pression and Temperature models (GPT and GPT2)
  • geomagnetic field (WMM, IGRF)
  • geoid model from any gravity field
  • displacement of ground points due to tides
  • tessellation of zones of interest as tiles
  • sampling of zones of interest as grids of points
• Customizable data loading
  • loading from local disk
  • loading from classpath
  • loading from network (even through internet proxies)
  • support for zip archives
  • automatic decompression of gzip compressed (.gz) files upon loading
  • automatic decompression of Unix compressed (.Z) files upon loading
  • plugin mechanism to add filtering like custom decompression algorithms, deciphering or monitoring
  • plugin mechanism to delegate loading to user defined database or data access library

3. Dependency

OREKIT has only one dependency: the Hipparchus open-source library. This library provides mathematical tools for many purposes: geometry, polynomial equations, differential equations, and more... It is distributed under the business-friendly Apache Software License version 2.0.

OREKIT is based on several Hipparchus packages:

• geometry, which provides very useful objects as vectors and rotations (internally represented by quaternions)
• ode, which provides numerical solutions to solve Ordinary Differential Equations (ODE)
• optim, which provides multi-dimensional optimization
• solvers, which provides root-finding algorithms
• differentiation, which provides analytical computation of partial derivatives to arbitrary order and arbitrary number of free parameters

The use of Hipparchus is hidden in OREKIT as much as possible so users don't need to fully master this library. If they wish, they can limit themselves to understanding the simple classes Vector3D and Rotation from the geometry package, and the interface FirstOrderIntegrator from the ode package.