Star Tracker Sensor Model FMUs

This repository contains compiled Functional Mock-up Units (FMUs) for a system-level star tracker sensor model. A BibTeX entry template for citing the associated publication is provided in CITATION.bib; publication-specific fields are left open until the paper is published.

The FMUs are included in bin/ for Linux and Windows:

File	Platform	FMI mode
bin/startracker_error_model_n16_clk0p1_v140_linux.fmu	Linux 64 bit	Co-Simulation
bin/startracker_error_model_n16_clk0p1_v140_win.fmu	Windows 64 bit	Co-Simulation

The exported model is intended for system-level, closed-loop simulation of guidance, navigation, and control algorithms. It is not an image-level optical star tracker simulator.

Download

Please download the binaries from the latest release on the Github page (right side, under releases). There are known issues with FMUs that are synchronized via git.

Model Overview

The model represents the attitude-relevant behaviour of a star tracker at vector level. It uses catalogue star directions, the spacecraft position and attitude, the sensor mounting, field-of-view geometry, directional measurement noise, and analytical Sun, Earth, and Moon geometry to produce:

• an estimated spacecraft attitude quaternion,
• a geometry-dependent covariance estimate,
• visible catalogue star directions and identifiers,
• Boolean flags indicating Sun, Earth, or Moon intrusion into the configured avoidance region.

The model omits pixel-level image formation, optics, detector physics, centroid extraction, and explicit star-identification failures. These effects are represented only indirectly through directional disturbance of the identified star vectors. Consequently, the FMU is most appropriate for closed-loop prototyping where downstream algorithms consume attitude, covariance, and availability information.

Internally, the model performs the following operations:

1. The true spacecraft attitude qTrue and position rBody_eci define the body frame with respect to the Earth-centred inertial frame.
2. The sensor mounting measToBodyEuler and line of sight lineOfSight_meas define the measurement frame and boresight.
3. Catalogue stars from the Bright Star Catalogue are selected if they lie within the configured field of view.
4. The selected star vectors are perturbed by an angular disturbance with mean muDist and standard deviation sigmaDist.
5. The perturbed body-frame vectors and the corresponding inertial catalogue vectors are used in a QUEST attitude-estimation step.
6. Analytical ephemerides are used to evaluate Sun, Earth, and Moon field-of-view intrusion flags.

The number of tracked stars and the model clock period are fixed in this FMU export. This repository provides an export with:

Quantity	Value
Maximum number of tracked stars	16
Model clock period	0.1 s
Nominal update rate	10 Hz

The fixed star count is visible in the interface dimensions, for example visibleStarsECI[3,16] and visibleStarsID[16]. Changing the tracked-star limit or clock period requires a new FMU export.

Coordinates and Conventions

The model uses an Earth-centred inertial frame (ECI), a spacecraft body frame, and a star tracker measurement frame. The catalogue frame and ECI frame are treated as aligned for the intended system-level simulations.

Quaternions use the ordering:

{p1, p2, p3, p0}

where p0 is the scalar component. Both qTrue and qEst represent the rotation from the ECI frame into the body frame.

Angles are provided in radians unless otherwise stated. The Euler mounting parameter measToBodyEuler follows an intrinsic x-y-z roll-pitch-yaw sequence and describes the rotation from the body frame into the measurement frame.

FMU Interface

Inputs

Variable	Size	Type	Unit	Description
rBody_eci	3	Real input	m	Position of the spacecraft body frame origin in ECI coordinates.
qTrue	4	Real input	-	True spacecraft attitude quaternion {p1,p2,p3,p0} rotating ECI into the body frame.

Outputs

Variable	Size	Type	Unit	Description
visibleStarsECI	3 x 16	Real output, discrete	-	Unit direction vectors of the selected visible catalogue stars, resolved in ECI coordinates. Columns correspond to tracked stars.
visibleStarsID	16	Real output, discrete	-	Identifiers of the selected visible stars. These are HR numbers from the Bright Star Catalogue.
qEst	4	Real output, discrete	-	Estimated attitude quaternion {p1,p2,p3,p0} rotating ECI into the body frame.
earthInFOV	1	Boolean output, discrete	-	true if Earth lies inside the configured Earth avoidance region; the measurement should be treated as invalid.
sunInFOV	1	Boolean output, discrete	-	true if the Sun lies inside the configured Sun avoidance region; the measurement should be treated as invalid.
moonInFOV	1	Boolean output, discrete	-	true if the Moon lies inside the configured Moon avoidance region; the measurement may be invalid.
covEst	3 x 3	Real output, discrete	-	Estimated covariance matrix of the small attitude-error vector with respect to the body axes.

The covariance estimate is geometry-dependent. It should be interpreted as a relative indicator of attitude-observation quality.

Parameters

Variable	Size	Default	Unit	Description
lineOfSight_meas	3	[0, 0, 1]	-	Sensor line-of-sight vector in the measurement frame. The default corresponds to the positive measurement-frame z-axis.
measToBodyEuler	3	[0, 0, 0]	rad	Intrinsic x-y-z Euler angles defining the body-to-measurement mounting rotation.
earthAvoidanceAngle	1	0.34906585039887	rad	Minimum allowed angular separation between Earth's horizon and the sensor boresight.
sunAvoidanceAngle	1	0.45378560551853	rad	Minimum allowed angular separation between the Sun and the sensor boresight.
MoonAvoidanceAngle	1	0	rad	Minimum allowed angular separation between the Moon and the sensor boresight.
muDist	1	0	rad	Mean angular bias of the directional disturbance applied to visible star vectors.
sigmaDist	1	1.7453292519943e-05	rad	Standard deviation of the angular directional disturbance applied to visible star vectors. The default is 0.001 deg.
FOVAngle	1	0.34906585039887	rad	Full characteristic field-of-view angle. The default is 20 deg.
year	1	2000	-	Gregorian simulation start year for the analytical ephemeris model.
month	1	1	-	Gregorian simulation start month, 1 to 12.
day	1	1	-	Gregorian simulation start day, 1 to 31.
hour	1	0	-	Gregorian simulation start hour, 0 to 23.
minute	1	0.0	min	Gregorian simulation start minute, including fractional minutes for seconds.
localSeed	1	13300988	-	Local seed for random-number generation.
globalSeed	1	39941994	-	Global seed for random-number generation.

Notes on Visibility and Validity

The FMU returns up to 16 visible catalogue stars per update. If more than 16 stars satisfy the FOV criterion, the retained subset is determined by the catalogue search order. The model does not sort visible stars by brightness, expected centroid quality, or geometric conditioning.

The earthInFOV, sunInFOV, and moonInFOV flags indicate geometric intrusion into the corresponding avoidance region. The FMU does not automatically suppress or replace qEst when a flag is true. Downstream simulation code should decide how to handle flagged measurements, for example by rejecting the attitude update or increasing measurement uncertainty.

Limitations

The FMU is a system-level abstraction. It does not model optical image formation, detector noise, saturation, point-spread functions, centroiding, motion blur, catalogue-matching failures, or hardware-specific processing. Directional noise and covariance are not calibrated to a particular flight sensor in this repository. Quantitative validation against image-level simulation or hardware measurements is outside the scope of the provided FMUs.

The model is therefore suitable for reproducible closed-loop prototyping and algorithm studies, but it should not be interpreted as a flight-qualified or sensor-vendor-specific performance model.

License

See LICENSE for repository licensing information. Each FMU also contains third-party license files in its documentation/ directory.

Contact

Tobias Kamp @tkmamp

tobias.kamp@dlr.de

German Aerospace Center Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)

Institute of Robotics and Mechatronics

Münchener Straße 20

D-82234 Wessling, Germany