ERK'2021, Portorož, 91-95 91
Improving Attitude Determination of a Satellite with
Photodiodes for Sun Position Estimation using TRISAT data
and Earth Albedo model
Nejc Kosaniˇ c
1
, dr. Iztok Kramberger
2
1
LaboratoryforElectronicandInformationSystems,FacultyofElectricalEngineeringandComputerScience,
UniversityofMaribor
E-mail: nejc.kosanic@um.si
Figure 1: Block sheme of the ADCS onboard TRISAT func-
tions during stabilisation period (PD - photodiodes, ADC - ana-
log to digital converter, OBC - on-board computer, GYRO -
gyroscope, MAG - magnetometer, ACT - actuators).
Abstract
InordertoimproveSun-positionestimationinlowEarth
orbits (LEO), an Earth albedo model [1] was designed,
whichhelpstodecipherthetotalsolarandEarth-reglected
current on solar sensors and improves Sun position es-
timation to a higher accuracy. In this short paper the
methodofimprovingtheSunpositionestimationwithso-
larsensorsisdiscussed.
1 Introduction
Satellite attitude determination and control systems (ADCS)
are placed on satellites in order to be able to track the
satellite and describe its movement. Positional estimation
is usually done with the help of GNSS, while primary atti-
tude control is done by a star tracker. During stabilisation
periods, when GNSS and star-tracker are inactive, pho-
todiodes serve as solar sensors and predict Sun position.
Since light sensors are calibrated and have a strict lin-
ear response, data from three orthogonally-placed Sun-lit
sensors results in a sun position estimation with a rela-
tively high accuracy. The ADCS on board the TRISAT
satellite uses photodiode data during stabilisation phase
and accounts for a constant albedo factor of Earth re-
ﬂected light. Currently an Earth albedo model is being
built and tested, to provide for a better albedo factor esti-
mation in regards to the satellite position in LEO.
2 Photodiodes and sun estimation
ADCS systems onboard TRISAT include a global nav-
igation satellite systems (GNSS), a star tracker, a gyro-
scope, a magnetic sensor, and 6 photodiodes to record
the amount of incoming light (Fig. 1). While star tracker
returns high-accuracy satellite attitude it has to be ofﬂine
when using magnetorques to correct satellite orientation.
Photodiodes return values from which Sun vectors are be-
ing calculated to account for Suns position in relation to
the satellite during that time.
The diodes on board TRISAT have been calibrated
and have a strict linear power-to-current response, with
best responsitivity around 360 nm (Fig. 3). Diodes have
a viewing angle of about 160°.
As stated before, current Sun vector estimation takes
into account a constant albedo factor, whereas data from
TRISAT shows that abledo factor is much more com-
plex to estimate. While the albedo constant is the correct
time-average, the effect of a non-constant albedo factor
is prominent (Fig. 4). The TRISAT satellite at the al-
titude of around 500 km takes several measurements at
the same time (photodiodes, magnetometer, gyroscope).
The measurement frequency is entirely dependant on the
speed of change in rotation: the faster the rotation, the
more data samples are acquired to increase the accuracy
and validity of data, the lower the speed of rotation, the
slower is the rate of data sampling. Keep in mind there is
a maximum speed of data transfer to ground control and
to increase the relevance of data sent, some threshold on
rotation information is set in order to conserve the size of
data.
The main problem in photodiodes lies in maximum
values, where the maxime can not be properly estimated,
which in turn translates to a discrepancy between actual
Sun position and satellite-calculated Sun vector. Although
the error between the real and calculated Sun position is
small, even if the sun were 15° from the normal to so-
lar panels, the amount of light that falls on panels is still
above 95% of what it would be, had the Sun been on the
normal.
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Figure 2: Recorded magnetic ﬁeld vector (dots, ’sat’) data interpolated (dashed lines through dots, ’sat’) compared to WMM2020
prediction of magnetic ﬁeld at the same trajectory (dashed lines, ’mag’).
Figure 3: TOP: Photodiode responsitivity in power spectrum,
BOTTOM: photodiode responsitivity in wavelength spectrum.
Figure 4: Normalised solar sensor values for a short data sam-
ple. It can be seen that satellite makes a nice rotation with
”Zneg” values going to 0 and ”Zpos” values starting to go up
at roughly the same time.
3 Magnetic ﬁeld data
Three orthogonal Sun sensors are needed to accurately
predict Sun position, where an overshadowed photodi-
ode results in an sun vector inaccuracy over a half-sphere
around the satellite. To circumvent this problem we have
turned our focus to other on-board sensors, speciﬁcally
the magnetometer, which records the magnetic ﬁeld vec-
tor around the satellite. With the help of an Earth mag-
netic ﬁeld model - World Magnetic Model 2020 [2] - we
can calculate the satellite orientation by comparing the
recorded vector to that of the model.
As the magnetometer on-board the satellite has some
unknown bias, the ﬁrst step in checking the data validity
was made by choosing a data sample that has little change
in magnetic vector direction and then re-sampling and in-
terpolating the data set over shorter, equal time intervals
(Fig. 2). By doing this and subtracting zero-values from
the data sample, we can assume to have gotten rid of some
93
Figure 5: Visualisation of TRISAT path (with orientation vec-
tors) over Earth.
of the data noise, while still maintaining quite an accu-
rate dataset. Furthermore we have used the interpolated
dataset to calculate the satellite rotation and compared it
to the recorded rotation from gyroscopes (Fig. 6). There
is some bias in the comparison, but the data is compa-
rable, which shows that magnetic ﬁeld data is accurate
to a high enough degree that it can be used directly for
satellite attitude estimation.
4 Earth albedo model
The main goal of the model is to properly account for the
Earth reﬂected light and get an accurate estimate of the
maximal Sun-only values on the solar sensors [3],[4],[5].
That way we can predict the Sun vector with a large ac-
curacy and are ultimately able to rotate the satellite to get
better Sun coverage over solar panels.
The model takes into consideration the surface of Earth
in the form of a spherical albedo map. It then places the
satellite above the surface and based on the telemetry data
positions the Sun in respect to the satellite and the Earth
(Fig. 5). On the ﬁrst step the amount of satellite-visible
Sun-lit Earth surface is estimated, where the lit surface
is later divided to multiple smaller areas and integrated
over to get the amount of reﬂected light. Then the view-
ing angles of all the photodiodes as well as all shadowing
objects on TRISAT are taken into account (Fig. 7).
The model is being extensively tested and has shown
great promise in providing useful data (Fig. 8). Based
on comparing model data with satellite data, the basic
”satellite is lit/is not lit” function is accurate to within
seconds, while the problems start with sensor orientation
and longer time samples: while quaternions are used to
rotate the satellite based on its recorded magnetic data,
there are some inaccuracies in satellite attitude estima-
tion.
One of the larger problems is also the WMM2020 in-
accuracy over the magnetic poles, which makes the mag-
netic ﬁeld data unusable for satellite attitude estimation
over at least one third of the orbit.
94
Figure 6: Recorded rotation (x, ’satelite rotation’ ) compared to rotation from magnetic ﬁeld data (ful line, ’magnetic rotation’) for
x-axis (TOP), y-axis (MIDDLE), z-axis (BOTTOM), different and longer time sample than on ﬁgures before.
95
Figure 7: TOP: Modeled viewing angles for X+ solar sensor
with recorded light intensity on the right. BOTTOM: modeled
viewing angles for Z+ solar sensor with recorded light intensity
on the right. Geometrical properties of the satellite which cause
shading can be clearly distinguished in both ﬁgures.
Further work is needed to verify the model to account
for the ever-changing albedo factor needed in the ADCS.
Once the already collected data has been processed and
veriﬁed with the albedo model, the plan is to implement
the model on future TRISAT missions.
5 Conclusion
Since many (comercial) satellites are being produced to
be ﬂown in LEO, the need for a simple solution during
satellite stabilisation period, when GNSS and star tracker
are inactive, is needed. In this short paper we have shown
that simple method with photodiode sensors and the help
of an Earth albedo model in combination with real-time
magnetic sensor and gyroscope data provides a high ac-
curacy solution for Sun vector estimation. As the satel-
lites in LEO are prone to Earth reﬂected light, the albedo
model can account for reﬂected light and shine light on
true Sun values thus providing accurate Sun vector esti-
mations. Further testing of the model with more of TRISAT
data is required for ﬁnal model veriﬁcation, with the end
goal to produce an accurate model to be incorporated into
ADCS on-board future TRISAT satellites.
References
[1] T. W. Flatley, W. A. Moore: NASA Technical Memoran-
dum 104596, january 1994, Greenbelt, Maryland, USA
[2] https://www.ngdc.noaa.gov/geomag/WMM/
Figure 8: TOP: Normalised solar sensor values for a short data
sample. BOTTOM: normalised solar sensor value for the same
interval from albedo model. ’Yneg’ line in bottom ﬁgure can
not be seen in the top ﬁgure, because the solar sensor is blocked
by a solar panel. Not all lines are drawn..
[3] S. A. O’Keefe: Autonomous Sun-Direction Estimation Us-
ing Partially Underdetermined Coarse Sun Sensor Conﬁg-
urations, 2015, Department of Aerospace Engineering Sci-
ences, Faculty of the Graduate School of the University of
Colorado
[4] D. D. V . Bhanderi: Modeling Earth Albedo Currents on Sun
Sensors for Improved Vector Observation, AIAA Guid-
ance, Navigation, and Control Conference and Exhibit, 21.-
24. August 2006, Keystone, colorado
[5] P. M. Akhmet’ev, A. Y . Smirnov: Determination of the Ori-
entation of an Artiﬁcial Satellite from Magnetic Field Data
in Orbit, Geomagnetism and Aeronomy, V ol. 60, No. 3, pp-
289-291, 2020