Analysis of the Feasibility of Demonstrating Pulsed Plasma
Thrusters on FalconSAT-3
C1C Andrea M. Johnson
United States Air Force Academy
Abstract
FalconSAT-3 is a small satellite being assembled, integrated, and tested by cadets at the United
States Air Force Academy. Among the payloads on FalconSAT-3 are pulsed plasma thrusters
(PPT’s). When it became clear that the actual thrust produced by the PPT’s was lower than
initially estimated, concern arose regarding the ability of ground control or the on-board
computer to detect changes in attitude that could be attributed to PPT firing. With the suggestion
that the PPT’s could not be used for attitude control, it became necessary to find alternative
means of demonstrating that the PPT’s were firing. A Kalman filter and Batch filter were tested
with simulated attitude data generated with Simulink. Even with extremely pessimistic thrust
data, noisy attitude data, and pessimistic disturbance torques values, the Batch filter was able to
accurately estimate the torque produced by the PPT’s. The Kalman filter, although providing a
solution faster than the batch filter, was significantly less accurate.
Nomenclature List
a1i , a2i , a3i , a4i
a
â
A
Ai
Bi
C
Ci
D sun
Di
Nutation coefficients
Vector a, average a value, predicted measurement of a
Unit vector a, measurement of a
Satellite drag area and angle for calculating polar motion component
Nutation coefficient
Nutation coefficient
Angle for calculating polar motion component
Nutation coefficient
Mean elongation from the sun
Nutation coefficient
Ê
EQequinox
Unit vector from the satellite center of mass to the earth
Equation of equinoxes
M moon
M sun
Mean anomaly of the moon
Mean anomaly of the sun
N̂
Ŝ
Tbylo
Unit vector normal to surface
Unit vector from the spacecraft center of mass to the sun
Transformation matrix from local orbital to body
Tloecf
TAI
TDB
TDT
u moon
xp
yp
z



 AST
 moon
Transformation matrix from earth-centered, fixed to local orbital
coordinate frame
International atomic time
Terrestrial barycentric time
Terrestrial dynamical time
Mean argument of latitude of the moon
Polar motion component, measured positive from the North pole along 0o
longitude
Polar motion component, measured positive from the North pole along 90o
west longitude
Final precession angle to align J2000 and earth-centered, inertial
coordinate frames
Orbital energy and obliquity of the ecliptic
Mean obliquity of the ecliptic
Pitch angle, coelevation, and angle between mean equator at epoch and
mean equator of date
Apparent sidereal time
Longitude of the ascending node of the mean lunar orbit
Introduction
FalconSAT-3 is a small satellite being assembled, integrated, and tested by cadets at the United
States Air Force Academy. It is scheduled for launch in 2006 aboard a Lockheed-Martin AtlasV rocket, a medium-class evolved expendable launch vehicle (EELV), owned by the United
States Air Force. It will “piggyback” along with five other small satellites on an EELV
secondary payload adapter (ESPA) ring. The following are the specifications for FalconSAT-3:
Total Mass:
Inertia Tensor (Deployed Boom):
Coefficient of Drag (Cd):
Spacecraft Dipole:
Orbit:
46.1 kg
0
0 
67.40
 0
67.45 0  kg-m2

 0
0
1.31
2.6
0.05 A-m2
Altitude = 560 km
Semimajor axis = 6938.137 km
Inclination = 35o
Eccentricity = 0
Right Ascension = 0o
Table 1: FalconSAT-3 Specifications
Figure 1: FalconSAT-3 Dimensions
Experimental Methods
In order to follow the calculations made, various coordinate frames must first be defined.
Coordinate Frames
Body frame: Same as local orbital when pitch, roll, and yaw = 0
Local orbital frame:
Origin: Satellite center of mass
Fundamental plane: Satellite’s orbital plane
x in the direction of satellite velocity,
y in the direction of orbit normal,
z completes right-handed system
Earth-Centered, Fixed:
Origin: Center of the earth
Fundamental plane: Earth’s true of date equator
x points toward the prime meridian
z points along the earth’s true of date rotational axis, positive north
y completes right-handed coordinate system
Earth-Centered, Inertial (J2000):
Origin: Center of the earth
Fundamental plane: Mean of earth’s equator of epoch
I in the direction of the mean vernal equinox of epoch,
K points toward the mean rotational axis of epoch, positive north
J completes right-handed coordinate system
Perifocal Coordinate System (quasi-inertial, PQW):
Origin: Center of the earth
Fundamental Plane: Satellite’s orbital plane
P in the direction of the first point of Aries,
Q 90 degrees away from P in the direction of satellite orbit,
W axis completes right-handed system
Spiral Orbit Transfer
In determining whether or not a change in semimajor axis is feasible, the total change in velocity
provided by a single PPT, assuming 24 hours of firing, perfect alignment of the thrust in the
direction of the velocity vector, instantaneous firing, and no thruster decay is made. In this
analysis, third-body effects are neglected, the mass of the satellite is assumed to be negligible
compared to the mass of the earth, and the only perturbing force taken into consideration is the
PPT thrust.
To determine the total change in velocity, the peak thrust is multiplied by the time of firing for
the entire 24 hours and divided by the mass of the satellite:
160e 6 N * 15e 6 sec* 2 Hz * 24hrs * 60 min* 60 sec
V 
 8.9960954446855e 6 m / s
46.1kg
The initial velocity of the spacecraft, assuming the orbital elements above are accurate is
calculated:
Vcircle 

 7.5796208888927km / sec
R
In which V is velocity in km/sec, μ is the gravitational parameter of the earth, and R is the
magnitude of the position vector. The final velocity is used to determine the energy of the new
orbit at that position:
(7.5796208978888km / sec) 2 
    28.725326341481
2
R
The energy is used to determine the semimajor axis of this new orbit:


 a  6938.1370164696  a  1.64696cm
2a
The force of drag causes deceleration according to the following equation:
1 C A
a drag     d V 2
2  m 
In which a is acceleration,  is the air density, C d is the coefficient of drag on the satellite, A
is the area of the satellite susceptible to drag, m is the mass of the satellite and V is the velocity
of the satellite.
Assuming the minimum amount of drag on the satellite and only one panel is susceptible to drag,
the acceleration is given to be:
3 2
1
 4  2.6 * (0.46e ) 

7.5796 2  4.9611e 11km / sec 2
adrag   *1.488e 
2
47.4


From these calculations, the change in velocity possible from air drag over the same 24 hour
period of time that the PPT’s are firing is around -4.2864e-3 m/s. The force of drag on the
satellite even in the best-case scenario is three orders of magnitude greater than the force of
thrust from the PPT’s.
Lacking an accurate model for air density and a GPS receiver, even estimation theory cannot be
used to provide an accurate answer. Even if a GPS receiver could be mounted on FalconSAT-3,
it would not provide the accuracy necessary to measure such a small change in semimajor axis.
Attitude Control
Equations of Motion:
To determine whether or not changes in attitude due to PPT firing could be detected, Simulink
was used to model the behavior of the satellite with and without disturbance torques using
Euler’s moment equations. Assuming no products of inertia, the equations of motion are:
I11  ( I 3  I 2 ) 23  T1
I 2 2  ( I 1  I 3 )13  T2
I 3 3  ( I 2  I1 )12  T3
Solving for  :
( I  I )   T
1  2 3 2 3 1
I1
( I  I )   T
 2  3 1 1 3 2
I2
( I  I )   T
 3  1 2 1 2 3
I3
Simulink then integrates the above equations using initial conditions specified by the user.
Taking the results, the transformation matrix from the body frame to the local orbital is
calculated. Initially user-defined initial roll, pitch, and yaw angles are used. Subsequently, the
calculated angles are used. To perform a 2-1-3 rotation:
 cos cos   sin  sin  sin  sin  cos   cos sin   sin  sin  cos  
Tbylo   sin  cos   cos sin  sin  cos cos  sin  sin   cos sin  cos  


cos  sin 
 sin 
cos  cos 
The rates in the roll, pitch, and yaw directions are then calculated:
 lo   by  Tbylo o for which o  0 o
0 and  o 
T

a3
So     Tlobylo to put the rates with respect to the local orbital frame.


Disturbance Torques:
The first disturbance torque taken into account is the gravity-gradient torque. The equations
describing the torque in each axis assume no products of inertia:
2
N xGG  3 o ( I z  I y )Tbylo 23Tbylo 33
N yGG  3 o ( I x  I z )Tbylo 33Tbylo13
2
N zGG  3 o ( I y  I x )Tbylo13Tbylo 23
2
The second disturbance torque taken into account is atmospheric drag. If roll, pitch, and yaw are
not zero (or a limited number of specific angles), there will be a torque caused by drag. The drag
torque is calculated as follows:
1
C d Ac p  V 
2
For which Cd is the coefficient of drag for the satellite, ρ is the density of air at the altitude of the
satellite’s orbit, A is the area of the satellite normal to the velocity vector, c p is the vector from
N drag 
the center of mass to the center of pressure, and V is the unit velocity vector of the satellite. To
calculate the torque correctly, the velocity magnitude should be in the body frame and units must
agree (if area is in meters, the velocity must be in meters per second). For this analysis, the
international standard atmosphere model developed in 1976 is used. As more complex models
generate minimal to no improvement over this model, the sacrifice of computation time is not
justifiable.
To obtain a more precise estimate of what the drag torque is, the simplified model of
FalconSAT-3 is used and the drag force on six planes and two cylinders is calculated:
1
Fdrag, plane   C d V 2 A Nˆ  Vˆ Vˆ
2
2
1
Fdrag,cylinder   C d V 2 DL 1  Zˆ  Vˆ Vˆ
2




n
N drag   ci p  Fi drag
i 1
For this simulation, since the center of pressure for each element of the satellite and the overall
center of pressure are not known, the center of pressure for the satellite main body is assumed to
be off by 1 cm from the geometric center of the element. The centers of pressure for the boom
and the tip mass are assumed to correspond with the geometric centers of those elements.
The third disturbance torque taken into account is solar pressure. The equation for the solar
pressure disturbance torque is very similar to that of drag:
d
N solar  o Ac p  V 
c
For which d o is the average solar radiation constant and c is the speed of light. Once again, to
obtain a more accurate estimate of the solar pressure torque, the following equations are used:

1  

Fsolar, plane   Psun A cos  sun 1  C s Sˆ  2 C s cos  sun  C d  Nˆ  
3  


Fsolar,cylinder

1  

Pearth A cos  earth 1  C s Eˆ  2 C s cos  earth  C d  Nˆ 
3  






 1  
 4

  Psun  sin  sun 1  C s   Cd  ASˆ    C s sin  sun  C d  cos sun A1 Zˆ  
6
 3  6 
 3







 1  
 4

Pearth  sin  earth 1  C s   C d  AEˆ    C s sin  earth  C d  cos earth A1 Zˆ 
6
 3  6 
 3



For which
Psun 
Fsun
c
and
Fsun 
1358
W 2
1.0004  0.0334 cos D m
While
Pearth  Pearth,reflect  Pearth,rad
For which
Pearth,reflect  600W
and Pearth,rad  150 W 2
m2
m
Finding the total torque is then exactly the same as finding the drag torque:
n
N solar   ci p  Fi solar
i 1
The fourth disturbance torque taken into account is magnetic moment caused by the interaction
of the spacecraft dipole with the earth’s magnetic field. The equation for this torque follows:
N magnetic  M  B
For which M is the magnetic dipole of the satellite and B is the magnetic field of the earth at the
satellite’s position. For this analysis, the International Geomagnetic Reference Field (IGRF) 10th
generation model is used.
The Gaussian coefficients used for this analysis include terms up to the 13th degree and 13th order
and secular terms up to the 8th degree and 8th order. The earth’s magnetic field can be
represented fairly well as the gradient of a scalar potential function:
B  V
The equations for B in terms of the distance of the satellite from the center of the earth,
coelevation, and azimuth (spherical coordinate frame) are:
Br  
k
V
a
  
r n 1  r 
n2
n  1 g n,m cos m  h n,m sin m P n,m  
n
m 0
k
1 V
a
B  
   
r 
n 1  r 
n2 n
 g
n ,m
cos m  h
n ,m
m 0
n2
P n ,m  
sin m


n
1 V
1 k a
B  




 m  g n,m sin m  h n,m cos m P n,m  
r sin  
sin  n 1  r  m 0
For which a is the equatorial radius of the earth defined as 6371.2 km for the IGRF, r is the
distance from the center of the earth, θ is the coelevation (angle from the spin axis of the earth to
the position vector), and  is azimuth, measured east from Greenwich. K is the maximum order
of the Gaussian coefficients used, gn,m and hn,m are the Schmidt normalized Gaussian
coefficients, n and m are the degree and order (respectively) of the Gaussian coefficients, and
P n ,m  
n,m


and
are the associated Legendre functions and partial derivatives thereof,
P 

respectively.
A recursive algorithm can be used to find the respective Schmidt coefficients:
S 0,0  1


 2n  1
S n , 0  S n 1, 0 
 n 
S n ,m  S n ,m 1
n  m  1 m1  1
nm
The Schmidt normalized coefficients are defined as
g n,m  S n,m g nm
h n,m  S n,m hnm
For which g n ,m and h n ,m are the Schmidt normalized coefficients, g nm and hnm are Gaussian
coefficients and S n ,m is the respective Schmidt function.
A similar algorithm can be used to find the Legendre functions and their derivatives:
P n ,m
P 0, 0  1
P n ,n  sin P n 1,n 1
 cos P n 1,m  K n ,m P n  2,m
For which
K n,m
K 1,m  0
2

n  1  m 2

2n  12n  3
And
P 0,0
0

P n,n
P n 1,n 1
 sin  
 cos  P n 1,n 1


n,m
n 1, m
n  2,m
P
P
n 1, m
n , m P
 cos  
 sin  P
K



To make the magnetic field values useful, they must be in body coordinates. Converting from
the spherical earth-fixed coordinate frame to the Cartesian earth-fixed coordinate frame is the
first step.
Figure 2: Spherical Coordinate to Cartesian Coordinate Transformation
Using simple geometry, the magnetic field equations become:
B x  Br sin  cos   B cos  cos   B sin   Br sin   B cos   cos   B sin 
B y  Br sin  sin   B cos  sin   B cos   Br sin   B cos  sin   B cos 
Bz  Br cos   B sin 
A conversion from the earth-centered fixed coordinate frame to the earth-centered inertial
coordinate system is then necessary. Although a simpler conversion algorithm would have
sufficed for this simulation, the following was developed so that the program could be used again
for calculations requiring more precise solutions.
Given the year, month, day, hour, minute, and second at which the calculations are to be made,
Julian date can be found using the following formula:
 
month  9   
 7 year  floor 
  
12
 

 
 275 * month 
JD  367 * year  floor 
 floor 


4
9








sec
 min
60
 hour
60
 day  1721013.5 
24
Precession:
Three rotations are necessary to account for the change in coordinate frame from that of epoch to
that of the true of date because of precession.
rwprecession  Rot 3( z ) Rot 2( ) Rot 3( )rJ 2000
For which
  0.011180860TTDB  1.464e 6TTDB 2  8.7e 8TTDB 3
z  0.011180860TTDB  5.308e 6TTDB  8.9e 8TTDB
2
3
  0.009717173TTDB  2.068e 6TTDB 2  2.02e 7TTDB 3
TTDB represents the number of centuries in TDB that have passed since epoch. The method for
determining this value is outlined later.
Nutation:
Again, three rotations are necessary:
rwnutation  Rot1( ) Rot 3() Rot1( )r wprecession
The angles through which the vectors are rotated can be found as follows:
  0.40909280  0.000226966TTDB  2.86e 9TTDB 2  8.80e 9TTDB 3
M moon
r  2
2
3
 2.355548394  (1325r  3.470890872)TTDB  0.000151795TTDB  3.103e 7TTDB
M sun  6.2400359  (99r  6.2666106)TTDB  0.0000027974TTDB  5.81e 8TTDB
2
3
umoon  1.627901934  (1342r  1.431476084)TTDB  0.000064272TTDB  5.34e 8TTDB
2
Dsun  5.198469514  (1236r  5.36010650)TTDB  0.0000334086TTDB  9.22e 8TTDB
2
 moon  2.182438624  (5r  2.341119397)TTDB  0.000036142TTDB  3.87e 8TTDB
2
106
   ( Ai  Bi TTDB ) sin a1i M moon  a 2i M sun  a ei u moon  a 4i Dsun  a5i  moon 
i 1
106
   (Ci  Di TTDB ) cosa1i M moon  a 2i M sun  a ei u moon  a 4i Dsun  a5i  moon 
i 1
    
3
3
3
Sidereal Time:
Only one rotation is necessary to account for sidereal time:
EQequinox   cos 
 AST   GST  EQequinox
rwopolar  Rot 3( AST )rwprecession
Polar Motion:
Two rotations are necessary to account for polar motion:
x p  0.0373  0.0206 cos A  0.0794 sin A  0.1075 cos C  0.0803 sin C
y p  0.3454  0.0678 cos A  0.0209 sin A  0.0803 cos C  0.1075 sin C
A  2 MJD  53173 / 365.25
C  2 ( MJD  53173) / 435
recf  Rot 2( x p ) Rot1( y p )rwopolar
To transform the vector into the local orbital:
U x

Tloecf   V x
W x

For which
Uz

Vz 
W z 
Uy
Vy
Wy

 V
U  V  W   U x
T
V 
R V
R V
W 

R
 Rx
R
x
Uy
Uz
V y Vz
Ry
Rz



For which R is the satellite’s position vector in earth-centered inertial coordinates and V is the
satellite’s velocity vector in earth-centered inertial coordinates.
Time Conversion
All inputs into the simulation are assumed to be in coordinated universal time (UTC), but in
order to generate accurate data, some time conversions must be made.
To convert from universal time corrected for longitudinal variations (UT1) to UTC:
UTC  UT1  UT1
Values for UT1 are published and updated by the Naval Observatory on a regular basis. Since
the simulation is run for a date in 2006, a date for which this value is not yet provided, an
estimate is used:
UT1  0.5 sec 0.03sec
To calculate terrestrial barycentric time (TDB), the international atomic time (TAI) and
terrestrial dynamical time (TDT) must be calculated.
TAI  UTC  AT
Values for AT are also provided by the Naval Observatory. At this time, AT  32 sec .
TDT  TAI  32.184 sec
TDB  TDT   0.002 sec
The short duration of calculations does not warrant the computational expense of finding TDB
more accurately.
For many of the above calculations, Julian centuries are used. To determine this value for any
time frame, the following equation can be used:
JDa  2,451,545.0
Ta 
36,525
For which Ta is the number of Julian centuries from epoch in the given time frame and JDa is
the Julian date in the given time frame.
Estimation Theory
Since the PPT thrust is very small, determining whether or not the PPT’s are firing is difficult to
do. A simple linearized Kalman filter is used to estimate the value of N PPT about the yaw axis.
The dipole of the satellite is also uncertain and because of the strength of the effect of the
magnetic interaction, m1 and m2 are also considered unknowns. The algorithm then follows the
following format. For this algorithm, drag and solar pressure are assumed to be known from the
equations above. Any variations from these values to the actual disturbance torques are assumed
to be noise.
Equation of motion for yaw axis:
2
I z  z  3o I y  I x Tbylo Tbylo  M x B y  M y Bx   I y  I x  x y  N zdrag  N zsolar  N oPPT  gk

13
23

z
I z  z  I y  I x  3o Tbylo13Tbylo23   x y  M x B y  M y Bx   N
N
N
 gk
For which
N zPPT  N oPPT
 gk
z
For which g is the decay rate of the average PPT thrust. Although not explicitly known, it is too
small to estimate, so a rough number from measured data is used to account for measurable
decay over long simulation times.
The state for this Kalman filter is then
 N oPPT

z


X   Mx 
 My 


and the measured and predicted values are calculated by
2
zˆ  I z  z  I y  I x  3o Tbylo13Tbylo23   x y
2
drag
z


z  M x B y  M y Bx   N zdrag  N zsolar  N oPPT
 gk
z
z
Since the H matrix is defined as
X
 z
z
z 
H 

 N M x M y 

H  1 By
 Bx

solar
z
PPT
oz
Assuming that X is constant, the state transition matrix is
1 0 0
  0 1 0
0 0 1
Propagating the covariance matrix:
Pk  Pˆk 1  Q
Since X  0 propagating the state is simply:
X k  Xˆ k 1
Calculating the measured and predicted values:
2
zˆ  I z ,k  z ,k  I y  I x  3o Tbylo,k13Tbylo,k23   x,k  y ,k


solar
z  M x B y ,k  M y Bx,k   N zdrag
 N oPPT
 gk
,k  N z ,k
z
This program is meant to read in data containing  z , Tbylo1 3 , Tbylo2 3 ,  x ,  y , B x , and B y for each time
step.
The H matrix is constant and the Kalman gain is calculated by:

K k  Pk H kT H k Pk H kT  R
To update the state:

1
Xˆ k  X k  K k zˆ k  z k 
To update the covariance:
Pˆk  I  K k H k Pk
This process is repeated for as many data points as the user desires.
When noise is added, the Kalman filter will produce values that oscillate about a bias (for this
case in which the state is constant). To determine the bias, a simple smoothing function is
implemented which truncates the data and takes the mean of the remaining data. Assuming the
noise is white Gaussian, the filter will provide a decent amount of accuracy.
Since it can be assumed that X is constant, another viable option for estimation is using a batch
ˆ z and H remain the same as those for the Kalman filter.
filter. For this filter, z,
HTH
H T WH   k k
R
k
T
H zˆ  z k 
H T W O  C    k k
R
k
After the preceding has been performed for all of the data points:


X  H T WH H T W O  C 
If X   (user defined), then exit the loop. If not:
1
X  X  X
Results and Discussion
To demonstrate the accuracy of the numerical integrator, a 24-hour simulation is run without any
disturbance torques. Energy and angular momentum should remain constant. Plotting the
following will demonstrate the integrator accuracy.
Attitude:
h  I
1
2
   T I
Orbit:

Normalized error:
V2 

2 R
 o   t 
o
h  R V
and
ho  ht 
ho
If plots of the above remain less than the smallest disturbance torque plotted, the integrator is
sufficiently accurate for the simulation being performed. The maximum error is on the order of
10e-14, sufficiently small to model the PPT thrust on the order of 10e-9 N.
To validate that the simulation and gravity gradient disturbance torque is correct, a simulation
including only the gravity gradient disturbance torque is performed and compared to a known Cprogram developed by Surrey Satellite Technology Limited. The results are slightly different
because of slightly different initial conditions and because of slightly different coordinate
frames, but graphs of the results from both models clearly show that the simulation is correct.
The magnetic field disturbance torque program is compared numerically to the output produced
by the SSTL gravity gradient disturbance torque program. Differences in orbit propagation
prevented graphical comparison. The drag and solar pressure disturbance torque programs are
verified using hand calculations as SSTL does not have programs to which the output could be
compared.
Several 24-hour simulations were run with various noise values, generating the following results:
No Noise
Actual
PPT torque
0.0000
Dipole (x)
0.0000
Dipole (y)
0.0500
Table 2: Simulation Values without Noise
Percent Error Kalman w/o
Smoothing
Percent Error Kalman w/
Smoothing
Percent Error Batch
N/A
N/A
N/A
N/A
N/A
N/A
3.4001E-10
8.6001E-10
0.0000E+00
Table 3: Simulation Results with No Noise
0.3E-6 on B field
Actual
PPT torque
0.0000
Dipole (x)
0.0000
Dipole (y)
0.0500
Table 4: Simulation Values with B Field Noise
Percent Error Kalman w/o Percent Error Kalman w/
Smoothing
Smoothing
Percent Error Batch
N/A
N/A
N/A
N/A
N/A
N/A
2.0709
2.2331
0.0318
Table 5: Simulation Results with B Field Noise
No PPT's
With PPT's
Noise
Percent error
Noise
Percent error
0.3E-3 on w
0.379488
0.3E-3 on w
10.07
1.33E-6 on wdot 0.379488
1.33E-6 on wdot 10.07
Table 6: Batch Filter Simulation Results with Various Noise
Conclusion
The integration error for the simulation is small enough that even the thrusters on the order of
10e-9 N will be accurately modeled.
Comparisons of gravity gradient and magnetic field disturbance torques as well as earthcentered, inertial to earth-centered, fixed conversions to programs developed in C by other
programmers show that they are accurate and data generated by this simulation may be
considered truth.
A batch filter provided more accurate results than the Kalman filter and the Kalman filter with
smoothing.
Using a batch filter to process noisy attitude data, it can be verified that the PPT’s are firing as
long as the data noise stays within appropriate limits.
Recommendations
For 24 hours, the PPT’s should be fired with no other active attitude control. The satellite should
be operating on minimal systems. Magnetometer readings and attitude data from a six or seven
state Kalman filter are necessary. Data from the 24 hour period must then be saved and sent to
the ground station or streamed down during periods of contact and saved during blackout
periods. A file containing all 24 hours worth of data is necessary for the batch filter to function
properly. The program itself can be altered as necessary for the file format.
To increase the accuracy of this model for longer simulations or for even more precise numbers,
orbital perturbations should be included. For use with NORAD two line elements, the NORAD
SGP4 orbit model should be used. If the model will only be used for simulations and/or will not
be processing NORAD data (if the satellite will instead be using GPS data), numerically
integrating the perturbing forces may be a better choice.
Acknowledgements
Cappellari, J.O., et. all. Mathematical Theory of the Goddard Trajectory Determination
System. Goddard Space Flight Center: Greenbelt, MD, 1976.
Hashida, Yoshi. ADCS for Future UoSAT Standard Platform. Surrey Satellite
Technology, Ltd.: University of Surrey, England, 1997.
IERS Bulletin-A. 29 June, 2004. ftp://maia.usno.navy.mil/ser7/ser7.dat.
LeapSecond.com 29 June, 2004. http://www.leapsecond.com/java/gpsclock.htm
Oersted Field Model. 29 June, 2004.
http://www.dsri.dk/Oersted/Field_models/IGRF2000/igrf2000.cof
Steyn, W.H. A Multi-Mode Attitude Determination and Control System for Small
Satellites. University of Stellenbosch, December 1995.
Vallado, David A. Fundamentals of Astrodynamics and Applications. McGraw-Hill
Companies, Inc.: New York, 1997.
Wertz, James R. Spacecraft Attitude Determination and Control. Kluwer Academic
Publishers: London, 2002.