An autonomous navigation system is considered that provides a satellite with sufficient numbers and types of sensors, as well as computational hardware and software, to enable it to track itself. Considered are attitude type sensors, meteorological cameras and scanners, one way Doppler, and image correlator

Desai, P. S.

English

NASA Technical Reports Server

AUTONOMOUS NAVIGATION FOR ARTIFICIAL SATELLITES 
Phmv s. Desai 
Computer Sciences Corkwutioti 
Siber Spritg. Mcuylmd 
The term ‘autonomous navigation” refers to the possibility of providing a satellite with the 
sufficient number and type of sensors, as well as cowputational hardware and software. to  
enable it to track itself. In other words. there is no ground trackkg involved. 
There are two classes of such autonomous navigation: passive and active. Paszive means 
that the satellite does not get cooperation from the ground or from other satellites; active 
means that the satellite doos get active cooperation fram either the ground or from another 
satelhte like the Trackir Data Relzy Satellite Systen RSS). This active coopera- 
tion could come in t:.? .adio signals. laser beams, oI ather kir:c!s of si~fials o r  b c x c w .  
The basic reason for usi- .tonornous navigation is to reduce the neessily ior gr--wd track- 
ing, thereby reducing th, o w .  --ding of ground tracking facilities and also redwny, the cost. 
There are also other techrLa1 reasons. For example, with a fast satellite, if there is a gap 
in the ground tracking data set, especially if there are drag and other prominent effects 
present, an autonomous navigation system could increase the accuracy of prediction between 
the two data sets. Another reason could be that the reaction time for noticing changes in 
the satellite orbit would be reduced by autonomous navigation. even if it is used as a 
backup to ground tracking. 
This work is a conceptualization effort made by Don Novak, Paul Beaudet, and the author 
at Computer Sciences Corporation. The literature is not exhaustive. but it should be noted 
that Howard Garcia’s paper has a summary of sensors as well as some discussion of the new 
sensor interferometer landmark tracker. 
The following considerations are important in such a feasibility study: First of all, it is t- 
necessary to  be aware of what types of sensors are available (or could be made available) on 
a satellite to help in autonomous navigation. Then the observability arising from combina- 
tions or configurations of these sensors should be checked. In other words, it shocld be 
determined whether a given set of sensors is sufficient under various conditions for 
determination of attitude and orbit of the satellite. The accuracy of the selectcd system 
and its reliability should then be studied to  determine that, should one of the components 
fail, the other components would be enough to  back it up. The choice of sensors basically 
depends on the estimation algorithm, in that we might choose either a coupled attitude 
and orbit determination scheme or a decoupled scheme. The computational hardware is 
still another factor. 
33 
https://ntrs.nasa.gov/search.jsp?R=19760003083 2020-03-22T19:28:23+00:00Z
Some potential Sensors for use in autonomous navigation are listed below, but this is 
by no means an exhaustive list. Some satellites that have used, ar are presently using, these 
sensors are listed: 
0 Inertial measurement unit-ATSF, OAO-2, O A W  
0 Star mapper-ATS-F, CrS,  OAO-2, OAOC, OSO-I, OSO-7, SAS-B, S A X ,  SSS-A 
0 Magnetometer-AE. AEROS, CEO$€, OSW. 0-7, SAS-A, SAS-B, S A X  
0 Sohr sensor-SE, AEROS, ATS-F, CTS, GEOSC, IMP-H, I, J, RAE-2, SASB. 
C, S S A ,  Nimbus 
0 Horizon senscrs-optical-IMP-H, I, J, RAE-2, SSS-A 
0 Horizon sensors-infrared-AE, AEROS, ATSF, CTS, S A X ,  TIROS, Nimbus 
0 Interferometer iandmark tracker-ATS-F 
0 Scannerlcamera-SMS, Nimbus, Landsat 
Thc first is an inertial measurement unit, which is a system of gyros and accelerometers 
for determining inertial attitude and inertial acceleration of the spacecraft; it has been 
used on the Orbiting Astronomical Observatory (OAO). The star mapper is probably the 
most accurate of the attitude sensors for determining inertial attitude and has been used 
on many satellites. The magnetometer determines attitude with respect t o  the magnetic 
field of the earth, or the central body, and if there is a good model available for the 
magnetic field of the central body, it indirectly determines the satellite attitude. The 
solar sensor comes in many varieties, but basically it provides angles to the sun from the 
spacecraft frame. Horizon sensors can be either optical or  infrared. For example. an 
optical horizon Sensor was used on the Radio Astronomy Explorer-2 (RAE-:) mission; but 
infrared is more common and is used in a large number of missions. The interferometer 
landmark tracker (ILT), a new type of sensor. will be discussed later. 
So far the discussion has been limited to attitude-type sensors: however. they are by no 
means the only Sensors that could be used for autonomous navigation. We could consider 
using non-attitude- or non-navigational-type sensors, including meteorological cameras 
and scanncn that could be used in a landmark determination scheme, in which there is 
currently an interest. 
There are two other sensors t o  be considered: the one-way Doppler and the image correlator 
(IC); however, the image correlator has not yet been put on board. The one-way Doppler 
would determine range rate t o  known radio stations on the ground or to a tracking satellite. 
The image cornlator is an advanced version of the landmark determination-type scheme 
where a computer would determine, through pattern recognition, the direction cosines in 
the spacecraft axes to a known landmark. 
34 
It is also necessary to decide how to combine the Sensors for autonomous navigation, and 
a decision has to be made as to whether attitude and orbit should be determined in a 
coupled Qr decoupled scbme. There is an argument in favor of a decoupled scheme be- 
cause orbital parameters, on the whole, vary less rapidly than attitude parameters. There- 
fore, longer spans of data can be used for orbit determination than for attitude. A 
coupled scheme would not take into account this difference in the memory span require- 
ment of the two. However, an initial determination could very well be coupled, so perhaps 
the best method would be to first determine a coarse orbit and attitude in a coupled 
determination, followed by fine attitude determination, followed by fine orbit determina- 
tion. So, for this discussion, it is assumed that we are going to  determine attitude first, then 
orbit. 
The ILT (figure la) has a pair of antennas (at A and B), and its functicn is to determine the 
phase difference between the received signals that arrive at the antennas. The ILT must 
be initialized as t o  what radio signal frequency it is looking for, which means that the 
approximate position in orbit must be known. If the satellite is geosynchronous, orbit 
determination does not have to be done continuously. 
I d I 
ANTENNAS AT A. B IBASELLNE AB = d) 
(a) 
Fgum 1. 
etry and circie of ambiguity. 
01) ILT circle of ambiguity. 
lntrrferomaar landmark tradrers phrse shift wonk 
(I) ILT ph8S shift w r y ;  
35 
We determine the path difference, d cos 0, by determining the phase difference, because 
the two are proportional. and this gives us the angle 8 between the direction line to  the 
emitter and the baseline of the ILT. However, as seen in figure 1 b, there is a conical 
ambiguity left in the direction to  the emitter, because that angle is all that is known. 
To reduce ambiguity, we also have another pair of antennas (not shown in figure) where 
the baseline is perpendicdar t o  the fmt baseline; we will have an intersection of two 
cones and, therefore, will reduce the ambiguity to just two lines. A little further analysis, 
perhaps over a period of time or using multiple landmark determination, might reduce the 
twofold ambiguity as well. 
In fire 2, we begin examining some sensor configurations from the point of view of observ- 
ability. Suppose we were trying t o  determine the satellite inertial attitude using a star 
sensor that determines the direction to one star only, and then supplement that with a 
landmark determination scheme. In other words, the direction cosines in the spacecraft axis 
t o  one landmark on the central body are determined using either the ILT or some other 
means such as a scanner or a camera. 
IbJ 
STAR 
GRAZING OF W CIRCLES 
Figure 2. Star sensor configuration. (a) One-star, single landmark 
symmetry; (bl poor resolution geomctry. 
36 
In a scheme like this, the star determines the satellite attitude ambiguous to  the -011 
around the axis from the satellite to the star. Normally, the roll ambiguity is further 
reduced by having a second star, but suppose that second star is replaced by a landmark. 
In that case, all that is known is the angle between the star direction and the landmark 
direction, and that does not give the absolute attitude of the spacecraft unless its position 
is known. Spacecraft position can be ambiguous to  within that circle (figure 2a), in fact, 
to within the whole cone, which indirectly results in ambiguity in the attitude. That would 
be considered an untenable or unobservable condition. 
Suppose we tried to  reduce the ambiguity by looking at  the central body horizon and 
obtaining indirectly the direction to  the center of the central body. This could remove the 
ambiguity, but occasionally there is a situation where the resolution is poor, because we 
are now on two circles that graze, and as can be seen in fiiure 2b, the graze is quite large. 
If the ILT station was not placed in the plane formed by the line to the center of the 
central body and the line to the star, then the circles would intersect at two points instead 
of grazing, and that would be a better resolution geometry. 
Based on this discussion, we can eliminate as untenable those confirat ions for attitude 
determination which use only one star and one landmark and such other combinations 
which are conceptually equivalent, for example: 
0 One star-ILT/IC (single station) 
0 Sun-ILT/IC (single station) 
0 One star-central body horizon 
0 Sun-central body horizon 
0 Moon horizon-central body horizon 
0 Moon 1L.T-central body ILT (single station) 
The following are weakly-orbit-coupled configurations for attitude determination: 
One star-central body horizon-ILT/IC (single station) 
0 Sun-central body horizon-ILT/IC (single station) 
Moon horizon-central body horizon-ILT/IC (single station) 
0 One star-ILT/IC (multiple stations) 
0 Sun-ILT/IC (multiple stations) 
0 Moon horizon-ILT/IC (multiple stations) 
Moon ILT-central body ILT (multiple stations) 
37 
We are still speaking of attitude determination, and we would like it to be orbit decoupled, 
but these configurations are weakly orbit coupled in the sense that the ILT. for example. 
would need to  be initialized with an approximate knowledge of orbit so that we would 
know which station to tune to. This list includes a one star/central body horizonlone land- 
mark configuration as well as a one-star/multiple station configuration for the same reason. 
In summary, t o  have orbit decoupled attitude determination, perhaps two star sensors 
would be needed, and they could have an associated inertial measurement unit to  back 
them up. 
We will now examine the information that can be derived by determining the direction 
to the landmark in the spacecraft frame. Figure 3 shows the spacecraft position, the 
line from the spacecraft t o  a known landmark, and 0 and 7 ,  which are the latitude and 
longitude of the landmark. The unknown subpoint of the satellite is (ee, 7o ), the distance 
of the satellite is r, and the satellite-to-landmark range is p. The following equations are 
based on the fact that this line intersects this sphere, and they show that the direction 
cosines of that line ought to be 1 x ,  1 y ,  1 z ,  in the earth frame of rzference: 
cosBsin7 = pP Y + r c o s ~ o s i r ~ y ,  
sin0 = pP2 +rsin8, 
where 
Equations 1 to 3 can be solved to get the range explicitly; therefore, for every landmark, 
the three equations reduce t o  two equations. If 6 and 7 ,  the position of the landmark 
on the earth, are known, then there are three unknowns: r, e, and T ~ .  If we are 
interested in orbit determination, and the attitude is already determined. then we have 
three unknowns and two equations per landmark, so that we need at least two landmarks 
for orbit or position determination. 
If we could determine the subpoint (ee, 7,)  on a continuous basis, then, by studying a 
history of the subpoint, we could get a track of the satellite on the ground and its 
characteristics would suggest a period. By using Kepler’s Third Law, for example, the 
semimajor axis could be derived indirectly from the period. In that case, even one 
landmark is, in principle, sufficient for orbit determination. 
38 
*NORTHPOLE / 
.-. 
b r  
SATELLITE 
Figure 3. Spaecrah/landmark geometry. 
We have assumed that attitude was already known, but suppose we were trying t o  use 
this ILT for a coupled attitude and orbit determination, perhaps in a coarse way, for 
preliminary locking on. How many unknowns would then be had? 
In figure 3, we have these directional cosines to the landmark, which are supposed to be 
in the geographc frame. What we really would know from the satellite instruments would 
be the direction cosines in the satellite frame of reference. Therefore, indirectly there 
are three unknowns involved here which represent the transformation from the satellite 
frame to  the geogrdp?ic frame, which e5seqtially means the satellite attitude, that is, the 
three attitude angles of the satellite. We then have six unknowns-the three satellite 
attitude angles plus three positional unknowns-and two equations per landmark, so we 
still would need only three landmarks. If we had strategically located a sufficient number 
of landmarks, accounting for possible cloud cover, even then perhaps just a few would be 
enough for a coupled attitude and orbit determination. (Expressions for the sensitivity of 
this kind of determination kave been developed in our report and are available for anyone 
interested in performing their error analysis.) 
In summary, it seems that by using a variety of sensors it is conceptually possible to have 
autonomous navigation. However, the details would have to be worked out for each type 
of orbit. For example, a geosynch 'onous orbit would require a different type of configura- 
tion, perhaps, than the 2-hour satellite, so we do not ha-re a general conclusion or recom- 
mendation valid for all types of satellites. 
The second part of this paper presents a standardized autonomous navigation system 
(figure 4) which was designed by Computer Sciences Corporation personnel for possible 
future use in a standardized type of satellite. In the base are the computer, electronics, and 
some gyro hardware. On the two sides of that base are two gimbal units. The right-hand 
gimbal unit is a two-star sensor, located near the beam splitter, which would determine 
the satellite's inertial attitude. The main navigational unit (lower left) consists of a gimbal 
unit with thEe arrays of infrared detectors arranged conically at the tip of the unit. One 
small section of that array is high resolution, and two outside sections are low resolution. 
This is supposed to determine three directions to three points on the horizon of the central body. 
39 
Figure 4. Possible configuration for the proposed standardized autonomous navigation system. 
As seen in figure 5 ,  three lines of sight to  the central body horizon determine a uni iue cone, 
so that the sateliite position is known. The f o l l o w ~ g  are the equations for xi, yi, i i, the 
central body coordinates in the sracecraft axes: 
hllxi  t h,,y, t h,,p = (r2 - R2)% 
$,xi t h2,yi t h,,zi = (r2 - R2)% 
h,, xi t h,,yi t h,,zi = (r2 - R2)% 
By using the information from the star sensors, the equations can be transformed into 
inertial coordinates. 
Figures 6 and 7 show the degree of accuracy we can get from this system. Depending on 
the angular accuracy of the IR detectors, different errors are obtained at different altitudes. 
At 1000 krn altitude, and with a 0.1 angular precision, we have less than a IO-km error, 
in fact, close to  a 5-km error in altitude (figure 7). In faure 6, the horizontal component 
error, the curves are flatter, but again we have the same order of magnitude accuracy. 
Figure 5. Three lines of sight to the central body 
horizon determine a unique cone. 
-- I I 1 I 
0 1000 2000 3000 4000 5Ooo 6000 
41 
Y) = I  c 
3 3 30- 
Y 
a 
0 a a 
n 
I& 
20- z 
r -1 
a 
10 - 
I 
I 
I I I 
0 loo0 zoo0 3000 4Ooo 5000 6Ooo 
SPACECRAFT ALTITUDE~KILOYETERS 
Figure 7. Variations in altitude error 
as a function of altitude. 
BIBLIOGRAPHY 
Dambeck, W. J., Geostationary Satellite Position arid A ttitude Determination Using 
Picture Landmarks, NOAA TM NESS-2 1 , August 1972. 
Garcia, H. A., “An Analysis of Recent Advances in Autonomous Navigation,” (Presented 
at AIAA Guidance and Control Conference, Key Biscayne, Florida, 1973). 
(3), p. 338, 1968. 
Reznikov, B. A., “Parametric Observability of Space Vehicles,” Kosmich. Issled., 6 
42 
IDEAL ELEMENTS FOR PEW? URBED KEPLERIAN MOTIONS 
A. Deprit 
University of Cincinnati 
Cincinnati, Ohio 
The motion is referred to  Hansen’s ideal frame, its attitude being defined by its Eulerian 
parameters. The parameters selected to  determine the motion in the orbital plane cause no 
singularities or indeterminacies for small eccentricities; they have been chosen with a view 
of making the right-hand members of the equations as simple to  program as possible. 
43 


Autonomous navigation for artificial satellites

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