1. Introduction
Design of Satellite
Constellations for Optimal
Continuous Coverage
D.C. BESTE, Member, IEEE
General Research Corporation
Abstract
A satellite-borne sensor can view a region at or above the Earth's
surface. The size of this region depends on the satellite's altitude,
the maximum range and scan angle of the sensor, the minimum
above-the-horizon viewing angle required, the extent in altitude of
the region to be viewed, and the maximum altitude of sensor obscuration by the atmosphere. Except for geosynchronous satellites this
region moves relative to the Earth, so that constellations of satellites are generally necessary for continuous coverage. Satellite
constellations which minimize the number of satellites required
for continuous coverage are derived as a function of the angle
subtended at the Earth's center by the coverage of a single satellite. This is done for single and triple continuous coverage of the
entire Earth and of the polar regions extending to arbitrary latitude. Simple, cogent approximations for the configurations and
numbers of satellites are found. Expressions which relate sensor
capabilities and surveillance requirements to are presented.
Examples are given to illustrate the use and accuracy of the results.
Manuscript received September 6, 1977; revised November 28, 1977.
Author's address: General Research Corporation, P.O. Box 6770,
Santa Barbara, CA 93111.
0018-9251/78/0500-0466 $00.75
466
1978 IEEE
In the first twenty years of the space age we have witnessed a dramatic increase in the number of satellite-based
systems. We can expect this trend to continue with the
advent of the Space Shuttle [ 1,2] Many of these systems
will require that the entire Earth, or certain regions of the
Earth, be continuously within sight of one or more satellites. For example, the NAVSTAR global positioning
system (GPS) [3] requires that every user be able to observe
four satellites simultaneouslv.
It is of interest to know the configuration of satellites
which requires the fewest satellites with sensors of given
range and scan angle. Emara and Leondes [4] addressed
this problem for a mission which requires quadruple coverage (i.e., GPS). Liuders [5] addressed the problem of continuous single coverage. His results are widely used [6, 7, 8].
This paper is directed toward designing optimum satellite configurations for continuous coverage of the entire
Earth or of polar regions extending to arbitrary latitude. It
is shown that the method developed here requires about 15
percent fewer satellites than the classical Luders configurations. It is also showin that orbital planes which have a
common intersection (e.g., polar orbits) are preferred,
and that the number of satellites required for continuous
coverage between latitude X and the pole can be approximated by
N
-
4 cos X/(1- cos4')
where 4iis the Earth-centered half-cone-angle of coverage
for each of the N satellites (see Fig. 1).
A comparison is also made with the number of satellites required if the satellites could remain "stationary."
This unrealizable situation is useful for establishing an
absolute lower bound on the number of satellites.
Surveillance systems which employ angle-only or timedifference-of-arrival techniques require simultaneous viewing by three satellites. For this reason triple coverage is
also addressed. Although the analysis is approached
differently, the results are similar to those for single coverage except that approximately 24 times as many satellites
are required. Triple coverage with somewhat fewer than
3 times as many satellites is in good agreement with intuition since, ideally, the additional satellites should be placed
to take advantage of the overlap which occurs with single
coverage..
In this paper the optimum corifiguration of satellites is
first determined for continuous single and triple coverage
of two polar regions extending to the latitudes ±X. Given
that the sensor on each satellite can cover a circular region
defined by an Earth-centered cone of half-angle 4, an
expression is derived for the number of satellite orbital
planes (n) and the number of satellites per plane (m) which
yield the smallest total number of satellites (N = nm).
After establishing the relationship between q4 and N for
single and triple coverage, the relationship between 4 and
the required sensor range R and maximum scan angle a is
derived under a number of different constraints of interest.
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
AES-14, NO. 3
MAY 1978
SATELLITE
IL. Single Coverage
Two approaches to satellite constellation design were
considered. The first approach was to place the satellites
in orbital planes which have a common intersection (e.g.,
polar orbits) and to adjust the plane separation and satellite
spacing so as to minimize the total number required. This
approach can be considered to be an extension of the
Liiders method, and leads to some very simple expressions
which relate the number of satellites to the sensor require-
ments.
Polar orbits result in higher satellite densities at the
poles than at the equator. It seerns intuitive that orbital
configurations which result in a more uniform distribution
of satellites over the Earth would lead to more efficient
covering. Therefore the second approach was to select
orbital planes which result in as uniform a distribution of
satellites as possible (e.g., three mutually orthogonal
obital planes).
A. Single Coverage With Polar Orbits
Fig. 1. Region observed by a satellite.
Fig. 2. Coverage geometry. [n = orbital planes, m satellites per
plane, 4, = angular coverage, 4, + A = plane separation between codirectional orbits (separation is 2A between opposite-moving
=
The geometry is shown in Fig. 2. The angle 4 is the
Earth-centered half-cone-angle corresponding to the coverage of one satellite, or equivalently, the radius of the coverage circle (measured in angular units) on the surface of the
Earth. This region will be referred to as the coverage circle
of radius 4. Satellites in adjacent orbital planes move in
the same direction, and the satellites of one plane are
shifted relative to those of the adjacent plane by one-half
of the intraorbit satellite spacing (i.e., r/rm, where m is the
number of satellites per orbit). This configuration clusters
the satellites in an optimal manner at the equator. At the
two boundaries where adjacent orbital chains move in
opposite directions, the relative geometry is not constant,
so that the angular separation between orbital planes must
be smaller than the angular separation between orbital
planes of satellites moving in the same direction. The most
demanding requirement on 4 occurs at the equator, where
the following equation must be satisfied:
(n-1)o + (n + )A =Tr
CIRCLE OF
chains).]
(1) Note that in all cases the ratio is nearly equal to 2.
The
implication is that the coverage averaged over the entire
where n is the number of orbital planes, 4 is the angular
sphere is double. The result, which holds for ratios of m
radius of the coverage circle, and A = cos-m [cos 4/
to n in the approximate range of 1.3 to 2.2, leads to a
(cos 7r/m)] . The n orbital planes are separated in angle by
simple formulation for specifying the relationship between
4 where
the numbers of satellites and their orbital configurations
(2) and coverage requirements.
¢,= , + A.
Since the solid angle Q corresponding to the circle 4, is
= 27r (1 - cos 4,), the preceding result suggests the followQ
This results in an orbital-plane separation of 2A at the
ing approximation for the number of satellites for a
boundaries where satellites in adjacent orbital planes move
4,:
given
in opposite directions.
Equation (1) was evaluated for a wide range of combi1.3n < m < 2.2n.
(3)
nations of n orbital planes and m satellites per orbital plane. N nm 4/(l Cos IP),
The results are summarized in Table I, which also shows the
This expression is shown as a dashed line in Fig. 3 along with
orbital-plane separation 4,. The last column gives the ratio
data points corresponding to the solution of (1).
of the total solid angle covered by all satellites to 47r sr.
=
-
BESTE: DESIGN OF SATELLITE CONSTELLATIONS FOR OPTIMAL CONTINUOUS COVERAGE
467
TABLE
Requirements for Single Coverage of the Entire Earth
n
m
2
2
3
3
3
4
4
4
5
5
5
3
4
4
5
6
6
7
8
8
9
10
j (deg)
66.7
57.6
48.6
42.3
38.7
33.6
(deg)
104.5
98.4
69.3
66.1
64.3
49.4
48.3
47.6
38.6
38.1
37.7
nmE./4ir
1.81
1.86
2.03
1.95
1.97
2.00
1.97
1.99
1.98
1.97
1.99
0
30.8
28.9
25.7
24.2
23.0
NUMBER OF ORBITAL PLANES (n)
50
40
30
Fig. 4. Coverage geom,etry at latitude X.
TABLE 11
Requirements for Single Coverage of Polar Regions Extending to
Latitude X
20
22
N
=
-
4o
Cos
n
m
i (deg)
p (deg)
nm2'4 ir
3
4
5
64.1
53.4
48.1
39.9
35.8
33.3
28.9
26.8
25.3
22.6
111.8
103.1
98.7
68.4
66.0
64.5
38.8
1.69
1.62
1.66
1.75
1.70
1.72
1.74
1.72
1.73
1.73
49.6
43.2
39.4
30.0
111.2
104.4
100.4
66.9
65.4
64.4
49.2
48.4
47.9
47.4
1.41
1.35
1.37
1.41
1.40
1.42
1.42
1.41
1.41
1.43
X = 300
0o
20
30
40
,
degrees
50
60
2
2
2
3
3
3
4
4
4
5
70
Fig. 3. Number of satellites required for single coverage of the
Earth.
Note that the approximation of (3) degrades gracefully
for n and m outside the indicated range. For this reason it
is sometimes worthwhile to try combinations of n and m
outside this range. For example, if the maximum coverage
of one satellite corresponds to 4 = 380, (3) yields N 18.9.
The smallest value of N (a product of integers) which exceeds this and satisfies the inequality is N = 24 (n = 4,
m = 6). However, it can be seen from Fig. 3 that n = 3,
m = 7 (N = 21), which does not satisfy the inequality, also
provides total coverage with 4 < 380.
It should be concluded that (3) gives a simple, nearly
exact relationship between 4' and N when the inequality
between n and m is satisfied. In situations where the inequality leads to values of N much larger than that required
to satisfy (3) (as in the example above), it may be worthwhile to consider combinations of m and n not satisfying
the inequality. This requires a trial-and-error evaluation of
(1).
X
The preceding analysis can be extended to coverage between latitude X and the north pole, and between latitude
468
6
7
7
8
9
9
450
2
2
2
3
3
3
4
4
4
4
-
B. Full Coverage Beyond Latitude X
5
4
5
6
7
8
9
9
10
11
12
28.0
26.5
22.9
21.6
20.6
19.9
49.6
48.5
47.8
-X and the south pole. Fig. 4 shows the geometry; it is the
same as in Fig. 2 except that coverage must be achieved at
X degrees latitude rather than at the equator. In this case
the requirement (1) becomes
(n -1)
+
(n+ 1)A =rrcosX
(4)
where A is defined as in (1). Table II summarizes the evaluation of (4). Fig. 5 shows a plot of 4 versus n m for X= 0,
30, and 45 degrees. These results indicate that (3) may be
generalized to
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
AES-14, NO. 3
MAY 1978
N=nm 4 cosX(l -cos4), 1.3 n <m cos X< 2.2n.
450 300 0°
-5 5//
NUMBER OF
'
A
50
(5)
The accuracy and implications of this approximation will
be discussed later.
=
ORBITAL
PLANES (n)
5 5
40
44
4
C. Nonpolar Orbits
55
4\
-j
\
An alternative approach to achieving total coverage is to
\ \5\
30 [
use orbits distributed in some uniform manner. In general
L.
these are very difficult to analyze for arbitrary numbers of
N-1 4CosA~
co
\ 4\\\
44
satellites. However, a few specific cases were individually
3
m:
\ 3 \ 3\
examined and it was found that the polar-orbit configura20 [
\33 3 93
tion was superior.
Two orbital planes have one intersection and are thus equivalent to the polar case described above. In that case it was
21 -z .32-J)
shown that the optimum angle between satellite planes was
Iu
20
30
40
50
not 900 but depended on the number of satellites per orbit
p, degrees
plane. The optimum angle approaches 90° only in the limit
Fig. 5. Number of satellites required for single coverage beyond
of an infimite number of satellites per plane.
latitude X.
Three mutually orthogonal orbital planes were investigated for the case of m = 4 (total of 12 satellites). The
Fig. 6. Comparison of LUders and Beste results.
method used was to adjust the interorbit relative phase,
while maintaining the intraorbit spacing of 900 so as to
60r
minimize the maximum distance from a satellite to a point
in any quadrant. The resulting coverage angle 4 is 50.80.
50F
This angle compares with 48.60 required for 12 satellites in
3 polar orbits as given in Table I.
1.1 40
BESTE
N = 4 (E + 1)
n
1
LUDERS
2
-j
D. Comparison With Previous Results
Luders' paper in 1961 [5] addressed inclined as well as
polar orbits in which orbital planes were uniformly separated.
He concluded that polar orbits were optimum. His results
were given in terms of minimum satellite altitude (a monotonic function of 4) and expressed in nautical miles. A
comparison of his results with those of this paper is shown
in Fig. 6. Note that the method described here leads to a
substantial reduction in the number of satellites (10-20 percent in most cases). A similar conclusion holds for coverage
between the poles and latitudes ±X. The reason for the difference is that Luders' restriction to equally separated orbital
planes leads to an unnecessarily large overlap between satellites in adjacent orbital chains which move in the same
direction.
-j
< 30
u
20
iok
n
200
400
600
800
1000
II
1200 1400
n mi
ALTITUDE,
1600
1800
2000
with two great circles (corresponding to 2 satellites diametrically opposite and at infinity) where the ratio of the
solid angle of coverage to 47r sr is 1. Other efficient coverings occur for satellites which are positioned according to
the faces and vertices of regular polyhedra. The most efficient of these occur for 4, 6, 12, and 32 circles. In the limit
as the number of circles grows to infinity, the optimum
pattern is that of a hexagonal grid on a planar surface. Table
III summarizes the required 4 and amount of excess coverE. Comparison With Stationary Satellite Coverage
age for these configurations.
Fig. 7 compares the relationship between 4 and the total
Because the satellites are in motion (in their respective
number
of satellites obtained in this study with that of
orbits) a considerable amount of overlap must be experiLuders'
paper
and with the stationary bound.
enced in order to ensure coverage at all times. It is therefore
of interest to investigate the numbers of "stationary" satellites required to cover the Earth. This represents an unIll. Triple Coverage
achievable (except for 2 satellites) lower bound.
Different numbers of circles cover a sphere with different
There appears to be no reasonable analytical approach to
efficiency. That is, some combinations of circles having a
the triple coverage problem. Therefore the method used in
common radius 4, cover the sphere with a smaller fraction of this study is to calculate the required 4 by using an iterative
overlap. In particular, the most efficient coverage occurs
search.
BESTE: DESIGN OF SATELLITE CONSTELLATIONS FOR OPTIMAL CONTINUOUS COVERAGE
469
TABLE IIl
Sphere Coverage by Circles
Number of
Circles
2
4
6
12
Radius of
Coverage y (deg)
90.0
54.7
37.4
1.0
1.3
1.3
1.2
32
22.7
1.2
lim
N-oo
cos 1(1- 2.42/N)
1.2
Nfl/4ir
70.5
Configuration
diametrically opposite
faces of a tetrahedron
faces of a cube
faces of a dodecahedron
faces and vertices of a
dodecahedron (or
icosahedron)
hexagonal pattern on
a plane surface
6Or50
V)
U.j
LUDERS V2
40k
cos-
Co~q
4lm/(n ±I+ '/4O)
-j
LLJ
.::c
Ln
30 F-
4
Li-
CD
cl.
LLJ
co
M:
20k
.2-1
10
0
STATIONARY
COVERING BOUND
2.5 i
( l -cos; )
10
20
30
40
50
60
70
;, degrees
Fig. 7. Comparison of number of satellites required for total
Earth coverage.
A basic assumption is that, as in the case of single coverage, it is desirable to keep the satellites spaced as uniformly
as possible in a fixed relative orientation. The configuration
is thus similar to that used for single coverage (Fig.2) except
that the circles must overlap to a much greater extent. Adjacent orbital planes have equal angular separation, and
satellites in adjacent planes travel in the same direction
(except at the two boundaries) and are staggered by onehalf of the intraorbit separation.
The required angle of coverage (4) per satellite is determined as follows: m satellites are placed uniformly in each
orbital plane; n polar orbital planes are placed uniformly
around the equator. The satellites in adjacent orbital planes
are shifted in latitude by one-half of the intraorbit spacing
(iT/m). A set of points is chosen at the equator. The set
extends one-half the interorbital separation in longitude.
Each point of the set is successively examined to determine
the value of 4 such that three satellites are within a distance
4 of that point. The satellites are then moved along their
orbits by a small fraction of their orbital spacing and the
procedure is repeated. The largest value of 4 thus obtained
is chosen. Satellites having this angle of coverage are necessary and sufficient for triple coverage of the points in the
set; that is, points between orbital planes in which satellites
move in the same direction. This value of 4i is called 4i.
470
The value of ; required for points falling between orbital planes in which satellites move in opposite directions
is called 'o-. 4o is determined by using the same set of
points as before. However, in this case, each point is examined repeatedly as the satellites in one adjacent orbital
plane are incrementally moved along their orbital path.
Qo is of course equal to or larger than 4i.
For the equally spaced orbits chosen above, the required
angle 4 per satellite must equal 40. This would result in
excess coverage between planes in which satellites inove
in the same direction. Clearly the value of 4 required for
triple coverage can be reduced if the distance between adjacent codirectional orbital planes is increased at the expense of the distance between adjacent opposing orbital
chains. Since the ratio of the number of intervals between
oppositely moving orbital chains to the number of intervals
between codirectional orbital chains is 1 /(n- 1), the first
iteration solution to the optimum orbital plane separation
0 and satellite coverage 4 is
=
(6)
[41.(n 1) + 24 o ] /(n + 1).
(7)
-
In principle the procedure can be repeated, leading to better
and better approximations to the optimum solution. This
was done for a small number of cases and it was found that
the results changed negligibly or not at all after the first
iteration.
Table IV summarizes the triple-coverage requirements in
the same form as Table I for single coverage. Note that the
ratio of the total solid angle of coverage of all satellites to
4mT sr remains close to 5.5. In other words, a point is in
view of 5.5 satellites on the average when this average is
taken over the entire Earth.
Satellite requirements were also determined for triple
coverage between the poles and ±X degrees latitude. The
procedure was the same as for total coverage. Fig. 8 shows
the number of satellites required as a function of 41 for
X = 00, 450, and 600. Also shown in the figure are curves
for the approximate relationship
N= nm
=
11 cos X/(1- cos 1), 1.4n < m cos X < 2.4n.
(8)
IV. Sensor Requirements
In this section, the single-satellite coverage 4 is related to
the range and scan angle required for a sensor on-board the
satellite. Fig. 9 depicts the geometrical relation for a satellite at altitude H providing coverage of the half-cone-angle
4' at a surveillance altitude A. As can be seen from the
figure, the satellite's altitude can be increased or decreased
to provide various combinations of required sensor range R
and scan angle o. As H is increased the sensor's maximum
scan angle decreases at the expense of a longer required
sensor range R.
Although there is no upper limit to the satellite altitude,
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
AES-14, NO. 3
MAY 1978
TABLE IV
Requirements for Triple Coverage of the Entire Earth
n
3
3
3
3
m
4
5
6
7
;p (deg)
80.7
70.3
63.9
61.1
4
4
5
5
5
6
6
7
8
8
9
10
52.2
6
4
9
10
X = 600
450
48.3
43.7
41.1
38.8
37.5
35.8
45.4
36.9
36.6
36.2
5.04
(A
a)
(1)
I
0)
0)
-0
5.42
5.36
5.42
5.35
5.54
45.9
d
LU
-j
30.8
30.5
\6
4\4
c<: 40
3
3
3
\6
-r-
m
L.)
V)
C)
C)
V)
2-1
Li
L/)
4
40
Fig. 10. Sensor range and scan angle as a function of satellite
altitude.
Using the law of cosines and law of sines, the following
expressions can be derived for the required sensor range and
scan angle as a function of the satellite altitude H:
\5
4
\,
3
y,
4
50
60
60
50
40
30
70
70
R-= [(Ref
R=
(Re+ A)2
[(Re+IHI2 ++(+X)
degreess
-2(Re + H) (Re + A) cos ]1/2
Fig. 8. Number of satellites required for triple coverage.
a
Fig. 9. Sensor range and
30
20
10
SATELLITE HEIGHT (H), 1000 km
0
5
\
v,
_
scan
sin -I {[(R
+ A)/R ] sin
(9)
4}
(10)
where
H>
SCAN ANGLE, ,x
REQUIRED SENSOR
SATELLITE
HEIGHT, H
=
angle requirements.
SATELLITE
MINIMUM
cY-
5\
3
20
C-1
m
.:x
Ci
NUMBER OF ORBITAL
-, PLANES (n)
5\
\4
4
)k
CD
.u
5.55
5.52
5.59
5.66
\5
50 l
30
46.9
-
8 SATELLITES
15 SATELLITES
32 SATELLITES
5.03
4.98
NN_- 1 1 cos X
1 - cos )
6
v)
E
56.4
-.
nmQ2/47r
(deg)
64.5
62.3
60.3
60.0
-
0O
60 F
L-1
0
--
=
[(Re
+A
min )/cos(4i-cos'
e)]
Re
(11)
and
RANGE, R
=
SATELLITE\
HEIGHT, HMIN
SURVEILLANCE
MINIMUM
/
PENETRATION
ALTITUDE,
Hmin
ALTITUDE, A
AMI N
(Re + A min)/(Re +A).
The required sensor range and scan angle are shown in
Fig. 10 as functions of satellite altitude for single coverage
of the entire Earth's surface with 8, 15, and 32 satellites
600, 42.80, and 290, re[from (3) this corresponds to
spectively]
Equations (9) through (11) provide a means of trading
off between sensor range and sensor scan angle. In some
applications it is desirable to minimize the sensor range
without regard to scan angle; in these situations the
required sensor range is given by
.
EARTH
R
~~~~~~SURFACE
EARTH
CENTER
there is a lower limit Hmin below which the satellite loses
its line-of-sight to the desired surveillance altitude A. The
line-of-sight can be obstructed either by the Earth's surface
or by the atmosphere near the Earth's surface. The dashed
line in Fig. 9 shows the minimum satellite altitude required
to ensure a line-of-sight above Am in.
R
(Re + A) sin
41,
cos
>a
cos
<R.
=
(Re +Hmin )Sin 4,
(12)
The corresponding satellite altitude at which the required
sensor range is minimized is as follows:
BESTE: DESIGN OF SATELLITE CONSTELLATIONS FOR OPTIMAL CONTINUOUS COVERAGE
471
cc
ot
-z
Cu>
6
4
Fig. 11. Sensor
range
and
scan
12
8
10
SATELLITE ALTITUDE, 1000 km
angle requirements for global
14
coverage
16
18
20
(example 2).
TABLE V
System Characteristics for Minimum-Range Single Coverage With
15 Satellites
(3). This yields 14.8, which when rounded up to the nearest
product of the integers (n = 3, m = 5), results in N = 15.
Therefore three orbital planes of five satellites each are reUsing
Using
quired.
Approximate Q, Exact Q
Parameter
For N = 15 the exact value of according to Table I is
5930
5820
Sensor range (R) in kilometers
42.30 and the approximate value according to (3) is
47.7
47.2
Sensor scan angle (cr) in degrees
= 42.80. Using these exact and approximate values of 4,
2330
2250
Satellite altitude (H) in kilometers
66.1
67.8
Orbital plane separation (¢) in degrees
the various system characteristics shown in Table V were
42.8
42.3
Circle of coverage (V) in degrees
derived using (2), (9), (10), and (13). From the table it can
be concluded that for most analysis purposes the approximate value of is adequate.
Example 2: The sensor requirements for single coverage
(Re+A)cos -Re, cos > GS
(13) of an altitude region extending from 20 to 900 km over the
H=
entire Earth, with 8 and 15 satellites, is determined. The
H in.
Cos <.R
variation of these requirements as satellite altitude is increased is also shown.
V. Examples
The approximate half-cone-angle of satellite coverage for
each satellite is found by inverting (3), using N = 8, 15;
To illustrate the preceding results examples are given
600 and
42.8°,
which use the approximate relationship (5) between and
A = 0;Re = 6400. The results are
respectively. These compare with exact values of 57.60 and
N. For comparison the equivalent results will also be ob42.30, respectively, from Table I. The sensor range and scan
tained from the more complex exact relationship (1).
Example 1: Given a maximum sensor range of 6000 km, angles are found by using (9) and (10). These results are
the satellite constellation which provides single coverage of shown in Fig. 11 (the curves based on exact and approximate values for are nearly coincident). In this figure the
the entire Earth with the minimum number of satellites is
sensor scan angles are shown for coverage at 20 km and 900
found.
The required number of satellites is obtained by first
km; the required sensor range is essentially the same for both
using (12) to find for A =Amin = 0, Re = 6400 km, and
altitudes. The effect of a constraint corresponding to atR = 6000 km and then substituting the resulting value into
mospheric obscuration below 20 km is also indicated.
=
472
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
AES-14, NO. 3
MAY 1978
References
[1
[2]
[3]
[4]
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David C. Beste (S'60-M'65) received the B.S. and M.S. degrees in physics and mathematics
from the University of Michigan, and the Ph.D. degree in electrical engineering from the
University of Southern California in 1970.
He is presently with General Research Corporation, Santa Barbara, Calif. His professional interests include radar and communication systems, advanced radar concepts,
extraordinary space-based systems, detection and tracking, and electronic countermeasures.
Dr. Beste is a member of Sigma Xi and Eta Kappa Nu.
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