Note: Descriptions are shown in the official language in which they were submitted.
~ k~ ~9
1 B~CKGROI]ND OF THE INVENTION
. _
1) Field of the Invention
This invention relates to determining the relative
positions of two or more objects; and, more particularly, to
radiating a field from each object, detecting the field at
the other objects and analyzing the field to determine the
position of the radiating object.
2) Description of the Prior Art
The use of orthogonal coils for generating and
sensing magentic fields is known. Such apparatus has received
wide attention in the area of mapping magnetic fields to pro-
vide a better understanding of their characteristics, for
example. If a magnetic field around generating coils can be
very accurately mapped through use of sensing coils, it has
also been perceived that it might be possible to determine the
location of the sensing coils relative to the generating coils
based on what is sensed. However, a problem associated with
doing this is that there is more than one location and/or
orientation within a usual magnetic dipole field that will
provide the same characteristic sensing signals in a sensing
coil. In order to use a magnetic field for this purpose,
additional information must therefore be provided.
One approach to provide the additional information
required for this purpose is to have the generating and
sensing coils move with respect to each other, such as is
taught in U.S. Patent No. 3,644,825 issued February 22, 1972
to Paul D. Davis Jr. and Thomas E. McCullogh. The motion
of the coils generates changes in the magnetic field and the
resulting signals then may be used to determine direction of
the movement or the relative position of the generating and
sensing coils. While such an approach removes some ambiguity
--2--
.
,
~ d . 2 ~
1 about the position on the basis of the field sensed, its
accuracy is dependent on the relative motion, and it cannot
be used at all without the relative motion.
Another approach that has been suggested to pro-
vide the additional required information is to make the
magnetic field rotate as taught in Kalmus, "A New Guiding
and Tracking System", IRE Transactions on Aerospace and
Navigational Electronics, March 1962, pages 7-10. To deter-
mine the distance between a generating and a sensing coil
accurately, that approach requires that the relative orien-
tation of the coils be maintained constant. It therefore can-
not be used to determine both the relative transla~ion and re-
lative orientation of the generating and sensing coils.
U.S. Patent No. 3,868,565 issued February 25, 1975
in the name of Jack Kuipers teaches a tracking system for
continuously determining at the origin of a reference
coordinate system the relative translation and orientation
of a remote object. The tracking system includes radiating
and sensing antenna arrays each having three orthogonally
positioned loops. Properly controlled excitation of the
radiating antenna array allows the instantaneous com-
posite radiated electromagnetic field to be equivalent
to that of a single loop or equivalent stub antenna
oriented in any desired direction. Further, control of
the excitation causes the radiated field to nutate about
an axis denoted a pointing vector.
The tracking system is operated as a closed loop
system with a computer controlling the radiated field orien-
tation and interpreting the measurements made at the sensing
antenna array. That is, an information feedback loop from
the sensing antenna array to the radiating antenna array
3-
.. ; . ' ` ~: ' ' :' ' '
,. . , ~
~ s3~ ~
1 provides information for pointing the axis o-f the nutating
field toward the sensing antenna array. Accordingly, the
pointing vector gives the direction to the sensing antenna
array from the radiating ante~na array. The proper orien-
s tation of the pointing vector is necessary for computation
of the orientation of the remote'object. ~he signals de-
tected at the sensing antenna include a nutation component.
The nutating Eield produces a different nutation component
in the signals detected in each of the three orthogonal
loops of the sensing antenna array. The orientation of the
sensing antenna array relative'to the radiated signal is
determined from the relati~e'magnitudes and phase of these
modulation components.
~hile the art;of determining position and orien-
tation of remote ohjects is a well devel'oped one, there
still remains a nee'd to determine the'relative position and
orientation of a first obj'ect with resp-ect to a second
remote object without requiring hard wire feedback between
the'two objects and also without imposing movement and
orientatisn constraints on the'remote object or the' radiated
electromagnetic field. Further, the`re is a need or con-
tinuously and simultaneously determining at a plurality of
objects the relative positions and orientation of the
objects with'res'pect to each othe'r.
' SUMM~RY O~'THE I'NVENTION
_
In accordance with an embodiment of thi's inven-
tion, independently oriented field receiving means located
at a first object are used to sense a field radiated by
independently oriented transmitting means located at a
3~ second remote object. ~he' field is characteriæed in that
one direction of the transmitted field can be uniquely
-4-
1 determined at the field receiving means. Although more
easily explained with respect to far-field or plane ~aves,
it also is true for near-field waves, intermediate-ficld
waves, and far-field waves. For example, if the distance to
wavelength ratic of the field radiated by the' transmitting
means i5 such that at the receiving means the $ield has far-
field characteristics, ~ratio > 5) which means essentially a
planar wave front, the orthogonal direction to this planar
wave front can be determined and also easily and intuitively
understood. Coordinate transformation of the signals
received by the recei~ing means can be used to co~pute the
pointing angles to the second obj'ect from the' irst object.
Such an embodiment can be useful for having one aircraft
determine the~rel'ative direction to another aircraft for
such purposes as aircraft collision avoidance.
An embodiment of this invention can also include
the determination at the first object receiving means of
whethe'r the''second object transmitting means has correctly
computed the pointing angles to the first- obj'ect from the
second object. This is accomplished by using a nutating
field transmitted from the second object having an axis of
nutation defined by a pointing vector. If the` magnitude of
the field received at the first obj'ect is constant over the
nutation cycle,' the` pointing vector from the second object
is pointing towa'rd the' first objec* and the pointing angles
from the second obj;ect to the' first object have been cor-
rectly computed. As a result, not only can the position of
the second obj'ect be determined rel'ative to the first
object, but the' first object can determine whether the
second object has computed the position o$ the~ first object
relative to the second object.
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~32~t3~9
1 A transmitted nutating field can be characterized
in one direction at a receiving means by the component that
establishes the pointing vector from the receiving means to
the transmitting means and can have far-field, intermediate-
field or near-field characteristics. Furthe'r, a nutating
field can be used to determine relative roll angle about the
pointing vecto.r betwe.en the receiving means at the first
object and the transmitting means at the second object in
addition to determining the pointing angles characterizing
the pointing vector direction. Relative roll wo:uld be
obtained from the comparision of the received signal with an
a priori knowledge of the st~rt of the nutation cycle.
A further embo:diment of this invention can include
transmitting coded information in the transmitted field
signals giving the' local pointing angles of, for example,
the pointing vector of a.nutating field or the normal to the
plane:of a rotating field transmitted b~ the' ob.j'ect. These
pointing angles are'sufficient::for determining the orienta-
. tion o$ the transmitting object relative to the receiving
object. ~ccordingly, if the transmitting and receiving
obj:ec.ts. establ:ish that the pointing vector of the trans-
mitt:ing obj:ect is alqng a line connecting th.e transmitting
and receiving obj:ects~ then the relative orientation of each
object can be' det~ermined, wi:th respect to each'other. This
embodiment, in this instance:, is a five degree-of-freedom
measurement system and the computational strategy can be
.sel:ected such that the' measured angles provided in each of
the bodies' are'referen.ced to the' coordinate frame of the`
transmitting object:and/or the coordinate fr'ame o~ the
receiving obj:e~ct.: Such an application can be:'used for air-
craft formation control, robo:t control, hel'icopter and/or
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1 aircraft landing, rendez~ous, etc. A further embodiment can
include means for phase locking on some appropriate modula-
tion frequency (which may be the nutation frequency? in both
bodies thereby enabling each body to make a measure of the
round trip phase shift of the modulation envelope. This
measured phase shift is proportional to the distance between
the two bodies. The modulation frequency would be selected
to avoid ambiguities in the measured distance. For this
particular embodiment the invention is a full six-degree-o~-
freedom position and orientation measurement system operating
cooperativel~ between two or more bodies. Applications of
this embodiment can be used for aircraft collision a~oid-
ance, aircraft formation control, helicopter and/or aircraft
landing, rendevous, robot control and the like.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 describes the geometry of a simple coordi-
nate transformation called a rotation;
Fig. 2 is the block diagram representation of a
single rotation operator called a resolver;
Fig. 3 is a schematic representation of an elec-
tromagnetic field from a single dipole along a plane through
the dipole;
Fig. 4 shows the two pointing angles defined for
three dimensional pointing;
Fig. 5 is a representation of the nutating move-
ment of an intensity or excitation vector of an electro-
magnetic field about a pointing vector in accordance with an
embodiment of this invention;
~ Fig. 6 is a block diagram of the path of a re-
ference nutating electrical input signal to an antenna
positioned at the origin o a coordinate frame and a sche-
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1 matic diagram of a generated pointing vector;
Fig. 7 is a block diagram of an excitation circuit
for providing a pointing vector in accordance with Fig. 6
and Fig. 4;
Fig. 8 is a schematic diagram of the relative
coordinates of a first body and a second body and a sequence
of rotation relating the two coordinate frames;
Fig. 9 is a block diagram of a pair of antennas
acting as both transmitting means and receiving means and
associated coordinate transformations in accordance with an
embodiment of this invention;
Fig. 10 is a block diagram of an antenna means and
associated means for transmitting electromagnetic radiation,
receiving electromagnetic radiation and performing coordi-
nate transformations in accordance with an embodiment of
this invention; and
Fig. 11 is a schematic representation of a system
in accordance with an embodiment of this invention which
will compute the position or direction and the relative
angular orientation of two bodies free to move in three
dimensions.
DETAILED DESCRIPTION OF THE INVENTION
This invention includes an object tracking and
orientation determination means, system and process. The
invention can provide in each of two independent body frames
a measure of the pointing angles and range to the other body
when a field transmitted from one body to the other body
includes means for determining the direction to the source
of radiation of the field. In accordance with one embodi-
ment of this invention a nutating field is the means by
which the direction to the radiating source can be determined.
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~ 9 ~,
1 A field nutatin~ about a pointing vector can
additionally provide in each of two independent bod~ frames
a measure of the relative angular orientation of the other
body frame. Although the invention can be used in a plural-
ity of embodi~ents, only an embodiment for determining
relative pointing angles, range and relative orientation
between two bodies will be described. However, it should be
recognized that the in~ention is not limited to this embodi-
ment and that it may be advantageous to determine the
pointing angles, range and orientations of a plurality of
objects with respect to one another. Further, it should be
recognized that two dimensional embodiments can be advan-
tageously used where objects are restricted in motion to a
single plane. In connection with such a two dimensional
embodiment, subsequent discussion of nutation includes two-
dimensional nodding. Other embodiments can be used where
only pointing angles of one object relative to another
object are desired.
To determine pointing angles from the reference
coordinate frame of a receiving object to a transmitting
object~ the transmitted field must have oscillating field
components in directions perpendicular to the line connect-
ing the transmitting and receiving bodies. For example, in
a three dimensional situation, the field can be rotating in
a plane or nutating about a pointing vector. Orthogonal
receiving means, such as coils 11, 12 and 13 shown in Fig.
4, at the receiving object detect spatial components of the
transmitted field. A transformation performed on the
detected components is used to establish a direction with no
modulation when the field is nutating. A tracking system
including a transmitted field nutating about a pointing
g
1 vector is described belo~ and inclu~es a discussion of the
characteristics of a nutating field.
Radiating coils or dipoles need not necessarily be
mutually orthogonal, but must be independently oriented.
That is, a vector representing the orientation of one of the
coils can not be formed from a linear combination of two
other vectors representing the orientation of the other two
coils. However, the orthogonal case will be described
because it is simpler and easier to explain and implement.
Therefore, apparatus in accordance with an em-
bodiment of this invention or generating a directable,
nutating, electromagnetic field alon~ a pointing vector
includes three orthogonally positioned coils or stub dipoles
through which excitation currents can be passed. The
mutually orthogonal coils at a transmitting body define a
radiator reference coordinate frame. Mutually orthogonal
coils at a receiving body define a sense reference coordi-
nate frame. An orthogonal radiator pointing coordinate
frame is defined as having an x-axis coincident with the
pointing vector and a y-axis in the x-y plane of the re-
ference frame and orthogonal to the x-axis of the pointing
coordinate frame. The z-axis of the radiator pointing
coordinate frame is mutually orthogonal to the abo~e men-
tioned x and y axes, sensed according to the right-hand
rule. ~ith all pointing and orientation angles equal to
zero, the radiator pointing frame, the radiator reference
frame and the sense reference frame are all coincident in
orientation. The nutating E~ field can be described by a
conical motion (continuous or intermittent) of the intensity
or excitation vector about a direction called the pointing
direction or axis of nutation of the composite nutating
-10-
1 field, the conical apex being defined at the intersection of
the radiator or excitor coils. Such a nutating field can be
generated by a carrier signal modulated by the combination
of a DC signal in one of the coils, an AC signal in a second
coil, and another AC signal having a phase in quadrature
with the phase of the first AC signal, passed through the
third coil, all three coils being mutually, spacially
orthogonal. That is, as can readily be appreciated, the DC
signal refers to an alternating current carrier having a
constant modulation envelope and the AC signals refer to an
alternating current carrier having a variable, for example,
sinusoidal amplitude modulation envelope. The pointing
vector is fixed to the composite direction of the axis of
the resultant DC signal. To make this nutating field direct-
able, a signal processing means known as a coordinate
transformation circuit must operate on the reference AC and
DC excitation signals in order to point the nutating field
in the desired direction. The generation of a nutating
field is described in U.S. Patent No. 4,017,858 issued
on April 12, 1977 in the name of Jack Kuipers. A brief dis-
cussion of the coordinate transformation known as a rotation
is presented as background in order to properly teach the
principles underlying the techniques employed in this inven-
tion.
A vector transformed by pure rotation from one
coordinate frame into another coordinate frame is also said
to be resolved from the one into the other coordinate frame.
Resolve and resolution in this context are synonyms for
transform and transformation. The operator which transforms
the comp~nents of a given vector in one coordinate frame
into its components in another coordinate frame where the
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~ 9
l two coordinate -frames are related by a simple angular
rotation is defined as a resolver. The equations governing
this transfor~ation are:
x2 = x,cos ~ + vlsin A
Y2 = ylcos A -x~sin A
2 Z I
where in this case the z -axis is the axis of rotation. The
equations are readily verified from the geometry illustrated
in Fig. 1. Note that when the two components operated on by
the resolver are ordered positively (zxyzxy... ) then the
first component of the positively ordered pair always has
the positive sine term when the angle of rotation is posi-
tive. If the angle of rotation is negative then the sign of
the sine term reverses. A convenient notation for a re-
solver is the block shown in ~ig. 2 where the rotation in
this case is shown as negative about the y-axis. The y
component is therefore not affected by the transformation
and this fact is indicated in this notation by passing that
component directly through the box as shown, whereas, the
resolver block representing Fig. 1 would show the z axis
passing directly throu~h the box. This notation should be
regarded as a signal flow or block diagram for rector
components, particularly useful in describing the compu-
tational strategy employed in this invention.
A process in accordance with an embodiment of this
invention includes the generation of a directable, nutating
field, nutating about an axis called the pointing axis or the
pointing vector. The reference nutation excitation vector
consists of three components: a DC and two AC signals
quadrature related. The pointing vector and its entire
nutating magnetic field structure are pointed in any desired
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1 direction defined in terms of angles A and B, in this
case. Figures 4 and 7 illustrate the pointing geometry and
the computation coordinate transformation circuitry
necessary for achieving the desired pointing direction by
operating on the given three reference excitation signals.
A more detailed explanation of coordinate transformations,
calculations and applications is contained in Kuipers, J.,
Solution and_Simulation_of Certain Kinematics and Dynamics
Problems Using Resolvers, Proceedings of the Fifth Congress
of the International Association for Analog Computation,
Lausanne, Switzerland, August 28 - September 2, 1967, pages
125-134.
Discussing the nature of a generated field, for
simplicity, first consider the nature and intensity of a
signal at a body 20 when sent from a body 10 having a single
radiator 13 equivalent to simple dipole. Referring to Fig.
3, radiator 13 is a dipole aligned along the z-axis with the
radiation center at the origin. Assume that vector P is
pointing at body 20 and also assume that the distance to
body 20 is at least about 5 wavelengths of the radiated
field, so that plane wave conditions prevail. This means
that essentially all the radiated energy lies in a plane
normal to vector P. The intensity of the signal detected at
body 20 is independent of an angle A (Fig. 4, z-axis only),
the angle between the x-axis and the projection of vector P
on the x-y plane, but is proportional to the cosine of the
angle B, the elevation of vector P from the x-y plane. The
signal processing strategy of the signal received at body 20
is based upon the properties of ~1) plane wave and ~2) in-
tensity proportional to cosB. The relative signal strength
in the direction of vector P is illustrated in Fig. 3. The
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~ ~?~
1 intensity locus is r = Kcos B, where K is merely the pro-
portionality constant representing the level of the excita-
tion on the dipole antenna.
Referring to Fig. 4 for a discussion of a pointing
vector capable of pointing in any direction, an antenna
triad 15 of body 10 shows three coils which are the equiva-
lent of three dipole-stub antennas 11, 12 and 13 ortho-
gonally arranged along x, y and z-axes, respectively. Let
the radiation centers of coils 11, 12 and 13 be coincident
at the origin. This x, y and z-axes frame for antenna triad
15 is fixed to body 10 and will be regarded as the reference
frame. The body frame of body lO'to which antenna triad 15
is fixed differs from the reference frame by at most a
constant matrix.
The excitation vector of a signal applied to a
single coil 13, such'as illustrated in Fig. 3, is f = col
C, 0,' K~, where the x and r co~ponents are zeroes because
there is only a z-axis antenna and K is the excitation level
or intensity of reference excitation vector f. The notation
"col" is used to indicate a single column matrix defining
the three components of a vector. Accordingly, the excita-
tion vector for antenna triad 15 is
f - col ~n, cos mt, sin mt) Cl~
where n is greater than or equal to 0 and where' m is the
radian frequency of the modulation of the carrier. ~hen n
is greater than zero, this excitation on antenna triad 15
results in what is e~quivalent to a nutating dipole. For
example, as shown in Fig. 5, whe'n n is equal to one, this
nutating dipole can be ~isualized as being equi~alent to an
3~ actual physical dipole oriented such that it makes a fixed
angle'of 45 with'respect to the x-axis and nutates about
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'
l this x-axis with a nutation rate equal to the sinusoidal or
other modulation frequency indicated in the components of
the excitation vector. When n is equal to zero the excita-
tion vector f rotates about antenna triad 15 in the plane
excited by the y and z antenna components. As a result, an
embodiment of this invention need not necessarily include
nutation in a true sense. Nevertheless, when nutation is
used more information is available than when rotation is
used. When n is equal to zero, there is no measure of
transmitted pointing angle error available at the receiver.
For example, with nutation of the radiated field it can be
determined at the receiving body whether or not the radiator
is pointing the radiated field at the receiver. As n in
equation (1) gets larger in magnitude, the receiver is able
to be more sensitive to pointing errors at the transmitter.
The radiation pattern associated with this nu-
tating dipole, of course, also nutates in the fixed x, y, z
coordinate frame. Because of this, the signal at every
point off the x-axis in the pointing frame x, y, z space is
modulated at the nutation frequency. The magnitude of the
signal detected at any point on the x-axis of the pointing
frame, defined by the pointing vector, is invariant over the
nutation cycle. This fact forms the basis for a signal
processing strategy of a nutating field in accordance with
an embodiment of this invention. Moreover, this unique
direction of magnitude invariance with respect to the
nutating electromagnetic field structure defines the direc-
tion of the pointing vector in this tracking system. The
discussion follows or n equal to one.
In accordance with an embodiment of this invention
the excitation vector as defined in equation (1) need not be
-15-
1 continuous over the nutation cycle. That is, it ~ay be
convenient to employ a d;screte state representation. For
e~ample, the nutation cycle can be defined in terms of the
four states:
x y z
f (tl) 1 1 0
f (t2) 1 0 l (2)
f (t3) 1 -1 0
f (t4) 1 0 -1
where the vector f at the our discrete times, tl to t4, has
x, y and z values as indicated. The order and duration of
each of these states can be modified OT coded to contain
meaningful system information such as direction of nutation,
reference axis, an angle measure, etc. A simple example is
encoding one pointing angle on the relative durations of the
first and second states of the our state sequence and
encoding the other pointing angle on the relative durations
of the third and fourth states. Such coding will be sub-
sequently discussed in more detail. ~hen the excitation
vector uses discrete states between two bodies free to move
in three dimensions, at~least three discrete states per
nutation cycle must be used to establish three independent
directions so one body can be related to the other body.
~hen determination of relative roll is desired, the coding
of the vector f includes identification of one of the states
of the nutating or rotating field so a reference state can
be established at which time it can be determined at the
receiver in what direction the radiated field is pointing
relative to the radiator reference frame. ~or example, if
there are four states in one nutat~on cycle transmitted in a
known sequence, a reference state can be identified by
-16-
1 having a longer time gap between each sequence of the four
states than between the individual states in a sequence.
If the nutating field is contlnuous 7 instead of discrete, a
phase shift can be used to establish a reference state.
When both bodies have transmitting means so each
receives informatian from the other, the bodies can alter-
nate sending discrete states or they could be duplexed to
send and receive simultaneously. For example, a first body
can send a first state, a second body can send a first state
and the first body can send a second state. Alternatively,
the states can be sent as groups of twos or threes. Con-
siderations for choosing among these possibilities include
providing for storing information at the receiving body and
the desired frequency of updating relati~e orientati-on and
pointing angles.
A nutating electromagnetic field with a pointing
vector coincident with the x-axis of the radiator reference
frame is the result of the excitation vector of equation ~1)
on antenna triad 15 and is shown in Fig. 5. H~wever, in
general, body 20 will not be on the radiator reference frame
x-axis (see Fig. 8~. Thereore, it is desirable to position
or direct the pointing vector to be colinear with a line
connecting bodies 10 and 20. This means *hat the tracking
system must have the capability of pointing the nutation
axis of the nutating electromagnetic field arbitrarily over
a sphere surrounding body 10. This is accomplished by an
orthogonal coordinate transformation Tl-l shown in Fig. 6.
It consists of two rotations T, = (TB~ TA~ = TAl
TB ', operating on the nutation input excitation reference
vector f. The letter T represents a transformation and the
letters A and B represent angles. The subscripts to the
-17-
1 Ietters T, A and B identify the body associated with the
particular transformation or pointing angle. As shown in
Fig. 7, TA _l and TB l are the transformations through
angles A and B, respectively. Transformation T l is the
combination of transformations TA -I and TB -I and relates
the reference input excitation vector f to the actual
e~citations required on the radiator elements to give the
desired pointing ~ector. The coordinate transformations
corresponding to the t~o rotations relating the input vector
to the vector P are defined as follows:
cos Al sin Al 0 cos Bl 0 -sin B
TAl = -sin Al cos Al 0 and TB = 1 0 ~3)
0 0 1 ' sin Bl 0 cos B ~
The output of this operation gives the correct composite DC
and AC modulated carrier excitation to each of the elements
in the antenna triad such that the pointing vector P is
directed in accord ance with two specified angles Al and B ,
as shown. Thus, with pointing angles A = B = 0 as shown in
Fig. 5 the resultant electromagnetic fieId nutates about the
reference x-axis while in Fig. 6 the identical electromag-
netic field structure nutates about a pointing vector P,
directed in accordance with pointin~ angles Al and B,.
Referring to Fig. 8, a tracking system in accor-
dance with an embodiment o this invention operates by
sending a signal from a body 10 to a body 20 and from body
20 back to body 10. This transponding process or its equi-
valent continues in order to provide a continuous measure in
each of the two bodies, of the pointing angles to the other
body. That is, the angular tr~nsormation shown in Fig. 7
for determining the direction of the pointing vector is
generated by sensing a fie~d transmitted from the other
-18-
~ 7
1 body. For example, if hody 10 sends a nutating signal to
body 20, body 20 can determine the direction of body 10 from
body 20 and can direct the pointing vector of a nutating
field transmitted from body 20 toward body 10. Advanta-
geously, bodies 10 and 20 both have transmitting and re-
ceiving capabilities. Further, in steady-state with both
bodies 10 and 20 having transmitting and receivi.ng means,
the pointing vector of body 10 points to body 20 and the
pointing vector of body 20 points to body lO.
The relative orientation of body 2Q with respect
to the body frame (radiator reference frame) of body 10 is
defined by the transformation T:
1 0 0 cos~ 0 -sin3 cos~ sinll~ 0
T = 0 cos~ sin~ 0 1 0 -sinll) cos~ 0 (4)
0 -sin~ cos~ sin9 0 cos~ L n 1
That is, the orien*ation of body 20 can be related to the
frame of body 10 by a sequence of three ro*ations as illu-
strated in Fig. 8. The se~quence of a rotation about zl'
through an angle ~ follo,wed by a rotation about the new y-
axis through an angle ~, and inally a rotation about the
x -axis through an angle ~, es'tablishes the' orientation o
the x2y2z2' frame of body 20 with'respec't t~ the xlylzl frame
of body 10. The' independent pointing geometry is shown in
the lower portion of Fig. 8. It should be noted that the
axes ldentified as x2yzz2 in Fig. 8, are translate~d from the
origin at body 20 merely to avoid diagramatic congestion in
an attempt to clearly illustrate the Euler angles ~, ~, and
involved in the relative orientation geometry.
A summary ,of the coordinate frame relationships
involved in a *racking system in accordance ~ith an em-
bodiment of this invention is illustrated in Fig. 9. The
-19-
1 upper block diagram shows the reference nutating excitation
vector fl defined in the frame of body 10. Operating on
this excitation vector with the pointing transfo'rmation
Tll produces the proper excitations for antenna triad 15 o~
body 10 such that the nutating signal is continuously
pointed at body 20. In body 20 a receiving antenna triad 25
detects the nutating field components. By processing the
signal to determine a direction having no nutation signal
component, the direction of the' "normal" to the' received
plane-ware is determined. This direction is defined by two
computed pointing angles, as in Fig. 6, and establishes the
pointing transformation T2. Actually, Tz is that trans-
formation that produces the plane-wave vector equivalent
f2' of the transmitted vector ~. That is, wh'e'n there is
no pointing error and ideal free' space transmission is
assumed, the normalized tangential components of f, are
equal to the normalizéd tangential components of fz~. The
radial component of the transmitted vector f~ is lost
because of the assumed far-fiel'd condition and the received
vector f2' then after being properly transformed and pro-
cessed it also has a zero radial component. Whether near-
field, intermediate-field, or far-fiel'd signals are re-
ceived, the signal processing strategy is or may be the
same. That is~ either the radial component is non-zero as
in the near-field, intermediate-'field or zero as in far-
field. The processing which'determines the'pointing angles
is that no modulati'on or nutation components exist in the
radial direction, in all three cases. When the Teceiver
body is pointing at the transmitting body confirmation that
the tran's~itting body's pointing angles to the receiver body
are CoTreCt is provided by modulation components of the
-20-
l nutating ield at the receiver body being a vector of con-
stant magnitude and rotating in the plane no'rmal to the
pointing vector from the receiver body to the transmitter
body thus describing a circular pattern. Deviation of the
modulation components from such a circular pattern can be
used as an alternative control law for a tracking system.
The upper block diagram in Fig. 9 represents
coordinate frame relationships when operating or trans-
mitting from body lO and received in body 20. Similarly,
lQ the lower block diagram represents coordinate ;Erame rela-
tionships when operating or transmitting from body 20 and
received in body 10. Between body 10 and body 20 is an
implicit coordinate transformation T representing the
relative orientation of body 20'with res~pect to the frame of
body 10. The two bl'ock diagrams are, in a sense, inverses
of one anothe'r and indicate the transponding nature of this
tracking system. Thes'e coordinate frame relationships form
the basis for the' signal processing strategy of this tracking
system.
If the matrix product of the transformations be-
tween the excitation vector , and the reconstructed or
reprocessed' vector f~'were the identity matrix, then clear-
ly, f2' = f~. The~situation is not this simple primarily
because of nonlinear attenuation characteristics of the
vector components of eIectromagnetic radiation. These
attenuation characteristics are a function of wavelength and
distance. The explanation o the system concepts is, how-
ever, simplified by the' plane-wave assumption, even though
valid for all circumstances. ~ith the assumption that
plane-wave conditions prevail, that is, the radial component
of the received signal is zero, the plane containing the
-21 -
~ 2 ~
1 radiated energy is nor~al to the line connecting body 10 and
body 20. This is so even if large errors are present in the
pointing.
An error in the pointing angles of the pointing
vector originating at the receiver is indicated when the
magnitude of the received signal component sensed in the
pointing direction is not invariant over the nutation cycle.
The frequency of this variation due to the pointing error is
equal to the nutation rsquency. The magnitude of the
variation is proportional to the magnitude of the pointing
error. And the phase of this periodic error function
resolves into two components which'are related to the' erTors
in the two pointing angles A and B.
Phase discr'imination circuitry, similar to that
commonly used in flight' control applications, can provide a
continuous measure of the angular errors in the'two pointing
angles. Howe~ver, the phase measure of the error requires a
cyclic reference'agains* ~hich the measure of the phase is
to be compared. Therefore, there'is advantageously provided
a continuous identification of either a positive going zero-
crossing whe'n a continuous nutation vector is used to
generate the' nutating field or of an extended duration of
the reference state when a discrete state excitation ~ector
is use-d to generate the nutating field. The' resulting
measure'of angular error is used for correcting the angles
in the'pointing transor~ation, such that the pointing
errors tend toward zero. As a result of kno~ing the se-
quence'of nutation states ~either continuously or dis-
cretely~ about the pointing vector, the relative angular
displacement ~or roll~ about the pointing vector of the
receiving body with'respect to the trans~itting body can be
-22-
~ 3 ~9
1 determined. Subse~uent notation of a transformatlon R
refers to such a roll angle relationship bet~een body 10 and
body 20 about the pointing axis.
Referring again to Fig. 9, the indicated opera-
tions on the excitation vectors in the two block diagram
which illustrate the transponding scheme, can be written:
f2 R2T2T T~lf~ = R2Bf (5)
f '= R,TlT-lT~lf2 = RlB f2 ~6)
where B = T2T Tll and therefore B-l =TITelT2' ~7)
Moreover, since in equations ~5) and ~6)
R2T2TT~ I = RITlT lT2 ' = Identity ~16)
it is easily concluded that
RlR2 = R2Rl ~ Identity (17)
Both of the excitation vectors, fl and f2, and
both of the output vectors f2'and f,'are defined in their
respective pointing frames and normalized. The pointing
frame x-axis is directed such that it contains body 10 and
body 20. ~s noted above, the y-axis, orthogonal to x, lies
in the reference frame xy plane; the z-axis is mutually
orthogonal ~in the right-handed sense) to the pointing frame
x and y axes.
In summary, the steady-state vectors defined at
each point in the upper block diagram of Fig. 9 are:
fl points from body 10 to body 20; its components
are defined in the pointing frame by equation
T~-~ fl ls the same vector with components defined in
the reference frame o body 10 for exciting
antenna triad 15 of body 10.
TTl-l f~ is again the same vector whose components are
ideally detected in and therefore defined in
-Z3-
?~5~
1 the reference frame of body 20, where T is the
spacial transformation bet~een bodies 10 and
20.
R2T2TTl -'fl is the same vector whose components are re-
produced in the pointing frame by choosing,
after computation, the appropriate pointing
transformation T 2 relative to the frame of
body 20. The transformation R2 is required
to correct for the relative roll angle about
the pointing vector and is ~generated by
satisfying the control law that the field
components of vector fl and f2' orthogonal
to the pointing rector are equal, except
for an attenuation constant, or that the
sequence of transormation between fl and
f2' must be equivalent to the identity, a
constant.
The output vector f for a steady-state far-field
condition will have all zeroes or its x components. For
example, if the input vector f " over one nutation cycle, is
represented by
1 1 1 1 .
fl= 1 Q -1 (8)
O 1 0 -1 L
then the output vector f2' is, over one nutation cycle,
O O O O
f2 = 1 0 -1 0 (9?
o 1 o -1 ,
However, if the tracking system is not operating so the
field has far-field characteristics at the receiver, the x-
components (i.e. the first- row of f2l) will be non-zero,
-24-
1~ 2~
l constant, and equal in each state. The product of the roll
transformation R2 at body 20, and the roll transformation Rl
at body 10 is equal to the identity matrix because each body
has the same roll with respect to the other body except for
sign. More specifically,
: 1 0 0
R2 1 = Rl = 0 cosp sinp ~10)
0 -sinP cosp l
To compute the errors in the pointing angles A and
B and the roll angle P, the input and output vectors are
processed using scalar product notation as follows:
~A = (elf2 .e2f~
~B = ~e f '.e f ) (12)
~ e2f2'-e3f2~ - (e3f2'-e2fl) (13)
where el = row vector (1 0 0)
e2 = row ~ector (0 1 0)
e~ = row vector (0 0 1)
and fl and f2 ? are the matrices representing the nutation
sequence over one cycle as shown in ~8) and (9), respec-
tively. This signal processing can be used for nutating EM
fields, whether far-ield~ intermediate-ield, or near-
field. Equations 11, 12 and 13 describe processing in body
20 of signals which have a dlrection parallel to a line
between bodies 10 and 20. As noted beore, additional
information, namely, regarding the pointing errors of body
10 can be obtained in body 20 by processing in body 20
signals present in the plane perpendicular to the line
between bodies 10 and 20.
It is clear that an analogous summary of vector
definitions can be stated or the lower block diagram of
Fig. 9 indicating the signal going from body 20 back to body
-25-
1 10. The signal flow from body 10 to body 20 and back to
body 10 completes one transponding cycle. This cyclic
transponding behavior continues so that under dynamic
conditions, such as whe-re two bodies are in relative motion,
the pointing angles to the other body may be determined in
each of the two bodies. Over one transponding cycle, with
the requirements that the respective y and z components of
vector fl and f2'are equal, the computability of the desired
pointing angles A2 and B2 and the relative roll angle P in
body 20 is assured. ~ similar discussion applies to the
computation in body 10 of the pointing angles A, and Bl to
body 20 and also the relative roll p. Further, in accord-
ance with an embodiment of this invention, the tracking
system can be, for example, multiplexed or time-shared to
include processing Qf the data related to n number of bodies
such that the pointing angles to n-l bodies can be deter-
mined in the kth body, or each of the n bodies. This can
have application in formation control, multiple refueling of
aircraft in flight and general use as an aircraft navigation
and landing aid and aircraft collision avoidance.
In addition to all o~ the capabilities discussed
above a tracking system in accordance with an embodiment of
this invention can have the capability of providing, in each
body, a measure of the remote body relative orientation
angles. The pointing angles and relative roll of each body
are available in the body. Further, the orientation of one
body with respect to the other body can be computed. How-
ever, to do this computation it is necessary to send from
one body to the other body information defining the pointing
angles of the pointing ~ector of the transmitting body.
Upon receipt of information defining the pointing angles of
-26-
. ~ 2 ~
1 the transmitting body, the recei~ing body can compute the
relative orientation between the transmitting body and the
receiving body. Going from body 10 to body 20
R2T2 = T~T-I or T-~ = T -lR T ~14)
is computed at body 20 and going from body 20 to body lO
R T = T T or T = T2l RlT, (15
is computed at body 10.
Tabulated below are four options involving per-
mutations of ~ariables such as the body whose orientation is
desired, the body whose coordinate frame is used to express
the orientation and the body where the orientation is
computed or made available.
Option Orientation o Body~ade~ ~vailable
I 10 with respect to 20 in 10
20 with respect to 10 in 20
II 20 with respect to 10 in 10
10 with respect to 20 in 20
III 10 with respect to 20 in 10
10 wi:th respect to 20 in 20
20 IV 10 with respect to 20 in 10
20 with respect to 10 in 10
Up to this point, the orientation o body -frame 20
with respect to body rame 10 was defined by the transfor-
mation T ~see equation 4~. A more precise notation is
required in order to clearly define the orientation trans- :
formations tabulated above, in terms of the appropriate
product of matrices available in the indicated body. ~et
the transformation Tij define the orientation of body frame
i with respect to the body frame j. Then using equations
(1~), (15~ and (17), the orientation transformations appear-
ing in the four options tabulated above are:
-27-
~ 9
1T2, = T2'R2'Tl computed in body 20 (18~
T2 Rl Tl computed in body 10 (19)
Tl 2 = TIlR,lT2 computed in body 10 (20)
= TllR2 T2 computed in body 20 ~21~
Notice that the computation of the orientation
transformations specified by equations ~18~ and (21) re-
quires the pointing angles computed in body 10, and that in
equations ~19) and (20), the pointing angles computed in
body 20 are required. This means that the pointing angles
Al and Bl defining the pointing transformation T" must be
made available in body 20; and pointing angles A2 and B2,
which define the pointing transformation T2, must be made
available in body 10. That is, these angles must be sent to
the other body in order to compute the desired body orienta-
tion angles, in the body frame in which they are desired.
The transformation T defined in (4) relates the
orientation of the ~sense) reerence frame of body 20 re-
lative to the ~radiator) reference frame of body lO. If it
is desired to compute the orientation of body 20 relative to
body 10 at body 20, computations at body 20 would use the
algorithm specified in Equation ~18), namely,
T - T -lR 'IT
The above transformation T can be determined at:bady 20 if
the body 10 pointing angles defining transformation Tl are
sent from body 10 to body 20, since the angles defining the
transformation T2l and R2l can be determined at body 20. If
on the other hand, the orientation of body 10 relative to
the reference frame of body 20 is desired at body 20, the
algorithm s:pecified in Equation ~21~ is:used at body 20.
The computation of the set of Euler angles ~ defining
the relati~e orientation between the two bodies is well
-28-
~.2 ~
1 known and is shown, for example, by the conneçtions within
dotted line 500 in Fig. 11. For a more complete discussion
of these computations see Kuipers' referenced paper.
There are, of course, several schemes for getting
a measure of the two angles, camputed in one body, sent to
the other body such as, for example, using multiplexing
techniques on the carrier. Advantageously, the components
of the nutating signals already transmitted between the two
remote bodies are coded. For example, the pointing angles
A~ and B, defining a pointing vector from body 10 can be
sent to body 20 on separate states of the nutating excita-
tion vector fl. Similarly, pointing angles A2 and B2 de-
fining a pointing vector from body 20 can be sent to body 10
on separate states of the vector f2. The actual measure of
the angles can be related to state-duration differences, for
example, which could be determined by up/down CQUnting on
the carrier.
The angular error signals measured at the receiver
are relative to and deined in the sense pointing frame.
However, in order to determine a measure of the errors in
the pointing angles and roll of the receiver body frame, it
is desirable to have the measured errors in the sense
pointing frame transformed into intermediate coordinate
frames. This is because these directions in the particular
intermediate frames~ which CQnStitute the Euler angle frame,
are specifically appropriate or determining and making the
required corrections in each of these three respective Euler
angles ~pointing angles and relative roll~.
The orientation o the three orthogonal a~es of
the receiver body or sense referenced frame can be specified
with respect to the radiator pointing frame by an Euler
-29-
~ 3
1 angle-axis sequence. Consequently, in accordance with an
embodiment of this invention, there is included an apparatus
which can transform the sensed pointing angle and roll
errors from the pointing frame of the radiated field into
the corresponding angular corrections required by the
respective Euler angle frame.
It can be appreciated that when the radiator
pointing frame and the sense reference frame are coincident
then the aforementioned transformation is not necessary.
When this coincidence occurs, the pointing vector is along
the x-axis of the radiator pointing frame and along the x-
axis of the sense reference frame. In this case, errors
sensed in the sense reference frame can be used directly to
correct the receiving body pointing angles. It can there-
fore be appreciated that there can be some, say, small angle
deviation from having the radiator pointing frame coincident
with the sense reference frame and still use errors measured
in the sense reference frame to correct the sense reference
frame pointing angles directly. However, for example, in a
situation ~here the x-axis of the radiator pointing frame is
coincident with the z-axis of the sense reference frame, it
is clear that an error about the x-axis of the receiver or
sense pointing frame (defined further later) cannot be
corrected by simply introducing an angular change about the
x-axis of the sense reference frame. It can be appreciated
that the correction should be made about the z-axis of the
sense reference frame. A coordinate transformer apparatus
2Sl (Fig. 11) in accordance with an embodiment of this
invention is introduced into the orientation and tracking
system to make sure that proper corrections are made.
Fig. 11 illustrates a tracking and orientation
-30-
~ 9
] determination system using coordinate transformation means.
The system includes in this instance mutually orthogonal
magnetic field generating coils 158, 64 and 66 mutually
orthogonal magnetic field sensing coils 248, 52 and 54.
For ease of understanding, the three coils in each case have
been shown as spatially separated. In actuality, the
magnetic axes of both the generator coils and the sensor
coils advantageously intersect in a mutually orthogonal
relationship and their centers in triad are advantageously
coincident as shown by the cartesian coodinate frames 84,
86, 160, the radiator reference frame, and 90, 92, 170, the
sense reference frame, respectively. Pointing frame excita-
tion signals ACl and AC2 are quadrature related or 90
degrees phase related. They may be considered as sinusoids
of equal amplitude but 90 degrees out of phase, although the
two signals ACl and AC2 need not necessarily be sinusoidal
in the practical embodiment of the system. Reference is
again made to Fig. 4 which was related to the earlier
discussion of coordinate transformation circuitry and which
shows the three dimensional pointing geometry. Ihe ability
to point the pointing vector 180 in any direction in which
the assembly of sensing coils 52, 54 and 248 are free to
move enables the sensing coils to be tracked. The pointing
excitation DC, ACl and AC2 signals from sources 68, 70 and
140, respectively, define a conically nutating magnetic
field 164 about a pointing axis 180 which is coincident with
the axis of the DC component of the field. It should be
emphasized again that the pointing of the vector 180 is
accomplished electrically by the circuit to be described
while the physical generating coils 64, 66 and 158 maintain
a fixed orientation physically.
-31-
~ 3~
1 Sources 68~ 70 and 4~ are connected by leads 141,
145 and 143 to a pointing angle encoder 219 for encoding the
po:inting angles of the radiated field with respect to the
radiator reference frame. Encoder 219 is connected by leads
142 and 144 to resolver 220, whose output lead 148 and
output lead 146 from encoding 219 are connected to a re-
solver 222. The output leads 154 and 156 provide reference
frame excitation signals from resolver 222 to generator
coils 64 and 66, respectively. Generator coil 158 is
excited through connection 152 from the output of resolver
220. The two angles A and B of resolver 222 and 220,
respectively, are thus operating on the radiator pointing
frame nutating field vector input whose components are the
pointing frame excitations from sources 68, 70 and 140, so
as to provide reference frame excitations to point the
pointing vector 180 and its attendant nutating field struc-
ture in accordance with *he geometry shown in Fig. 4.
The pointing vector 18Q is presumed to be pointing
nominally at the sensor which is fixed to the remote object
to be trac~ed by the system. ~ore specifically, a pointing
vector from the radiator to the sensor defines the x-axis of
a radiator pointing frame and a pointing vector from the
sensor to the radiator deines the x-axis of a sense point-
ing frame. The sensor consists of the three mutually ortho-
gonal sensor coils 52, 54 and 248, which are fixed to the
remote object and in the preferred embodiment are aligned to
the principal axes of the remote object, so that in the
process of determining the orientation of the sensor triad
the orientation of the remote~ object is therefore deter-
3Q mined. The signals induced in the sensor coils 52, 54 and
248 depend on the orientation of their sensor coordinate
-32-
~ ~ 2 ~
1 frame, defined by the mutually orthogonal coordinate axes
90, 92 and 170, relative to the pointing axis 180 and its
two orthogonal nutation components of the nutating field.
In other words, the particular mixing of the three excita-
tion signals DC, ACl and AC2 from sources 68, 70 and 140,
induced in each of the three sensor coils 52, 54 and 248,
depends not only upon the two pointing angles Al and Bl
relating the radiator frame to sense pointing frame, but
also upon the three Euler angles, ~ defining the
relative angular orientation of the remote object (i.e.
sense reference frame) relative to the radiator reference
frame.
The principal function of the coordinate trans-
formation circuit 250 in the overall computational strategy
of the system is unmixing that part of the reference signal
mix induced in the sensor coils attributable to the pointing
angles, A2 and B2. If the three angles defining coordinate
transformation circuit 250 properly represent the orienta-
tional relationship between the sensor coordinate frame and
the sensor pointing frame, then the relative magnitudes of
the signals sensed by the sense circuits 26 will correspond,
except for an attenuation factor, to the unmixed pointing
frame signals DC, ACl and AC2, respectively, from sources
68, 70 and 140, i.e. what is now termed the radiator point-
ing frame.
Sensor coils 52, 54 and 248 are connected to a
pointing angle decoder 249 by leads 167, 165 and 171,
- respective]y. Decoder 249 is used to determine the encoder
pointing angles Al and Bl of the radiated field whenever
such information is encoded onto the field. Decoder 249 is
connected to resolvers 230 and 232 by leads 229 and 231,
-33-
1 respectively, and connected to resolver 224 by leads 168 and
172. An output 166 of decoder 244 and one output from
resolver 224 connect to resolver 226 by leads 166 and 174,
respectively. One output from resolver 224 and one output
from resolver 226 connect to resolver 228 by leads 176 and
178, respectively. The two outputs from resolver 228 are
connected to sense circuit 26 by leads 186 and 188, re-
spec~ively. One output from resolver 226 connects to sense
circuit 26 on leads 184. Ou~puts 172, 168 and 166 from
decoder 249 carry the same information as leads 165, 167 and
171 because decoder 249 couples decoded information, if any,
only to resolvers 230 and 232 by output leads 229 and 231,
respectively.
Sense circuits 26 operate on the three input
signals, provided by leads 184, 186 and 188, to sense devi-
ations from their nominally correct values which should cor-
respond to the radiator pointing frame excitation signals com-
ponents 68, 70 and 140, respectively. The operation of sense
circuits 26 is described in U.S. Patent No. 3,868,565, issued
on February 25, 1975 in the name of Jack Kuipers. Basically,
sense circuits 26 compare an input vector in the radiator
pointing frame from sources, 68, 70 and 140 to an output
vector in the sense reference frame from inputs 184, 186 and
188. If this comparison manifests an error then the orienta-
tion of the sense reference frame is displaced from where it
was assumed to be. This error is expressed as three angular
errors. Accordingly, the out~ut of sense circuits 26 are
three angular errors which are related to the errors in the
Euler angles p , B and A . That is, the errors appearing on
the x, y and z-axes of the intermediate frame correspond to the
-34-
4~
1 errors in the P2, B2 and A2 Euler angles, respectively.
Once Euler angles P2, A2 and B2 have been corrected, the
orientation of sense reference frame is defined with respect
to the sense pointing frame.
Accordingly, each of the angular errors defined in
the radiator pointing frame is subjected to appropriate
transformation to give the desired angular errors appropriate
to the Euler angles in the transformation. As shown in Fig.
11, they are operated on by resolvers 315 and 316. Sense
circuit 26 is connected to resolver 315 by an output line
317; resolver 315 is connected to resolver 316 by an output
line 318; resolver 316 is connected to angle measuring
circuit 100 by an output line 319. Sense circuit ~6 is also
connected to resolver 315 by an output line 321. Resolver
315 is connected by an output line 322 to angle measuring
circuit 100. Sense circuit 26 is connected to a summer 323
by an output line 324. Summer 323 is connected by an output
line 325 to resolver 316. Resolver 316 is connected to a
high gain feedback amplifier or equivalent sample/hold
integrator or summer 326 by an output line 327. Amplifier
326 is connected to an integrator or angle measuring circuit
100 by an output line 328. Amplifier 326 is also connected
to summer 323 by an output line 402. Resolver 315 has an
input 406 supplying angle p from an ouput 218 of circuit
100. Resolver 316 has an input line 407 supplying angle B
from an output 216 of circuit 100. In operation, inputs on
lines 317, 321 and 324 are transformed into the angular
errors relating to P 2 and B2 and A2 as defined in the sense
reference or receiver body frame.
The techniques used to derive the transformations
performed on the outputs of sense circuit 26 are discussed
-35-
1 in greater detail in U.S. Patent 3,983,474 issued on
September 28, 1976 in the name of Jack Kuipers.
It is also desired to calculate the Euler angles
relating the sense reference frame to radiator reference
frame, i.e. ~, 0 and ~. Given the availability of A and
B on leads 229 and 231 coupled to resolvers 230 and 232,
respectively, techniques for such calculations are taught in
Kuipers' referenced paper. The connections for such a
calculation are enclosed within dotted line 500 in Fig. 11.
As shown in Fig. 11 resolver 232 is followed by a row of
resolvers 501, 502, 503, 504, 505 and 506. These resolvers
are connected in a closed loop from which information is
taken and computed within a computer 507 having outputs 508,
509, 510 corresponding to the three Euler angles ~, ~ and
~. Resolvers 501, 502 and 503 are connected to output
leads 218, 216 and 214, respectively. Resolvers 504, 505
and 506 are connected to output leads 510, 509 and 508,
respectively. Resolver 230 is connected to resolver 232 by
a lead 511 and to resolver 501 by a lead 512. Resolver 232
is connected to resolver 502 by a lead 513 and to resolver
501 by a lead 514. Resolver 501 is connected to 503 by a
lead 515 and to resolver 502 by a lead 516. Resolver 502 is
connected to 503 by a lead 517 and to resolver 505 by a lead
518. Resolver 503 is connected to resolver 504 by a lead
519 and by a lead 520. Resolver 504 is connected to
resolver 505 by a lead 521 and to resolver 506 by a lead
522. Resolver 505 is connected to resolver 506 by a lead
523 and by a lead 524. Resolver 506 is connected to
resolver 230 by a lead 525 and 526 and to resolver 232 by
a lead 527.
It can be appreciated that if only the Euler
-36-
1 angles p , B and A are desired, encoder 219 and decoder
249 as well as all the circuitry within line 500 can be
omitted. The aforementioned components are only necessary
if the Euler angles ~, ~ and ~ are desired relating the
sense reference frame to the radiator reference frame.
It should be pointed out that the sequence of
angles and their corresponding axes of rotation, for the
pointing coordinate transformation circuit 252 and the
relative orientation coordinate transformation circuit 250
]o are not unique. That is, other angle definitions and
rotation sequences can be used for the transformations
subject to their having the required pointing and relative
orientation freedom.
It should be pointed out that the implementation
of the invention can be done using state-of-the-art tech-
niques using digital, analog or hybrid circuitry.
In the discussion above, it is to be understood
that the sense circuits 26 are internally supplied with the
components of the excitation signals from sources 68, 70 and
140 in order to logically perform the discriminating sensing
function required of sensing circuits 26.
The resolvers which form components of the cir-
cuitry described herein may be fabricated, by way of example,
in accordance with the teachings of United States Patent
Nos. 3,187,169 issued June 1, 1965 to Robert D. Trammell, Jr.
and Robert S. Johnson and 2,927,734 issued March 8, 1960
to Arthur W. Vance. The sensing circuits, again by way of
example, may be fabricated in accordance with the teachings
of a circuit diagram appearing on page 67 of the book
entitled "Electronics Circuit Designers Casebook", published
by Electronics, Mc-Graw Hill, No. 14-6. The angle measuring
-37-
1 circuitry may take the form of any of a vast number of
closed-loop control circuits. There are, of course, num-
erous alternate constructions available for each of these
components as will be readily appreciated by those skilled
in the art.
An embodiment of this invention can also include
the capability of being a full-six-degree-of-freedom mea-
surement system. That is, in addition to measuring the two
pointing angles in each of the two remote bodies and the
three angles measuring their relative orientation also
available in each of the two bodies, a precise measure of
the distance between the two bodies can be provided in each
of the two bodies. This can be done using the internally
generated and sensed nutating electromagnetic field struc-
ture alreadly established and pointing between the two
bodies or an appropriate subcarrier can be used for this
purpose.
Using phase-locking techniques, ~such as those
described in Alain Blanchard, Phase-Locked Loops: Ap~
cation_to Coherent Receiver Design, John Wiley ~ Sons, 1976,
page 351), on the modulation ~nutation) signal sent between
the two bodies, a precise measure of the distance between
the two bodies can be determined. With reference to Fig. 9,
body 10 sends the nutating signal to body 20. Body 10 also
establishes a reference point such as, for example, the
positive-going, zero-crossing of the modulated signal sent
to body 20. Body 20 receives the modulated signal from body
10 and phase-locks on this modulation. When body 20 returns
its modulated signal back to body 10, body 20 will make
certain that the phase of the modulation is locked to the
phase of the modulated signal that is received from body
-38-
l'~.if~ 3
l 10. The phase of the signal received fro~ body 20 is
compared with the phase of the signal sent by body 10 to
body 20 and the phase difference between the two signals is
a measure which can be used for determining the distance
between the two bodies. If, however, the actual distance
between the two bodies exceeds one-half the wavelength of
the nutation frequency then potential ambiguities exist in
the measurement of the distance. One way to avoid ambigui-
ties is to choose the modulation frequency such that its
wavelength is equal to two times the maximum distance
expected in a given application. Distance is equal to
[~phase difference) ~velocity of light)] divided by [~4
nutation frequency)].
For example, if the maximum expected distance in
lS some given application is 10 kilometers, then the nutation
frequency of the system might be chosen as 15 kilohertz or
less. This choice would have the advantage that the total
measured phase shift would lie within the range 0 to 360;
this phase shift is linearly related to the separation
distance measured in the range zero to 10 kilometers.
Establishing the phase reference can be accomplisbed within
block 219 labeled pointing angle encoding and comparison of
the phases of the transmitted and received signals can be
accomplished within block 249 labeled pointing angle de-
coding.
Alternatively, if, for example, a nutation cycle
includes discrete states, other coding can be used to
determine distance between receiver and transmitter. That
is, block 219 can include a means for establishing a re-
ference state signal and block 249 can include means for
initiating the radiation of a return signal in response to
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1 the reference state signal and determining the time delay
between the radiation of the reference state signal and the
reception of the return signal.
Referring to Fig. 10, even though the receiving
and transmitting antennas can be two different physical
structures, bodies 10 and 20 can advantageously have sub-
stantially identical receiving, transmitting and computa-
tional systems so bodies 10 and 20 can each transmit and
receive signals to and from the other. Transmission and
reception using the same antenna can be done using known
multiplexing techniques which include time division, fre-
quency division, and phase division. As used here frequency
division is meant to include using two different carrier
frequencies for transmission and reception.
For example, in one multiplexing system, antenna
triad 15 is coupled to a switching means 31. Switching
means 31 is, in turn, coupled to a coordinate transfor-
mation, ranging and control means 32 through a first series
path including a demodulator and preamplifier 33 and an
analog to dlgital converter 34, and a second series path
including a modulator and power amplifier 35 and a digital
to analog conv~rter 36. For reception, switching means 31
selectively couples coordinate transformation, ranging and
control means 32 to antenna triad 15 through the first
series path. For transmission, switching means 31 selec-
tively couples coordinate transformation, ranging and
control means 32 to antenna triad 15 through the second
series path. Coordinate transformation, ranging and control
means 32 has an output for providing the value of the range
3G and the pointing and orientation angles ~or monitoring,
display or further processing. Coordinate transformation,
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3L~..2~ f3
1 ranging and control means 32 is also coupled directly to 31
and controls switching between the two series paths.
Various modifications and variations will no doubt
occur to those skilled in the various arts to which this
invention pertains. For example, in addition to electro-
magnetic fields such fields as ultrasonic and optical may be
used with appropriate radiating means such as diaphragms or
light sources. Further, the particular coding means em-
ployed in the nutating electromagnetic field may be chosen
from any of numerous alternatives. Still further, the
number of users of the tracking system and the coupling of
the transmitting and receiving means may be varied from that
disclosed above. These and all other variations which
basically rely on the teachings through which this dis-
closure has advanced the art are properly considered within
the scope of this invention as defined by the appended
claims.
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.. . .
