CA1124369A - Method and apparatus for tracking objects - Google Patents

Abstract

METHOD AND APPARATUS FOR TRACKING OBJECTS

ABSTRACT OF THE DISCLOSURE
Two spaced bodies each including three indepen-dently oriented radiating antennas are in communication with each other by such means as an electromagnetic or a sonic field. A first body receives radiation transmitted from a second body and establishes the pointing angles to the second body with respect to the first body. Further, the radiation received by the first body can include information defining the second body's pointing angles to the first body. These pointing angles are sufficient for determining the orientation of the second body relative to the first body. Analogously, radiation received by the second body can include information defining the first body's pointing angles to the second body for determining the orientation of the first body relative to the second body. Distance between the two bodies can be determined by phase-locking techniques thus providing the capability of a full six-degree-of-freedom measurement system.

Description

~ 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 .
, ~ 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.

~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 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-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.

~ 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 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 ~ 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

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 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 ~ ~?~

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 ' 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 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 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 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 ~ 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 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 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 ~ 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 ~ 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 ?~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) 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, 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 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 . ~ 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:

~ 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 ~.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 ~ 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 ~ 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.

~ 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 ~ ~ 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, 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 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 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 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 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 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 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, 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.

.. . .

Claims

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

Apparatus for determining the direction between and relative orientation of first (10) and second (20) bodies relative to one another, each body having a coordinate reference frame (84, 86, 160, 92, 90, 170), said apparatus comprising:
means (64, 66, 158) for radiating a first field from said first body, said first field having components receivable at said second body from which said second body:
(a) can determine the direction to the first body with respect to the second body coordinate frame;
(b) can define the relative rotation between said first body and said second body coordinate reference frames;
means (52, 54, 248.) at said second body for receiving said first field, said receiving means including:
(a) means for determining the direction to the first body with respect to the second body coordinate frame;
(b) means for defining the relative rotation between said first body and said second body coordinate reference frames;
means (52, 54, 248) for radiating a second field from said second body, said second field having components receivable at said first body from which said first body:
(a) can determine the direction to the second body with respect to the first body coordinate frame;
(b) can define relative rotation between said second body and said first body coordinate reference frames;
means (64, 66, 158) at said first body for receiving said second field, said receiving means including:
(a) means for determining the direction to the second body with respect to the first body coordinate frame;
and (b) means for defining the relative rotation between said second body and said first body coordinate reference frames.

Apparatus as recited in claim 1 wherein:
said means for radiating each cycle of said first field comprises means (68, 70, 140) for applying first actuating signals to at least two independently oriented first body electromagnetic field generating members; and said means for radiating each cycle of said second field comprises means for applying second actuating signals to at least two independently oriented second body electromagnetic field generating members.

Apparatus as recited in claim 2 wherein:
said means for applying first actuating signals includes means for applying a first set of signals to said first body generating members, each cycle of said signals providing at the second body as many independently measurable quantities as there are unknowns to be determined at the second body; and said means for applying second actuating signals includes means for applying a second set of signals to said second body generating members, each cycle of said signals providing at the first body as many independently measurable quantities as there are unknowns to be determined at the first body.

Apparatus as recited in claim 3 wherein:
said means for radiating each cycle of said first field from said first body includes means for directing (220, 222) the field so as to track said second body, said first directable field characterizing the direction of a first pointing vector (180) defined by first body pointing angles with respect to the first coordinate reference frame; and said means for radiating each cycle of said second field from said second body includes means for directing the field so as to track said first body, said second directable field characterizing the direction of a second pointing vector defined by second body pointing angles with respect to the second coordinate reference frame.

Apparatus as recited in claim 4 wherein:
said means for applying first actuating signals includes means for applying during each cycle a set of discrete signals to said first generating members for radiating first discrete field pulses from said first body generating members, said discrete pulses containing at least two coordinate component carriers; and said means for applying second actuating signals includes means for applying during each cycle a set of discrete signals to said second generating members for radiating second discrete field pulses from said second body generating members, said discrete pulses containing at least two coordinate component carriers.

Apparatus as recited in claim 4 wherein:
said means for applying first actuating signals includes means for applying during each cycle four discrete signals to said first generating members for radiating four discrete field pulses from said first body generating members, said discrete pulses containing at least two coordinate component carriers; and said means for applying second actuating signals includes means for applying during each cycle four discrete signals to said second generating members for radiating four discrete field pulses from said second body generating members, said discrete pulses containing at least two coordinate component carriers.

Apparatus as recited in claim 4 wherein:
said means for applying first actuating signals to said first body radiating means includes means for producing in each cycle of said first field a radial component along said first pointing vector defined by first body pointing angles with respect to said first body coordinate reference frame thereby forming a first nutating field; and said second means for applying second actuating signals to said second body radiating means includes means for producing in each cycle of said second field a radial component along a second body pointing vector defined by second pointing angles with respect to said second body coordinate reference frame thereby forming a second nutating field.

Apparatus as recited in claim 3 wherein said first body receiving means includes a first means for determining the relative roll of one of said first and second bodies relative to the other of said first and second bodies about one of said directions and said second body receiving means includes a second means for determining the relative roll of one of said first and second bodies relative to the other of said first and second bodies about the other of said directions.

Apparatus as recited in claim 1 wherein:
said means for applying first actuating signals to said first body generating members includes means (219) for including in each cycle of said first field information from which the second body receiving means can determine the distance from said second body to said first body;
said means for applying second actuating signals to said second body generating members includes means for including in each cycle of said second field information from which the first body receiving means can determine the distance from said first body to said second body; and which further comprises means at said first and second bodies for determining said distance.

Apparatus as recited in claim 9 wherein said means for applying first actuating signals to said first body generating members includes means for including in each cycle of said first field phase reference means (219) for establishing a reference point, said means for applying second actuating signals to said second body generating members includes means for including in each cycle of said second field phase reproduction means (249) for establishing the same radiated phase in said second field as the phase of said first field when received at said second body, and said first body receiving means includes phase comparison means (32) for comparing at said first body the phase difference between the phase of said reference point of said first field and the phase of said first field when said second field is received with the phase of said reference point, thereby determining the separation distance between said first body and said second body.

Apparatus as recited in claim 2 wherein each of said radiating means includes at least three independently oriented electromagnetic field generating members and further comprises:
a first multiplexing means (31) coupled to said first body generating members, coupled to said means for applying first actuating signals and coupled to said first receiving means, for permitting use of said first body generating members as said first body receiving means; and a second multiplexing means coupled to said second body generating members, coupled to said means for applying second actuating signals and coupled to said second receiving means, for permitting use of said second body generating members as said second body receiving means.

Apparatus as recited in claim 2 wherein:
said first and second fields having a :Erequency such that the ratio of the wavelength to the distance separating said bodies results in far-field characteristics at said receiving means, said characteristics being utilized by said receiving means for determining said directions.

Apparatus as set forth in claim 2 wherein each cycle of said first and second fields produces at the receiving body at least five independent measurements.

A process for determining the direction between and relative orientation of first and second bodies relative to one another, each body having a coordinate reference frame, said process comprising the steps of:
radiating a first vector field from said first body, said first field having components receivable at said second body from which said second body:
(a) can determine the direction to the first body with respect to the second body coordinate frame;
(b) can define the rotation of said first body coordinate reference frame with respect to said second body coordinate reference frame;
receiving said first field at said second body and:
(a) determining the direction to the first body with respect to the second body coordinate frame;
(b) defining the rotation of said first body coordinate reference frame;
radiating a second vector field from said second body, said second field having components receivable at said first body from which said first body:
(a) can determine the direction to the second body with respect to the first body coordinate frame;
(b) can define the rotation of said second body coordinate reference frame with respect to said first body coordinate reference frame;
receiving said second field at said first body and:
(a) determining the direction to the second body with respect to the first body coordinate frame; and (b) defining the rotation of said second body coordinate reference frame with respect to said first body coordinate reference frame.

The process as set forth in claim 14 wherein said radiating steps include the step of applying actuating signals to at least two independently oriented magnetic field generating members.

The process as set forth in claim 15 which further comprises the step of directing said first and second vector fields toward said second and first bodies, respectively.

The process as set forth in claim 15 wherein said first and second fields have components receivable and processable at the receiving body to produce at least five independent measurements.

The process as set forth in claim 14 further comprising the step of determining the distance between said first and second bodies at one of said bodies.