Method and apparatus for tracking objects

• US 4,298,874 A
• Filed: 10/24/1978
• Issued: 11/03/1981
• Est. Priority Date: 01/17/1977
• Status: Expired due to Term

• Current Assignee: Kaiser Aerospace & Electronics Corporation (Rtx Corporation)
• Original Assignee: The Austin Company (Kajima Corporation)
• Inventors: Kuipers, Jack
• Primary Examiner(s): Blum, Theodore M.
• Application Number:
  US05/954,126
• Time in Patent Office: 1,106 Days
• Field of Search: 343/100 R, 343/112 D, 343/100 CS, 343/112 R
• US Class Current: 342/463
• CPC Class Codes: G01S 1/42 Conical-scan beacons transmitting signals which indicate at a mobile receiver any displacement of the receiver from the conical-scan axis, e.g. for "beam-riding" missile control

Abstract

Two spaced bodies, each including at least two independently oriented radiating antennas, are in communication with each other by such means as an electromagnetic field. The first body receives radiation transmitted from the second body and establishes the pointing angles to the second body with respect to the first body coordinate reference frame. The field received by the first body can include information defining the second body'"'"'s pointing angles to the first body with respect to the second body'"'"'s coordinate reference frame and the relative roll about their mutually aligned pointing axis. These pointing angles and relative roll are sufficient for determining the orientation of the first body relative to the second body. The second body receives radiation transmitted from the first body and establishes the pointing angles to the first body with respect to the second body. Analogously, radiation received by the second body can include information defining the first body'"'"'s pointing angles with respect to the first body coordinate reference frame to the second body and the relative roll between their mutually aligned pointing axes. As before, this information is sufficient for the second body to determine its orientation relative to the first 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.

A third body, known and defined in the coordinate frame of the first body, can be defined at the second body with respect to the frame of the second body. That is, information is transmitted from the first body and received at the second body which establishes a vector from the second body to the third body thus defining the location of the third body at the second body.

Claims

1. Apparatus for determining a pointing angle to a first body from a second body comprising:

at least two independently oriented first body radiating means coupled to said first body and defining a first reference coordinate frame;

a first means for applying to said first body radiating means first actuating signals for producing a first field radiated in response to said first signals oscillating along a first line of generation and characterizing a first body pointing angle of a first pointing vector with respect to said first reference frame, said first field having receivable components characterized in that at said second body one direction in said first field has unique characteristics with respect to all other directions in said first field;

at least two independently oriented second body receiving means coupled to said second body and defining a second reference coordinate frame for detecting and measuring the receivable components of said first field; and

a second body analyzing means coupled to said second body receiving means for converting said first field components into a second body pointing angle, from said second body to said first body, relative to said second reference coordinate frame.

2. Apparatus as recited in claim 1 further comprising:

at least two independently oriented second body radiating means coupled to said second body;

a second means for applying to said second body radiating means second actuating signals for producing, in response to said second signals, a second field oscillating along a second line of generation and characterizing said second pointing angle of said second pointing vector with respect to said second reference frame;

said second field having receivable components characterized in that at said first body one direction in said second field has unique characteristics with respect to all other directions in said second field;

at least two independently oriented first body receiving means centered about the origin of said first reference coordinate frame for detecting and measuring the receivable components of said second field; and

a first body analyzing means coupled to said first body receiving means for converting said second field components into a first body pointing angle, from said first body to said second body, relative to said first reference coordinate frame.

3. Apparatus as recited in claim 2 wherein said first means for applying signals includes means for including in said signals information characterizing said first body pointing angle from said first body to said second body with respect to said first reference coodinate frame.

4. Apparatus for determining second body pointing angles to a first body from a second body comprising:

independently oriented first body radiating means coupled to said first body and defining a first reference coordinate frame;

a first means for applying to said first body radiating means first actuating signals for radiating first field components rotating in a plane denoted a first plane of rotation and characterizing a first field, said first field having receivable components characterized in that, at said second body, one direction in said first field has unique characteristics with respect to all other directions in said first field and for at least partially characterizing the relative roll angle about an axis between said first and second bodies;

independently oriented second body receiving means coupled to said second body and defining a second reference coordinate frame for detecting and measuring the spatial components of said first field; and

a second body analyzing means coupled to said second body receiving means for using said first field components to determine second body pointing angles, from said second body to said first body, relative to said second reference coordinate frame and for determining the relative roll angle about said axis.

5. Apparatus as recited in claim 4 wherein said first means for applying actuating signals includes means for at least partially characterizing the relative orientation between said first plane of rotation and said first reference coordinate frame.

6. Apparatus as recited in claim 5 further comprising:

independently oriented second body radiating means coupled to said second body;

a second means for applying to said second body radiating means second actuating signals for radiating second field components rotating in a plane denoted a second plane of rotation, and characterizing a second field, said field having receivable components characterized in that, at said first body, one direction in said second field has unique characteristics with respect to all other directions in said second field and for at least partially characterizing the relative roll angle between said first and second bodies about said axis, and the relative orientation between said second plane of rotation and said second reference coordinate frame;

independently oriented first body receiving means coupled to said first body for detecting and measuring spatial components of said second field; and

a first body analyzing means coupled to said first body receiving means for using said second field components to determine first body pointing angles relative to said first reference coordinate frame, and determining the relative roll angle about said axis.

7. Apparatus for determining the direction and roll angle between first and second bodies relative to one another, each body having a coordinate reference frame, said apparatus comprising:

means 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 roll angle between said first body and said second body about said direction;

means 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 roll angle between said first body and said second body about said direction;

means 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 the relative roll angle between said second body and said first body about said direction;

means 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 roll angle between said second body and said first body about said direction.

8. Apparatus as recited in claim 7 wherein:

said means for radiating each cycle of said first field comprises means 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.

9. Apparatus as recited in claim 8 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.

10. Apparatus as recited in claim 9 wherein:

said means for radiating each cycle of said first field from said first body includes means for directing the field so as to track said second body, said first directable field characterizing the direction of a first pointing vector 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.

11. Apparatus as recited in claim 10 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.

12. Apparatus as recited in claim 10 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.

13. Apparatus as recited in claim 10 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 acutating 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.

14. Apparatus as recited in claim 9 wherein said first body receiving means includes a first means for determining the relative orientation of one of said first and second bodies relative to the other of said first and second bodies and said second body receiving means includes a second means for determining the relative orientation of one of said first and second bodies relative to the other of said first and second bodies.

15. Apparatus as recited in claim 7 or 14 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 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.

16. Apparatus as recited in claim 15 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 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 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 receiving means includes phase comparison means 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.

17. Apparatus as recited in claim 8 wherein each of said radiating means includes at least three independently oriented electromagnetic field generating members and further comprises:

a first multiplexing means coupled to said first body generating member, 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.

18. Apparatus as recited in claim 8 wherein:

said first and second fields having a frequency 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.

19. The apparatus as set forth in claim 8 which further comprises:

means at said first body for defining pointing angles from said first body to a remote object relative to said first body coordinate reference frame; and

means at one of said bodies for translating said angles from the first body to said second body coordinate reference frame.

20. The apparatus as set forth in claim 8 which further comprises:

means at said first body for defining a first body object vector to a remote object, said vector being defined initially relative to the coordinate reference frame of said first body;

means at one of said bodies for translating said vector from the first body to the second body coordinate reference frame.

21. The apparatus as set forth in claim 20 wherein said translating means comprises:

means for determining the distance between said first and second bodies at said first body, said distance along with said direction to the second body establishing a reference vector between said first and second bodies;

means at said first body for determining a third vector, said third vector being the third side of a vector triangle including said reference vector and said first body-object vector;

means for establishing at said first body a pseudo coordinate reference frame, said frame having one of its axes defined by said third vector and being displaced from said first body coordinate reference frame through a series of two angles; and

means for transmitting to said second body from said first body;

(a) the pointing angles to the second body from the first body relative to said pseudo frame; and

(b) the magnitude of said third vector.

22. The apparatus as set forth in claim 8 which further comprises:

a remote object;

means at said first body for measuring the distance between said first and second bodies, said distance, in conjunction with said direction to said second body defining a reference vector between said first and second bodies, said reference vector forming one side of a vector triangle, the points of which are coincident with said first and second bodies and said remote object;

means for supplying to said first body at least two component values of said triangle other than said reference vector rendering the same solvable; and

means at said first body for solving said triangle for the desired component value.

23. Apparatus for determining the direction between and relative orientation of a second body relative to a first body, each body having a coordinate reference frame, said apparatus comprising:

means for radiating a first vector field from said first body, the frequency of said field being such that the ratio of the wavelength to the distance separating said bodies results in far-field reception characteristics at said second body, each cycle of said first field having components receivable at said second body and processable to produce at said second body at least five independent measurements from which said second body;

(a) can compute the direction to the first body with respect to the second body coordinate reference frame; and

(b) can compute the rotation of said first body coordinate reference frame with respect to said second body coordinate reference frame;

means at said second body;

(a) for receiving and processing said first field to produce said five independent measurements;

(b) for computing the direction to the first body with respect to the second body coordinate reference frame, said direction computing means utilizing the far-field characteristics of said field; and

(c) for computing the rotation of said first body coordinate reference frame with respect to said second body reference frame.

24. Apparatus as recited in claim 23 wherein:

said means for radiating each cycle of said first field comprises means for applying first actuating signals to at least two independently oriented first body electromagnetic field generating member.s

25. Apparatus as recited in claim 24 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.

26. Apparatus as recited in claim 24 wherein:

said means for radiating each cycle of said first field from said first body includes means for directing the field so as to track said second body;

said first directable field characterizing the direction of a first body pointing vector defined by first body pointing angles with respect to said first coordinate reference frame.

27. Apparatus as recited in claim 26 wherein:

said means for applying first actuating signals includes means for applying a set of discrete signals to said first generating member for radiating first discrete field pulses from said first body generating members, said discrete pulses containing at least two coordinate component carriers.

28. Apparatus as recited in claim 26 wherein:

said means for applying first actuating signals includes means for applying 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.

29. Apparatus as recited in claim 26, 27 or 28 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.

30. Apparatus as recited in claim 26 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 information characterizing said first body pointing angles from said first body to said second body with respect to said first body reference coordinate frame.

31. Apparatus as set forth in claim 24 for further determining the direction between and relative orientation of said first body relative to said second body, said apparatus comprising:

means for radiating a second field from said second body, the frequency of said field being such that the ratio of the wavelength to the distance separating said bodies results in far-field reception characteristics at said first body, each cycle of said second field having components receivable at said first body and processable to produce at said first body at least five independent measurements from which said first body;

(a) can compute the direction to the second body with respect to the first body coordinate reference frame; and

(b) can compute the rotation of said second body coordinate reference frame with respect to said first body coordinate reference frame;

means at said first body;

(a) for receiving and processing said second field to produce said five independent measurements;

(b) for computing the direction to the second body with respect to the first body coordinate reference frame, said direction computing means utilizing the far-field characteristics of said field; and

(c) for computing the rotation of said second body coordinate reference frame with respect to said first body coordinate reference frame.

32. Apparatus as set forth in claim 31 wherein 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.

33. Apparatus as recited in claim 23 further comprising means at said second body for determining the distance from said second body to said first body.

34. Apparatus as recited in claim 32 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 information with which the second body receiving means can determine the distance from said second body to said first body; and

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 with which the first body receiving means can determine the distance from said first body to said second body.

35. Apparatus as recited in claim 34 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 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 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 receiving means includes phase comparison means 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.

36. Apparatus as recited in claim 29 wherein each of said radiating means includes at least three independently oriented electromagnetic field generating members and which further comprises:

a first multiplexing means coupled to said first body generating member, 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 by both said first actuating means and said first 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 receiver means, for permitting use of said second body generating members by both said second actuating means and said second receiving means.

37. The apparatus as set forth in claim 23 which further comprises means at said first body for defining pointing angles from said first body to a remote object relative to said first body coordinate reference frame;

and

means at one of said bodies for translating said angles from the first body to said second body coordinate reference frame.

38. The apparatus as set forth in claim 23 which further comprises means at said first body for defining a first body object vector to a remote object, said vector being defined initially relative to the coordinate reference frame of said first body;

means at one of said bodies for translating said vector from the first body to the second body coordinate reference frame.

39. The apparatus as set forth in claim 23 which further comprises:

a remote object;

means at said second body for measuring the distance between said first and second bodies, said distance, in conjunction with said direction defining a reference vector between said second and first bodies, said reference vector forming one side of a vector triangle, the points of which are coincident with said first and second bodies and said remote object;

means for supplying to said second body at least two component values of said triangle other than said reference vector rendering the same solvable; and

means at said second body for solving said triangle for the desired component value.

40. Apparatus 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 apparatus comprising:

means for radiating a first field from said first body, each cycle of said first field having components receivable at said second body and processable to produce at said second body at least five independent measurements from which said second body;

(a) can compute the direction to the first body with respect to the second body coordinate reference frame; and

(b) can compute the rotation of said first body coordinate reference frame with respect to said second body coordinate reference frame;

means at said second body;

(a) for receiving and processsing said first field to produce said five independent measurements;

(b) for computing the direction to the first body with respect to the second body coordinate reference frame; and

(c) for computing the rotation of said first body coordinate reference frame with respect to said second body coordinate reference frame;

means for radiating a second field from said second body, each cycle of said second field having components receivable at said first body and processable to produce at said first body at least five independent measurements from which said first body;

(a) can compute the direction to the second body with respect to the first body coordinate reference frame; and

(b) can compute the rotation of said second body coordinate reference frame with respect to said first body coordinate reference frame;

means at said first body;

(a) for receiving and processing said second field to produce said five independent measurements;

(b) for computing the direction to the second body with respect to the first body coordinate reference frame; and

(c) for computing the rotation of said second body coordinate reference frame with respect to said first body coordinate reference frame.

41. Apparatus as recited in claim 40 wherein:

said means for radiating each cycle of said first field comprises means 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.

42. Apparatus as recited in claim 41 wherein:

said means for radiating each cycle of said first field from said first body includes means for directing the field so as to track said second body, said first directable field characterizing the direction of a first pointing vector defined by first body pointing angles with respect to said 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 said second coordinate reference frame.

43. Apparatus as recited in claim 42 wherein:

said means for applying first actuating signals includes means for applying 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 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.

44. Apparatus as recited in claim 43 wherein:

said means for applying first actuating signals to said first body radiating means further includes means for producing in each cycle of said first field a radial component along said first pointing vector, thereby forming a first nutating field; and

said second means for applying second actuating signals to said second body radiating means further includes means for producing in each cycle of said second field a radial component along said second body pointing vector, thereby forming a second nutating field.

45. Apparatus as recited in claim 42 wherein:

said means for applying first and second actuating signals to said first and second generating members further includes means for including in each cycle of said fields information from which said first and second body receiving means can determine the relative roll angle between said first and second bodies about their mutually aligned pointing vectors; and

means at said first and second body receiving means for determining the relative roll angle between said first and second bodies about their mutually aligned pointing vectors.

46. Apparatus as recited in claim 45 wherein:

said means for applying first actuating signals to said first body generating members includes means for including in said first field information characterizing said first body pointing angles from said first body to said second body with respect to said first body reference coordinate frame; and

said means for applying second actuating signals to said second body generating members includes means for including in said second field information characterizing said second body pointing angles from said second body to said first body with respect to said second body reference coordinate frame.

47. Apparatus as set forth in claim 41 which further comprises means at at least one of said bodies for determining the distance between said first and second bodies.

48. Apparatus as recited in claim 41 wherein each of said radiating means includes at least three independently oriented electromagnetic field generating members and which further comprises:

a first multiplexing means 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 by both said first actuating means and said first 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 by both said second actuating means and said second receiving means.

49. The apparatus as set forth in claim 40 which further comprises means at said first body for defining pointing angles from said first body to a remote object relative to said first body coordinate reference frame;

and

means at one of said bodies for translating said angles from the first body to said second body coordinate reference frame.

50. The apparatus as set forth in claim 40 which further comprises means at said first body for defining a first body object vector to a remote object, said vector being defined initially relative to the coordinate reference frame of said first body;

means at one of said bodies for translating said vector from the first body to the second body coordinate reference frame.

51. The apparatus as set forth in claim 50 wherein said translating means comprises:

means for determining the distance between said first and second bodies at said first body, said distance along with said direction to the second body establishing a reference vector between said first and second bodies;

means at said first body for determining a third vector, said third vector being the third side of a vector triangle including said reference vector and said first body-object vector;

means for establishing at said first body a pseudo coordinate reference frame, said frame having one of its axes defined by said third vector and being displaced from said first body coordinate reference frame through a series of two angles; and

means for transmitting to said second body from said first body;

(a) the pointing angles to the second body from the first body relative to said pseudo frame; and

(b) the magnitude of said third vector.

52. The apparatus as set forth in claim 40 which further comprises:

a remote object;

means at said second body for measuring the distance between said first and second bodies, said distance, in conjunction with said direction to said first body defining a reference vector between said second and first bodies, said reference vector forming one side of a vector triangle, the points of which are coincident with said first and second bodies and said remote object;

means for supplying to said second body at least two component values of said triangle other than said reference vector rendering the same solvable; and

means at said second body for solving said triangle for the desired component value.

53. Apparatus for determining a second body object vector from a second body to a remote object, said apparatus including a first body, said first and second bodies having coordinate reference frames, said first body having a priori knowledge of the angles and magnitude of a first body object vector between the first body and the object, said apparatus comprising:

means 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 roll angle between said first body and said second body about said direction;

means at said second body for receiving said 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 roll angle between said first body and said second body about said direction;

means for radiating a second field from said second body, said second field having components receivable at said first body from which said first body can determine the direction to the second body with respect to the first body coordinate frame;

means at said first body for receiving said field, said receiving means including means for determining the direction to the second body with respect to the first body coordinate frame;

means at said first body for determining the distance between said first body and said second body, said distance along with said direction to the second body establishing a reference vector between said first and second bodies;

means at said first body for determining a third vector, said third vector being the third side of a vector triangle including said reference vector and said first body object vector, the direction of said third vector being determined relative to said first body coordinate reference frame;

means for establishing at said first body a pseudo coordinate reference frame, said pseudo frame having one of its axes defined by said third vector and being displaced from said first body coordinate reference frame through a series of two angles;

means for transmitting to said second body from said first body;

(a) the direction to the second body from the first body relative to said pseudo frame; and

(b) the magnitude of said third vector.

54. The apparatus as set forth in claim 53 wherein one of said first body receiving and second body radiating means comprises at least two independently oriented electromagnetic field antennas;

wherein the other of said first body receiving and second body radiating means comprises at least three independently oriented electromagnetic field antennas;

wherein one of said first body radiating and second body receiving means comprises at least two independently oriented electromagnetic field antennas; and

wherein the other of said first body radiating and second body receiving means comprises at least three independently oriented electromagnetic field antennas.

55. Apparatus as set forth in claim 54 wherein said means for radiating includes means for directing the field so as to track the receiving body.

56. Apparatus as set forth in claim 55 wherein each of said fields comprises a set of discrete field pulses, said pulses containing at least two coordinate component carriers.

57. Apparatus as set forth in claim 56 wherein each discrete pulse contains a radial component, thereby forming a nutating field.

58. Apparatus as set forth in claim 54 wherein said receiving and radiating antennas at each body comprise single antennas and which further includes means for multiplexing said antennas between receiving and radiating functions.

59. A process for determining the direction and roll angle between 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 relative roll angle between said first body and said second body about said direction;

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 relative roll angle between said first body and said second body about said direction;

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 relative roll angle between said second body and said first body about said direction;

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 relative roll angle between said second body and said first body about said direction.

60. The process as set forth in claim 59 wherein said radiating steps include the step of applying actuating signals to at least two independently oriented magnetic field generating members.

61. The process as set forth in claim 60 which further comprises the step of directing said first and second vector fields toward said second and first bodies, respectively.

62. The process as set forth in claim 60 wherein said first and second fields have components receivable and processable to produce at least five independent measurements and which further comprises the steps of computing the rotation of each coordinate reference frame with respect to the other.

63. The process as set forth in claim 59 further comprising the step of determining the distance between said first and second bodies at one of said bodies.

64. A process for determining the direction between and relative orientation of a second body relative to a first body, each body having a coordinate reference frame, said process comprising the steps of:

radiating a first vector field from said first body, the frequency of said field being such that the ratio of the wavelength to the distance separating said bodies results in far-field reception characteristics at said second body, each cycle of said first field having components receivable at said second body and processable to produce at said second body at least five independent measurements from which said second body;

(a) can compute the direction to the first body with respect to the second body coordinate reference frame; and

(b) can compute the rotation of said first body coordinate reference frame with respect to said second body coordinate reference frame;

receiving and processing said first field at said second body to produce said five independent measurements;

computing at said second body the direction to the first body with respect to the second body coordinate reference frame, said direction computing step utilizing the far-field characteristics of said field; and

computing at said second body the rotation of said first body coordinate reference frame with respect to said second body reference frame.

65. The process as set forth in claim 64 wherein said radiating step includes the step of applying actuating signals to at least two independently oriented magnetic field generating members.

66. The process as set forth in claim 65 which further comprises the step of directing said first and second vector fields toward said second and first bodies, respectively.

67. A process for determining the direction between and the 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, each cycle of said first field having components receivable at said second body and processable to produce at said second body at least five independent measurements from which said second body;

(a) can compute the direction to the first body with respect to the second body coordinate reference frame; and

(b) can compute the rotation of said first body coordinate reference frame with respect to said second body coordinate reference frame;

receiving and processing said first field at said second body to produce said five independent measurements;

computing at said second body the direction to the first body with respect to the second body coordinate reference frame; and

computing at said second body the rotation of said first body coordinate reference frame with respect to said second body coordinate reference frame;

radiating a second vector field from said second body, each cycle of said second field having components receivable at said first body and processable to produce at said first body at least five independent measurements from which said first body;

(a) can compute the direction to the second body with respect to the first body coordinate reference frame; and

(b) can compute the rotation of said second body coordinate reference frame with respect to said first body coordinate reference frame;

receiving and processing said second field at said first field to produce said five independent measurements;

computing at said first body the direction to the second body with respect to the first body coordinate reference frame; and

computing at the first body the rotation of said second body coordinate reference frame with respect to said first body coordinate reference frame.

68. The process as set forth in claim 67 wherein said radiating steps include the step of applying actuating signals to at least two independently oriented magnetic field generating members.

69. The process as set forth in claim 68 which further comprises the step of directing said first and second vector fields toward said second and first bodies, respectively.

70. The process as set forth in claim 69 further comprising the step of determining the distance between said first and second bodies at one of said bodies.