METHOD AND APPARATUS FOR GEOMETRICAL DETERMINATION

• US 3,691,560 A
• Filed: 04/21/1969
• Issued: 09/12/1972
• Est. Priority Date: 02/02/1961
• Status: Expired due to Term

• Current Assignee: Calvin M. Hammack
• Original Assignee: Calvin M. Hammack
• Inventors: Calvin M. Hammack, P.O. Box 516
• Primary Examiner(s): Benjamin A. Borchelt
• Assistant Examiner(s): Richard E. Berger
• Application Number:
  US04/817,765
• Time in Patent Office: 1,240 Days
• Field of Search: 343/113DE,106D
• US Class Current: 342/387
• CPC Class Codes: G01S 1/08 Systems for determining direction or position line
• CPC Class Codes: G01S 1/302 Systems in which the direction is determined by using an interferometric type transmitting antenna array
• CPC Class Codes: G01S 11/02 using radio waves G01S19/00 takes precedence
• CPC Class Codes: G01S 11/10 using Doppler effect
• CPC Class Codes: G01S 13/4454 phase comparisons monopulse, i.e. comparing the echo signals received by an interferometric antenna arrangement
• CPC Class Codes: G01S 13/46 Indirect determination of position data
• CPC Class Codes: G01S 13/58 Velocity or trajectory determination systems; Sense-of-movement determination systems
• CPC Class Codes: G01S 13/582 adapted for simultaneous range and velocity measurements
• CPC Class Codes: G01S 13/584 adapted for simultaneous range and velocity measurements
• CPC Class Codes: G01S 13/66 Radar-tracking systems; Analogous systems
• CPC Class Codes: G01S 13/726 Multiple target tracking
• CPC Class Codes: G01S 13/87 Combinations of radar systems, e.g. primary radar and secondary radar
• CPC Class Codes: G01S 13/878 Combination of several spaced transmitters or receivers of known location for determining the position of a transponder or a reflector G01S13/874 takes precedence
• CPC Class Codes: G01S 13/931 of land vehicles
• CPC Class Codes: G01S 2013/466 by Trilateration, i.e. two antennas or two sensors determine separately the distance to a target, whereby with the knowledge of the baseline length, i.e. the distance between the antennas or sensors, the position data of the target is determined
• CPC Class Codes: G01S 2013/932 using own vehicle data, e.g. ground speed, steering wheel direction
• CPC Class Codes: G01S 2205/03 Airborne
• CPC Class Codes: G01S 2205/04 Nautical
• CPC Class Codes: G01S 3/46 using antennas spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
• CPC Class Codes: G01S 5/02 using radio waves using satellite radio beacon systems for determining position G01S19/00
• CPC Class Codes: G01S 5/04 : Position of source determined by a plurality of spaced direction-finders
• CPC Class Codes: G01S 5/14 : Determining absolute distances from a plurality of spaced points of known location

Abstract

This invention relates to a method and means of determining at least one dimension of the position-motion state of one or more points relative to a number of reference points by performing measurements of angular variations or angular differences, or of functions of such angular variations or angular differences. The position-motion state of said point or points is unknown and unbounded by any '"'"''"'"''"'"''"'"'a priori'"'"''"'"''"'"''"'"' information. The apexs of such angular variations or differences are located at the reference points.

Claims

1. A method of determining the direction of a continuous plane wave incident upon an apparatus, said apparatus containing two apertures sensitive to said wave comprising:

Action 1. Mounting said two apertures on an axis sufficiently close together to assure the validity of the assumption that said wave is planar;

Action 2. Rotating the axis through said apertures about an axis of rotation that is nonparallel with said axis joining said apertures;

Action 3. Measuring increment of a trigonometric function resultant from said rotation by measuring increment of the difference of the phases of the signals from said apertures occurring during said rotation;

Action 4. Concurrently with Action 3 measuring increment of the angular orientation of said aperture axis about said axis of rotation relative to the direction of propagation of said wave, said increment of angular orientation being associated with said increment of the difference of the phases;

Action 5. Determining from the results obtained in Action 3 and Action 4 the direction of propagation of said wave relative to said aperture axis.

2. A method of determining the direction of a plane wave incident upon an apparatus, said apparatus comprising a reference frame relative to which the variation of the direction of said wave is unknown and relative to which the direction of said wave is to be determined, said apparatus containing at least two apertures sensitive to said wave comprising:

Action 1. MouNting two of said apertures on an axis sufficiently close together to assure the validity of the assumption that said wave is planar;

Action 2. Rotating the axis through said apertures about an axis of rotation that is nonparallel with said axis joining said apertures;

Action 3. Determining the variation of trigonometric function resultant from said rotation by measuring the variation of the difference of the phases of the signals from said apertures occurring during said rotation;

Action 4. Concurrently with Action 3 measuring the variation of the angular orientation of said aperture axis about said axis of rotation relative to the direction of propagation of said wave, said variation of angular orientation of said aperture axis being associated with said variation of the difference of the phases;

Action 5. Concurrently with Action 3 and Action 4 the further and separate action of measuring the angular orientation of the aperture axis about the axis of revolution relative to said reference frame, said angular orientation of the aperture axis associated with the occurrence of said variation of difference of phases;

Action 6. Employing the results obtained in Action 3, Action 4 and Action 5 determining the direction of propagation of said wave relative to said reference frame.

3. A method of determining the direction of a plane wave as recited in claim 2 further limited by:

In Action 3;

said variation of a trigonometric function being an increment of a trigonometric function;

In Action 4;

said variation of the angular orientation being an increment of the angular orientation.

4. A method of determining the direction of a plane wave as recited in claim 2 further limited by:

In Action 3;

said variation of a trigonometric function being a rate of change of a trigonometric function;

In Action 4;

said variation of the angular orientation being a rate of change of the angular orientation.

5. A method of determining the direction of a plane wave as recited in claim 2 further limited by:

In Action 3;

performing said measuring during a fractional part of a complete revolution of said aperture axis;

In Action 6;

determining said direction relative to said fractional part of a complete revolution of said axis.

6. A method of determining the direction of plane waves incident upon an apparatus comprising a plurality of apertures sensitive to said waves comprising the following actions;

Action 1. Mounting a first pair of said apertures on a first aperture axis sufficiently close together to assure the validity of the assumption that said waves are planar;

Action 2. Mounting a second pair of said apertures on a second aperture axis sufficiently close together to assure the validity of the assumption that said waves are planar, one of which apertures of said second pair of apertures may be common to said first pair of apertures;

Action 3. Mounting said pairs of apertures in an array such that said first aperture axis is nonparallel to said second aperture axis and so that the array may be rotated about an axis of rotation that is nonparallel to two parallel planes, each said plane containing one of said aperture axes and which planes may be coincident;

Action 4. Rotating said array about said axis of rotation;

Action 5. Measuring relative to each of said aperture pairs the variation of a trigonometric function of the bearing of the direction of propagation of said waves relative to said each aperture pair by measuring, relative to each said pair of apertures, the variation of the difference of the phases of the signals from the apertures of each said pair of apertures;

Action 6. Determining from the results obtained in Action 5 a bearing of the direction of wave propagatiOn relative to one of said aperture axes, said last-mentioned bearing lying in a plane perpendicular to said axis of rotation.

7. A method of determining direction data relative to a plurality of separate simultaneous plane waves incident upon an apparatus comprising a plurality of apertures sensitive to said waves comprising the following actions:

Action 1. Mounting one pair of said apertures on an axis sufficiently close together to assure the validity of the assumption that said waves are planar;

Action 2. Mounting another pair of said apertures on a second axis sufficiently close together to assure the validity of the assumption that said waves are planar, one of which apertures of said second pair of apertures may be common to said first pair of apertures;

Action 3. Mounting said two pairs of apertures in an array such that said first aperture axis is non-parallel to said second aperture axis;

Action 4. Measuring relative to each of said aperture pairs the difference between trigonometric functions of the bearings of the directions of propagation of said waves relative to said each aperture pair by measuring the difference between the difference of the phases of the signals from the apertures of each said pair of apertures;

Action 5. Determining from the results obtained in Action 4 a bearing of the direction of propagation of at least one of said plane waves relative to at least one said aperture axes.

8. A method as in claim 7 further defined in that said direction data comprises the direction of at least one of said waves.

9. A method as in claim 7 further defined in that said direction data comprises the angular relationship between two of said plane waves.

10. A method of determining the direction of plane waves incident upon an apparatus comprising a plurality of apertures sensitive to said waves comprising the following actions;

Action 1. Mounting a first pair of apertures on a first axis sufficiently close together to assure the validity of the assumption that said waves are planar;

Action 2. Mounting a second pair of apertures on a second axis sufficiently close together to assure the validity of the assumption that said waves are planar, one of which apertures of said second pair of apertures may be common to said first pair of apertures;

Action 3. Mounting said first pair of apertures and said second pair of apertures in an array such that said first axis is non-parallel to said second axis and so that the array may be rotated about an axis of rotation that is non-parallel to two parallel planes, each said plane containing one of said aperture axes, and which planes may be coincident;

Action 4. Rotating said array about said axis of rotation;

Action 5. Measuring relative to said first pair of apertures and said second pair of apertures the variation of trigonometric function of the bearing of the direction of propagation of said waves relative to said each aperture pair by measuring the variation of the difference of the phases of the signals from the apertures of each said pair of apertures;

Action 6. Determining from the results of Action 5 the bearing of the direction of propagation of said wave relative to the axis of rotation of said aperture array.

11. A method as in claim 10 further defined in that said measurements are rate measurements.

12. A method as in claim 10 further defined in that said measurements are measurements of incremental variations.

13. A method of determining the direction of a receiving equipment from a transmitting equipment and relative to at least one axis determined by said transmitting equipment, said receiving equipment being sufficiently remote from said transmitting equipment that all wave fronts arriving at said receiver from said transmitter may be regarded for practical purposes as being planar and parallel with each other, compRising the following actions:

Action 1. At said transmitting equipment transmitting waves from a plurality of wave apertures;

Action 2. Arranging said apertures in an array of at least two pairs of apertures, at least one of said pairs of apertures being mounted on a separate axis, which axis is non-parallel to the axis of any other of said aperture pairs, and holding the array of said apertures in fixed form so that the positions of any of said apertures with respect to the rest of said apertures is fixed;

Action 3. Rotating said array of apertures about an axis that is non-parallel with the axis of any of said pairs of apertures;

Action 4. Measuring the variation of a trigonometric function of the bearing of said receiver from said transmitting equipment by measuring the variation of the difference between arrival times of waves arriving at the receiver from each aperture of each of said pairs of apertures;

Action 5. Determining from the results obtained in Action 4 the bearing of said receiver relative to at least one of said axes.

14. A method of determining the direction of a receiving equipment from a transmitting equipment and relative to at least one axis determined by said transmitting equipment, said receiving equipment being sufficiently remote from said transmitting equipment that all wave fronts arriving at said receiver from said transmitter may be regarded for practical purposes as being planar and parallel with each other, comprising the following actions;

Action 1. At said transmitting equipment transmitting waves from a plurality of waves apertures;

Action 2. Arranging at least three apertures in an array of at least two pairs of apertures, each of said pairs of apertures being mounted on a separate axis, which axis is nonparallel to the axis of any other of said pairs of aperture, and holding the array of apertures in fixed form so that the positions of any of said apertures with respect to the rest of said apertures is fixed;

Action 3. Rotating said array of apertures about an axis that is nonparallel to the axis of any of said pairs of apertures;

Action 4. Measuring the variation of a trigonometric function of the bearing of said receiver from said transmitting equipment by measuring the variation of the difference between arrival times of waves arriving at the receiver from each aperture of each of said pairs of apertures;

Action 5. Determining the angular orientation of said array of apertures relative to a reference frame. Action 6. Employing the results of Action 4 and Action 5, determining the direction of said receiving apparatus relative to said reference frame.

15. A method of determining the direction of a propagated plane wave or wave group relative to an array of at least three wave apertures coupled to the propagation environment of said wave, said array of apertures being of sufficiently small dimensions that the assumption of a planar wave at pertinent points of the environment is valid, comprising the following actions:

Action 1. Arranging said apertures in an array of apertures, said array being arranged in at lease two pairs of said apertures, each of said pairs of apertures being mounted on a separate axis, which axis is nonparallel to the axis of any other of said aperture pairs, and holding the array of said apertures in fixed form so that the positions of any of said apertures with respect to the rest of said apertures is fixed;

Action 2. Rotating said array of apertures about an axis that is non-parallel with the axis of any of said pairs of apertures;

Action 3. Measuring the variation of a trigonometric function of the bearing of the direction of propagation of said wave or wave group relative to the axis of each aperture pair by measuring the variation of the difference between the phases of signals, which signals are phase dependent upon said rotation;

Action 4. Determining from the results obtained in Action 3 the direction of propagation of said waves relative to at least one of said axes.

16. A method of determining the direction of a propagated plane wave or wave group relative to a plurality of wave apertures coupled to the propagation environment of said wave, the distances between said apertures being sufficiently small that the assumption of a planar wave at pertinent points of the environment is valid, comprising the following actions:

Action 1. Arranging in an array at least one pair of said apertures, each pair of apertures being mounted on a separate axis, which axis is nonparallel to the axis of any other of said aperture pairs, and holding the array of said apertures in fixed form so that the positions of any of said apertures with respect to the rest of said apertures is fixed;

Action 2. Rotating said array of apertures about an axis that is non-parallel with the axis of any of said pairs of apertures;

Action 3. Measuring the variation of a trigonometric function of the bearing of the direction of propagation of said wave or wave group relative to the axis of each aperture pair by measuring the variation of the difference between the phases of signals, which signals are phase dependent upon said rotation;

Action 4. Determining the angular orientation of the array relative to a reference frame;

Action 5. Employing the results of Action 3 and Action 4, determining the direction of the propagation of said wave relative to said reference frame.

17. In an apparatus for determining the at least one dimension of the directional characteristic of a plane wave whose direction is varying, said characteristic comprising direction and variation of direction, said plane wave being incident upon said apparatus, said direction being relative to at least one axis through said apparatus, the combination comprising a first pair of apertures mounted on a first axis and a second pair of apertures mounted on a second axis, separate mixing means connected between the apertures of each pair of said apertures, the output of said mixing means being dependent upon the variation of direction of the incident plane wave, each of said mixing means mixing signals derived from said apertures connected thereto to obtain a difference frequency signal therefrom, separate cycle counting means connected to the output of each of said mixing means counting the cycles of the difference frequency signal derived from said mixing means, means controlling the time during which all of said counting means operate simultaneously, said counting means having means indicating the data determining at least one dimension of said directional characteristic of the incident plane wave.

18. An apparatus as set forth in claim 17 further characterized in that an aperture of said first pair of apertures is common to said second pair of apertures.

19. In an apparatus as in claim 18 further defined in that said directional characteristic comprises at least one bearing between the direction of propagation of said wave and an axis of said apparatus.

20. In an apparatus as in claim 18 further defined in that said directional characteristic comprises the variation of at least one bearing between the direction of propagation of said wave and an axis of said apparatus.

21. An apparatus as set forth in claim 17 further characterized in that there is provided a third pair of apertures mounted on a third axis, and mixing and counting means connected to said last mentioned apertures, said axes so arranged that direction of the said wave is determined in three-dimensional space.

22. An apparatus as set forth in claim 21, further characterized in that an aperture of each of said pairs of apertures is common to the other of said pairs of apertures.

23. In an apparatus for determining at lEast one dimension of the directional characteristic of a plane wave whose direction is varying, said characteristic comprising direction and variation of directions, said plane wave incident upon said apparatus, the combination comprising a first pair of apertures mounted on a first axis and a second pair of apertures mounted on a second axis, said apertures mounted sufficiently close together to insure that the approximation of a plane wave front across the entire group of apertures is valid, separate means sensitive only to variation of the phase difference between the output terminals of the apertures of each pair of said apertures connected thereto, said last mentioned means including means for producing output signals resulting only from the variation of direction of the incident plane wave, means controlling the duration of operation of said last mentioned means, and means associated with said signal producing means indicating data determining at least one dimension of said directional characteristic of the incident plane wave.

24. In an apparatus as in claim 23 further defined in that said directional characteristic comprises at least one bearing between the direction of propagation of said wave and an axis of said apparatus.

25. In an apparatus as in claim 23 further defined in that said directional characteristic comprises the variation of at least one bearing between the direction of propagation of said wave and an axis of said apparatus.

26. An apparatus as set forth in claim 23, further characterized in that an aperture of said first pair of apertures is common to said second pair of apertures.

27. An apparatus as set forth in claim 23, further characterized in that there is provided a third pair of apertures mounted on a third axis and connected thereto similar sensitive and indicating means, said third axis lying at an angle to parallel planes, each said plane containing one of said axes and which planes may be coincident, said third pair of apertures similarly closely spaced to all other of said apertures, said third axis so arranged that the direction of said wave is determined in three-dimensional space.

28. An apparatus as set forth in claim 27, further characterized in that an aperture of each of said pairs of apertures is common to the other two of said pairs of apertures.

29. An apparatus for determining the rate of change of a transcendental function of the angle between the direction of propagation of a plane wave incident on said apparatus, comprising in combination:

two separate antenna means held rigidly a fixed distance apart from each other and remote from any point source of said wave, phase measuring means measuring the phase difference between signals separately derived from said two antennas, the signal level of the instantaneous output of said phase measuring means being linearly related to said phase difference, differentiating means connected to said phase sensitive means, signal amplitude measuring means connected to the output of said differentiating means, all of said means being so arranged that the output indication of the said measuring means indicates the rate of change of a transcendental function of the angle between the line between the phase centers of said two antenna means and the direction of propagation of waves impinging upon said antennas.

30. In a system of apparatus for determining the variation of a trigonometric function of the bearing of a receiver from a transmitter relative to at least one axis through said transmitter, a plurality of transmitting apertures mounted on each of a plurality of axes through said transmitter, means for altering the character of the signal radiated from individual apertures so that the radiation of each aperture may be separately identified at the receiver, means at said receiver determining the variation of the relative times of arrival at said receiver of the signals from the said transmitting apertures as said bearings vary.

31. An apparatus as set forth in cLaim 30, further characterized in that at least two of said axes of apertures intersect each other and one of said transmitting apertures is located at the point of this intersection.

32. In a system of apparatus for determining the variation of trigonometric function of the bearing of a receiver from a transmitter relative to an axis through said transmitter, a pair of transmitting apertures mounted on said axis, means transmitting waves from said apertures at frequencies different from each other, plural detecting means at said receiver, each said detecting means separately detecting the signals from a separate one of said transmitting apertures, measuring means connected to said detecting means measuring the variation with respect to time of the relative phase between said detected signals as said bearing varies.

33. In a system of apparatus as in claim 32, further defined in that said measuring means comprises cycle counting means.

34. In a system of apparatus as in claim 32 defined in that all of said variations are incremental type variations.

35. In a system of apparatus as in claim 32 further defined in that said array comprises only two apertures.

36. In an apparatus for measuring the change of the cosine of the angle between a plane wave incident upon said apparatus and a selected axis, two wave apertures sensitive to said incident wave mounted on said axis, means for supporting said apertures on said axis, mixing means connected between said apertures, cycle counting means connected to said mixing means for counting the cycles of the difference frequency signal from said apertures, and timing means associated with said counting means for regulating the period over which said counting means performs its counting operation.

37. In an apparatus for finding the direction of plane waves incident upon said apparatus, a plurality of aperture means sensitive to said waves, said apertures forming an array of apertures, means rotating said array relative to a reference frame which reference frame is fixed relative to the direction of propogation of said plane wave, and means connected to said apertures measuring the increment type variation of the differences of the arrival times of identical points on said waves at said apertures, said variations resulting from the rotation of said array.

38. An apparatus as described in claim 37, further comprising angle measuring means indicating angular orientation of said array relative to said reference frame.

39. An apparatus as described in claim 37, further comprising means indicating the variation of the angular orientation of said array relative to said reference frame.

40. In an apparatus for finding the direction of plane waves incident upon said apparatus, a plurality of spaced aperture means sensitive to said waves, said apertures forming an array of apertures, said direction being found relative to said array, measuring means connected to said apertures measuring the variation of difference of arrival times of identical points on said waves at said apertures, said variations resulting from the rotating of said array.

41. In an apparatus as recited in claim 40, further comprising:

means for determining the angular variation of said array relative to the direction of said waves occurring during said variation of differences.

42. In an apparatus as recited in claim 40 further defined in that said apparatus is an omnidirectional apparatus.

43. In an apparatus as recited in claim 40 further defined in that said variation of differences of arrival times is change of differences of arrival times.

44. In an apparatus as recited in claim 43 further comprising:

means for determining the angular change of said array relative to the direction of said waves occurring during said change of differences.

45. In an apparatus for finding the direction of plane waves incident upon said apparatus, a plurality of aperture means sensitive to said waves mounted upon a plurality of separate aperture axes, means For rotating said axes, means connected to said apertures measuring the variation of the differences of the arrival times of identical points on said waves at pairs of said apertures, said variations resulting from said rotating.

46. In an apparatus for beaconing and attitude indication, a multidimensional array of wave transmitting apertures;

means for energizing said apertures, means for modifying the signals transmitted from at least some of said apertures so that said signals may be separately identified, and means for rotating said array.

47. An apparatus as described in claim 46, further comprising means for indicating the angular orientation of said array relative to a known reference frame.

48. In a system for beaconing and navigating, a beaconing apparatus located at a known point on a known reference frame, a receiving apparatus located in a navigating craft, said beaconing apparatus comprising at least three wave transmitting apertures disposed in at least two dimensions, means for energizing said apertures, means modifying the signals transmitted from at least some of said apertures so that said signals may be separately identified, means rotating said apertures about a selected point, said receiving apparatus comprising means detecting the signals radiated from said apertures, and means connected to said detecting means determining variations of the differences of the times of arrival at said detecting means of waves transmitted from said apertures, which variations are resultant from the rotation of said array.

49. An omnidirectional system for determining at least one dimension of the otherwise unknown varying directional relationship between apparatus at a first point and apparatus at a second point remote from said first point said relationship comprising unknown angular motion, said system comprising elements as follows:

Element 1. At one of said points wave generating apparatus and at the other of said points wave detecting apparatus responsive to waves generated by said wave generating apparatus;

Element 2. Connected to the apparatus at said first point an array of apertures functional with respect to the waves generated by said wave generating apparatus, the maximum dimension of said array being made negligible relative to the distance between said points;

Element 3. Connected to said detecting apparatus measuring apparatus receiving signals from said detecting apparatus and measuring the variation of at least one trignometric function of the direction of said second point relative to said array and insensitive to any particular direction of said second point relative to said array;

Element 4. Connected to said measuring apparatus recited in Element 3 and receiving information therefrom third apparatus for determining from said information the direction of said second point relative to said array.

50. A system as recited in claim 49 further defined in that said variation is an incremental variation.

51. A system as recited in claim 50 further defined in that said measuring apparatus comprises cycle counting means.

52. A system as recited in claim 49 further defined in that said array is a multidimensional array comprising at least three apertures.

53. A system as recited in claim 49 further defined in said array comprising at least three apertures and at least two aperture axes.

54. A system as recited in claim 49 for determining the directional relationship between apparatus at a first point and apparatus at a second point remote from said first point further defined in that apparatus at said first point is wave receiving apparatus and apparatus at said second point is wave transmitting apparatus.

55. A system as recited in claim 49 for determining the directional relationship between apparatus at a first point and apparatus at a second point remote from said first point further defined in that apparatus at said first point is wave transmitting apparatus and apparatus at said second point is wave receiving apparatus.

56. A system as recited in claim 49 further comprising:

means for rotating said array.

57. An omnidirectional method of determining at least one dimension of the otherwise unknown directional relationship between first apparatus at a first point and second apparatus at a second point remote from said first point, said method comprising the following elements:

Element 1. Establishing at the first one of said points an array of apertures comprising at least two axes of apertures functional with respect to waves transmitted in at least one direction between said first point and said second point, the maximum dimension of said array being negligible relative to the distance between said points;

Element 2. Using signals from said array, measuring the variation of at least one trigonometric function of the angle between said array and said waves and non-responsive to any particular direction of said second point relative to said array;

Element 3. By processing said signals determining at least one dimension of the directional relationship between said second point and said array located at said first point.

58. A method as recited in claim 57 further defined in that said variation is an incremental type variation.

59. A method as recited in claim 58 further defined in Element 2 by using cycle counting means in measuring said incremental type variation.

60. A method as recited in claim 57 further defined in using a multidimensional array comprising at least three apertures.

61. A method as recited in claim 57 further defined in using an array comprising at least three apertures and at least two aperture axes.

62. The method as recited in claim 57 wherein apparatus at said first point is wave receiving apparatus and apparatus at said second point is wave transmitting apparatus.

63. The method as recited in claim 57 wherein the apparatus at said first point is wave transmitting apparatus and the apparatus at said second point is wave receiving apparatus.

64. The method as recited in claim 57 wherein the geographical position of said first point is known and the geographical position of said second point is unknown.

65. The method as recited in claim 57 wherein the geographical position of said second point is known and the geographical position of said first point is unknown.

66. The method as recited in claim 57 further comprising rotating said array to achieve said angular motion.

67. The method as recited in claim 57 further comprising:

Element 4. Rotating said array, Element 5. Measuring precisely the direction of said array relative to a reference frame. Element 6. Using the information resulting from Element 3 and Element 5 determining the direction of said second point from said first point relative to said reference frame.