METHOD AND APPARATUS FOR AUTOMATICALLY DETERMINING POSITION-MOTION STATE OF A MOVING OBJECT

• US 3,866,229 A
• Filed: 09/12/1972
• Issued: 02/11/1975
• Est. Priority Date: 02/02/1961
• Status: Expired due to Term

• Current Assignee: Calvin Miles Hammack
• Original Assignee: Calvin Miles Hammack
• Inventors: Hammack, Calvin Miles
• Primary Examiner(s): Wilbur, Maynard R.
• Assistant Examiner(s): Berger, Richard E.
• Application Number:
  US05/288,429
• Time in Patent Office: 882 Days
• Field of Search: 235/150.27,150.271 343/112R,15,112C,9,16R 356/141
• US Class Current: 342/451
• 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 13/46 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 13/66 Radar-tracking systems; Analogous systems
• CPC Class Codes: G01S 13/87 Combinations of radar systems, e.g. primary radar and secondary radar
• 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 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 at least one reference point by performing a plurality of measurements comprising measurements of angular variations or angular differences, or of functions of such angular variations or angular differences. The apexes of such angular variations or differences are located at the reference points.

Claims

1. A meThod of determining at least one otherwise unknown dimension of the position-motion state of at least one selected point of a plurality of points in space relative to the position of at least one other of said plurality of points;

said plurality of points being divided into two groups of points, each group of points comprising at least one point of said plurality of points;

each point of the first group of points, hereinafter called an apex point, being the apex of at least one angle;

each point of the second group of points, hereinafter called an arm point, being contained in one arm of at least one of said angles and being a point along the trajectory of a moving object;

at least one dimension of the position-motion state of at least one of said second group of points being known a priori;

said method comprising the following elements;

Element 1. Determining relative to a particular one of said apex points angular data related to said particular apex point and at least one said arm point, said angular data being dependent upon the variation of direction of said moving object relative to said apex point which variation is resultant of the motion of said moving object at said last mentioned arm point, Element 2. Performing a plurality of determinations as described in Element 1 such that at least one dimension of the position-motion state of at least one selected point of said plurality of points becomes physically defined relative to the position-motion state of other of said plurality of points by the values of said plurality of determinations, by the known parameters related to said determinations, and by at least one said dimension which one said dimension is at least bounded by a priori data, Element 3. Computing at least one dimension of the positionmotion state of at least one selected point of said plurality of points using the information obtained in Element 1 and Element 2 and at least one said dimension known a priori.

2. A method as described in claim 1 further characterized in that the position of at least one of said apex points is known.

3. A method as described in claim 1 further characterized in that said selected point is an arm point.

4. A method as recited in claim 1, further defined in that said selected point is an apex point.

5. A method as described in claim 1, further defined in that Element 2 comprises performing a redundancy of said determinations, and computing in Element 3 the most probable values for the coordinates of the position of said selected point.

6. A method as described in claim 1, comprising Element 1A. Determining the differences between selected ranges from at least one of said apex points to said arm points, said ranges each being between one of said arm points and one of said apex points;

and further comprising using the information derived in Element 1A in Element 2 and in Element 3.

7. A method as recited in claim 1, further defined in accomplishing Element 2 in such a manner that there exists a finite number of points, hereinafter called false points, whose positions are defined, as well as the position of said selected point, by the determined data and a priori data described in Element 2;

and further defined in performing Element 2 in such a manner that a redundancy of said data is made available; and

employing said redundant data in Element 3 to determine the true selected point.

8. A method as recited in claim 1, further defined in accomplishing Element 2 in such a manner that there exists a finite number of points, hereinafter called false points, whose positions are defined, as well as the position of said selected point, by the determined data and a priori data described in Element 2;

and further defined in that said selected point is at the position of an object and that none of said false points is necEssarily located at the position of any such object; and

determining from physical and mechanical considerations the impossibility or improbability of the existence of the said object at said each false point.

9. A method as described in claim 1, further comprising in Element 3, computing at least one of the coordinates of the position of said selected point in any desired coordinate system.

10. A method as described in claim 1, further defined in that Element 1 comprises determining the range from a single apex point to each arm point.

11. A method as described in claim 1, further defined in that said selected point is an arm point and the position of said last mentioned arm point being determined relative to other of said arm points.

12. A method as described in claim 1, further defined in said selected point being an apex point and at least one dimension of the position-motion state of said last mentioned apex point being determined relative to other of said apex points.

13. A method as recited in claim 1, further comprising;

Element 1A, using the laws of motion and determining thereby relationships between said arm points; and

further defined in using the information derived in Element 1A in performing Element 2 and Element 3.

14. A method as recited in claim 1, further defined in comprising:

Element 1A, determining the variations of selected ranges, said ranges each being between one of said arm points and one of said apex points; and

further defined in using the information derived in Element 1A in performing Element 2 and Element 3.

15. A method as recited in claim 1, further defined in that said unknown dimension is a dimension of position of said selected point.

16. A method as recited in claim 1, further defined in that said unknown dimension is a dimension of motion.

17. A method as recited in claim 1, further defined in employing inertial means at said apex points in performing Element 1.

18. A method as recited in claim 1, further defined in that said dimension known a priori is a dimension of position.

19. A method as recited in claim 1, further defined in that said dimension known a priori is a dimension of motion.

20. A method as recited in claim 1, further defined in Element 1 by determining the variation of at least one trigonometric function of an angle whose apex is at each said apex point, using for the purpose of this determining single aperture wave means.

21. A method as recited in claim 1, further defined in that a plurality of position dimensions define the position of a starting arm point on the path of said moving object;

and further defined in that said last mentioned position dimensions are known a priori.

22. A method as recited in claim 1, further defined in performing Element 1 and Element 2 in such a manner that said unknown dimension of the position-motion state of said selected point in space is redundantly determined and further defined in performing Element 3 in such a manner that the value of said unknown dimension is separately computed using a plurality of separate combinations of the data determined in Element 1 and of the dimensions known a priori;

and further defined in Element 3 in determining weights to be applied to each such last mentioned computation indicating the relative merit of said last mentioned computation; and

further defined in Element 3 in computing a best estimate of the true value of said unknown dimension employing the weighted values separately determined.

23. A method as recited in claim 1 further defined in there being but a single apex point, further defined in employing apparatus at said single apex point which apparatus establishes at least one axis through said single apex point, further defined in employing said apparatus in the peformance of Element 1 and Element 2, and further defined in saId angular data being dependent upon said axis.

24. A method as recited in claim 1 further defined in there being but a single apex point, further defined in Element 1 employing apparatus responsive to the variations of the cosine of the angle between an axis through said apex point and the direction of an arm point from said apex point, and further defined in performing Element 2 employing apparatuses responsive to the variations of angles relative to at least two separate axes through said apex point.

25. A method as recited in claim 1 further defined in there being a plurality of apex points, further defined in performing Element 1 employing apparatus responsive to the variations of the cosine of the angle between an axis through said particular one of said apex points and the direction of an arm point from said particular one of said apex points, and further defined in performing Element 2 employing at least one of such apparatuses at each of said apex points.

26. A method as recited in claim 1 further defined in there being a plurality of said apex points, further defined in there being a plurality of axes through each apex point, each axis of said plurality of axes being established by apparatus responsive to the variations of the cosine of the angle beween said each axis and the direction from said each apex point to said arm point, further defined in all of said axes being fixed relative to one another, and further defined in all of said apex points being fixed in position relative to one another.

27. A method as recited in claim 1 further defined in each apex point being traversed by at least one fixed axis;

there being at each apex point at least two angles hereinafter called '"'"''"'"''"'"''"'"'bearings'"'"''"'"''"'"''"'"' associated with each axis through said each apex point;

one arm of each bearing being coincident with said last mentioned axis and the other arm including one of said arm points;

performing Element 1 by determining relative to a first apex point and a first axis through said first apex point the value of function of a first and a second bearing associated respectively with a first and a second arm point, such a function hereinafter called a '"'"''"'"''"'"''"'"'bearing function'"'"''"'"''"'"''"'"'; and

in Element 2, comprising determining the values of a plurality of bearing functions, all of said plurality of points being included in the arms and apexes of the bearings associated with said plurality of bearing functions.

28. A method as recited in claim 27 further defined in there being but a single apex point;

further defined in there being established by plural wave aperture means a plurality of axes through said single apex point;

further defined in that said bearing function is the difference between the cosines of two bearings relative to the same axis.

29. A method as recited in claim 27 further defined in there being a plurality of apex points;

further defined in there being established by plural wave aperture means a plurality of axes through each said apex point;

further defined in that each said bearing function is the difference between the cosines of two bearings relative to the same axis.

30. A method as recited in claim 1 further defined in said unknown dimension of the position-motion state is a dimension of position;

further defined in that said selected point is an arm point;

further defined in there being established by plural wave aperture means a plurality of axes through each said apex point;

further defined in each said axis being established by two wave apertures spaced from each other;

further defined in there being at each apex point at least two angles hereinafter called '"'"''"'"''"'"''"'"'bearings'"'"''"'"''"'"''"'"' associated with each axis through said each apex point, one arm of each said bearing being coincident with said last-mentioned axis and the other arm including one of said arm points further defined in Element 1 in said angular data being the difference between the cosines of two bearings relative to the same axis;

further defined in Element 2 comprising determining a multiplicity of such data, all the points of said plurality of points being included in the arms and apexes of the bearings associated with said multiplicity of such data.

31. A method as recited in claim 30, further defined in there being but a single apex point and further defined in at least one dimension of position of at least one arm point being known a priori.

32. A method as recited in claim 30 further defined in there being a plurality of apex points and further defined in at least one dimension of position of at least one of said arm points being known a priori.

33. A method of determining at least one dimension of the position-motion state of a moving object relative to a reference frame established by the positions of a plurality of wave apertures;

there being at least one dimension of said position-motion state known a priori;

said moving object constituting a wave aperture defining the position of said moving object and cooperative with said plurality of wave apertures;

said method comprising the following elements;

Element 1. Performing a plurality of simultaneous measurements of only the variations of trigonometric functions of angles whose apexes are at a plurality of separate points on said reference frame and which points on said reference frame are determined by the locations of said wave apertures, each said angle being defined relative to an axis through said point by the locations of the wave apertures which define the position of the apex of said angle, said variations of trigonometric functions being dependent upon the motion of said moving object relative to said reference frame;

Element 2. Computing at least one dimension of the position-motion state of said moving object using simultaneously the dimensions of its position-motion state known a priori and the data resultant of said plurality of simultaneous measurements.

34. A method recited in claim 33 further defined in that said dimension of the position-motion state known a priori is a dimension of position and the dimension of the positive-motion state of the moving object determined by the claimed process is also a dimension of position.

35. A method as recited in claim 33 further defined in that said dimension of the position-motion state of said moving object known a priori is a dimension of position and the dimension of the position-motion state of the moving object determined by the claimed process is a dimension of motion.

36. A method as recited in claim 33 further defined in that said dimension of the position-motion state of said moving object known a priori is a dimension of motion and the dimension of the position-motion state of the moving object determined by the claimed process is a dimension of position.

37. A method as recited in claim 33 further defined in that said dimension of the position-motion state of said moving object known a priori is a dimension of motion and the dimension of the position-motion state of the moving object determined by the claimed process is also a dimension of motion.

38. A method of determining at least one dimension of the position-motion state of a moving object relative to a reference frame upon which is already known at least one dimension of the position-motion state of said moving object;

the position on said reference frame of said moving object being defined by a wave aperture which is a part of said moving object;

said method comprising the following elements;

Element 1. Performing a plurality of simultaneous measurements of only the variations of angles whose apexes are established at a plurality of separate points on said reference frame by a plurality of wave apertures cooperative with the wave aperture of said moving object;

the measured angular variations being variations dependent upon the variations of the directions of said moving object from said separate points owing to the motioN of said moving object on said reference frame. Element 2. Computing at least one dimension of the position-motion state of said moving object using simultaneously at least one known dimension of the position-motion state of said moving object and the data resultant of said plurality of simultaneous measurements.

39. a method as recited in claim 38 further defined in that said one dimension of the position-motion state which is already known is a dimension of position and the dimension of the position-motion state of the moving object determined by the claimed process also is a dimension of position.

40. A method as recited in claim 38 further defined in that said one dimension of the position-motion state which is already known is a dimension of position and the dimension of position-motion state of the moving object determined by the claimed process is a dimension of motion.

41. A method as recited in claim 38 further defined in that said one dimension of the position-motion state which is already known is a dimension of motion and the dimension of position-motion state of the moving object determined by the claimed process is a dimension of position.

42. A method as recited in claim 38 further defined in that said one dimension of the position-motion state which is already known is a dimension of motion and the dimension of the position-motion state of the moving object determined by the claimed process also is a dimension of motion.

43. A system of apparatus for the determination of the position of a moving object in space, comprising a plurality of means measuring the angular variation of a line between said moving object and the point of location of each of said means;

all of said means being located on a common frame relative to which said variation is measured;

said variation being measured from a known direction of said line; and

computing means determining the position of said moving object from said measurements.

44. A system of apparatus for the determination of the variation of position of a moving object in space, comprising a plurality of means measuring the angular variation of a line between said moving object and the point of location of each of said means;

all of said means being located on a common frame relative to which said variation is measured;

said variation being measured from a known direction of said line; and

computing means determining the variation of position of said moving object from said measurements.

45. A multistatic method of determining at least one unknown dimension of the position-motion state of at least one selected point of a plurality of points in space relative to the position of at least one other of said plurality of points;

said plurality of points comprising a first group of points and a second group of points;

said first group of points comprising at least two points;

said second group of points comprising at least one point;

at least one point of said first group of points, hereinafter called an apex point, being the apex of at least one angle;

each point of the second group of points, hereinafter called an arm point, being contained in one arm of at least one of said angles and being a point along the trajectory of a moving object;

said method comprising the following elements;

Element 1. Automatically determining relative to a particular one of said apex points angular data related to an angle at said particular apex point and at least one said arm point, said angular data being dependent upon the variation of the direction of said moving object relative to said apex point which variation is resultant of the motion of said moving object at said last mentioned arm point;

Element 2. Automatically determining independently of any function as described in Element 1 and independently of any angle determining apparatus at any apex point, relative to a plurality of points in said first group of points and relative to at least one Of said arm points, nonvariational geometric data which geometric data is dependent upon at least one dimension of the otherwise unknown position of said moving object;

Element 3. Automatically performing a plurality of determinations as described in Element 1 and in Element 2 such that there exists at least one unknown dimension of the position-motion state of at least one selected point of said plurality of points defined relative to the dimensions of the position-motion state of other of said plurality of points by the values of said plurality of determinations and by the known parameters related to said determinations;

Element 4. Automatically computing at least one dimension of the position-motion state of at least one selected point of said plurality of points using the data obtained in Element 1, Element 2, and Element 3.

46. A method as recited in claim 45 further defined in that said geometric data determined in Element 2 comprises at least one element of data that is linearly dependent upon at least one range to at least one of said arm points from one of said first group of points.

47. A method as recited in claim 45 further defined in that said geometric data determined in Element 2 comprises at least one dimension of the position-motion state of said moving object.

48. A method as recited in claim 45 further defined in that said geometric data determined in Element 2 comprises at least one element of angular data.

49. A method as recited in claim 45 further defined in performing Element 1, Element 2, and Element 3 in such a manner that said unknown dimension of the position-motion state of said selected point in space is redundantly determined, and further defined in performing Element 4 in such a manner that the value of said unknown dimension is separately computed using a plurality of separate combinations of the data determined in Element 1 and in Element 2;

and further defined in Element 3 in determining weights to be applied to each such last mentioned computation indicating the relative merit of said last mentioned computation; and

further defined in Element 4 in computing a best estimate of the true value of said unknown dimension employing the weighted values separately determined.

50. A method as recited in claim 45 further defined in said second group of points comprising but a single arm point, said single arm point being the location of said moving object and further defined in Element 1 in said angular variations being rate variations.

51. A method as recited in claim 45 further defined in that the angular variations recited in Element 1 are incremental variations.

52. A method as recited in claim 45 further defined in that said selected point is a point of said first group of points.

53. A method as recited in claim 45 further defined in that said selected point is a point of said second group of points.

54. A method as recited in claim 45 further defined in that said moving object is a vehicle and further defined in comprising in Element 2 using apparatus aboard said moving vehicle determining relative to a plurality of points in said first group of points nonvariational geometric data which geometric data is dependent upon at least one dimension of the position of said moving object.

55. A method as recited in claim 54 further defined in that said nonvariational geometric data is data relative to at least one angle whose apex is at the point of the position of said moving object.

56. A method as recited in claim 45 further defined in performing Element 2 in such a manner that separate measurement means used in the performance of separate parts thereof operate simultaneously.

57. A method as recited in claim 45 further defined in performing Element 1 in such a manner that separate measurement means used in thE performance of separate parts thereof operate simultaneously.

58. A method as recited in claim 45 further defined in performing Element 1 and Element 2 in such a manner that separate means functional in the performance of each of these elements operates simultaneously with separate means used in the performance of the other element.

59. A method of determining at least one dimension of the otherwise unknown and unbounded position-motion state of at least one selected point of a plurality of points in space relative to the position of at least one other of said plurality of points;

said plurality of points being divided into two groups of points, a first group of points and a second group of points, said first group of points comprising at least two points, said second group of points comprising at least one point;

at least one point of said first group of points, hereinafter called an apex point, being the apex of at least one angle;

each point of the second group of points, hereinafter called an arm point, being contained in one arm of at least one of said angles and being a point along the trajectory of a moving vehicle;

comprising the following elements;

Element 1. Automatically determining relative to a particular one of said apex points angular data related to an angle at said particular apex point and at least one said arm point, said angular data being dependent upon the variation of the direction at said particular apex point of said moving vehicle relative to said particular apex point which variation is resultant of the motion of said moving vehicle at said last mentioned arm point;

Element 2. Using means aboard said moving vehicle independently of any function as described in Element 1 or apparatus used therefor determining at least one dimension of the otherwise unknown and unbounded position-motion state of said vehicle independently of any measurement of direction of said moving vehicle relative to any axis through any apex point which axis does not include an arm point;

Element 3. Automatically performing a plurality of determinations as described in Element 1 and in Element 2 such that at least one unknown dimension of the position-motion state of at least one selected point of said plurality of points is physically defined, geometrically and dynamically, relative to the position-motion state of other of said plurality of points by the values of said plurality of determinations and by the known parameters related to said determinatioins;

Element 4. Automatically computing at least one dimension of the position-motion state of at least one selected point of said plurality of points using the data obtained in Element 1, Element 2, and Element 3.

60. A method as recited in claim 59 further defined in said means aboard said moving vehicle comprises inertial elements.

61. A method as recited in claim 59 further defined in said means aboard said moving vehicle comprising angle determining apparatus.

62. A method as recited in claim 59 further defined in said means aboard said moving vehicle comprising apparatus for determining angles whose apexes are at the position point of said moving vehicle.

63. A method as recited in claim 59 further defined in said means aboard said moving vehicle comprising apparatus for determining variational angular data relative to at least one angle whose apex is at the position point of said moving vehicle.

64. A method as recited in claim 59 further defined in said means aboard said moving vehicle comprising apparatus for determining nonvariational angular data relative to at least one angle whose apex is at the position point of said moving vehicle.

65. A method as recited in claim 59 further defined in said means aboard said moving vehicle comprising inertial apparatus for determining at least one axis through the position point of said vehicle and further comprising means for determining angular data relative to said axis.

66. A method as recited in claim 59 further defined in said means aboard said moving vehicle comprising means cooperative with apparatus at at least one point of said first group of points.

67. A method as recited in claim 59 further defined in said means aboard said mving vehicle comprising means cooperative with means at at least one point of said first group of points for determining nonvariational data linearly dependent upon the range between said last mentioned point and said moving vehicle.

68. A method as recited in claim 59 further defined in said means aboard said moving vehicle comprising means cooperative with means at at least one point of said first group of points for determining variational data linearly dependent upon the range between said last mentioned point and said moving vehicle.

69. A method as recited in claim 59 further defined in said dimension of the position-motion state recited in Element 2 being nominally the same as that dimension of the position-motion state recited in Element 3 and Element 4, and further defined in that the derived value of said dimension computed in Element 4 is the weighted combination of redundant independent determinations of said dimension and is of improved accuracy.

70. A method as recited in claim 59 further defined in employing doppler means in Element 2.

71. A method as recited in claim 59 further defined in performing Element 2 in such a manner that the position of one of said arm points is determined, and further defined in that the dimension of the position-motion state computed in Element 4 is not one of the dimensions of the position determined in Element 2.

72. A method of determining at least one dimension of the otherwise unknown and unbounded position-motion state of at least one selected point of a plurality of points in space relative to the position of at least one other of said plurality of points;

said plurality of points comprising a first group of points and a second group of points;

each of said first group of points comprising at least one point;

each of said second group of points comprising at least one point;

each point of said first group of points hereinafter being called a group one point;

each point of said second group of points hereinafter being called a group two point;

each group two point being a point along the path of a moving object;

said method comprising the following elements;

Element 1. Determining variational angular data relative to at least one angle whose apex is at at least one group two point and at least one of whose arms includes a particular one of said group one points said data being such that the direction of said particular one of said group one points is not determined independently by said data alone relative to any known axis;

Element 2. Performing a plurality of determinations as described in Element 1 such that resultant thereof there becomes physically defined at least one dimension of the position-motion state of at least one selected point of said plurality of points relative to the position-motion state of other of said plurality of points by the values of said plurality of determinations and by the known parameters related to said determinations; and

Element 3. Computing at least one dimension of the position-motion state of at least one selected point of said plurality of points using the information obtained in Element 1 and in Element 2.

73. A method as recited in claim 72 further defined in that the position of at least one of the group one points is known.

74. A method as recited in claim 72 further defined in that the position of at least one of the group two points is known.

75. A method as recited in claim 72 further defined in that said selected point is a group one point.

76. A method as recited in claim 72 further defined in that said selected point is a group two point.

77. A method as recited in claim 72 further defined in that Element 2 comprises performing a redundancy of said determinations, and computing in Element 3 the most probable value for at least one dimension of the position-motion state of said selected point.

78. A method as described in claim 72 further characterized in that said selected point is a group one point and the position of said last mentioned group one point being determined relative to other of said group one points.

79. A method as recited in claim 72 further characterized in that said selected point being a group two point and at least one dimension of the position-motion state of said last mentioned group two point being determined relative to the other of said group two points.

80. A method as recited in claim 72 further comprising Element 1A, determining characteristics of motion of said moving object;

and further characterized in that the information derived in Element 1A is utilized in Element 2 and Element 3.

81. A method as recited in claim 72 further comprising Element 1A, using laws of motion relative to the moving object and determining thereby relationships between said group two points;

and further characterized in using the information derived in Element 1A in performing Element 2 and Element 3.

82. A method as recited in claim 72 further defined in that said moving object is a moving vehicle, and further defined in performing Element 1 using apparatus aboard said moving vehicle.

83. A method as recited in claim 72 further defined in that said moving object is a moving vehicle and further defined in performing Element 1 using inertial mechanisms aboard said moving vehicle.

84. A method as recited in claim 82 further defined in performing Element 1 using star tracking mechanisms aboard said moving vehicle.

85. A method as recited in claim 72 further defined in said angular data being data of the variations of angles between directions of said group one points from said moving object.

86. A method as recited in claim 72 further defined in said angular data being data of variations of angles between at least one axis through said moving object and the directions of said group one points from said moving object.

87. A method as recited in claim 72 further defined in said angular data being data of variations of angles between at least one known axis through said moving object and the directions of said group one points from said moving object.

88. A method as recited in claim 72 further defined in said angular data being data of the variation of trigonometric functions of angles whose apexes are at said moving objects and at least one of whose arms include a group one point.

89. A method as recited in claim 72 further defined in said angular data being data of incremental measurements relative to variations of angles whose apexes are at said moving object and at least one of whose arms includes a group one point.

90. A method as recited in claim 72 further defined in said angular data being data of rate type measurements relative to variations of angles whose apexes are at said moving object and at least one of whose arms include a group one point.

91. A method as defined in claim 72 further comprising Element 1A, by process independent of any process employed in Element 1 determining at least one dimension of the position-motion state of said moving object;

and further defined in employing the data derived in Element 1A, in Element 2 and in Element 3.

92. A method as recited in claim 91 further characterized by the use of inertial means in the performance of Element 1A.

93. A method as recited in claim 91 further characterized by use of doppler means in the performance of Element 1A.

94. A method as recited in claim 91 further characterized by use of automatic navigation means in the performance of Element 1A.

95. A method as recited in claim 91 further characterized by use of ranging means in the performance of Element 1A.

96. A method as recited in claim 91 further characterized by use of star tracking means in the performance of Element 1A.

97. A method as recited in claim 91 further characterized by use of angle measuring means in the performance of Element 1A.

98. A method as recited in claim 72 further comprising Element 1A:

by processes independent of processes employed in Element 1 determining geometric data by doppler means, and further defined in employing data from Element 1A in Element 2 and Element 3.

99. A method as recited in claim 72 further comprising Element 1A:

by processes independent of processes employed in Element 1 determining geometric data by ranging means, and further defined in employing data from Element 1A in Element 2 and Element 3.

100. A method as recited in claim 72 further comprising Element 1A:

by processes independent of processes employed in Element 1 determining geometric data by star tracking means, and further defined in employing data from Element 1A in Element 2 and in Element 3.

101. A method as recited in claim 72 further comprising Element 1A:

by processes independent of processes employed in Element 1 determining geometric data by automatic navigation means, and further defined in employing data from Element 1A in Element 2 and in Element 3.

102. A method as recited in claim 72 further comprising Element 1A:

by processes independent of processes employed in Element 1 determining geometric data by angle measuringn means, and further defined in employing data from Element 1A in Element 2 and in Element 3.

103. A method as recited in claim 72 further comprising Element 1A:

by processes independent of processes employed in Element 1 determining geometric data by inertial means, and further defined in employing data from Element 1A in Element 2 and in Element 3.

104. A method as recited in claim 91 further defined in said dimension of the position-motion state recited in Element 1A being nominally the same as that dimension of the position-motion state recited in Element 2 and Element 3, and further defined in that the derived value of said dimension computed in Element 3 is the weighted combination of redundant independent determinations of said dimension and is of improved accuracy.