Plural information display for navigation

• US 5,369,589 A
• Filed: 09/15/1993
• Issued: 11/29/1994
• Est. Priority Date: 09/15/1993
• Status: Expired due to Fees

• Current Assignee: Trimble Navigation Limited (Trimble Inc.)
• Original Assignee: Trimble Navigation Limited (Trimble Inc.)
• Inventors: Steiner, Glenn C.
• Primary Examiner(s): Black, Thomas G.
• Assistant Examiner(s): NGUYEN, TAN QUANG
• Application Number:
  US08/121,990
• Time in Patent Office: 440 Days
• Field of Search: 364/449, 364/444, 364/429, 364/424.02, 364/451, 364/458, 364/459, 364/424.06, 364/447, 340/988, 340/990-995, 340/705, 340/722, 340/724, 224/164, 224/177, 342/47-49, 342/119, 342/160
• US Class Current: 701/200
• CPC Class Codes: G01C 21/203 Specially adapted for sailing ships
• CPC Class Codes: G01C 23/00 Combined instruments indicating more than one navigational value, e.g. for aircraft; Combined measuring devices for measuring two or more variables of movement, e.g. distance, speed or acceleration
• CPC Class Codes: G01S 7/22 Producing cursor lines and indicia by electronic means
• CPC Class Codes: G05D 1/106 Change initiated in response to external conditions, e.g. avoidance of elevated terrain or of no-fly zones

Abstract

Apparatus for visually displaying simultaneously on one screen two variables that characterize the path followed by a land, marine or airborne vessel with reference to a preselected or ideal path that extends from a beginning point to an ending point. Using two distinguishable icons or other indicia for the two variables, the screen displays a single one-dimensional scale and displays the two indicia, each of which represents one of the following differences: (1) the difference between at least one of the two horizontal location coordinates for the present vessel location and for a nearest point on the preselected path; (2) the difference between the elevation coordinates for the present vessel location and for a nearest point on the preselected path; (3) the difference between the present horizontal bearing angle of the vessel path and the horizontal bearing angle along the preselected path at a nearest point on the preselected path; and (4) the difference between the present vertical bearing angle of the vessel path and the vertical bearing angle along the preselected path at a nearest point on the preselected path. Alternatively, the screen may display two one-dimensional scales with either two indicia, three indicia or two mutually exclusive sets of two indicia. Alternatively, two indicia may be used to define the size of a rectangle and the quadrant it appears in, for representation of the two indicia.

Claims

1. Apparatus for display of variables that characterize a path followed by a land, marine or airborne vessel, the apparatus comprising:

a computer having an associated memory unit that contains at least two of the following four vessel path variables for a preselected path that extends between a beginning path point and an ending path point;

(1) first and second horizontal location coordinates, determined in a selected approximately horizontal plane, of a location on the preselected path;

(2) an elevation coordinate, determined approximately perpendicular to the selected approximately horizontal plane, of a location on the preselected path;

(3) horizontal bearing angle ("horizontal angle") in the selected horizontal plane at a location along the preselected path; and

(4) vertical bearing angle ("vertical angle") in a selected vertical plane approximately perpendicular to the selected horizontal plane, at a location along the selected path;

vessel path characterization means for determining, at each of a sequence of two or more times, at least two of the following four vessel path variables;

(1) first and second horizontal location coordinates, determined in the selected approximately horizontal plane, of the present vessel location;

(2) an elevation coordinate, determined in the selected vertical plane, of the present vessel location;

(3) the present horizontal angle of the vessel path; and

(4) the present vertical angle of the vessel path;

first comparator means, connected to the microprocessor and to the vessel path characterization means, for determining a point on the preselected path for which preselected path vessel variable values are available in the microprocessor memory and for which that point is nearest to the present vessel location (referred to as the nearest point on the preselected path);

second comparator means, connected to the first comparator means, for determining the differences, between a value for the present vessel location and the corresponding value for the nearest point on the preselected path, of at least two of the following four variables;

(1) a linear combination of least two of the first horizontal location coordinate, a second horizontal location coordinate and the elevation coordinate;

(2) a choice of one of the first horizontal location coordinate, the second horizontal location coordinate and the elevation coordinate;

(3) the horizontal angle of the vessel; and

(4) the vertical angle of the vessel; and

a display screen, connected to the second comparator means and having two one-dimensional scales that lie along a single axis and are interleaved with each other, the first and second scales having movable first and second variable indicia, where the first indicium visually displays a first variable difference and the second indicium displays a second variable difference that is distinct from the first variable difference, as determined by the second comparator means.

2. The apparatus of claim 1, wherein said linear combination is formed from said first horizontal coordinate difference and said second horizontal coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said horizontal angle along said preselected path.

3. The apparatus of claim 1, wherein said linear combination is formed from said first horizontal coordinate difference and said elevation coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said vertical angle along said preselected path.

4. Apparatus for display of variables that characterize a path followed by a land, marine or airborne vessel, the apparatus comprising:

a computer having an associated memory unit that contains at least two of the following four vessel path variables for a preselected path that extends between a beginning path point and an ending path point;

(1) first and second horizontal location coordinates, determined in a selected approximately horizontal plane, of a location on the preselected path;

(2) an elevation coordinate, determined approximately perpendicular to the selected approximately horizontal plane, of a location on the preselected path;

(3) horizontal bearing angle ("horizontal angle") in the selected horizontal plane at a location along the preselected path; and

(4) vertical bearing angle ("vertical angle") in a selected vertical plane approximately perpendicular to the selected horizontal plane, at a location along the selected path;

vessel path characterization means for determining, at each of a sequence of two or more times, at least two of the following four vessel path variables;

(1) first and second horizontal location coordinates, determined in the selected approximately horizontal plane, of the present vessel location;

(2) an elevation coordinate, determined in the selected vertical plane, of the present vessel location;

(3) the present horizontal bearing angle of the vessel path; and

(4) the present vertical angle of the vessel path;

first comparator means, connected to the microprocessor and to the vessel path characterization means, for determining a point on the preselected path for which preselected path vessel variable values are available in the microprocessor memory and for which that point is nearest to the present vessel location (referred to as the nearest point on the preselected path);

second comparator means, connected to the first comparator means, for determining the differences, between a value for the present vessel location and the corresponding value for the nearest point on the preselected path, of at least two of the following four variables;

(1) a linear combination of least two of the first horizontal location coordinate, a second horizontal location coordinate and the elevation coordinate;

(2) a choice of one of the first horizontal location coordinate, the second horizontal location coordinate and the elevation coordinate;

(3) the horizontal angle of the vessel; and

(4) the vertical angle of the vessel; and

a display screen, connected to the second comparator memos and having first and second approximately perpendicular one-dimensional scales with movable first and second variable indicia on the first and second scales, respectively, where the first indicium visually displays a first variable difference and the second indicium displays a second variable difference that is distinct from the first variable difference, as determined by the second comparator means.

5. The apparatus of claim 4, wherein said linear combination is formed from said first horizontal coordinate difference and said second horizontal coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said horizontal angle along said preselected path.

6. The apparatus of claim 4, wherein said linear combination is formed from said first horizontal coordinate difference and said elevation coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said vertical angle along said preselected path.

7. Apparatus for display of variables that characterize a path followed by a land, marine or airborne vessel, the apparatus comprising:

a computer having an associated memory unit that contains at least two of the following four vessel path variables for a preselected path that extends between a beginning path point and an ending path point;

(1) first and second horizontal location coordinates, determined in a selected approximately horizontal plane, of a location on the preselected path;

(2) an elevation coordinate, determined approximately perpendicular to the selected approximately horizontal plane, of a location on the preselected path;

(3) horizontal bearing angle ("horizontal angle") in the selected horizontal plane at a location along the preselected path; and

(4) vertical bearing angle ("vertical angle") in a selected vertical plane approximately perpendicular to the selected horizontal plane, at a location along the selected path;

vessel path characterization means for determining, at each of a sequence of two or more times, at least three of the following four vessel path variables;

(1) first and second horizontal location coordinates, determined in the selected approximately horizontal plane, of the present vessel location;

(2) an elevation coordinate, determined in the selected vertical plane, of the present vessel location;

(3) the present horizontal angle of the vessel path; and

(4) the present vertical angle of the vessel path;

first comparator means, connected to the microprocessor and to the vessel path characterization means, for determining a point on the preselected path for which preselected path vessel variable values are available in the microprocessor memory and for which that point is nearest to the present vessel location (referred to as the nearest point on the preselected path);

second comparator means, connected to the first comparator means, for determining the differences, between a value for the present vessel location and the corresponding value for the nearest point on the preselected path, of at least three of the following four variables;

(1) a linear combination of least two of the first horizontal location coordinate, a second horizontal location coordinate and the elevation coordinate;

(2) a choice of one of the first horizontal location coordinate, the second horizontal location coordinate and the elevation coordinate;

(3) the horizontal angle of the vessel; and

(4) the vertical angle of the vessel; and

a display screen, connected to the second comparator means and having first and second one-dimensional scales that lie along a single axis and are interleaved with each other, the first and second scales having movable first and second variable indicia, respectively, where the first indicium visually displays a first variable difference and the second indicium displays a second variable difference that is distinct from the first variable difference, and having a third one-dimensional scale that extends in a direction different from that of the first and second scales, where the third scale has a movable third indicium that visually displays a third variable difference that is distinct from the first variable difference and from the second variable difference, as determined by the second comparator means.

8. The apparatus of claim 7, wherein said linear combination is formed from said first horizontal coordinate difference and said second horizontal coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said horizontal angle along said preselected path.

9. The apparatus of claim 7, wherein said linear combination is formed from said first horizontal coordinate difference and said elevation coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said vertical angle along said preselected path.

10. Apparatus for display of variables that characterize a path followed by a land, marine or airborne vessel, the apparatus comprising:

a computer having an associated memory unit that contains at least two of the following four vessel path variables for a preselected path that extends between a beginning path point and an ending path point;

(1) first and second horizontal location coordinates, determined in a selected approximately horizontal plane, of a location on the preselected path;

(2) an elevation coordinate, determined approximately perpendicular to the selected approximately horizontal plane, of a location on the preselected path;

(3) horizontal bearing angle ("horizontal angle") in the selected horizontal plane at a location along the preselected path; and

(4) vertical bearing angle ("vertical angle") in a selected vertical plane approximately perpendicular to the selected horizontal plane, at a location along the selected path;

vessel path characterization means for determining, at each of a sequence of two or more times, the following four vessel path variables;

(1) first and second horizontal location coordinates, determined in the selected approximately horizontal plane, of the present vessel location;

(2) an elevation coordinate, determined in the selected vertical plane, of the present vessel location;

(3) the present horizontal angle of the vessel path; and

(4) the present vertical angle of the vessel path;

first comparator means, connected to the microprocessor and to the vessel path characterization means, for determining a point on the preselected path for which preselected path vessel variable values are available in the microprocessor memory and for which that point is nearest to the present vessel location (referred to as the nearest point on the preselected path);

second comparator means, connected to the first comparator means, for determining the differences, between a value for the present vessel location and the corresponding value for the nearest point on the preselected path, of the following four variables;

(1) a linear combination of least two of the first horizontal location coordinate, a second horizontal location coordinate and the elevation coordinate;

(2) a choice of one of the first horizontal location coordinate, the second horizontal location coordinate and the elevation coordinate;

(3) the horizontal angle of the vessel; and

(4) the vertical angle of the vessel; and

a display screen, connected to the second comparator means and having first and second one-dimensional scales that lie along a single first axis and are interleaved with each other, the first and second scales having movable first and second variable indicia, respectively, where the first indicium visually displays a first variable difference and the second indicium displays a second variable difference that is distinct from the first variable difference, and having third and fourth one-dimensional scales that lie along a single second axis and are interleaved with each other, the third and fourth scales having movable third and fourth variable indicia, respectively, where the third indicium visually displays a third variable difference that is distinct from the first and second variable differences, and the fourth indicium displays a fourth variable difference that is distinct from the first, second and third variable differences, as determined by the second comparator means, where the second axis extends in a direction different from that of the first axis.

11. The apparatus of claim 10, wherein said linear combination is formed from said first horizontal coordinate difference and said second horizontal coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said horizontal angle along said preselected path.

12. The apparatus of claim 10, wherein said linear combination is formed from said first horizontal coordinate difference and said elevation coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said vertical angle along said preselected path.

13. Apparatus for display of variables that characterize a path followed by a land, marine or airborne vessel, the apparatus comprising:

a computer having an associated memory unit that contains at least two of the following four vessel path variables for a preselected path that externals between a beginning path point and an ending path point;

(1) first and second horizontal location coordinates, determined in a selected approximately horizontal plane, of a location on the preselected path;

(2) an elevation coordinate, determined approximately perpendicular to the selected approximately horizontal plane, of a location on the preselected patio;

(3) horizontal bearing angle ("horizontal angle") in the selected horizontal plane at a location along the preselected path; and

(4) vertical bearing angle ("vertical angle") in a selected vertical plane approximately perpendicular to the selected horizontal plane, at a location along the selected path;

vessel path characterization means for determining, at each of a sequence of two or more times, the following four vessel path variables;

(1) first and second horizontal location coordinates, determined in the selected approximately horizontal plane, of the present vessel location;

(2) an elevation coordinate, determined in the selected vertical plane, of the present vessel location;

(3) the present horizontal angle of the vessel path; and

(4) the present vertical angle of the vessel path;

first comparator means, connected to the microprocessor and to the vessel path characterization means, for determining a point on the preselected path for which preselected path vessel variable values are available in the microprocessor memory and for which that point is nearest to the present vessel location (referred to as the nearest point on the preselected path);

second comparator means, connected to the first comparator means, for determining the differences, between a value for the present vessel location and the corresponding value for the nearest point on the preselected path, of the following four variables;

(1) a linear combination of least two of the first horizontal location coordinate, a second horizontal location coordinate and the elevation coordinate (the "linear combination difference");

(2) a choice of one of the first horizontal location coordinate, the second horizontal location coordinate and the elevation coordinate (the "chosen coordinate difference");

(3) the horizontal angle of the vessel (the "horizontal angle difference"); and

(4) the vertical angle of the vessel (the "vertical angle difference"); and

a display screen, connected to the second comparator means, having first and second axes that are approximately perpendicular to each other and having third and fourth axes that are approximately parallel to the first and second axes, respectively, where the intersection of the first and second axes ("first intersection") represents the present location of the vessel and the intersection of the third and fourth axes ("second intersection") represents the nearest point to the present vessel location on the ideal path, where the parallel projections of the second intersection on the first axis and on the second axis are proportional to the linear combination difference and to the chosen coordinate difference, respectively.

14. The apparatus of claim 13, wherein said linear combination is formed from said first horizontal coordinate difference and said second horizontal coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said horizontal angle along said preselected path.

15. The apparatus of claim 13, wherein said linear combination is formed from said first horizontal coordinate difference and said elevation coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said vertical angle along said preselected path.

16. The apparatus of claim 13, wherein said display screen also displays an indicium with location coordinates, expressed with reference to said first and second axes, that are proportional to said horizontal angle difference and to said vertical angle difference, respectively.

17. Apparatus for display of variables that characterize a path followed by a land, marine or airborne vessel, the apparatus comprising:

a computer having an associated memory unit that contains at least two the following four vessel path variables for a preselected path that extends between a beginning path point and an ending path point;

(1) first and second horizontal location coordinates, determined in a selected approximately horizontal plane, of a location on the preselected path;

(2) an elevation coordinate, determined approximately perpendicular to the selected approximately horizontal plane, of a location on the preselected path;

(3) horizontal bearing angle ("horizontal angle") in the selected horizontal plane at a location along the preselected path; and

(4) vertical bearing angle ("vertical angle") in a selected vertical plane approximately perpendicular to the selected horizontal plane, at a location along the selected path;

vessel path characterization means for determining, at each of a sequence of two or more times, the following four vessel path variables;

(1) first and second horizontal location coordinates, determined in the selected approximately horizontal plane, of the present vessel location;

(2) an elevation coordinate, determined in the selected vertical plane, of the present vessel location;

(3) the present horizontal angle of the vessel path; and

(4) the present vertical angle of the vessel path;

first comparator means, connected to the microprocessor and to the vessel path characterization means, for determining a point on the preselected path for which preselected path vessel variable values are available in the microprocessor memory and for which that point is nearest to the present vessel location (referred to as the nearest point on the preselected path);

second comparator means, connected to the first comparator means, for determining the differences, between a value for the present vessel location and the corresponding value for the nearest point on the preselected path, of the following four variables;

(1) a linear combination of least two of the first horizontal location coordinate, a second horizontal location coordinate and the elevation coordinate (the "linear combination difference");

(2) a choice of one of the first horizontal location coordinate, the second horizontal location coordinate and the elevation coordinate (the "chosen coordinate difference");

(3) the horizontal angle of the vessel (the "horizontal angle difference"); and

(4) the vertical angle of the vessel (the "vertical angle difference"); and

a display screen, connected to the second comparator means, having first and second axes that are approximately perpendicular to each other, the screen displaying a sequence of M (≧

1) rectangles R₁ , . . . , R_M with first and second sides approximately parallel to the first and second axes, respectively, where the first and second sides of rectangle R_m (m=1,2, . . . , M) have length Δ

w_m and Δ

e_m, respectively, with Δ

w_m ≦

Δ

w_m-1 and Δ

e_m ≦

Δ

e_m-1 for m=2, . . . , M, and the lengths Δ

w_m and Δ

e_m are proportional to selected maximum permitted errors in the linear combination difference and in the chosen coordinate difference, respectively, at a location along the vessel path corresponding to the integer m, and where the interior of the rectangle R_m contains an indicium I_m whose location has Cartesian coordinates, expressed with reference to the first and second axes, are proportional to the linear combination difference and to the chosen coordinate difference, respectively.

18. The apparatus of claim 17, wherein said linear combination is formed from said first horizontal coordinate difference and said second horizontal coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said horizontal angle along said preselected path.

19. The apparatus of claim 17, wherein said linear combination is formed from said first horizontal coordinate difference and said elevation coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said vertical angle along said preselected path.

20. Apparatus for display of variables that characterize a path followed by a land, marine or airborne vessel, the apparatus comprising:

a computer having an associated memory unit that contains at least two the following four vessel path variables for a preselected path that extends between a beginning path point and an ending path point;

(1) first and second horizontal location coordinates, determined in a selected approximately horizontal plane, of a location on the preselected path;

(2) an elevation coordinate, determined approximately perpendicular to the selected approximately horizontal plane, of a location on the preselected path;

(3) horizontal bearing angle ("horizontal angle") in the selected horizontal plane at a location along the preselected path; and

(4) vertical bearing angle ("vertical angle") in a selected vertical plane approximately perpendicular to the selected horizontal plane, at a location along the selected path;

vessel path characterization means for determining, at each of a sequence of two or more times, the following four vessel path variables;

(1) first and second horizontal location coordinates, determined in the selected approximately horizontal plane, of the present vessel location;

(2) an elevation coordinate, determined in the selected vertical plane, of the present vessel location;

(3) the present horizontal angle of the vessel path; and

(4) the present vertical angle of the vessel path;

first comparator means, connected to the microprocessor and to the vessel path characterization means, for determining a point on the preselected path for which preselected path vessel variable values are available in the microprocessor memory and for which that point is nearest to the present vessel location (referred to as the nearest point on the preselected path);

second comparator means, connected to the first comparator means, for determining the differences, between a value for the present vessel location and the corresponding value for the nearest point on the preselected path, of the following four variables;

(1) a linear combination of least two of the first horizontal location coordinate, a second horizontal location coordinate and the elevation coordinate (the "linear combination difference");

(2) a choice of one of the first horizontal location coordinate, the second horizontal location coordinate and the elevation coordinate (the "chosen coordinate difference");

(3) the horizontal angle of the vessel (the "horizontal angle difference"); and

(4) the vertical angle of the vessel (the "vertical angle difference"); and

a display screen, connected to the second comparator means, having first and second axes that are approximately perpendicular to each other and that form first, second, third and fourth quadrants of the screen, the screen displaying a rectangle with first and second sides approximately coinciding with portions of the first axis and the second axis, respectively, with the length of the first side and of the second side being proportional to the magnitudes of the linear combination difference and the chosen coordinate difference, respectively, where the rectangle generally lies (i) in the first quadrant, (ii) in the second quadrant, (iii) in the third quadrant or (iv) in the fourth quadrant if the linear combination difference LCD and the chosen coordinate difference CCD satisfy the respective relations (i) LCD>

0 and CCD>

0, (ii) LCD<

0 and CCD>

0, (iii) LCD<

0 and CCD<

0, and (iv) LCD>

0 and CCD<

0.

21. The apparatus of claim 20, wherein said linear combination is formed from said first horizontal coordinate difference and said second horizontal coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said horizontal angle along said preselected path.

22. The apparatus of claim 20, wherein said linear combination is formed from said first horizontal coordinate difference and said elevation coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said vertical angle along said preselected path.

23. Apparatus for display of variables that characterize a path followed by a land, marine or airborne vessel, the apparatus comprising:

a computer having an associated memory unit that contains at least two the following four vessel path variables for a preselected path that extends between a beginning path point and an ending path point;

(1) first and second horizontal location coordinates, determined in a selected approximately horizontal plane, of a location on the preselected path;

(2) an elevation coordinate, determined approximately perpendicular to the selected approximately horizontal plane, of a location on the preselected path;

(3) horizontal bearing angle ("horizontal angle") in the selected horizontal plane at a location along the preselected path; and

(4) vertical bearing angle ("vertical angle") in a selected vertical plane approximately perpendicular to the selected horizontal plane, at a location along the selected path;

vessel path characterization means for determining, at each of a sequence of two or more times, the following four vessel path variables;

(1) first and second horizontal location coordinates, determined in the selected approximately horizontal plane, of the present vessel location;

(2) an elevation coordinate, determined in the selected vertical plane, of the present vessel location;

(3) the present horizontal angle of the vessel path; and

(4) the present vertical angle of the vessel patio;

first comparator means, connected to the microprocessor and to the vessel path characterization means, for determining a point on the preselected path for which preselected path vessel variable values are available in the microprocessor memory and for which that point is nearest to the present vessel location (referred to as the nearest point on the preselected path);

second comparator means, connected to the first comparator means, for determining the differences, between a value for the present vessel location and the corresponding value for the nearest point on the preselected path, of the following four variables;

(1) a linear combination of least two of the first horizontal location coordinate, a second horizontal location coordinate and the elevation coordinate (the "linear combination difference");

(2) a choice of one of the first horizontal location coordinate, he second horizontal location coordinate and the elevation coordinate (the "chosen coordinate difference");

(3) the horizontal angle of the vessel (the "horizontal angle difference"); and

(4) the vertical angle of the vessel (the "vertical angle difference"); and

a display screen, connected to the second comparator means, having first and second axes that are approximately perpendicular to each other and that form first, second, third and fourth quadrants of the screen, the screen displaying a rectangle with first and second sides approximately coinciding with portions of the first axis and the second axis, respectively, with the length of the first side and of the second side being proportional to the magnitudes of the linear combination difference and the chosen coordinate difference, respectively, where the rectangle generally lies (i) in the first quadrant, (ii) in the second quadrant, (iii) in the third quadrant or (iv) in the fourth quadrant if the linear combination difference LCD and the chosen coordinate difference CCD satisfy the respective relations (i) LCD<

0 and CCD<

0, (ii) LCD CCD<

0, (iii) LCD>

0 and CCD<

0, and (iv) LCD<

0 and CCD>

0.

24. The apparatus of claim 23, wherein said linear combination is formed from said first horizontal coordinate difference and said second horizontal coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said horizontal angle along said preselected path.

25. The apparatus of claim 23, wherein said linear combination is formed from said first horizontal coordinate difference and said elevation coordinate difference, and said linear combination has weighting coefficients that depend upon the sine and cosine of said vertical angle along said preselected path.