Method and System For Determining Altitude, Longitude, and Lattitude From Earth Orthogonal Coordinate System
AssigneeHoneywell International Inc.
InventorsSafet SH Hodzic, Harry Melville Dougherty, III
Life of this patent
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Abstract
A method and system for a method and system is provided for transforming geocentric, rectangular coordinates to geodetic coordinates. A meridian plane containing a given point reckoned in geocentric rectangular coordinates is determined, and a line though the given point and normal to a reference ellipsoid of a geodetic coordinate system is determined. An algebraic solution to intersection of the line with the reference ellipsoid is used to determine the coordinates of the point of intersection, which in turn are used to determine the geodetic latitude and altitude of the given point.
Claims20
In a system comprising a computer processor coupled with a computer-readable storage medium, a method of transforming and outputting geographic location coordinates, the method being implemented in a computer program (i) comprising machine-language logic instructions stored on the computer-readable storage medium and (ii) being executable by the computer processor, the method comprising:
- providing to the computer program spatial coordinates of a given point reckoned in a geocentric rectangular coordinate system, the geocentric rectangular coordinate system comprising three mutually orthogonal axes X, Y, and Z, wherein the spatial coordinates of the given point are X=x0, Y=y0, and Z=z0;
- providing a geodetic coordinate system comprising a reference ellipsoid with (i) a center at X=0, Y=0, and Z=0, (ii) an equatorial plane coincident with the X-Y plane, (iii) a semi-major axis a in the equatorial plane and (iv) a semi-minor axis b in the Z-axis, the ellipsoid thereby being of the form:
- X
- 2
- a
- 2
- +
- Y
- 2
- a
- 2
- +
- Z
- 2
- b
- 2
- =
- 1
- ,
- the surface of the reference ellipsoid being a smooth representation of the surface of the Earth;
- in the geodetic coordinate system, determining a meridian plane containing the given point;
- determining spatial coordinates X=x1, Y=y1, and Z=z1 of a second point lying on the ellipsoid, wherein a line passing through both the second point and the given point lies in the meridian plane and is normal to the ellipsoid at the second point;
- storing machine-logic representations of x1, y1, and z1 in the computer-readable storage medium;
- determining a geodetic longitude 20 of the given point from a longitude function Λ(X, Y) evaluated at X=x0 and Y=y0 according to λ0=Λ(x0, y0)=tan−1(y0/x0);
- determining a geodetic latitude φ0 of the given point using the stored representations of x1, y1, and z1 to evaluate a latitude function φ(X, Y, Z) at X=x1, Y=y1, and Z=z1, the latitude function giving an angle between the line and the equatorial plane at a point of intersection between the line and the equatorial plane;
- determining a geodetic altitude h0 of the given point using the stored representations of x1, y1, and z1 to evaluate an altitude function H(X, Y, Z) at X=x1, Y=y1, and Z=z1, the altitude function giving a length of the line between the given point and the second point;
- and
- outputting a signal representing the determined geodetic latitude φ0, longitude λ0, and altitude h0, wherein φ0, λ0, and h0 are the spatial coordinates of the given point transformed to coordinates of the geodetic coordinate system.
A system for transforming and outputting geographic location coordinates, the system comprising:
- a computer-readable storage medium;
- a computer processor coupled with the computer-readable storage medium;
- machine-language logic instructions stored on the computer-readable storage medium and executable by the computer processor to:
- receive spatial coordinates of a given point reckoned in a geocentric rectangular coordinate system, the geocentric rectangular coordinate system comprising three mutually orthogonal axes X, Y, and Z, wherein the spatial coordinates of the given point are X=x0, Y=y0, and Z=z0;
- render a geodetic coordinate system comprising a reference ellipsoid with (i) a center at X=0, Y=0, and Z=0, (ii) an equatorial plane coincident with the X-Y plane, (iii) a semi-major axis a in the equatorial plane and (iv) a semi-minor axis b in the Z-axis, the ellipsoid thereby being of the form:
- X
- 2
- a
- 2
- +
- Y
- 2
- a
- 2
- +
- Z
- 2
- b
- 2
- =
- 1
- ,
- the surface of the reference ellipsoid being a smooth representation of the surface of the Earth;
- determine a meridian plane containing the given point;
- determine spatial coordinates X=x1, Y=y1, and Z=z1 of a second point lying on the ellipsoid, wherein a line passing through both the second point and the given point lies in the meridian plane and is normal to the ellipsoid at the second point;
- store machine-logic representations of x1, y1, and z1 in the computer-readable storage medium;
- determine a geodetic longitude 21 of the given point from a longitude function Λ(X, Y) evaluated at X=x0 and Y=y0 according to λ=Λ(x0, y0)=tan−1(y0/x0);
- determine a geodetic latitude φ0 of the given point using the stored representations of x1, y1, and z1 to evaluate a latitude function φ(X, Y, Z) at X=x1, Y=y1, and Z=z1, the latitude function giving an angle between the line and the equatorial plane at a point of intersection between the line and the equatorial plane;
- determine a geodetic altitude h0 of the given point using the stored representations of x1, y1, and z1 to evaluate an altitude function H(X, Y, Z) at X=x1, Y=y1, and Z=z1, the altitude function giving a length of the line between the given point and the second point;
- and
- output a signal representing the determined geodetic latitude φ0, longitude λ0, and altitude h0, wherein φ0, λ0, and h0 are the spatial coordinates of the given point transformed to coordinates of the geodetic coordinate system.
Dependencies are inferred from the claim text.