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Positional Coordinate Conversion

IP.com Disclosure Number: IPCOM000115402D
Original Publication Date: 1995-Apr-01
Included in the Prior Art Database: 2005-Mar-30

Publishing Venue

IBM

Related People

Bryne, FT: AUTHOR [+3]

Abstract

The positional coordinate conversion algorithm is used to convert radar slant range, azimuth and altitude measurements into X and Y coordinates in a common planar coordinate system known as the system plane. The method used is a conformal, azimuthal projection or a stereographic projection. As an azimuthal projection it is appropriate for small, approximately square areas. The conformal mapping preserves direction but with dilation errors introduced into distances.

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Positional Coordinate Conversion

      The positional coordinate conversion algorithm is used to
convert radar slant range, azimuth and altitude measurements into X
and Y coordinates in a common planar coordinate system known as the
system plane.  The method used is a conformal, azimuthal projection
or a stereographic projection.  As an azimuthal projection it is
appropriate for small, approximately square areas.  The conformal
mapping preserves direction but with dilation errors introduced into
distances.

      By convention the Earth centered coordinate system referenced
in the discussion is explicitly an Earth-centered, Earth-fixed (ECEF)
coordinate system.  The X axis points at Greenwich meridian, the Z
axis is true north and the Y axis points 90 degree   east of the X
axis.  All longitudes are measured from Greenwich, positive east.

      Throughout the positional coordinate conversion section the
variable 'Z' is assumed to represent the Z axis value relative to the
coordinate system of context.  The variable 'H' is assumed to
represent the height above the spheroid.  Since the algorithm
description applies to only the current target report, time notation
has been deleted from the variables.

      The algorithm accepts slant range, azimuth and altitude
measurements and must compute the corresponding X and Y measurements
in the system plane.  The conversion involves the following steps:
  1.  Convert radar target measurements to radar centered target
       Cartesian coordinates
  2.  Convert radar centered target Cartesian coordinates to ECEF
       target Cartesian coordinates
  3.  Convert ECEF target Cartesian coordinates to geodetic
coordinates
  4.  Convert geodetic coordinates to conformal coordinates
  5.  Perform stereographic projection

The following is a list of inputs required to perform coordinate
conversion: e = Earth's eccentricity NA1983 (e = .081819191) A =
semi-major Earth axis NA1983 (A = 3443.918467 nmi) k = correction
factor for Earth radius (k = .003348)

      The parameters e and A specify a reference spheroid and the
value k determined using the specified spheroid.  It is assumed that
the following latitude, longitude and height information is given
relative to the defined spheroid.  Should the reference spheroid
change, the values given must be adjusted.  Other necessary inputs
include:
  Knowing e and A, the semi-minor Earth axis, B (nmi) can be
   calculated.  The relationship between e, A, and B is

In implementation some data will be constant for a specific center.
Data such as the radar site, the coordinates of the stereoplane
tangency point and the radius of the conformal sphere will remain
constant.  Therefore, this data can be calculated once and stored.

Before the ECEF radar X, Y and Z can be found, the radius of
curvature of the spheroid surface in the east-west direction at the
radar location, N sub er (nmi) must be computed

Given the radar...