Add uvsim/wgs84.py: Convert WGS84 to ECEF/ENU coordinates

1 files changed, 97 insertions, 0 deletions

diff --git a/fg21sim/uvsim/wgs84.py b/fg21sim/uvsim/wgs84.py
new file mode 100644
index 0000000..f80e537
--- /dev/null
+++ b/fg21sim/uvsim/wgs84.py
@@ -0,0 +1,97 @@
+# Copyright (c) 2017 Weitian LI <weitian@aaronly.me>
+# MIT license
+
+"""
+WGS84 Earth geodetic coordinate conversion utilities.
+
+NOTE
+----
+The WGS84 coordinates (φ, λ, h) are *ellipsoidal*, not spheroidal
+(geocentric).
+
+References
+----------
+[1] Converting GPS Coordinates (φλh) to Navigation Coordinates (ENU)
+    http://digext6.defence.gov.au/dspace/bitstream/1947/3538/1/DSTO-TN-0432.pdf
+[2] Convert WGS-84 geodetic locations to Cartesian coordinates
+    in a local tangent plane
+    https://gist.github.com/govert/1b373696c9a27ff4c72a
+"""
+
+import numpy as np
+
+
+class Earth:
+    # WGS84 Earth semi-major & semi-minor axis [m]
+    a = 6378137.0
+    b = 6356752.3142
+    # Ellipsoid flatness
+    f = (a-b) / a
+    # Eccentricity
+    e2 = 1.0 - (b/a)**2
+    e = e2 ** 0.5
+
+
+def geodetic2ecef(p):
+    """
+    Convert the WGS84 geodetic coordinate to the ECEF (Earth Centered
+    Earth Fixed) Cartesian coordinate.
+
+    Parameters
+    ----------
+    p : (lon, lat, h)-tuple
+        The WGS84 geodetic point to be converted to ENU coordinate,
+        units: lon, lat -> [deg]; h -> [m]
+
+    Returns
+    -------
+    ecef : (x, y, z)-tuple
+        The converted ECEF coordinate. unit: [m]
+    """
+    lon, lat, h = p
+    phi, lam = np.deg2rad([lon, lat])
+    sin_phi, sin_lam = np.sin([phi, lam])
+    cos_phi, cos_lam = np.cos([phi, lam])
+    chi = np.sqrt(1.0 - Earth.e2 * sin_lam * sin_lam)
+    v = Earth.a / chi
+    x = (v + h) * cos_lam * cos_phi
+    y = (v + h) * cos_lam * sin_phi
+    z = (v*(1-Earth.e2) + h) * sin_lam
+    return (x, y, z)
+
+
+def geodetic2enu(p, ref):
+    """
+    Convert the WGS84 geodetic coordinate (longitude, latitude, height)
+    to East-North-Up coordinates in a local tangent plane that is
+    centered at the reference WGS84 geodetic point.
+
+    Parameters
+    ----------
+    p : (lon, lat, h)-tuple
+        The WGS84 geodetic point to be converted to ENU coordinate,
+        units: lon, lat -> [deg]; h -> [m]
+    ref : (lon0, lat0, h0)-tuple
+        The reference WGS84 geodetic point to determine the local
+        tangent plane.
+
+    Returns
+    -------
+    enu : (east, north, up)-tuple
+        The converted ENU coordinate in the determined local tangent
+        plane. unit: [m]
+    """
+    pxyz = np.array(geodetic2ecef(p))
+    pxyz0 = np.array(geodetic2ecef(ref))
+    dxyz = pxyz - pxyz0
+
+    lon0, lat0, h0 = ref
+    phi0, lam0 = np.deg2rad([lon0, lat0])
+    sin_phi0, sin_lam0 = np.sin([phi0, lam0])
+    cos_phi0, cos_lam0 = np.cos([phi0, lam0])
+    # Rotation
+    M = np.array([[-sin_phi0,          cos_phi0,          0.0],
+                  [-cos_phi0*sin_lam0, -sin_phi0*sin_lam0, cos_lam0],
+                  [cos_phi0*cos_lam0,  sin_phi0*cos_lam0,  sin_lam0]])
+    east, north, up = M.dot(dxyz)
+    return (east, north, up)