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geoloc.py
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geoloc.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright (c) 2011, 2012, 2013, 2014, 2015.
# Author(s):
# Martin Raspaud <martin.raspaud@smhi.se>
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
"""Module to compute geolocalization of a satellite scene.
"""
# TODO:
# - Attitude correction
# - project on an ellipsoid instead of a sphere
# - optimize !!!
# - test !!!
import numpy as np
from numpy import cos, sin, sqrt
from datetime import timedelta
from pyorbital.orbital import Orbital
a = 6378.137 # km
b = 6356.75231414 # km, GRS80
# b = 6356.752314245 # km, WGS84
def geodetic_lat(point, a=a, b=b):
x, y, z = point
r = np.sqrt(x * x + y * y)
geoc_lat = np.arctan2(z, r)
geod_lat = geoc_lat
e2 = (a * a - b * b) / (a * a)
while True:
phi = geod_lat
C = 1 / sqrt(1 - e2 * sin(phi)**2)
geod_lat = np.arctan2(z + a * C * e2 * sin(phi), r)
if np.allclose(geod_lat, phi):
return geod_lat
def subpoint(query_point, a=a, b=b):
"""Get the point on the ellipsoid under the *query_point*.
"""
x, y, z = query_point
r = sqrt(x * x + y * y)
lat = geodetic_lat(query_point)
lon = np.arctan2(y, x)
e2_ = (a * a - b * b) / (a * a)
n__ = a / sqrt(1 - e2_ * sin(lat)**2)
nx_ = n__ * cos(lat) * cos(lon)
ny_ = n__ * cos(lat) * sin(lon)
nz_ = (1 - e2_) * n__ * sin(lat)
return np.vstack([nx_, ny_, nz_])
class ScanGeometry(object):
"""Description of the geometry of an instrument.
*fovs* is the x and y viewing angles of the instrument. y is zero if the we
talk about scanlines of course. *times* is the time of viewing of each
angle relative to the start of the scanning, so it should have the same
size as the *fovs*. *attitude* is the attitude correction to apply.
"""
def __init__(self,
fovs,
times,
attitude=(0, 0, 0)):
self.fovs = np.array(fovs)
self._times = np.array(times)
self.attitude = attitude
def vectors(self, pos, vel, roll=0.0, pitch=0.0, yaw=0.0):
"""Get unit vectors pointing to the different pixels.
*pos* and *vel* are column vectors, or matrices of column
vectors. Returns vectors as stacked rows.
"""
# TODO: yaw steering mode !
# Fake nadir: This is the intersection point between the satellite
# looking down at the centre of the ellipsoid and the surface of the
# ellipsoid. Nadir on the other hand is the point which vertical goes
# through the satellite...
#nadir = -pos / vnorm(pos)
nadir = subpoint(-pos)
nadir /= vnorm(nadir)
# x is along track (roll)
x = vel / vnorm(vel)
# y is cross track (pitch)
y = np.cross(nadir, vel, 0, 0, 0)
y /= vnorm(y)
# rotate first around x
x_rotated = qrotate(nadir, x, self.fovs[:, 0] + roll)
# then around y
xy_rotated = qrotate(x_rotated, y, self.fovs[:, 1] + pitch)
# then around z
return qrotate(xy_rotated, nadir, yaw)
def times(self, start_of_scan):
tds = [timedelta(seconds=i) for i in self._times]
return np.array(tds) + start_of_scan
class Quaternion(object):
def __init__(self, scalar, vector):
self.__x, self.__y, self.__z = vector
self.__w = scalar
def rotation_matrix(self):
x, y, z, w = self.__x, self.__y, self.__z, self.__w
zero = np.zeros_like(x)
return np.array(
((w**2 + x**2 - y**2 - z**2,
2 * x * y + 2 * z * w,
2 * x * z - 2 * y * w,
zero),
(2 * x * y - 2 * z * w,
w**2 - x**2 + y**2 - z**2,
2 * y * z + 2 * x * w,
zero),
(2 * x * z + 2 * y * w,
2 * y * z - 2 * x * w,
w**2 - x**2 - y**2 + z**2,
zero),
(zero, zero, zero, w**2 + x**2 + y**2 + z**2)))
def qrotate(vector, axis, angle):
"""Rotate *vector* around *axis* by *angle* (in radians).
*vector* is a matrix of column vectors, as is *axis*.
This function uses quaternion rotation.
"""
n_axis = axis / vnorm(axis)
sin_angle = np.expand_dims(sin(angle / 2), 0)
if np.rank(n_axis) == 1:
n_axis = np.expand_dims(n_axis, 1)
p__ = np.dot(n_axis, sin_angle)[:, np.newaxis]
else:
p__ = n_axis * sin_angle
q__ = Quaternion(cos(angle / 2), p__)
return np.einsum("kj, ikj->ij",
vector,
q__.rotation_matrix()[:3, :3])
# DIRTY STUFF. Needed the get_lonlatalt function to work on pos directly if
# we want to print out lonlats in the end.
from pyorbital import astronomy
from pyorbital.orbital import *
def get_lonlatalt(pos, utc_time):
"""Calculate sublon, sublat and altitude of satellite, considering the
earth an ellipsoid.
http://celestrak.com/columns/v02n03/
"""
(pos_x, pos_y, pos_z) = pos / XKMPER
lon = ((np.arctan2(pos_y * XKMPER, pos_x * XKMPER) - astronomy.gmst(utc_time))
% (2 * np.pi))
lon = np.where(lon > np.pi, lon - np.pi * 2, lon)
lon = np.where(lon <= -np.pi, lon + np.pi * 2, lon)
r = np.sqrt(pos_x ** 2 + pos_y ** 2)
lat = np.arctan2(pos_z, r)
e2 = F * (2 - F)
while True:
lat2 = lat
c = 1 / (np.sqrt(1 - e2 * (np.sin(lat2) ** 2)))
lat = np.arctan2(pos_z + c * e2 * np.sin(lat2), r)
if np.all(abs(lat - lat2) < 1e-10):
break
alt = r / np.cos(lat) - c
alt *= A
return np.rad2deg(lon), np.rad2deg(lat), alt
# END OF DIRTY STUFF
def compute_pixels((tle1, tle2), sgeom, times, rpy=(0.0, 0.0, 0.0)):
"""Compute cartesian coordinates of the pixels in instrument scan.
"""
orb = Orbital("mysatellite", line1=tle1, line2=tle2)
# get position and velocity for each time of each pixel
pos, vel = orb.get_position(times, normalize=False)
# now, get the vectors pointing to each pixel
vectors = sgeom.vectors(pos, vel, *rpy)
# compute intersection of lines (directed by vectors and passing through
# (0, 0, 0)) and ellipsoid. Derived from:
# http://en.wikipedia.org/wiki/Line%E2%80%93sphere_intersection
# do the computation between line and ellipsoid (WGS 84)
# NB: AAPP uses GRS 80...
centre = -pos
a__ = 6378.137 # km
# b__ = 6356.75231414 # km, GRS80
b__ = 6356.752314245 # km, WGS84
radius = np.array([[1 / a__, 1 / a__, 1 / b__]]).T
xr_ = vectors * radius
cr_ = centre * radius
ldotc = np.einsum("ij,ij->j", xr_, cr_)
lsq = np.einsum("ij,ij->j", xr_, xr_)
csq = np.einsum("ij,ij->j", cr_, cr_)
d1_ = (ldotc - np.sqrt(ldotc ** 2 - csq * lsq + lsq)) / lsq
# return the actual pixel positions
return vectors * d1_ - centre
def norm(v):
return np.sqrt(np.dot(v, v.conj()))
def mnorm(m, axis=None):
"""norm of a matrix of vectors stacked along the *axis* dimension.
"""
if axis is None:
axis = np.rank(m) - 1
return np.sqrt((m**2).sum(axis))
def vnorm(m):
"""norms of a matrix of column vectors.
"""
return np.sqrt((m**2).sum(0))
def hnorm(m):
"""norms of a matrix of row vectors.
"""
return np.sqrt((m**2).sum(1))
if __name__ == '__main__':
# NOAA 18 (from the 2011-10-12, 16:55 utc)
# 1 28654U 05018A 11284.35271227 .00000478 00000-0 28778-3 0 9246
# 2 28654 99.0096 235.8581 0014859 135.4286 224.8087 14.11526826329313
noaa18_tle1 = "1 28654U 05018A 11284.35271227 .00000478 00000-0 28778-3 0 9246"
noaa18_tle2 = "2 28654 99.0096 235.8581 0014859 135.4286 224.8087 14.11526826329313"
from datetime import datetime
t = datetime(2011, 10, 12, 13, 45)
# edge and centre of an avhrr scanline
# sgeom = ScanGeometry([(-0.9664123687741623, 0),
# (0, 0)],
# [0, 0.0, ])
# print compute_pixels((noaa18_tle1, noaa18_tle2), sgeom, t)
# avhrr swath
scanline_nb = 1
# building the avhrr angles, 2048 pixels from +55.37 to -55.37 degrees
avhrr = np.vstack(((np.arange(2048) - 1023.5) / 1024 * np.deg2rad(-55.37),
np.zeros((2048,)))).transpose()
avhrr = np.tile(avhrr, [scanline_nb, 1])
# building the corresponding times array
offset = np.arange(scanline_nb) * 0.1667
times = (np.tile(np.arange(2048) * 0.000025 + 0.0025415, [scanline_nb, 1])
+ np.expand_dims(offset, 1))
# build the scan geometry object
sgeom = ScanGeometry(avhrr, times.ravel())
# print the lonlats for the pixel positions
s_times = sgeom.times(t)
pixels_pos = compute_pixels((noaa18_tle1, noaa18_tle2), sgeom, s_times)
print get_lonlatalt(pixels_pos, s_times)