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geolocation.py
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geolocation.py
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# -*- coding: utf-8 -*-
# geolocation.py
# Copyright (c) 2015-2018, Likun Wang (Likun.Wang@noaa.gov)
# Copyright (c) 2015-2018, Earth System Science Interdisciplinary
# Center/Univ. of Maryland
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# * Neither the name of the copyright holders nor the names of any
# contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
""" Accurate and fast geolocaiton coordinate transformation.
A collection of functions to handle geolocaiton coordinate transformation.
Basically, it follows the same functions from ADL common geolocation library
by calling the same library and using the same parameters for accuracy
consideration. In addition, to achieve the fast calculations, some functions
are vectorized.
:Author:
`Likun Wang <Likun.Wang@noaa.gov>`_
:Organization:
Earth System Science Interdisciplinary Center/Univ. of Maryland
:Version: 2018.9.5
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import numpy as np
from numpy import sqrt, sin, cos, tan, deg2rad, \
arctan2, arctan, arcsin, rad2deg, arccos
from numpy import arcsin as asin
from numpy import arctan2 as atan2
from datetime import datetime, timedelta
from functools import partial
from itertools import izip
import pyproj
from novas.compat import cel2ter, ter2cel
from astropy.time import Time, TimeDelta
from astropy.utils import iers
from pykdtree.kdtree import KDTree
from jpss import cris_sensor_info
import time
WGS84_A = 6378137.0
WGS84_F = 1.0 / 298.257223563
WGS84_B = WGS84_A*(1.0 - WGS84_F)
WGS84_E2 = 2 * WGS84_F - WGS84_F ** 2
eq_rad_km=6.37813700000000e+3; #/* equatorial radius, KM */
eq_radm=6.37813700000000e+6; #/* equatorial radius, meters */
pole_radm=6.35675231424518e+6; #/* polar_radius, meters */
eccen_sqr=6.69437999014132e-3; #/* e^2 = f(2 - f) */
detic2centric=9.93305620009859e-1; #/* 1 - e^2 */
centric2detic=1.00673949674228e+0; #/* 1 / (1 - e^2) */
delta=6.73949674227643e-3; #/* ( 1/(1-f)^2 ) - 1 */
#Rotational angular velocity of Earth in radians/sec from IERS
# Conventions (2003).
ANGVEL = 7.2921150e-5;
# Polar Wonder data
#iers.conf.auto_download = False
dat = iers.IERS_Auto.open()
# NPP/CrIS parameters
para = cris_sensor_info()
#####################################################################################
def rotationMatrixY(thePitch):
"""
Compute rotation matrix around Y axis
"""
thePitch = np.asarray(thePitch, dtype=np.float64)
pitchMatrix = np.zeros((thePitch.size, 3, 3), dtype=np.float64)
pitchMatrix[:, 0,0] = cos(thePitch)
pitchMatrix[:, 0,1] = 0
pitchMatrix[:, 0,2] = sin(thePitch)
pitchMatrix[:, 1,0] = 0
pitchMatrix[:, 1,1] = 1
pitchMatrix[:, 1,2] = 0
pitchMatrix[:, 2,0] = -sin(thePitch)
pitchMatrix[:, 2,1] = 0
pitchMatrix[:, 2,2] = cos(thePitch)
return np.squeeze(pitchMatrix)
def rotationMatrixX(theRoll):
"""
Compute rotation matrix around X axis
"""
theRoll = np.asarray(theRoll, dtype=np.float64)
rollMatrix = np.zeros((theRoll.size, 3, 3), dtype=np.float64)
rollMatrix[:, 0,0] = 1;
rollMatrix[:, 0,1] = 0;
rollMatrix[:, 0,2] = 0;
rollMatrix[:, 1,0] = 0;
rollMatrix[:, 1,1] = cos(theRoll);
rollMatrix[:, 1,2] = -sin(theRoll);
rollMatrix[:, 2,0] = 0;
rollMatrix[:, 2,1] = sin(theRoll);
rollMatrix[:, 2,2] = cos(theRoll);
return np.squeeze(rollMatrix)
def rotationMatrixZ(theYaw):
"""
Compute rotation matrix around Z axis
"""
theYaw = np.asarray(theYaw, dtype=np.float64)
yawMatrix = np.zeros((theYaw.size, 3, 3), dtype=np.float64)
yawMatrix[:, 0,0] = cos(theYaw)
yawMatrix[:, 0,1] = -sin(theYaw)
yawMatrix[:, 0,2] = 0
yawMatrix[:, 1,0] = sin(theYaw)
yawMatrix[:, 1,1] = cos(theYaw)
yawMatrix[:, 1,2] = 0
yawMatrix[:, 2,0] = 0
yawMatrix[:, 2,1] = 0
yawMatrix[:, 2,2] = 1
return np.squeeze(yawMatrix);
def dot_product(v, w):
"""
Dot product of two vectors
"""
return np.einsum('...j,...j->...', v, w)
def matrix_matrix_product(A, B):
"""
Product of two matrix
"""
return np.einsum('...jk,...kl->...jl', A, B)
def matrix_vector_product(M, v):
"""
Product of matrix with vector
"""
return np.einsum('...jk,...k->...j', M, v)
def normalize_vector(v):
"""
Unit vector of the vectors
"""
v = np.asarray(v, dtype=np.float64)
mag = np.sqrt(np.einsum('...i,...i', v, v))
if mag.size ==1: return v/mag
else: return v/np.expand_dims(mag, axis=-1)
def mag_vector(v):
"""
the magnitude of the vectors
"""
v = np.asarray(v, dtype=np.float64)
mag = np.sqrt(np.einsum('...i,...i', v, v))
return mag
def findAnglesBetweenTwoVectors(v1s, v2s):
"""
the angle of the two vectors
"""
v1s = np.asarray(v1s, dtype=np.float64)
v2s = np.asarray(v2s, dtype=np.float64)
dot_v1_v2 = dot_product(v1s, v2s)
dot_v1_v1 = dot_product(v1s, v1s)
dot_v2_v2 = dot_product(v2s, v2s)
return np.rad2deg(np.arccos(dot_v1_v2/(np.sqrt(dot_v1_v1)*np.sqrt(dot_v2_v2))))
def Triad (v1, v2, r1, r2):
"""
Derive transformation matrix from two vectors. The ideas are from
https://en.wikipedia.org/wiki/Triad_method
INPUTS: R = A V
A is Transformation matrix [3,3]
V1, V2: the two vector in reference coordinates
R1, R2: the two vector in transfomed coordinates
"""
vv1 = normalize_vector(v1)
vv2 = normalize_vector(v2)
vv3 = normalize_vector(np.cross(v1, v2))
vv4 = np.cross(vv1, vv3)
rr1 = normalize_vector(r1)
rr2 = normalize_vector(r2)
rr3 = normalize_vector(np.cross(r1, r2))
rr4 = np.cross(rr1, rr3)
a1 = np.column_stack((vv1, vv3, vv4))
a2 = np.column_stack((rr1, rr3, rr4))
a = matrix_matrix_product(a2, a1.T)
return a
def compute_alpha_beta(v, degree=False):
"""
Convert three-variable vector into two-variable degree for
perturbation purpose.
"""
v = np.asarray(v, dtype=np.float64)
if v.ndim == 1: v = np.expand_dims(v, axis=0)
if v.ndim >= 2:
sz = v.shape
v = v.reshape(-1, 3)
alpha = atan2(v[:, 0], v[:, 2])
beta = atan2(v[:, 1], v[:, 2])
if degree: alpha, beta = rad2deg(alpha), rad2deg(beta)
return alpha.reshape(sz[:-1]), beta.reshape(sz[:-1])
def haversine(lon1, lat1, lon2, lat2, R=None):
"""
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
if R is None: R=6367.0
# convert decimal degrees to radians
lon1, lat1, lon2, lat2 = map(deg2rad, [lon1, lat1, lon2, lat2])
# haversine formula
dlon = lon2 - lon1
dlat = lat2 - lat1
a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
c = 2 * arcsin(sqrt(a))
km = R * c
return km
def rotate_vec (rotationAxis, angle, oldVector, degree=True):
rotationAxis = np.asarray(rotationAxis, dtype=np.float64)
angle = np.asarray(angle, dtype=np.float64)
oldVector = np.asarray(oldVector, dtype=np.float64)
## check vector size
if rotationAxis.size != oldVector.size:
print ('The vector size does not match')
return
if rotationAxis.ndim == 1:
rotationAxis=np.expand_dims(rotationAxis, axis=0)
if oldVector.ndim == 1:
oldVector=np.expand_dims(oldVector, axis=0)
if angle.size != 1:
print('check angle input')
return
## we need to normalize rotationAxis
mag = np.linalg.norm(rotationAxis, axis=1)
rotationAxis= rotationAxis/np.expand_dims(mag, axis=1)
## check angle unit
if degree: angle = np.deg2rad(angle)
cosAngle = cos(angle) ;
sinAngle = sin(angle) ;
## 1st term
firstTerm = oldVector * cosAngle ;
## 2nd term
secondTerm = np.cross(oldVector, rotationAxis) * sinAngle
## 3rd term
temp= np.einsum('ij,ij->i', oldVector, rotationAxis)
temp= np.expand_dims(temp, axis=1)
thirdTerm = (temp * rotationAxis) * ( 1.0 - cosAngle) ;
newVector = firstTerm - secondTerm + thirdTerm ;
return newVector
def find_nearest(array, value):
array = np.asarray(array)
idx = (np.abs(array - value)).argmin()
return idx
def reject_outliers(data, m=2):
return data[abs(data - np.mean(data)) < m * np.std(data)]
#####################################################################################
def buildFovLosInSSMF(FlipFOV=False):
## from SBF_To_IAR
MatrixP = rotationMatrixY (para['SBFtoIAR_pitch']*1e-6)
MatrixR = rotationMatrixX (para['SBFtoIAR_roll']*1e-6)
MatrixY = rotationMatrixZ (para['SBFtoIAR_yaw']*1e-6)
Mat_SBFtoIAR = matrix_matrix_product(MatrixR, MatrixP)
Mat_SBFtoIAR = matrix_matrix_product(Mat_SBFtoIAR, MatrixY)
## from IAR_To_SSMR
MatrixP = rotationMatrixY (para['IARtoSSMR_pitch']*1e-6)
MatrixR = rotationMatrixX (para['IARtoSSMR_roll']*1e-6)
MatrixY = rotationMatrixZ (para['IARtoSSMR_yaw']*1e-6)
Mat_IARtoSSMR = matrix_matrix_product(MatrixR, MatrixP)
Mat_IARtoSSMR = matrix_matrix_product(Mat_IARtoSSMR, MatrixY)
## from SSMR_To_SSMF
MatrixP = rotationMatrixY (para['SSMRtoSSMF_pitch']*1e-6)
MatrixR = rotationMatrixX (para['SSMRtoSSMF_roll']*1e-6)
MatrixY = rotationMatrixZ (para['SSMRtoSSMF_yaw']*1e-6)
Mat_SSMRtoSSMF = matrix_matrix_product(MatrixR, MatrixP)
Mat_SSMRtoSSMF = matrix_matrix_product(Mat_SSMRtoSSMF, MatrixY)
Mat_SBFtoSSMF = matrix_matrix_product(matrix_matrix_product(Mat_SBFtoIAR, Mat_IARtoSSMR), Mat_SSMRtoSSMF)
## nominal optical axis direction
opticalAxis = np.array([1.0, 0, 0], dtype=np.float64)
LW_FOV5_inTrk = para['lw_losRelativePitch']
LW_FOV5_crTrk = para['lw_losRelativeYaw']
fov_inTrackAngle = np.asarray(para['lw_intrackOffsetAngle'], dtype=np.float64)
fov_crTrackAngle = np.asarray(para['lw_crosstrackOffsetAngle'], dtype=np.float64)
losInIOAR = np.zeros((fov_inTrackAngle.size, 3))
losInSSMF = np.zeros((fov_inTrackAngle.size, 3))
for i in range(0, fov_inTrackAngle.size):
ifov = i
if FlipFOV:
if i==0: ifov = 2
if i==2: ifov = 0
if i==3: ifov = 5
if i==5: ifov = 3
if i==6: ifov = 8
if i==8: ifov = 6
fovYaw = -1.0*(fov_crTrackAngle[ifov] + LW_FOV5_crTrk)*1.0e-6
fovPitch = (fov_inTrackAngle[ifov] + LW_FOV5_inTrk)*1.0e-6
losInIOAR[i, :] = matrix_vector_product(rotationMatrixZ(fovYaw), opticalAxis)
losInIOAR[i, :] = matrix_vector_product(rotationMatrixY(fovPitch), losInIOAR[i, :])
# Apply IOAR-SSMF transformation to account for pitch and yaw
# misalignments between interferometer and scan mechanism
losInSSMF[i, :] = matrix_vector_product(rotationMatrixZ(para['IFRboresighttoSSMF_yaw']*1e-6) , losInIOAR[i, :])
losInSSMF[i, :] = matrix_vector_product(rotationMatrixY(para['IFRboresighttoSSMF_pitch']*1e-6), losInSSMF[i, :])
return losInSSMF, Mat_SBFtoSSMF
#####################################################################################
def buildMatSCToSBF ():
## from SC_To_SBF
MatrixP = rotationMatrixY (para['SCtoSBF_pitch']*1e-6)
MatrixR = rotationMatrixX (para['SCtoSBF_roll']*1e-6)
MatrixY = rotationMatrixZ (para['SCtoSBF_yaw']*1e-6)
Mat_SCtoSBF = matrix_matrix_product(MatrixR, MatrixP)
Mat_SCtoSBF = matrix_matrix_product(Mat_SCtoSBF, MatrixY)
return Mat_SCtoSBF
#####################################################################################
def buildLosInSBF(forIET, servoErrCrTrk=None, servoErrInTrk=None):
forIET = np.asarray(forIET)
nScan, nFor = forIET.shape
nFov = 9
losInSSMF, Mat_SBFtoSSMF = buildFovLosInSSMF()
## unit vector of RMF
normalRMF = np.array([-1.0, 0, 1.0], dtype=np.float64)/sqrt(2.0)
commandedCrTrk = np.asarray(para['actualCrosstrackAngle'], dtype=np.float64)
commandedInTrk = np.asarray(para['actualIntrackAngle'], dtype=np.float64)
commandedCrTrk = np.broadcast_to(commandedCrTrk, (nScan, nFor))
commandedInTrk = np.broadcast_to(commandedInTrk, (nScan, nFor))
if servoErrCrTrk is None and servoErrInTrk is None:
commandedCrTrk = commandedCrTrk*1e-6
commandedInTrk = commandedInTrk*1e-6
else:
commandedCrTrk = (commandedCrTrk + servoErrCrTrk)*1e-6
commandedInTrk = (commandedInTrk + servoErrInTrk)*1e-6
## adding FOV elements
commandedCrTrk = np.broadcast_to(commandedCrTrk, (nFov, nScan, nFor))
commandedInTrk = np.broadcast_to(commandedInTrk, (nFov, nScan, nFor))
commandedCrTrk = np.transpose(commandedCrTrk, (1, 2, 0))
commandedInTrk = np.transpose(commandedInTrk, (1, 2, 0))
commandedCrTrk = commandedCrTrk.reshape(nScan*nFor*nFov)
commandedInTrk = commandedInTrk.reshape(nScan*nFor*nFov)
## Compute Normal of SSMF
normalSSMF = matrix_vector_product(rotationMatrixX(commandedCrTrk), normalRMF)
normalSSMF = matrix_vector_product(rotationMatrixY(commandedInTrk), normalSSMF)
## get FOV LOS in SSMF
losInSSMF, Mat_SBFtoSSMF = buildFovLosInSSMF()
losInSSMF = np.broadcast_to(losInSSMF, (nScan, nFor, nFov, 3))
losInSSMF = losInSSMF.reshape((nScan*nFor*nFov, 3))
dotProdAns = dot_product(losInSSMF, normalSSMF)
dotProdAns = dotProdAns.reshape(-1, 1) * normalSSMF
losInSBF = matrix_vector_product(Mat_SBFtoSSMF, losInSSMF - 2*dotProdAns)
losInSBF = losInSBF.reshape(nScan, nFor, nFov, 3)
return losInSBF
#####################################################################################
def buildQuatMatrix(Qw, Qi, Qj, Qk):
"""
//-------------------------------------------------------------------
// See the book edited by James R. Wertz, Library of Congress CIP Data:
// Computer Science Corporation. Attitude Systems Operation.
// Spacecraft Attitude Determination and Control.
// (Astrophysics and space library ; v. 73)
// 'Contract no. NAS 5-11999.'
// TL3260.C65 1978 629.47'42 78-23657
// ISBN 90-277-0959-9
// ISBN 90-277-1204-2 (pbk.)
// Published by D. Reidel Publishing Company. Copyright 1978.
// Last reprinted 1997. Appendix E, particullarly Page 762, E-8.
// See also: http://mathworld.wolfram.com/EulerAngles.html
//
// The spacecraft attitude quaternions provide the rotation from J2000 ECI
// coordinates to spacecraft coordinates.
"""
qMat2eci = np.zeros((Qw.size, 3, 3))
#If the sum of squares is 1, then the quaternion is already normalized.
mag = sqrt(Qi*Qi + Qj*Qj + Qk*Qk + Qw*Qw);
Qw /= mag;
Qi /= mag;
Qj /= mag;
Qk /= mag;
# first row of the matrix
qMat2eci[:, 0, 0] = (Qi*Qi) - (Qj*Qj) - (Qk*Qk) + (Qw*Qw);
qMat2eci[:, 0, 1] = 2.e0*( (Qi*Qj) + (Qk*Qw) );
qMat2eci[:, 0, 2] = 2.e0*( (Qi*Qk) - (Qj*Qw) );
# second row of the matrix
qMat2eci[:, 1, 0] = 2.e0*( (Qi*Qj) - (Qk*Qw) );
qMat2eci[:, 1, 1] = -(Qi*Qi) + (Qj*Qj) - (Qk*Qk) + (Qw*Qw);
qMat2eci[:, 1, 2] = 2.e0*( (Qj*Qk) + (Qi*Qw) );
# third row of the matrix
qMat2eci[:, 2, 0] = 2.e0*( (Qi*Qk) + (Qj*Qw) );
qMat2eci[:, 2, 1] = 2.e0*( (Qj*Qk) - (Qi*Qw) );
qMat2eci[:, 2, 2] = -(Qi*Qi) - (Qj*Qj) + (Qk*Qk) + (Qw*Qw);
## Return the spacecraft coordinates from J2000 ECI to SC matrix.
Mat_SCtoECI = qMat2eci.squeeze()
return Mat_SCtoECI
#####################################################################################
def LLA2ECEF(lonIn, latIn, altIn):
"""
Transform lon,lat,alt (WGS84 degrees, meters) to ECEF
x,y,z (meters)
"""
lonRad = deg2rad(np.asarray(lonIn, dtype=np.float64) )
latRad = deg2rad(np.asarray(latIn, dtype=np.float64) )
alt = np.asarray(altIn, dtype=np.float64)
a, b, e2 = WGS84_A, WGS84_B, WGS84_E2
## N = Radius of Curvature (meters), defined as:
N = a/sqrt(1.0-e2*(sin(latRad)**2.0))
##$ calcute X, Y, Z
x=(N+alt)*cos(latRad)*cos(lonRad)
y=(N+alt)*cos(latRad)*sin(lonRad)
z=(b**2.0/a**2.0*N + altIn)*sin(latRad)
return x, y, z
def RAE2ENU(azimuthIn, zenithIn, rangeIn):
"""
Transform azimuth, zenith, range to ENU x,y,z (meters)
"""
azimuth = deg2rad(np.asarray(azimuthIn, dtype=np.float64))
zenith = deg2rad(np.asarray(zenithIn, dtype=np.float64))
r = np.asarray(rangeIn, dtype=np.float64)
# up
up = r*cos(zenith)
# projection on the x-y plane
p = r*sin(zenith)
# north
north = p*cos(azimuth)
# east
east = p*sin(azimuth)
return east, north, up
def ENU2RAE(east, north, up):
"""
Transform ENU x,y,z (meters) to azimuth angle, zenith angle, and range
"""
p = sqrt(east**2 + north**2 + up**2)
zenith = rad2deg(arccos(up/p))
azimuth = rad2deg(arctan2(east, north))
return p, azimuth, zenith
#####################################################################################
def ENU2ECEF (east, north, up, lon, dlat):
"""
Convert local East, North, Up (ENU) coordinates to the (x,y,z) Earth Centred Earth Fixed (ECEF) coordinates
Reference is here:
http://www.navipedia.net/index.php/Transformations_between_ECEF_and_ENU_coordinates
Note that laitutde should be geocentric latitude instead of geodetic latitude
Note:
On June 16 2015
This note from https://en.wikipedia.org/wiki/Geodetic_datum
Note: \ \phi is the geodetic latitude. A prior version of this page showed use of the geocentric latitude (\ \phi^\prime).
The geocentric latitude is not the appropriate up direction for the local tangent plane. If the
original geodetic latitude is available it should be used, otherwise, the relationship between geodetic and geocentric
latitude has an altitude dependency, and is captured by ...
"""
x0 = np.asarray(east, dtype=np.float64)
y0 = np.asarray(north, dtype=np.float64)
z0 = np.asarray(up, dtype=np.float64)
lm = deg2rad(np.asarray(lon, dtype=np.float64))
ph = deg2rad(np.asarray(dlat, dtype=np.float64))
x=-1.0*x0*sin(lm)-y0*cos(lm)*sin(ph)+z0*cos(lm)*cos(ph)
y= x0*cos(lm) -y0*sin(lm)*sin(ph)+z0*sin(lm)*cos(ph)
z= x0*0 +y0*cos(ph) +z0*sin(ph)
return x, y, z
def ECEF2ENU (x, y, z, lon, dlat):
"""
From ECEF(x, y, z) to ENU (East, North, up) coordinates at a given location(lon, dlat)
Reference is here:
http://www.navipedia.net/index.php/Transformations_between_ECEF_and_ENU_coordinates
Note that laitutde should be geocentric latitude instead of geodetic latitude
"""
x = np.asarray(x, dtype=np.float64)
y = np.asarray(y, dtype=np.float64)
z = np.asarray(z, dtype=np.float64)
lm = deg2rad(np.asarray(lon, dtype=np.float64))
ph = deg2rad(np.asarray(dlat, dtype=np.float64))
east = -x*sin(lm) + y*cos(lm)
north = -x*cos(lm)*sin(ph) - y*sin(lm)*sin(ph) + z*cos(ph)
up = x*cos(lm)*cos(ph) + y*sin(lm)*cos(ph) + z*sin(ph)
return east, north, up
def GEO2ECEF( lon, lat, satAzimuth, satRange, satZenith, height = None):
"""
from geolocation fields including lon, lat, satAzimuth, satRange, satZenith to compute
LOS and satPos vectors in ECEF
"""
lon = np.asarray(lon, dtype=np.float64)
lat = np.asarray(lat, dtype=np.float64)
if height is None: height = np.zeros_like(lat)
satAzimuth = np.asarray(satAzimuth, dtype=np.float64)
satRange = np.asarray(satRange, dtype=np.float64)
satZenith = np.asarray(satZenith , dtype=np.float64)
savShape = lon.shape
# compute CrIS Pos Vector
pos_x, pos_y, pos_z = LLA2ECEF(lon, lat, height)
pos_x = np.expand_dims(pos_x, axis=-1)
pos_y = np.expand_dims(pos_y, axis=-1)
pos_z = np.expand_dims(pos_z, axis=-1)
# compute CrIS LOS Vector
east, north, up = RAE2ENU(satAzimuth, satZenith, satRange)
los_x, los_y, los_z = ENU2ECEF(east, north, up, lon, lat)
los_x = np.expand_dims(los_x, axis=-1)
los_y = np.expand_dims(los_y, axis=-1)
los_z = np.expand_dims(los_z, axis=-1)
pos = np.concatenate((pos_x, pos_y, pos_z), axis=-1)
los = np.concatenate((los_x, los_y, los_z), axis=-1)
satPos = pos + los
return pos, los, satPos
#####################################################################################
def ECEF2LLA(xIn, yIn, zIn):
"""
Transform ECEF x,y,z (meters) lon,lat,alt (WGS84 degrees, meters) to
"""
x = np.asarray(xIn, dtype=np.float64)
y = np.asarray(yIn, dtype=np.float64)
z = np.asarray(zIn, dtype=np.float64)
if x.size != y.size or x.size != z.size or x.ndim > 1:
print(x, y, z)
print(x.shape, y.shape, z.shape)
print ("check input x, y, z's shape")
return
ecef = pyproj.Proj(proj='geocent', ellps='WGS84', datum='WGS84')
lla = pyproj.Proj(proj='latlong', ellps='WGS84', datum='WGS84')
geoLon, geoLat, geoAlt = pyproj.transform(ecef, lla, x, y, z, radians=False)
return geoLon, geoLat, geoAlt
#####################################################################################
def IET2ATIME(iet):
"""
convert IET time into TIME
"""
aTime = Time('1958-01-01', scale='tai') + TimeDelta(iet*1e-6, format='sec')
return aTime
def TIME2IET(datetime):
"""
convert a DATETIME varible into IET
"""
t1= Time(datetime, scale='utc')
t0 = Time('1958-01-01', scale='tai')
dt = t1.tai-t0.tai
dt.format = 'sec'
iet = np.int64(dt.value*1e6)
return iet
def ATIME2IET(aTime):
"""
convert a TIME varible into IET
"""
t0 = Time('1958-01-01', scale='tai')
dt = aTime.tai-t0.tai
dt.format = 'sec'
iet = np.int64(dt.value*1e6)
return iet
#####################################################################################
def ECR2ECI_NOVAS (inTime, inPos, inVel, tflag='IET'):
"""
Transform Position and Velocity vector from ECR to ECI frame using NOVAS function.
"""
inPos = np.asarray(inPos, dtype=np.float64)
inVel = np.asarray(inVel, dtype=np.float64)
oneFlag = 0
if inTime.size == 1:
inTime = np.repeat(inTime, 2)
oneFlag = 1
if inPos.size ==3 :
inPos = np.broadcast_to(inPos, (2, 3))
if inVel.size == 3:
inVel = np.broadcast_to(inVel, (2, 3))
if tflag == 'IET':
inTime = np.asarray(inTime)
aTime = Time('1958-01-01', scale='tai') + TimeDelta(inTime*1e-6, format='sec')
if tflag == 'aTime': aTime = inTime
# set Polar Motion data
pmx, pmy = dat.pm_xy(aTime)
pmx=pmx.value
pmy=pmy.value
# set TT-UT1 data
delta_t = map(timedelta.total_seconds, aTime.tt.datetime-aTime.ut1.datetime)
# set jd_ut1 data
jd_ut1_high=aTime.ut1.jd
jd_ut1_low = np.zeros_like(jd_ut1_high)
inPos_List = inPos.tolist()
mapfunc = partial(ter2cel, method=1) # <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
s = map(mapfunc, jd_ut1_high, jd_ut1_low, delta_t, pmx, pmy, inPos_List)
outPos = np.asarray(s)
if inVel.size ==1 :
outVel = 0
else:
# counting Earth Rotation velocity
tempVec = np.cross(np.array([0,0, ANGVEL]), inPos, axisa=0, axisb=1)
vectorIn = inVel + tempVec
vectorIn_List = vectorIn.tolist()
s = map(mapfunc, jd_ut1_high, jd_ut1_low, delta_t, pmx, pmy, vectorIn_List)
outVel = np.asarray(s)
if oneFlag == 1:
outPos = outPos[0, :]
if isinstance(outVel, np.ndarray): outVel = outVel[0, :]
return outPos, outVel
def ECI2ECR_NOVAS (inTime, inPos, inVel, tflag='IET'):
"""
Transform Position and Velocity vector from ECI to ECR frame using NOVAS function.
"""
inPos = np.asarray(inPos, dtype=np.float64)
inVel = np.asarray(inVel, dtype=np.float64)
oneFlag = 0
if inTime.size == 1:
inTime = np.repeat(inTime, 2)
oneFlag = 1
if inPos.size ==3 :
inPos = np.broadcast_to(inPos, (2, 3))
if inVel.size == 3:
inVel = np.broadcast_to(inVel, (2, 3))
if tflag == 'IET':
inTime = np.asarray(inTime)
aTime = Time('1958-01-01', scale='tai') + TimeDelta(inTime*1e-6, format='sec')
if tflag == 'aTime': aTime = inTime
# set Polar Motion data
pmx, pmy = dat.pm_xy(aTime)
pmx=pmx.value
pmy=pmy.value
# set TT-UT1 data
delta_t = map(timedelta.total_seconds, aTime.tt.datetime-aTime.ut1.datetime)
# set jd_ut1 data
jd_ut1_high=aTime.ut1.jd
jd_ut1_low = np.zeros_like(jd_ut1_high)
inPos_List = inPos.tolist()
mapfunc = partial(cel2ter, method=1) # <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
s = map(mapfunc, jd_ut1_high, jd_ut1_low, delta_t, pmx, pmy, inPos_List)
outPos = np.asarray(s)
if inVel.size == 1 :
vectorOut = 0
else:
vectorIn_List = inVel.tolist()
s = map(mapfunc, jd_ut1_high, jd_ut1_low, delta_t, pmx, pmy, vectorIn_List)
vectorOut = np.asarray(s)
# counting Earth Rotation velocity
tempVec = np.cross(np.array([0,0, ANGVEL]), inPos, axisa=0, axisb=1)
vectorOut = vectorOut - tempVec
if oneFlag == 1:
outPos = outPos[0, :]
if isinstance(vectorOut, np.ndarray): vectorOut = vectorOut[0, :]
return outPos, vectorOut
#####################################################################################
def buildECIOrbFrame (inTime, posECR, velECR, tflag='IET'):
"""
NOTE: The "orbit frame" is a coordinate system describing the perfect
attitude. If the spacecraft frame(coordinate system) is exactly aligned
with the orbit frame, then the roll, pitch, and yaw would all be zero and
spacecraft attitude would be perfect. The orbit frame Z axis points down
to geodetic nadir, the Y axis is at a right angle to the Z axis, and the
spacecraft velocity vector (which means the Y axis is nearly at a right
angle to the orbit plane). The X axis completes a right handed cartesian
coordinate system, and is less than one degree away from the direction of
the spacecraft velocity vector. The X and Y axis of the orbit frame
form a plane which is geodetically horizontal.
"""
posECR = np.asarray(posECR, dtype=np.float64)
velECR = np.asarray(velECR, dtype=np.float64)
inTime = np.asarray(inTime)
if posECR.ndim ==1: posECR = np.expand_dims(posECR, axis=0)
if velECR.ndim ==1: velECR = np.expand_dims(velECR, axis=0)
if inTime.size == 1 and inTime.ndim == 0: inTime = np.expand_dims(inTime, axis=0)
if tflag == 'IET': aTime = Time('1958-01-01', scale='tai') + TimeDelta(inTime*1e-6, format='sec')
# compute satellite lon, geodetic lat, and altitude
sc_Lon, sc_dLat, sc_Alt = ECEF2LLA(posECR[:, 0], posECR[:, 1], posECR[:, 2])
# compute gedetic nadir position vector in ECR
nadir_p = np.zeros_like(posECR)
nadir_p[:, 0], nadir_p[:, 1], nadir_p[:, 2] =LLA2ECEF(sc_Lon, sc_dLat, np.zeros_like(sc_Lon))
# the vector from satellite to geodetic nadir
nadirVecECR = nadir_p - posECR
nadirVecECR = normalize_vector(nadirVecECR)
# convert all the vector from ECR to ECI
posECI, velECI = ECR2ECI_NOVAS(inTime, posECR, velECR)
nadirVecECI, tmpVel = ECR2ECI_NOVAS(inTime, nadirVecECR, 0)
orbFrameZ = nadirVecECI
orbFrameY = np.cross(orbFrameZ, velECI)
orbFrameY = normalize_vector(orbFrameY)
orbFrameX = np.cross(orbFrameY, orbFrameZ)
orbFrameY = normalize_vector(orbFrameY)
orbFrameX = normalize_vector(orbFrameX)
Mat_ECItoOrb = np.zeros((int(posECR.size/3), 3, 3), dtype=np.float64)
Mat_ECItoOrb[:,:, 0] = orbFrameX
Mat_ECItoOrb[:,:, 1] = orbFrameY
Mat_ECItoOrb[:,:, 2] = orbFrameZ
# return Rotation Matrix from Orbital Frame to ECI(J2000).
return np.squeeze(Mat_ECItoOrb)
#####################################################################################
def orb2sc(rollIn, pitchIn, yawIn):
"""
Now form the direction cosine matrix from the roll, pitch, and yaw.
This is a 3-1-2 matrix (i.e.: yaw, then roll, then pitch). This
forms a matrix which will rotate a vector in Orbit Frame Coordinates
to spacecraft coordinates.
input roll,pitch, yaw in radium
"""
roll = np.asarray(rollIn, dtype=np.float64)
pitch = np.asarray(pitchIn, dtype=np.float64)
yaw = np.asarray(yawIn, dtype=np.float64)
if np.asarray(roll).shape != np.asarray(pitch).shape or \
np.asarray(roll).shape != np.asarray(yaw).shape:
return None
matDC = np.zeros((np.asarray(roll).size, 3, 3), dtype=np.float64)
sin_roll = sin(roll)
cos_roll = cos(roll)
sin_pitch = sin(pitch)
cos_pitch = cos(pitch)
sin_yaw = sin(yaw)
cos_yaw = cos(yaw)
# Noted that it is from orbit to spacecraft
# First row of the matrix.
matDC[:, 0, 0] = (cos_yaw * cos_pitch) - (sin_yaw * sin_roll * sin_pitch)
matDC[:, 0, 1] = (sin_yaw * cos_pitch) + (cos_yaw * sin_roll * sin_pitch)
matDC[:, 0, 2] = -cos_roll * sin_pitch
# Second row of matrix
matDC[:, 1, 0] = -sin_yaw * cos_roll
matDC[:, 1, 1] = cos_yaw * cos_roll
matDC[:, 1, 2] = sin_roll
#Third row of matrix.
matDC[:, 2, 0] = (cos_yaw * sin_pitch) + (sin_yaw * sin_roll * cos_pitch)
matDC[:, 2, 1] = (sin_yaw * sin_pitch) - (cos_yaw * sin_roll * cos_pitch)
matDC[:, 2, 2] = cos_roll * cos_pitch
Mat_SPCtoOrb = np.squeeze(matDC)
# return Rotation Matrix from Orbital Frame to Spacecraft.
return Mat_SPCtoOrb
#####################################################################################
def calcGDRollPitchYaw(matDC):
## MatDC is Rotation Matrix from Orbital Frame to Spacecraft.
if matDC.ndim ==2 and matDC.size==9: matDC = np.expand_dims(matDC, axis=0)
roll = asin(matDC[:, 1, 2]);
cos_roll = cos(roll);
sin_pitch = (-matDC[:, 0, 2]) / cos_roll;
cos_pitch = matDC[:, 2, 2] / cos_roll;
pitch = atan2(sin_pitch, cos_pitch);
sin_yaw = (-matDC[:, 1, 0]) / cos_roll;
cos_yaw = matDC[:, 1, 1] / cos_roll;
yaw = atan2(sin_yaw, cos_yaw);
if matDC.size==9: return roll[0], pitch[0], yaw[0]
else: return roll, pitch, yaw
#####################################################################################
def conVec2LatLonAlt (Vec):
inVec = np.asarray(Vec, dtype=np.float64)
### WGS84 Parameters
a = WGS84_A
f = WGS84_F
b = WGS84_A
e2= WGS84_E2
ep = sqrt((a**2.0-b**2.0)/b**2.0)
MAX_LAT_DIFF = 1.0e-10
## Calculate square of radius from the Earth axis to the position.
## Get radius to position by adding the Z squared.