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geopos.py
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geopos.py
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''' Style Guide http://www.python.org/dev/peps/pep-0008/ '''
''' standard library imports '''
import math
''' related third party imports '''
import numpy as np
import pyproj
''' local application/library specific imports '''
''' Constants '''
A = 6378137.0
INVFLat = 298.257223563
F = 1.0/INVFLat
ESQUARED = (2.0*F - F**2)
ONE_MINUS_ESQUARED = 1.0 - ESQUARED
def loadIntrinsicParameters(fString = 'Data/Common/t.txt'):
'''
This function loads the intrinsic paremeters from file
and returns them as 3 numpy matricies
'''
File = open(fString, "r")
data= File.read().split()
File.close()
matrix = np.zeros((3,5))
for r in range(3):
for c in range(5):
matrix[r][c] = float(data[c+r*5])
Tne = matrix[:,0:3]
#INS-lidar translation
ins_lidar = matrix[:,3:4]
#INS-GPS translation
ins_gps = matrix[:,4:5]
Tne = np.matrix(Tne)
ins_lidar = np.matrix(ins_lidar)
ins_gps = np.matrix(ins_gps)
return(Tne,ins_lidar,ins_gps)
def buildCbnMatrix(Roll,Pitch,Yaw):
'''
# direct assignment
# body frame
# x == direction of travel
# y == to the right
# z == down
# Three rotations to transform the point
# vector from the body coordinate system
# to the navigation coordinate system.
#-----------------------------------------
#/*
#Cbn = [ cosd(Yaw)*cosd(Pitch) (cosd(Yaw)*sind(Pitch)*sind(Roll)-sind(Yaw)*cosd(Roll)) (cosd(Yaw)*sind(Pitch)*cosd(Roll)+sind(Yaw)*sind(Roll))
# sind(Yaw)*cosd(Pitch) (sind(Yaw)*sind(Pitch)*sind(Roll)+cosd(Yaw)*cosd(Roll)) (sind(Yaw)*sind(Pitch)*cosd(Roll)-cosd(Yaw)*sind(Roll))
# -sind(Pitch) cosd(Pitch)*sind(Roll) cosd(Pitch)*cosd(Roll)]
#*/
'''
#Cbn = np.matrix(np.zeros((3,3))) # body to nav frame rotation matrix
Cbn = np.zeros((3,3)) # body to nav frame rotation matrix
Roll = math.radians(Roll)
Pitch = math.radians(Pitch)
Yaw = math.radians(Yaw)
cos_Yaw = math.cos(Yaw)
cos_Pitch = math.cos(Pitch)
cos_Roll = math.cos(Roll)
sin_Yaw = math.sin(Yaw)
sin_Pitch = math.sin(Pitch)
sin_Roll = math.sin(Roll)
# row 1
Cbn[0,0] = cos_Yaw * cos_Pitch
Cbn[0,1] = cos_Yaw * sin_Pitch * sin_Roll - sin_Yaw * cos_Roll
Cbn[0,2] = cos_Yaw * sin_Pitch * cos_Roll + sin_Yaw * sin_Roll
# row 2
Cbn[1,0] = sin_Yaw * cos_Pitch
Cbn[1,1] = sin_Yaw * sin_Pitch * sin_Roll + cos_Yaw * cos_Roll
Cbn[1,2] = sin_Yaw * sin_Pitch * cos_Roll - cos_Yaw * sin_Roll
# row 3
Cbn[2,0] = -sin_Pitch
Cbn[2,1] = cos_Pitch * sin_Roll
Cbn[2,2] = cos_Pitch * cos_Roll
return(Cbn)
def buildCneMatrix(Lon,Lat):
# build Cne matrix
'''
% matrix of two rotations (3X3)
% Assumes X = north, Y = East, Z = up
Cne = [-sind(Lat)*cosd(Lon) -sind(Lon) -cosd(Lat)*cosd(Lon)
-sind(Lat)*sind(Lon) cosd(Lon) -cosd(Lat)*sind(Lon)
cosd(Lat) 0 -sind(Lat)]
This gives the point offset (dX, dY, dZ) from the nav frame origin.
'''
# transformation / rotation 3X3
#Cne = np.matrix(np.zeros((3,3))) # nav to ECEF rotation matrix
Cne = np.zeros((3,3)) # nav to ECEF rotation matrix
sinLat = math.sin(Lat)
cosLat = math.cos(Lat)
sinLon = math.sin(Lon)
cosLon = math.cos(Lon)
# row 1
Cne[0,0] = -sinLat * cosLon
Cne[0,1] = -sinLon
Cne[0,2] = -cosLat * cosLon
# row 2
Cne[1,0]= -sinLat * sinLon
Cne[1,1] = cosLon
Cne[1,2] = -cosLat * sinLon
# row 3
Cne[2,0] = cosLat
Cne[2,1] = 0.0
Cne[2,2] = -sinLat
return(Cne)
'''
def XYZtoLLH(pointX,pointY,pointZ):
p = math.sqrt(pointX**2+pointY**2)
r = math.sqrt(pointX**2+pointY**2+pointZ**2)
u = math.atan2((pointZ*(1.0-F+(ESQUARED*A)/r)),p)
sin_u = math.sin(u)
cos_u = math.cos(u)
Lon = math.atan2(pointY,pointX)
Lat = math.atan2((pointZ*(1-F)+ESQUARED*A*sin_u*sin_u*sin_u),((1-F)*(p-ESQUARED*A*cos_u*cos_u*cos_u)))
sin_Lat = math.sin(Lat)
pointHeight = p*math.cos(Lat) + (pointZ * sin_Lat) - A*math.sqrt(1.0 - (ESQUARED * sin_Lat**2))
pointLon = math.degrees(Lon)
pointLat = math.degrees(Lat)
return(pointLat,pointLon,pointHeight)
'''
def XYZtoLLH(X,Y,Z):
ecef = pyproj.Proj(proj='geocent', ellps='WGS84', datum='WGS84')
wgs84 = pyproj.Proj(proj='latlong', ellps='WGS84', datum='WGS84')
lon,lat, alt = pyproj.transform(ecef,wgs84, X,Y,Z)
return(lon, lat, alt)
def geoPos(Range,Angle,Lat,Lon,Height,Roll,Pitch,Yaw,Tne,ins_lidar,ins_gps):
''' This function ties together the data from the LiDAR with the GPS INS '''
Lat = math.radians(Lat)
Lon = math.radians(Lon)
Angle = math.radians(Angle)
sinLat = math.sin(Lat)
cosLat = math.cos(Lat)
sinLon = math.sin(Lon)
cosLon = math.cos(Lon)
''' Setting up some matricies '''
# coordinates 3X1
#Pb lidar point in body frame (== INS frame)
#Pn lidar point in navigation frame
#Ln Lidar - GPS offset in nav frame
#Pe lidar point offset from nav frame origin (dX dY dZ)
#Tne sensor to body frame rotation matrix
#Pecef lidar point in XYZ ECEF
NOe = np.zeros((3,1))# nav frame origin in XYZ ECEF
Ps = np.zeros((3,1))# lidar point in sensor frame
'''
# Tne is transformation matrix for body frame to local frame
# body frame = x direction of vehicle, y clockwise right, z down
# calcuLate body frame XYZ for target for all lidar measurements
# assume lidar is aligned to Y-Z body frame plane
'''
''' Position vector of point with respect to LiDAR'''
Ps[0] = Range*math.sin(Angle)
Ps[1] = 0.0
Ps[2] = Range*math.cos(Angle)
# rotate Ps by Tne to get Rbrt
Rbr = np.dot(Tne,Ps)
# transLate Rb by to get Pb
Pb = Rbr - ins_lidar
#create CbnMatrix
Cbn = buildCbnMatrix(Roll,Pitch,Yaw)
# rotate Pb by Cbn to get Pn
# This is three rotations around (in order) 1)Roll, 2)Pitch 3)Yaw
Pn = np.dot(Cbn,Pb)
'''
# Offset between GPS antenna and INS
#------------------------------------
# offset in body frame given in input file
# check if this data is not all 0
# as this indicates that this trasformation
# is either not wanted or not needed.
#if(ts->use_ins_gps)
#{
# calcuLate the INS - GPS offset for this epoch
# in the navigation frame
#mMultiply(&Ln, &Cbn, &ts->ins_gps)
'''
Ln = np.dot(Cbn,ins_gps)
# add Ln to Pn
Pn += Ln
# rotate Rn by Tne to get Rt
Cne = buildCneMatrix(Lon,Lat)
# rotate Pn by Cne to get Pe
Pe = np.dot(Cne,Pn)
# or Rt, if axis transformation is needed
# or the other way around
#mMultiply(&Rt, &Cne, &Pn)
#mMultiply(&Pe, &Tne, &Rt)
# build NOe
'''
transform nav frame origin to ECEF (WGS84) (3X1)
V is radius of curvature in meridian
normal section on ellipsoid
v = a/(sqrt(1-esq*(sind(Lat))**2))
NOe = [(v+h)*cosd(Lat)*cosd(Lon)
(v+h)*cosd(Lat)*sind(Lon)
(v*one_minus_esquared+h)*sind(Lat)]
'''
''' conversion to ECEF '''
v = A/(math.sqrt(1.0 - (ESQUARED * sinLat**2)))
NOe[0] = (v + Height) * cosLat * cosLon
NOe[1] = (v + Height) * cosLat * sinLon
NOe[2] = (v * ONE_MINUS_ESQUARED + Height) * sinLat
'''
Apply Range offset to origin in ECEF to obtain the XYZ coordinates of the target.
Recef = NOe + Pe %(3X1)
'''
Pecef = NOe+Pe
pointX = float(Pecef[0])
pointY = float(Pecef[1])
pointZ = float(Pecef[2])
lat,lon,height = XYZtoLLH(pointX,pointY,pointZ)
return(lat,lon,height)