def lossref_compute(P,h0,h1,k=4/3.) :
"""
compute loss and reflection rays on curved earth
Parameters
----------
P : float |list
if len(P) == 1 => P is a distance
if len(P) == 4 => P is a list of [lon0,lat0,lon1,lat1]
where :
lat0 : float |string
latitude first point (decimal |deg min sec Direction)
lat1 : float |string
latitude second point (decimal |deg min sec Direction)
lon0 : float |string
longitude first point (decimal |deg min sec Direction)
lon1 : float |string
longitude second point (decimal |deg min sec Direction)
h0 : float:
height of 1st point
h1 : float:
height of 2nd point
k : electromagnetic earth factor
Returns
-------
dloss : float
length of direct path (meter)
dref : float
length of reflective path (meter)
psy : float
Reflection angle
References
----------
B. R. Mahafza, Radar systems analysis and design using MATLAB, Third edition. Boca Raton; London: CRC/Taylor & Francis, chapter 8, 2013.
"""
if isinstance(P,float) or isinstance(P,int) :
#P is a distance
r=P
mode = 'dist'
elif isinstance(P,np.ndarray) or isinstance(P,list):
if len(P) == 1:
#P is a distance
r=P
mode = 'dist'
elif len(P) == 4:
#P is a lonlat
lat0=P[0]
lon0=P[1]
lat1=P[2]
lon1=P[2]
mode = 'lonlat'
else :
raise AttributeError('P must be a list [lat0,lon0,lat1,lon0] or a distance')
else :
raise AttributeError('Invalid P format ( list |ndarray )')
# if h0<h1:
# h1,h0 = h0,h1
r0 = 6371.e3 # earth radius
re = k*r0 # telecom earth radius
if mode == 'lonlat':
# r = distance curvilignenp.arcsin((h1/R1)-R1/(2.*re)) entre TXetRX / geodesic
r = gu.distance_on_earth(lat0, lon0, lat1, lon1)
else :
r=P
r=1.*r
# import ipdb
# ipdb.set_trace()
p = 2/(np.sqrt(3))*np.sqrt(re*(h0+h1)+(r**2/4.)) #eq 8.45
eps = np.arcsin(2*re*r*(h1-h0)/p**3) # eq 8.46
#distance of reflection on curved earth
r1 = r/2 - p*np.sin(eps/3) #eq 8.44
r2 = r -r1
phi1 = r1/re #8.47
phi2 = r2/re # 8.48
R1 = np.sqrt(h0**2+4*re*(re+h0)*(np.sin(phi1/2))**2) # 8.51
R2 = np.sqrt(h1**2+4*re*(re+h1)*(np.sin(phi2/2))**2) #8.52
Rd = np.sqrt((h1-h0)**2+4*(re+h1)*(re+h0)*np.sin((phi1+phi2)/2.)**2) # 8.53
# tangente angle on earth
psy = np.arcsin((h1/R1)-R1/(2.*re)) #eq 8.55
deltaR = 4*R1*R2*np.sin(psy)**2/(R1+R2+Rd)
dloss = Rd
dref = R1+R2
return psy,dloss,dref
def lossref_compute(P, h0, h1, k=4 / 3.):
"""
compute loss and reflection rays on curved earth
Parameters
----------
P : float |list
if len(P) == 1 => P is a distance
if len(P) == 4 => P is a list of [lon0,lat0,lon1,lat1]
where :
lat0 : float |string
latitude first point (decimal |deg min sec Direction)
lat1 : float |string
latitude second point (decimal |deg min sec Direction)
lon0 : float |string
longitude first point (decimal |deg min sec Direction)
lon1 : float |string
longitude second point (decimal |deg min sec Direction)
h0 : float:
height of 1st point
h1 : float:
height of 2nd point
k : electromagnetic earth factor
Returns
-------
dloss : float
length of direct path (meter)
dref : float
length of reflective path (meter)
psy : float
Reflection angle
References
----------
B. R. Mahafza, Radar systems analysis and design using MATLAB, Third edition. Boca Raton; London: CRC/Taylor & Francis, chapter 8, 2013.
"""
if isinstance(P, float) or isinstance(P, int):
#P is a distance
r = P
mode = 'dist'
elif isinstance(P, np.ndarray) or isinstance(P, list):
if len(P) == 1:
#P is a distance
r = P
mode = 'dist'
elif len(P) == 4:
#P is a lonlat
lat0 = P[0]
lon0 = P[1]
lat1 = P[2]
lon1 = P[2]
mode = 'lonlat'
else:
raise AttributeError(
'P must be a list [lat0,lon0,lat1,lon0] or a distance')
else:
raise AttributeError('Invalid P format ( list |ndarray )')
# if h0<h1:
# h1,h0 = h0,h1
r0 = 6371.e3 # earth radius
re = k * r0 # telecom earth radius
if mode == 'lonlat':
# r = distance curvilignenp.arcsin((h1/R1)-R1/(2.*re)) entre TXetRX / geodesic
r = gu.distance_on_earth(lat0, lon0, lat1, lon1)
else:
r = P
r = 1. * r
# import ipdb
# ipdb.set_trace()
p = 2 / (np.sqrt(3)) * np.sqrt(re * (h0 + h1) + (r**2 / 4.)) #eq 8.45
eps = np.arcsin(2 * re * r * (h1 - h0) / p**3) # eq 8.46
#distance of reflection on curved earth
r1 = r / 2 - p * np.sin(eps / 3) #eq 8.44
r2 = r - r1
phi1 = r1 / re #8.47
phi2 = r2 / re # 8.48
R1 = np.sqrt(h0**2 + 4 * re * (re + h0) * (np.sin(phi1 / 2))**2) # 8.51
R2 = np.sqrt(h1**2 + 4 * re * (re + h1) * (np.sin(phi2 / 2))**2) #8.52
Rd = np.sqrt((h1 - h0)**2 + 4 * (re + h1) * (re + h0) * np.sin(
(phi1 + phi2) / 2.)**2) # 8.53
# tangente angle on earth
psy = np.arcsin((h1 / R1) - R1 / (2. * re)) #eq 8.55
deltaR = 4 * R1 * R2 * np.sin(psy)**2 / (R1 + R2 + Rd)
dloss = Rd
dref = R1 + R2
return psy, dloss, dref