mirror of
https://gitlab.science.ru.nl/mthesis-edeboone/m.internship-documentation.git
synced 2024-11-14 03:13:37 +01:00
229 lines
7.3 KiB
Python
229 lines
7.3 KiB
Python
|
#!/usr/bin/env python3
|
||
|
|
|
||
|
|
__doc__ = \
|
||
|
|
"""
|
||
|
|
Create a figure showing the timing and geometry of 3+1 antennas,
|
||
|
|
and the triangles between them.
|
||
|
|
The additional antenna is to show that baselines are shared between
|
||
|
|
triangles.
|
||
|
|
|
||
|
|
In code (and on stdout), the antennas have time offsets which can be determined iteratively up to an overall offset.
|
||
|
|
"""
|
||
|
|
|
||
|
|
import matplotlib.pyplot as plt
|
||
|
|
import numpy as np
|
||
|
|
from itertools import combinations
|
||
|
|
|
||
|
|
c_light = 3e8 # m/s
|
||
|
|
|
||
|
|
def distance(x1, x2):
|
||
|
|
"""
|
||
|
|
Calculate the Euclidean distance between two locations x1 and x2
|
||
|
|
"""
|
||
|
|
|
||
|
|
assert type(x1) in [Antenna]
|
||
|
|
x1 = np.array([x1.x, x1.y, x1.z])
|
||
|
|
|
||
|
|
assert type(x2) in [Antenna]
|
||
|
|
x2 = np.array([x2.x, x2.y, x2.z])
|
||
|
|
|
||
|
|
return np.sqrt( np.sum( (x1-x2)**2 ) )
|
||
|
|
|
||
|
|
def phase_mod(phase, low=np.pi):
|
||
|
|
"""
|
||
|
|
Modulo phase such that it falls within the
|
||
|
|
interval $[-low, 2\pi - low)$.
|
||
|
|
"""
|
||
|
|
return (phase + low) % (2*np.pi) - low
|
||
|
|
|
||
|
|
|
||
|
|
class Antenna:
|
||
|
|
"""
|
||
|
|
Simple Antenna class
|
||
|
|
"""
|
||
|
|
def __init__(self,x=0,y=0,z=0,t0=0,name=""):
|
||
|
|
self.x = x
|
||
|
|
self.y = y
|
||
|
|
self.z = z
|
||
|
|
self.t0 = t0
|
||
|
|
self.name = name
|
||
|
|
|
||
|
|
self.offsets = []
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
cls = self.__class__.__name__
|
||
|
|
|
||
|
|
return f'{cls}(x={self.x!r},y={self.y!r},z={self.z!r},t0={self.t0!r},name={self.name!r})'
|
||
|
|
|
||
|
|
def antenna_triangles(antennas):
|
||
|
|
return combinations(antennas, 3)
|
||
|
|
|
||
|
|
def antenna_baselines(antennas):
|
||
|
|
return combinations(antennas, 2)
|
||
|
|
|
||
|
|
def plot_four_antenna_geometry(tx, ants, extra_ant=None, ax=None, line_kwargs={}, scatter_kwargs={}, scatter_zorder=5):
|
||
|
|
|
||
|
|
default_line_kwargs = dict( color='grey', lw=3, alpha=0.7)
|
||
|
|
default_scatter_kwargs = dict( color='grey', s=200)
|
||
|
|
|
||
|
|
if ax is None:
|
||
|
|
ax = plt.gca()
|
||
|
|
ax.set_aspect('equal')
|
||
|
|
ax.set_xlabel("x")
|
||
|
|
ax.set_ylabel("y")
|
||
|
|
|
||
|
|
line_kwargs = {**default_line_kwargs, **line_kwargs}
|
||
|
|
scatter_kwargs = {**default_scatter_kwargs, **scatter_kwargs}
|
||
|
|
|
||
|
|
# Plot Antennas + Tx
|
||
|
|
for i, ant in enumerate([tx] + ants + [extra_ant]):
|
||
|
|
ax.scatter(ant.x, ant.y, zorder=scatter_zorder, **scatter_kwargs)
|
||
|
|
ax.annotate(ant.name, (ant.x, ant.y), ha='center', va='center',zorder=scatter_zorder)
|
||
|
|
|
||
|
|
# Lines connecting Tx and ants
|
||
|
|
tmp_line_kwargs = line_kwargs
|
||
|
|
for ant in ants:
|
||
|
|
ax.plot([tx.x, ant.x], [tx.y, ant.y], **tmp_line_kwargs)
|
||
|
|
|
||
|
|
# Lines due to all Antennas (including extra_ant)
|
||
|
|
line_offset = 0.08*np.array([1,1])
|
||
|
|
for i, ant_triangle in enumerate(antenna_triangles(ants + [extra_ant])):
|
||
|
|
tmp_line_kwargs['color'] = None
|
||
|
|
tmp_line_kwargs['linestyle'] = '--'
|
||
|
|
tmp_line_kwargs['alpha'] = 0.4
|
||
|
|
for j, ant in enumerate(antenna_baselines(ant_triangle)):
|
||
|
|
a, b = ant[0], ant[1]
|
||
|
|
if j == 1: # fix ordering
|
||
|
|
a, b == b, a
|
||
|
|
|
||
|
|
dx, dy = (i-1)*line_offset
|
||
|
|
|
||
|
|
l = ax.plot([ a.x+dx, b.x+dx], [a.y+dy, b.y+dy], **tmp_line_kwargs)
|
||
|
|
line_kwargs['color'] = l[0].get_color()
|
||
|
|
|
||
|
|
# Lines internal to ants triangle
|
||
|
|
tmp_line_kwargs = line_kwargs
|
||
|
|
tmp_line_kwargs['color'] = 'green'
|
||
|
|
tmp_line_kwargs['alpha'] = 0.7
|
||
|
|
for j, ant_pair in enumerate(combinations(ants,2)):
|
||
|
|
a, b = ant_pair[0], ant_pair[1]
|
||
|
|
if j == 1: # fix ordering
|
||
|
|
a, b = b, a
|
||
|
|
|
||
|
|
ax.plot([ a.x, b.x], [a.y, b.y], **tmp_line_kwargs)
|
||
|
|
|
||
|
|
return ax
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
use_phase = False
|
||
|
|
correct_time = True
|
||
|
|
|
||
|
|
tx = Antenna(name="T", x=-8, y=2, t0=0)
|
||
|
|
|
||
|
|
ants = [
|
||
|
|
Antenna(name='1', x=0, y= 0, t0=1 ),
|
||
|
|
Antenna(name='2', x=2, y=-3, t0=4 ),
|
||
|
|
Antenna(name='3', x=1, y= 3, t0=10 ),
|
||
|
|
]
|
||
|
|
|
||
|
|
extra_ant = Antenna(name='4', x=4, y=-1, t0=-6)
|
||
|
|
|
||
|
|
|
||
|
|
if False:#correct_time: # taken from the output of this script
|
||
|
|
"""
|
||
|
|
Antenna Triangle(1,2,3)
|
||
|
|
j=0: 1,2
|
||
|
|
j=1: 3,1
|
||
|
|
j=2: 2,3
|
||
|
|
sigmas: [-2.99999999 9. -6.00000001]
|
||
|
|
sigmas sum: -8.881784197001252e-16
|
||
|
|
(Antenna(x=0,y=0,z=0,t0=1,name='1'), Antenna(x=2,y=-3,z=0,t0=4,name='2'), Antenna(x=1,y=3,z=0,t0=10,name='3')) : [0. 2.99999999 9. ]
|
||
|
|
Antenna Triangle(1,2,4)
|
||
|
|
sigmas: [-2.99999999 -7.00000001 10. ]
|
||
|
|
sigmas sum: 0.0
|
||
|
|
(Antenna(x=0,y=0,z=0,t0=1,name='1'), Antenna(x=2,y=-3,z=0,t0=4,name='2'), Antenna(x=4,y=-1,z=0,t0=-6,name='4')) : [ 0. 2.99999999 -7.00000001]
|
||
|
|
Antenna Triangle(1,3,4)
|
||
|
|
sigmas: [-9. -7.00000001 16.00000001]
|
||
|
|
sigmas sum: 0.0
|
||
|
|
(Antenna(x=0,y=0,z=0,t0=1,name='1'), Antenna(x=1,y=3,z=0,t0=10,name='3'), Antenna(x=4,y=-1,z=0,t0=-6,name='4')) : [ 0. 9. -7.00000001]
|
||
|
|
Antenna Triangle(2,3,4)
|
||
|
|
sigmas: [ -6.00000001 -10. 16.00000001]
|
||
|
|
sigmas sum: 0.0
|
||
|
|
(Antenna(x=2,y=-3,z=0,t0=4,name='2'), Antenna(x=1,y=3,z=0,t0=10,name='3'), Antenna(x=4,y=-1,z=0,t0=-6,name='4')) : [ 0. 6.00000001 -10.
|
||
|
|
"""
|
||
|
|
print("Running with pre-corrected times")
|
||
|
|
ants[1].t0 -= 2.99999999
|
||
|
|
ants[2].t0 -= 9
|
||
|
|
extra_ant.t0 -= -7
|
||
|
|
|
||
|
|
ax = plot_four_antenna_geometry(tx, ants, extra_ant=extra_ant)
|
||
|
|
|
||
|
|
fig = ax.get_figure()
|
||
|
|
|
||
|
|
### Lol, show my calculations are right
|
||
|
|
for i, triangle in enumerate(antenna_triangles(ants + [extra_ant])):
|
||
|
|
print("Antenna Triangle({},{},{})".format(*[ant.name for ant in triangle]))
|
||
|
|
|
||
|
|
sigma = np.zeros((3))
|
||
|
|
for j, ant_pair in enumerate(antenna_baselines(triangle)):
|
||
|
|
a, b = ant_pair[0], ant_pair[1]
|
||
|
|
if j == 1: # fix ordering
|
||
|
|
a, b = b, a
|
||
|
|
|
||
|
|
if i == 0: # print sigma pairing for first triangle
|
||
|
|
print('j={}: {},{}'.format(j, a.name, b.name))
|
||
|
|
|
||
|
|
phys_Dt = (distance(tx, a) - distance(tx, b))/c_light
|
||
|
|
meas_Dt = a.t0 - b.t0
|
||
|
|
|
||
|
|
if use_phase:
|
||
|
|
f_beacon = 50e6 # Hz
|
||
|
|
to_phase = lambda t: phase_mod(2*np.pi*f_beacon*t)
|
||
|
|
|
||
|
|
phys_Dt = to_phase(phys_Dt)
|
||
|
|
meas_Dt = to_phase(meas_Dt)
|
||
|
|
|
||
|
|
sigma[j] = meas_Dt - phys_Dt
|
||
|
|
|
||
|
|
if False:
|
||
|
|
print(
|
||
|
|
"Dt'_{},{} = ".format(a.name, b.name)
|
||
|
|
+ "{}".format(meas_Dt)
|
||
|
|
+ " = {} - {}".format(a.t0, b.t0)
|
||
|
|
)
|
||
|
|
print(
|
||
|
|
"Dt_{},{} = ".format(a.name, b.name)
|
||
|
|
+ "{}".format(phys_Dt)
|
||
|
|
+ " = {} - {}".format(distance(tx, a), distance(tx, b))
|
||
|
|
)
|
||
|
|
|
||
|
|
print(
|
||
|
|
"sigma_{},{} = ".format(a.name, b.name)
|
||
|
|
+ "{}".format(sigma[j])
|
||
|
|
)
|
||
|
|
print("sigmas:", sigma)
|
||
|
|
if use_phase:
|
||
|
|
print("sigmas sum:", phase_mod(np.sum(sigma)))
|
||
|
|
else:
|
||
|
|
print("sigmas sum:", np.sum(sigma))
|
||
|
|
|
||
|
|
# Take the first antenna as reference
|
||
|
|
ref_idx = 0
|
||
|
|
ref_sigma = sigma[ref_idx]
|
||
|
|
sigma = sigma - ref_sigma
|
||
|
|
|
||
|
|
ant_sigma = 1/3*np.array([0, sigma[1] + sigma[2], 2*sigma[1] - sigma[2]])
|
||
|
|
|
||
|
|
for i in [1,2]:
|
||
|
|
triangle[i].offsets.append(-ant_sigma[i])
|
||
|
|
if correct_time:
|
||
|
|
triangle[i].backup_t0 = triangle[i].t0
|
||
|
|
triangle[i].t0 += -ant_sigma[i]
|
||
|
|
|
||
|
|
if correct_time:
|
||
|
|
print(ants + [extra_ant])
|
||
|
|
for i, ant in enumerate(ants + [extra_ant]):
|
||
|
|
print(i, ant.name, ant.offsets)
|
||
|
|
|
||
|
|
plt.show()
|