def main():
# Verification 1
#file_root_name = 'raw/L1B/2015-02-11-H18'
#group = '000139'
#index = 839
# Verification 2
file_root_name = 'raw/L1B/2015-02-11-H18'
group = '000139'
index = 592
tds = tds_data(file_root_name)
tds.set_group_index(group, index)
tds.plot_ddm()
datenum = tds.metagrp.groups[tds.group].variables['IntegrationMidPointTime'][tds.index]
lat = tds.metagrp.groups[tds.group].variables['SpecularPointLat'][tds.index]
lon = tds.metagrp.groups[tds.group].variables['SpecularPointLon'][tds.index]
string = 'G: ' + group + ' I: ' + str(index) + ' - ' + \
str(datenum_to_pytime(float(datenum))) + \
' - Lat: ' + str(lat) + ' Lon: ' + str(lon) + '\n'
print(string)
plt.show(block=False)
plt.show()
def cdf4_search(file_root_name, target, search_error):
filename = os.path.join(os.environ['TDS_ROOT'],
file_root_name + '-metadata.nc')
print(filename)
search_output = filename + '\n'
tds = tds_data(file_root_name)
group_len = len(tds.metagrp.groups)
for group in tds.metagrp.groups:
step = 10
index_len = len(
tds.metagrp.groups[group].variables['IntegrationMidPointTime'])
for index in range(0, index_len, step):
print(
str(group) + '/' + str(group_len) + ' : ' + str(index) + '/' +
str(index_len))
tds.set_group_index(group, index)
datenum = tds.metagrp.groups[group].variables[
'IntegrationMidPointTime'][index]
# 0.5 deg error approx 55 km error
if (angle_between(tds.r_r, tds.r_t) <= search_error):
string = 'G: ' + group + ' I: ' + str(index) + ' - ' + \
str(datenum) + ' - ' + str(datenum_to_pytime(float(datenum))) + ' - Lat: ' + \
str(tds.lat_sp_tds) + ' Lon: ' + str(tds.lon_sp_tds) + \
'Angle (deg): ' + str(angle_between(tds.r_r, tds.r_t)*180/np.pi) + '\n'
print(string)
search_output = search_output + string
return search_output
def main():
# Di Simone Oil Platform Data
file_root_name = 'raw/L1B/2015-04-01-H00'
target = targets['hibernia']
group = '000095'
index = 525
tds = tds_data(file_root_name)
p = target_processor();
for i in range(index - 200, index + 10):
ddm = tds.rootgrp.groups[group].variables['DDM'][i].data
p.process_ddm(ddm)
def main():
# Di Simone
file_root_name = '2015-04-01-H00'
target = targets['hibernia']
group = '000095'
index = 525
# Hibernia
# Really good detection
#file_root_name = 'raw/L1B/2017-03-12-H18'
#target = targets['hibernia']
#group = '000035'
#index = 681
# Devils Tower
#file_root_name = 'raw/L1B/2015-12-04-H18'
#target = targets['devils_tower']
#group = '000066'
#index = 376
#file_root_name = 'raw/L1B/2016-11-14-H06'
#target = targets['petronius']
#group = '000057'
#index = 0
# 0.5 deg error approx 55 km error
if index == 0:
search_error = 0.7
cdf4_search(file_root_name, target, search_error)
target_delay_increment = 4
target_doppler_increment = 2000
tds = tds_data(file_root_name, group, index)
tds.set_group_index(group, index)
tds.plot_ddm()
print("t vel: {}".format(np.linalg.norm(tds.v_t)))
r_sp, lat_sp, lon_sp = tds.find_sp()
n_z = unit_vector(ellip_norm(r_sp))
n_x = unit_vector(np.cross(n_z, r_sp - tds.r_t))
n_y = unit_vector(np.cross(n_z, n_x))
#TODO: imporve sp auto calculation
h_r = np.dot((tds.r_r - r_sp), n_z)
print("h_r: {}".format(h_r))
h_t = np.dot((tds.r_t - r_sp), n_z)
print("h_t: {}".format(h_t))
elev = angle_between(n_y, tds.r_t - r_sp)
print("elev: {}".format(elev))
print("elev tds: {}".format(90 - tds.sp_incidence_tds))
print("elve: {0} elev: {1}".format(
elev * 180 / np.pi,
angle_between(-n_y, tds.r_r - r_sp) * 180 / np.pi))
print("h_r: {0} h_t: {1}".format(h_r, h_t))
def z_sp(x, y):
R = np.linalg.norm(r_sp)
print("r: {}".format(R))
return (R**2 - x**2 - y**2)**(1 / 2) - R
light_speed = 299792458 # m/s
def time_inc_eq(x, y):
return (np.sqrt(x**2 + (y + h_r / np.tan(elev))**2 + h_r**2) -
h_r / np.sin(elev) - y * np.cos(elev)) / light_speed
def doppler_eq(x, y):
# GPS L1 center frequency
f_0 = 10.23e6 # Hz
f_carrier = 154 * f_0
# 1575.42e6 Hz
v_tx = np.dot(tds.v_t, n_x)
v_ty = np.dot(tds.v_t, n_y)
v_tz = np.dot(tds.v_t, n_z)
v_rx = np.dot(tds.v_r, n_x)
v_ry = np.dot(tds.v_r, n_y)
v_rz = np.dot(tds.v_r, n_z)
# With the very far way transmitter approximation:
f_D_0 = f_carrier / light_speed * (
-v_ty * np.cos(elev) - v_tz * np.sin(elev) +
(v_rx * x + v_ry * (y + h_r / np.tan(elev)) - v_rz * h_r) *
(x**2 + (y + h_r / np.tan(elev))**2 + h_r**2)**(-0.1e1 / 0.2e1))
return f_D_0
def doppler_inc_eq(x, y):
return doppler_eq(x, y) - doppler_eq(0, 0)
extent = 200e3
extent_x0 = -extent
extent_x1 = extent
extent_y0 = -extent
extent_y1 = extent
linsapce_delta = 500
X, Y = np.meshgrid(np.linspace(extent_x0, extent_x1, linsapce_delta),
np.linspace(extent_y0, extent_y1, linsapce_delta))
delay_chip = 1 / 1.023e6 # seconds
Z_time_chip = time_inc_eq(X, Y) / delay_chip
Z_doppler = doppler_inc_eq(X, Y)
fig_surface, ax_surface = plt.subplots(1, figsize=(10, 4))
plt.xlabel('[km]')
plt.ylabel('[km]')
ticks_x = ticker.FuncFormatter(lambda x, pos: '{0:g}'.format(x / 1000))
ticks_y = ticker.FuncFormatter(lambda y, pos: '{0:g}'.format(y / 1000))
ax_surface.xaxis.set_major_formatter(ticks_x)
ax_surface.yaxis.set_major_formatter(ticks_y)
# Iso-Delay Contour
ax_surface.set_title('Time Delay Contour')
contour_delay = ax_surface.contour(X,
Y,
Z_time_chip,
np.arange(0, 15, 0.5),
cmap='viridis')
fig_surface.colorbar(contour_delay, label='C/A chips')
ax_surface.grid(c='k', ls='-', alpha=0.3)
plt.show(block=False)
# Iso-Doppler Contour
ax_surface.set_title('Doppler Shift Contour')
plt.xlabel('[km]')
plt.ylabel('[km]')
contour_doppler = ax_surface.contour(X,
Y,
Z_doppler,
np.arange(-5000, 5000, 500),
cmap='viridis')
fig_surface.colorbar(contour_doppler, label='Hz')
ax_surface.grid(c='k', ls='-', alpha=0.3)
target_iso_delay = ax_surface.contour(X,
Y,
Z_time_chip,
[target_delay_increment],
colors='red',
linewidths=2.5,
linestyles='dashed',
extent=(extent_x0, extent_x1,
extent_y0, extent_y1))
target_iso_doppler = ax_surface.contour(X,
Y,
Z_doppler,
[target_doppler_increment],
colors='red',
linewidths=2.5,
linestyles='dashed',
extent=(extent_x0, extent_x1,
extent_y0, extent_y1))
# TDS specular point in local coordinates
x_sp_tds = np.dot(n_x, (tds.r_sp_tds - r_sp))
y_sp_tds = np.dot(n_y, (tds.r_sp_tds - r_sp))
ax_surface.scatter(x_sp_tds,
x_sp_tds,
s=70,
marker=(5, 2),
zorder=4,
color='green')
# Target in ECEF coordinates
target_lat = target.lat_deg * np.pi / 180
target_lon = target.lon_deg * np.pi / 180
r_target_x = np.linalg.norm(r_sp) * np.cos(target_lat) * np.cos(target_lon)
r_target_y = np.linalg.norm(r_sp) * np.cos(target_lat) * np.sin(target_lon)
r_target_z = np.linalg.norm(r_sp) * np.sin(target_lat)
r_target = np.array([r_target_x, r_target_y, r_target_z])
# Target in local coordinates
x_target = np.dot(n_x, (r_target - r_sp))
y_target = np.dot(n_y, (r_target - r_sp))
ax_surface.scatter(x_target, y_target, s=70, zorder=4, color='black')
lon = np.arctan2(r_target[1], r_target[0]) * 180 / np.pi
lat = np.arcsin(abs(r_target[2] / np.linalg.norm(r_target))) * 180 / np.pi
print("lat target: {0} lon target: {1}".format(lat, lon))
# Intersection of target iso-delay and iso-doppler intersections
intersections = find_contour_intersection(target_iso_delay,
target_iso_doppler)
try:
for i in intersections:
ax_surface.scatter(i.x, i.y, s=70, zorder=4, color='orange')
r_i = np.array([i.x, i.y])
r_target = np.array([x_target, y_target])
print("error: {0}".format(np.linalg.norm(r_target - r_i) / 1e3))
r_sol = r_sp + n_x * i.x + n_y * i.y
lon = np.arctan2(r_sol[1], r_sol[0]) * 180 / np.pi
lat = np.arcsin(abs(
r_sol[2] / np.linalg.norm(r_sol))) * 180 / np.pi
print("lat: {0} lon: {1}".format(lat, lon))
except TypeError as te:
print('No intersections')
n_z = unit_vector(ellip_norm(tds.r_sp_tds))
n_x = unit_vector(np.cross(n_z, tds.r_sp_tds - tds.r_t))
n_y = unit_vector(np.cross(n_z, n_x))
v_tx = np.dot(tds.v_t, n_x)
v_ty = np.dot(tds.v_t, n_y)
v_tz = np.dot(tds.v_t, n_z)
v_rx = np.dot(tds.v_r, n_x)
v_ry = np.dot(tds.v_r, n_y)
v_rz = np.dot(tds.v_r, n_z)
sim_config = simulation_configuration()
sim_config.set_scenario_local_ref(
h_r=np.dot((tds.r_r - tds.r_sp_tds), n_z),
h_t=np.dot((tds.r_t - tds.r_sp_tds), n_z),
elevation=angle_between(n_y, tds.r_t - tds.r_sp_tds),
v_t=np.array([v_tx, v_ty, v_tz]),
v_r=np.array([v_rx, v_ry, v_rz]))
doppler_specular_point = eq_doppler_absolute_shift(np.array([0, 0, 0]),
sim_config)
delay = np.array([4 * delay_chip])
f_doppler = np.array([doppler_specular_point + 1800])
r_1, r_2 = spherical.delay_doppler_to_local_surface(
delay, f_doppler, sim_config)
print(r_1)
print(r_2)
ax_surface.scatter(r_1[0], r_1[1], s=70, zorder=4, color='blue')
ax_surface.scatter(r_2[0], r_2[1], s=70, zorder=4, color='blue')
plt.show(block=False)
plt.show()
def main():
sim_config = simulation_configuration()
sim_config.jacobian_type = 'spherical'
delay_chip = sim_config.delay_chip
# Decent noise results
file_root_name = '2017-03-12-H18'
target = targets['hibernia']
group = '000035'
index = 675 - 15
tds = tds_data(file_root_name, group, index)
mean_wind = tds.get_wind()
p = target_processor_power()
n = 1
p.n = n
for i in range(index - n, index + 2):
tds.set_group_index(group, i)
ddm_i = normalize(tds.rootgrp.groups[group].variables['DDM']
[i].data) * tds.peak_power()
p.process_ddm(ddm_i)
wind = tds.get_wind()
if (wind != None):
print("wind: {0}".format(wind))
mean_wind += wind
mean_wind /= 2
ddm_tds = np.copy(p.sea_clutter)
print("mean wind: {0}".format(mean_wind))
sim_config.u_10 = 15
sim_config.phi_0 = -200 * np.pi / 180
# Plot TDS DDM sea clutter
tds.set_group_index(group, index)
r_sp, lat_sp, lon_sp = tds.find_sp()
datenum = tds.rootgrp.groups[
tds.group].variables['IntegrationMidPointTime'][tds.index]
string = str(datenum_to_pytime(float(datenum))) \
+ ' Lat: ' + "{0:.2f}".format(tds.lat_sp_tds) \
+ ' Lon: ' + "{0:.2f}".format(tds.lon_sp_tds)
tds_number_of_delay_pixels = tds.metagrp.groups[
tds.group].NumberOfDelayPixels
tds_number_of_doppler_pixels = tds.metagrp.groups[
tds.group].NumberOfDopplerPixels
tds_delay_start = tds.calculate_delay_increment_chips(0)
tds_delay_end = tds.calculate_delay_increment_chips(
tds_number_of_delay_pixels - 1)
tds_delay_resolution = (tds_delay_end - tds_delay_start) / 128
tds_doppler_start = tds.calculate_doppler_increment(
-np.floor(tds_number_of_doppler_pixels / 2))
tds_doppler_end = tds.calculate_doppler_increment(
np.floor(tds_number_of_doppler_pixels / 2 - 0.5))
tds_doppler_resolution = 500
fig_tds, ax_tds = plt.subplots(1, figsize=(10, 4))
plt.title('TDS-1 Experimental Data')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
contour_tds = ax_tds.imshow(
ddm_tds,
cmap='jet',
extent=(tds_delay_start, tds_delay_end, tds_doppler_end,
tds_doppler_start),
aspect=(tds_number_of_doppler_pixels / tds_number_of_delay_pixels) /
np.abs(tds_doppler_start / tds_delay_start))
t = plt.text(0.01,
0.85,
string, {
'color': 'w',
'fontsize': 12
},
transform=ax_tds.transAxes)
cbar = fig_tds.colorbar(contour_tds, label='Power')
# Load TDS Geometry in simulation configuration
n_z = unit_vector(ellip_norm(tds.r_sp_tds))
n_x = unit_vector(np.cross(n_z, tds.r_sp_tds - tds.r_t))
n_y = unit_vector(np.cross(n_z, n_x))
v_tx = np.dot(tds.v_t, n_x)
v_ty = np.dot(tds.v_t, n_y)
v_tz = np.dot(tds.v_t, n_z)
v_rx = np.dot(tds.v_r, n_x)
v_ry = np.dot(tds.v_r, n_y)
v_rz = np.dot(tds.v_r, n_z)
sim_config.set_scenario_local_ref(
h_r=np.dot((tds.r_r - tds.r_sp_tds), n_z),
h_t=np.dot((tds.r_t - tds.r_sp_tds), n_z),
elevation=angle_between(n_y, tds.r_t - tds.r_sp_tds),
v_t=np.array([v_tx, v_ty, v_tz]),
v_r=np.array([v_rx, v_ry, v_rz]))
# DDM
sim_config.delay_increment_start = tds_delay_start * delay_chip
sim_config.delay_increment_end = tds_delay_end * delay_chip
sim_config.delay_resolution = (
sim_config.delay_increment_end -
sim_config.delay_increment_start) / tds_number_of_delay_pixels / 3
sim_config.doppler_increment_start = tds_doppler_start
sim_config.doppler_increment_end = tds_doppler_end + tds_doppler_resolution
sim_config.doppler_resolution = (
sim_config.doppler_increment_end -
sim_config.doppler_increment_start) / tds_number_of_doppler_pixels / 3
ddm_sim = (simulate_ddm(sim_config))
fig_ddm, ax_ddm = plt.subplots(1, figsize=(10, 4))
plt.title('DDM original simulation')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
contour_ddm = ax_ddm.imshow(ddm_sim,
cmap='jet',
extent=(sim_config.delay_increment_start,
sim_config.delay_increment_end,
sim_config.doppler_increment_end,
sim_config.doppler_increment_start),
aspect="auto")
cbar = fig_ddm.colorbar(contour_ddm, label='Normalized Power')
# Image downscaling to desired resolution:
fig_ddm_rescaled, ax_ddm_rescaled = plt.subplots(1, figsize=(10, 4))
plt.title('Simulation Rescaled')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
ddm_rescaled = rescale(ddm_sim, tds_number_of_doppler_pixels,
tds_number_of_delay_pixels)
ddm_rescaled[0, :] = ddm_rescaled[2, :]
ddm_rescaled[1, :] = ddm_rescaled[2, :]
ddm_rescaled[:, 0] = ddm_rescaled[:, 2]
ddm_rescaled[:, 1] = ddm_rescaled[:, 2]
# Noise
waf_delay_increment_values = list(
np.arange(
-tds_delay_end * delay_chip,
tds_delay_end * delay_chip + tds_delay_resolution * delay_chip,
tds_delay_resolution * delay_chip))
waf_doppler_increment_values = list(
np.arange(tds_doppler_start, tds_doppler_end + tds_doppler_resolution,
tds_doppler_resolution))
waf_delay_grid, waf_doppler_grid = np.meshgrid(
waf_delay_increment_values, waf_doppler_increment_values)
waf_matrix = woodward_ambiguity_function(waf_delay_grid, waf_doppler_grid,
sim_config)**2
T_noise_receiver = 225
k_b = 1.38e-23 # J/K
y_noise = 1 / sim_config.coherent_integration_time * k_b * T_noise_receiver
p1 = target_processor_power()
n = 500
p1.n = n
p1.tau = 0.08
ddm_noise = np.zeros(ddm_rescaled.shape)
for i in range(n + 1):
print("i: {0}".format(i))
noise_i = y_noise * (np.random.rand(ddm_rescaled.shape[0],
ddm_rescaled.shape[1]))
ddm_noise_i = np.abs(
signal.convolve2d(noise_i, waf_matrix, mode='same'))
p1.process_ddm(np.abs(ddm_rescaled + ddm_noise_i))
ddm_rescaled = p1.sea_clutter
contour_res = ax_ddm_rescaled.imshow(
ddm_rescaled,
cmap='jet',
extent=(tds_delay_start, tds_delay_end, tds_doppler_end,
tds_doppler_start),
aspect=(tds_number_of_doppler_pixels / tds_number_of_delay_pixels) /
np.abs(tds_doppler_start / tds_delay_start))
cbar = fig_ddm_rescaled.colorbar(contour_res,
label='Normalized Power',
shrink=0.35)
fig_diff, ax_diff = plt.subplots(1, figsize=(10, 4))
plt.title('Difference')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
ddm_diff = np.copy(ddm_rescaled)
for row_i, row in enumerate(ddm_diff):
for col_i, val in enumerate(row):
val_tds = ddm_tds[row_i, col_i]
val = ddm_rescaled[row_i, col_i]
ddm_diff[row_i, col_i] = np.abs((val - val_tds) / val_tds)
#np.place(ddm_diff, ddm_diff < 0, np.nan)
im = ax_diff.imshow(
ddm_diff,
cmap='jet',
extent=(tds_delay_start, tds_delay_end, tds_doppler_end,
tds_doppler_start),
aspect=(tds_number_of_doppler_pixels / tds_number_of_delay_pixels) /
np.abs(tds_doppler_start / tds_delay_start))
cbar = fig_diff.colorbar(im, label='Normalized Power', shrink=0.35)
plt.show()
def main():
sim_config = simulation_configuration()
sim_config.jacobian_type = 'spherical'
delay_chip = sim_config.delay_chip
file_root_name = '2015-12-04-H18'
target = targets['devils_tower']
group = '000066'
index = 385 - 10
tds = tds_data(file_root_name, group, index)
#sim_config.receiver_antenna_gain = lambda p1,p2: 12
'''
p = target_processor_power();
p.n = n
for i in range(index - n, index + 2):
tds.set_group_index(group, i)
ddm_i = normalize(tds.rootgrp.groups[group].variables['DDM'][i].data)*tds.peak_power()
p.process_ddm(ddm_i)
wind = tds.get_wind()
if (wind != None):
print("wind: {0}".format(wind))
mean_wind += wind
mean_wind /= 2
ddm_tds = np.copy(p.sea_clutter)
print("mean wind: {0}".format(mean_wind))
'''
sim_config.fresnel_coefficient = 0.8
n_tds = 20
n = n_tds
ddm_tds = np.zeros(
tds.rootgrp.groups[group].variables['DDM'][index].data.shape)
mean_wind = 0
n_wind = 0
noise_antenna_mean = 0
noise_rx_mean = 0
for i in range(n):
print("i: {0}".format(i))
tds.set_group_index(group, index + i)
power_i, noise_i = tds.peak_power()
ddm_i = normalize(
tds.rootgrp.groups[group].variables['DDM'][index +
i].data) * power_i
print("noise power estimate: {0}".format(noise_i))
ddm_tds += ddm_i
wind = tds.get_wind()
noise_antenna_mean_i = tds.metagrp.groups[group].variables[
'AntennaTemperature'][tds.index].data
if (np.isnan(noise_antenna_mean_i)):
noise_antenna_mean_i = tds.metagrp.groups[group].variables[
'AntennaTemperatureExtRef'][tds.index].data
if (np.isnan(noise_antenna_mean_i)):
noise_antenna_mean_i = 225.7
noise_rx_mean_i = tds.metagrp.variables['RxTemperature'][
tds.index_meta].data
if (np.isnan(noise_rx_mean_i)):
noise_rx_mean_i = 232.09
noise_antenna_mean += noise_antenna_mean_i
noise_rx_mean += noise_rx_mean_i
print("noise antenna : {}".format(noise_antenna_mean_i))
if (wind != None):
print("wind: {0}".format(wind))
mean_wind += wind
n_wind += 1
mean_wind /= n_wind
ddm_tds /= n
#np.flip(ddm_tds)
noise_antenna_mean /= n
noise_rx_mean /= n
noise_antenna_mean = 246.85
noise_rx_mean = 252.09
print("noise_antenna_mean: {0}".format(noise_antenna_mean))
print("noise_rx_mean: {0}".format(noise_rx_mean))
print("mean wind: {0}".format(mean_wind))
sim_config.u_10 = 2.35
#sim_config.phi_0 = 130*np.pi/180 # 0.547
sim_config.phi_0 = 45 * np.pi / 180 # max power diff: 0.58
# Plot TDS DDM sea clutter
tds.set_group_index(group, index)
r_sp, lat_sp, lon_sp = tds.find_sp()
datenum = tds.rootgrp.groups[
tds.group].variables['IntegrationMidPointTime'][tds.index]
string = str(datenum_to_pytime(float(datenum))) \
+ ' Lat: ' + "{0:.2f}".format(tds.lat_sp_tds) \
+ ' Lon: ' + "{0:.2f}".format(tds.lon_sp_tds)
tds_number_of_delay_pixels = tds.metagrp.groups[
tds.group].NumberOfDelayPixels
tds_number_of_doppler_pixels = tds.metagrp.groups[
tds.group].NumberOfDopplerPixels
tds_delay_start = tds.calculate_delay_increment_chips(0)
tds_delay_end = tds.calculate_delay_increment_chips(
tds_number_of_delay_pixels - 1)
tds_delay_resolution = (tds_delay_end - tds_delay_start) / 128
tds_doppler_start = tds.calculate_doppler_increment(
-np.floor(tds_number_of_doppler_pixels / 2))
tds_doppler_end = tds.calculate_doppler_increment(
np.floor(tds_number_of_doppler_pixels / 2 - 0.5))
tds_doppler_resolution = 500
fig_tds, ax_tds = plt.subplots(1, figsize=(10, 4))
plt.title('TDS-1 Experimental Data')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
contour_tds = ax_tds.imshow(
ddm_tds,
cmap='jet',
extent=(tds_delay_start, tds_delay_end, tds_doppler_end,
tds_doppler_start),
#aspect=(tds_number_of_doppler_pixels/tds_number_of_delay_pixels)/np.abs(tds_doppler_start/tds_delay_start)
aspect='auto')
t = plt.text(0.01,
0.85,
string, {
'color': 'w',
'fontsize': 12
},
transform=ax_tds.transAxes)
cbar = fig_tds.colorbar(contour_tds, label='Power')
# Load TDS Geometry in simulation configuration
n_z = unit_vector(ellip_norm(tds.r_sp_tds))
n_x = unit_vector(np.cross(n_z, tds.r_sp_tds - tds.r_t))
n_y = unit_vector(np.cross(n_z, n_x))
v_tx = np.dot(tds.v_t, n_x)
v_ty = np.dot(tds.v_t, n_y)
v_tz = np.dot(tds.v_t, n_z)
v_rx = np.dot(tds.v_r, n_x)
v_ry = np.dot(tds.v_r, n_y)
v_rz = np.dot(tds.v_r, n_z)
h_r = np.dot((tds.r_r - tds.r_sp_tds), n_z)
h_t = np.dot((tds.r_t - tds.r_sp_tds), n_z)
elevation = angle_between(n_y, tds.r_t - tds.r_sp_tds)
v_t = np.array([v_tx, v_ty, v_tz])
v_r = np.array([v_rx, v_ry, v_rz])
print("h_r: {}".format(h_r))
print("h_t: {}".format(h_t))
print("elevation: {}".format(elevation))
print("v_r: {}".format(np.linalg.norm(v_r)))
print("v_t: {}".format(np.linalg.norm(v_t)))
sim_config.set_scenario_local_ref(
h_r=np.dot((tds.r_r - tds.r_sp_tds), n_z),
h_t=np.dot((tds.r_t - tds.r_sp_tds), n_z),
elevation=angle_between(n_y, tds.r_t - tds.r_sp_tds),
v_t=np.array([v_tx, v_ty, v_tz]),
v_r=np.array([v_rx, v_ry, v_rz]))
# DDM
sim_config.delay_increment_start = tds_delay_start * delay_chip
sim_config.delay_increment_end = tds_delay_end * delay_chip
sim_config.delay_resolution = (
sim_config.delay_increment_end -
sim_config.delay_increment_start) / tds_number_of_delay_pixels / 4
sim_config.doppler_increment_start = tds_doppler_start
sim_config.doppler_increment_end = tds_doppler_end + tds_doppler_resolution
sim_config.doppler_resolution = (
sim_config.doppler_increment_end -
sim_config.doppler_increment_start) / tds_number_of_doppler_pixels / 4
ddm_sim = (simulate_ddm(sim_config))
fig_ddm, ax_ddm = plt.subplots(1, figsize=(10, 4))
plt.title('DDM original simulation')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
contour_ddm = ax_ddm.imshow(ddm_sim,
cmap='jet',
extent=(sim_config.delay_increment_start,
sim_config.delay_increment_end,
sim_config.doppler_increment_end,
sim_config.doppler_increment_start),
aspect="auto")
cbar = fig_ddm.colorbar(contour_ddm, label='Correlated Power [Watts]')
# DDM Rescaled
fig_ddm_rescaled, ax_ddm_rescaled = plt.subplots(1, figsize=(10, 4))
plt.title('Simulation Rescaled')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
ddm_rescaled = rescale(ddm_sim, tds_number_of_doppler_pixels,
tds_number_of_delay_pixels)
# Noise
waf_delay_increment_values = list(
np.arange(
-tds_delay_end * delay_chip,
tds_delay_end * delay_chip + tds_delay_resolution * delay_chip,
tds_delay_resolution * delay_chip))
waf_doppler_increment_values = list(
np.arange(tds_doppler_start, tds_doppler_end + tds_doppler_resolution,
tds_doppler_resolution))
waf_delay_grid, waf_doppler_grid = np.meshgrid(
waf_delay_increment_values, waf_doppler_increment_values)
waf_matrix = woodward_ambiguity_function(waf_delay_grid, waf_doppler_grid,
sim_config)**2
noise_temperature = noise_antenna_mean + noise_rx_mean
ddm_rescaled = add_thermal_noise(tds_number_of_doppler_pixels,
tds_number_of_delay_pixels, 1 * 1000,
noise_temperature, ddm_rescaled,
sim_config)
contour_res = ax_ddm_rescaled.imshow(
ddm_rescaled,
cmap='jet',
extent=(tds_delay_start, tds_delay_end, tds_doppler_end,
tds_doppler_start),
#aspect=(tds_number_of_doppler_pixels/tds_number_of_delay_pixels)/np.abs(tds_doppler_start/tds_delay_start)
aspect='auto')
cbar = fig_ddm_rescaled.colorbar(contour_res,
label='Correlated Power [Watts]')
# Difference
fig_diff, ax_diff = plt.subplots(1, figsize=(10, 4))
plt.title('Difference')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
ddm_diff = np.copy(ddm_rescaled)
for row_i, row in enumerate(ddm_diff):
for col_i, val in enumerate(row):
col_i_shift = col_i
row_i_shift = row_i
col_shift = 1
row_shift = 0
if (col_i + col_shift) >= 0 and (col_i + col_shift) < 128:
col_i_shift += col_shift
if (row_i + row_shift) >= 0 and (row_i + row_shift) < 20:
row_i_shift += row_shift
val_tds = ddm_tds[row_i_shift, col_i_shift]
val = ddm_rescaled[row_i, col_i]
if row_i == 0:
ddm_diff[row_i, col_i] = 0
elif col_i == 0:
ddm_diff[row_i, col_i] = 0
else:
rel = np.abs((val - val_tds) / val_tds)
ddm_diff[row_i, col_i] = rel
ddm_diff[:, -1] = 0
ddm_diff[0, 0] = 0
ddm_diff[0, 1] = 1
np.place(ddm_diff, np.abs(ddm_diff) > 2, 0.1)
print(file_root_name)
print("h_r: {}".format(h_r))
print("h_t: {}".format(h_t))
print("elevation: {}".format(elevation * 180 / np.pi))
print("v_r: {}".format(np.linalg.norm(v_r)))
print("v_t: {}".format(np.linalg.norm(v_t)))
print("max diff: {}".format(np.max(ddm_diff[1:, 1:])))
im = ax_diff.imshow(
ddm_diff,
cmap='jet',
extent=(tds_delay_start, tds_delay_end, tds_doppler_end,
tds_doppler_start),
#aspect=(tds_number_of_doppler_pixels/tds_number_of_delay_pixels)/np.abs(tds_doppler_start/tds_delay_start)
aspect='auto')
cbar = fig_diff.colorbar(im, label='Relative error')
# SNR
fig_snr, ax_snr = plt.subplots(1, figsize=(10, 4))
plt.title('SNR')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
T_noise_receiver = noise_antenna_mean + noise_rx_mean
k_b = 1.38e-23 # J/K
y_noise = 4 / sim_config.coherent_integration_time * k_b * T_noise_receiver / np.sqrt(
1000)
ddm_rescaled_snr = rescale(ddm_sim, tds_number_of_doppler_pixels,
tds_number_of_delay_pixels)
ddm_snr = np.copy(10 * np.log10(np.abs(ddm_rescaled_snr) / y_noise))
contour_snr = ax_snr.imshow(
ddm_snr,
cmap='jet',
extent=(tds_delay_start, tds_delay_end, tds_doppler_end,
tds_doppler_start),
#aspect=(tds_number_of_doppler_pixels/tds_number_of_delay_pixels)/np.abs(tds_doppler_start/tds_delay_start)
aspect='auto')
cbar = fig_snr.colorbar(contour_snr, label='dB')
plt.show()
def main():
sim_config = simulation_configuration()
delay_chip = sim_config.delay_chip
# Really good
#sim_config.u_10 = 4
#sim_config.phi_0 = 35*np.pi/180
#sim_config.u_10 = 4
#sim_config.phi_0 = 38*np.pi/180
sim_config.u_10 = 14.04
sim_config.phi_0 = -83*np.pi/180
file_root_name = 'raw/L1B/2015-04-01-H00'
target = targets['hibernia']
group = '000095'
index = 515
tds = tds_data(file_root_name, group, index)
# Sea clutter estimation.
#p = target_processor();
#for i in range(index - 30, index + 5):
# ddm = tds.rootgrp.groups[group].variables['DDM'][i].data
# p.process_ddm(ddm)
# Plot TDS DDM sea clutter
datenum = tds.rootgrp.groups[tds.group].variables['IntegrationMidPointTime'][tds.index]
string = str(datenum_to_pytime(float(datenum))) \
+ ' Lat: ' + "{0:.2f}".format(tds.lat_sp_tds) \
+ ' Lon: ' + "{0:.2f}".format(tds.lon_sp_tds)
number_of_delay_pixels = tds.metagrp.groups[tds.group].NumberOfDelayPixels
number_of_doppler_pixels = tds.metagrp.groups[tds.group].NumberOfDopplerPixels
delay_start = tds.calculate_delay_increment_chips(0)
delay_end = tds.calculate_delay_increment_chips(number_of_delay_pixels-1)
doppler_start = tds.calculate_doppler_increment(-np.floor(number_of_doppler_pixels/2))
doppler_end = tds.calculate_doppler_increment(np.floor(number_of_doppler_pixels/2 - 0.5))
delay_increment_start = sim_config.delay_increment_start
delay_increment_end = sim_config.delay_increment_end
delay_resolution = sim_config.delay_resolution
sim_config.delay_increment_start = delay_start*delay_chip + 2*delay_resolution
sim_config.delay_increment_end = delay_end*delay_chip
sim_config.doppler_increment_start = -5000
sim_config.doppler_increment_end = 5000
doppler_increment_start = sim_config.doppler_increment_start
doppler_increment_end = sim_config.doppler_increment_end
doppler_resolution = sim_config.doppler_resolution
fig_tds, ax_tds = plt.subplots(1,figsize=(10, 4))
plt.title('TDS-1 Experimental Data')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
im = ax_tds.imshow(p.sea_clutter, cmap='jet',
extent=(delay_start, delay_end, doppler_end, doppler_start),
aspect=(number_of_doppler_pixels/number_of_delay_pixels)/np.abs(doppler_start/delay_start)
)
t = plt.text(0.01, 0.85, string, {'color': 'w', 'fontsize': 12}, transform=ax_tds.transAxes)
# Load TDS Geometry in simulation configuration
r_sp, lat_sp, lon_sp = tds.find_sp();
n_z = unit_vector(ellip_norm(r_sp))
n_x = unit_vector(np.cross(n_z, r_sp-tds.r_t))
n_y = unit_vector(np.cross(n_z, n_x))
v_tx = np.dot(tds.v_t, n_x)
v_ty = np.dot(tds.v_t, n_y)
v_tz = np.dot(tds.v_t, n_z)
v_rx = np.dot(tds.v_r, n_x)
v_ry = np.dot(tds.v_r, n_y)
v_rz = np.dot(tds.v_r, n_z)
sim_config.set_scenario_local_ref(
h_r = np.dot((tds.r_r - r_sp), n_z),
h_t = np.dot((tds.r_t - r_sp), n_z),
elevation = angle_between(n_y, tds.r_t-r_sp),
v_t = np.array([v_tx,v_ty,v_tz]),
v_r = np.array([v_rx,v_ry,v_rz])
)
# DDM
ddm_sim = normalize(simulate_ddm(sim_config))
fig_ddm, ax_ddm = plt.subplots(1,figsize=(10, 4))
plt.title('DDM original simulation')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
im = ax_ddm.imshow(ddm_sim, cmap='jet',
extent=(delay_start, delay_end, doppler_end, doppler_start),
aspect="auto"
)
# Image downscaling to desired resolution:
# TODO: This is just an average of the pixels around the area
# This is not valid, summation i srequired:
# Di Simone > From a physical viewpoint,
# such an approach should call for summation instead of averaging
# https://stackoverflow.com/questions/48121916/numpy-resize-rescale-image
fig_ddm_rescaled, ax_ddm_rescaled = plt.subplots(1,figsize=(10, 4))
plt.title('Simulation')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
rescaled_doppler_resolution = tds.doppler_resolution
rescaled_delay_resolution_chips = tds.time_delay_resolution/delay_chip
ddm_rescaled = cv2.resize(ddm_sim,
dsize=(
128,
20
),
interpolation=cv2.INTER_AREA
)
ddm_rescaled = ddm_rescaled + 0.02*np.max(ddm_rescaled)*np.random.rand(ddm_rescaled.shape[0],ddm_rescaled.shape[1])
im = ax_ddm_rescaled.imshow(ddm_rescaled, cmap='jet',
extent=(delay_start, delay_end, doppler_end, doppler_start),
aspect=(number_of_doppler_pixels/number_of_delay_pixels)/np.abs(doppler_start/delay_start)
)
fig_diff, ax_diff = plt.subplots(1,figsize=(10, 4))
plt.title('Difference')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
ddm_diff = np.abs(ddm_rescaled-p.sea_clutter)
ddm_diff[0,0] = 0.35
im = ax_diff.imshow(ddm_diff, cmap='jet',
extent=(delay_start, delay_end, doppler_end, doppler_start),
aspect=(number_of_doppler_pixels/number_of_delay_pixels)/np.abs(doppler_start/delay_start)
)
cbar = fig_diff.colorbar(im, label='Normalized Power', shrink=0.35)
plt.show()
def main():
# Petronius Oil Platform
#file_dir = os.path.join(os.environ['TDS_ROOT'], 'raw/L1B/2017-11-26-H06-')
#rootgrp = Dataset(file_dir+"DDMs.nc", "r", format="NETCDF4")
#metagrp = Dataset(file_dir+"metadata.nc", "r", format="NETCDF4")
#group = '000047'
#start_0 = 590
file_root_name = 'raw/L1B/2015-04-01-H00'
group = '000095'
index = 525
tds = tds_data(file_root_name, group, index)
rootgrp = tds.rootgrp
metagrp = tds.metagrp
# The region of interest lies between delay column 60 and delay column 80
min_col = 60
max_col = 85
def datenum_to_pytime(matlab_datenum):
python_datetime = datetime.fromordinal(
int(matlab_datenum)) + timedelta(days=matlab_datenum %
1) - timedelta(days=366)
return python_datetime
def normalize(mat):
return (mat - np.min(mat)) / (np.max(mat) - np.min(mat))
def cut_noise_region(ddm, ddm_ref, new_value=0):
"""
For each pixel in ddm, replaces the pixel with new_value if the pixel
with same indeces in ddm_ref is less than 0.3
cut_threshold is computed as the mean of the noise region of the ddm_ref
(from column 0 to 40)
"""
ddm_cut = np.zeros(ddm.shape) + new_value
cut_threshold = 0.15
for row_i, row in enumerate(ddm_cut):
for col_i, val in enumerate(row):
if (col_i >= min_col and col_i <= max_col):
if (ddm_ref[row_i][col_i] >= cut_threshold):
ddm_cut[row_i][col_i] = ddm[row_i][col_i]
return ddm_cut
# 1. Original
ddm_original = normalize(
np.array(rootgrp.groups[group].variables['DDM'][index].data))
# 2. Sea clutter estimation.
# As target appear as bright spots, the initial estimation is based of the
# composition of the minimum values for each pixel for the last n measurements
n = 10
offset = 0
sea_clutter_0 = normalize(
np.array(rootgrp.groups[group].variables['DDM'][index - offset].data))
for i in range(n):
ddm_i = normalize(
np.array(rootgrp.groups[group].variables['DDM'][index - offset -
i].data))
sea_clutter_0 = normalize(sea_clutter_0)
for row_i, row in enumerate(sea_clutter_0):
for col_i, val in enumerate(row):
val_i = ddm_i[row_i][col_i]
val = sea_clutter_0[row_i][col_i]
min, max = np.sort([val_i, val])
sea_clutter_0[row_i][col_i] = 0.5 * min + 0.5 * max
sea_clutter_0 = normalize(sea_clutter_0)
# Using the sea_clutter_0 as initial estimation a low pass filter that gives
# more weight to the lower values is applied
n = 200
tau = 0.08
sea_clutter = np.array(sea_clutter_0)
for i in range(n):
ddm_i = normalize(
np.array(rootgrp.groups[group].variables['DDM'][index - offset -
i].data))
sea_clutter = normalize(sea_clutter)
for row_i, row in enumerate(sea_clutter):
for col_i, val in enumerate(row):
val_i = ddm_i[row_i][col_i]
val = sea_clutter[row_i][col_i]
#min,max = np.sort([val_i,val])
#new_val = 0.7*min + 0.3*max;
sea_clutter[row_i][col_i] = val + tau * (val_i - val)
sea_clutter = normalize(sea_clutter)
# Only the region of the wake is relevant for detection, so we cut the
# irrelevant region
sea_clutter_cut = cut_noise_region(sea_clutter, sea_clutter)
ddm_original_cut = cut_noise_region(ddm_original, sea_clutter)
# 3. Sea clutter substracted Difference Map
ddm_diff = ddm_original_cut - 0.85 * sea_clutter_cut
if (np.min(ddm_diff) < 0):
ddm_diff = ddm_diff - np.min(ddm_diff)
cut_value_fig = np.min(ddm_diff)
ddm_diff_fig = cut_noise_region(ddm_diff, sea_clutter, cut_value_fig)
ddm_diff = cut_noise_region(ddm_diff, sea_clutter)
# 4. Over threshold detection
ddm_detections = np.zeros(ddm_diff.shape)
threshold = 0.38
print(np.max(ddm_diff))
print(threshold)
print(index)
for row_i, row in enumerate(ddm_diff):
for col_i, val in enumerate(row):
if (col_i >= min_col and col_i <= max_col):
if (ddm_diff[row_i][col_i] >= threshold):
ddm_detections[row_i][col_i] = 1
# Plotting
x_start = -6
x_end = 15
y_start = 4500
y_end = -4500
number_of_delay_pixels = tds.metagrp.groups[tds.group].NumberOfDelayPixels
number_of_doppler_pixels = tds.metagrp.groups[
tds.group].NumberOfDopplerPixels
delay_start = tds.calculate_delay_increment_chips(0)
delay_end = tds.calculate_delay_increment_chips(number_of_delay_pixels - 1)
doppler_start = tds.calculate_doppler_increment(
-np.floor(number_of_doppler_pixels / 2))
doppler_end = tds.calculate_doppler_increment(
np.floor(number_of_doppler_pixels / 2 - 0.5))
fig_original = plt.figure(figsize=(10, 4))
im_original = plt.imshow(ddm_original,
cmap='viridis',
extent=(delay_start, delay_end, doppler_end,
doppler_start),
aspect='auto')
plt.xlim([x_start, x_end])
plt.ylim([y_start, y_end])
plt.xlabel('C/A chips')
plt.ylabel('Hz')
datenum = metagrp.groups[group].variables['IntegrationMidPointTime'][index]
lat = metagrp.groups[group].variables['SpecularPointLat'][index]
lon = metagrp.groups[group].variables['SpecularPointLon'][index]
#string = 'G: ' + group + ' I: ' + str(index) + ' - ' + \
# str(datenum) + ' - ' + str(datenum_to_pytime(float(datenum))) + ' - Lat: ' + \
# str(lat) + ' Lon: ' + str(lon) + '\n'
string = str(datenum_to_pytime(float(datenum))) \
+ ' Lat: ' + "{0:.2f}".format(tds.lat_sp_tds) \
+ ' Lon: ' + "{0:.2f}".format(tds.lon_sp_tds)
t = plt.text(-5.3, -3200, string, {'color': 'w', 'fontsize': 12})
plt.show(block=False)
fig_sea_clutter = plt.figure(figsize=(10, 4))
im_sea_clutter = plt.imshow(sea_clutter,
cmap='viridis',
extent=(delay_start, delay_end, doppler_end,
doppler_start),
aspect='auto')
plt.xlim([x_start, x_end])
plt.ylim([y_start, y_end])
plt.xlabel('C/A chips')
plt.ylabel('Hz')
plt.show(block=False)
fig_sub = plt.figure(figsize=(10, 4))
im_sub = plt.imshow(ddm_diff,
cmap='viridis',
extent=(delay_start, delay_end, doppler_end,
doppler_start),
aspect='auto')
plt.xlim([x_start, x_end])
plt.ylim([y_start, y_end])
plt.xlabel('C/A chips')
plt.ylabel('Hz')
plt.show(block=False)
fig_detections = plt.figure(figsize=(10, 4))
im_detections = plt.imshow(ddm_detections,
cmap='viridis',
extent=(delay_start, delay_end, doppler_end,
doppler_start),
aspect='auto')
plt.xlim([x_start, x_end])
plt.ylim([y_start, y_end])
plt.xlabel('C/A chips')
plt.ylabel('Hz')
plt.show(block=False)
all_labels = label(ddm_detections)
fig_labels, ax_labels = plt.subplots(1, figsize=(10, 4))
ax_labels.imshow(ddm_original, cmap='viridis', aspect='auto')
plt.show(block=False)
for region in regionprops(all_labels):
minr, minc, maxr, maxc = region.bbox
l = 1
rect = mpatches.Rectangle((minc - l, minr - l),
maxc - minc + 2 * l - 1,
maxr - minr + 2 * l - 1,
fill=False,
edgecolor='red',
linewidth=2)
ax_labels.add_patch(rect)
plt.show()
def main():
sim_config = simulation_configuration()
#sim_config.jacobian_type = 'spherical'
delay_chip = sim_config.delay_chip
# Really good
#sim_config.u_10 = 4
#sim_config.phi_0 = 35*np.pi/180
#sim_config.u_10 = 4
#sim_config.phi_0 = 38*np.pi/180
sim_config.u_10 = 3
sim_config.phi_0 = -83 * np.pi / 180
file_root_name = '2015-04-01-H00'
target = targets['hibernia']
group = '000095'
index = 415
tds = tds_data(file_root_name, group, index)
# Load TDS Geometry in simulation configuration
number_of_delay_pixels = tds.metagrp.groups[tds.group].NumberOfDelayPixels
number_of_doppler_pixels = tds.metagrp.groups[
tds.group].NumberOfDopplerPixels
delay_start = tds.calculate_delay_increment_chips(0)
delay_end = tds.calculate_delay_increment_chips(number_of_delay_pixels - 1)
doppler_start = tds.calculate_doppler_increment(
-np.floor(number_of_doppler_pixels / 2))
doppler_end = tds.calculate_doppler_increment(
np.floor(number_of_doppler_pixels / 2 - 0.5))
delay_increment_start = sim_config.delay_increment_start
delay_increment_end = sim_config.delay_increment_end
delay_resolution = sim_config.delay_resolution
sim_config.delay_increment_start = delay_start * delay_chip + 2 * delay_resolution
sim_config.delay_increment_end = delay_end * delay_chip
sim_config.doppler_increment_start = -5000
sim_config.doppler_increment_end = 5000
doppler_increment_start = sim_config.doppler_increment_start
doppler_increment_end = sim_config.doppler_increment_end
doppler_resolution = sim_config.doppler_resolution
r_sp, lat_sp, lon_sp = tds.find_sp()
n_z = unit_vector(ellip_norm(r_sp))
n_x = unit_vector(np.cross(n_z, r_sp - tds.r_t))
n_y = unit_vector(np.cross(n_z, n_x))
v_tx = np.dot(tds.v_t, n_x)
v_ty = np.dot(tds.v_t, n_y)
v_tz = np.dot(tds.v_t, n_z)
v_rx = np.dot(tds.v_r, n_x)
v_ry = np.dot(tds.v_r, n_y)
v_rz = np.dot(tds.v_r, n_z)
#sim_config.set_scenario_local_ref(
# h_r = np.dot((tds.r_r - r_sp), n_z),
# h_t = np.dot((tds.r_t - r_sp), n_z),
# elevation = angle_between(n_y, tds.r_t-r_sp),
# v_t = np.array([v_tx,v_ty,v_tz]),
# v_r = np.array([v_rx,v_ry,v_rz])
# )
# DDM
ddm_sim = simulate_ddm(sim_config)
fig_ddm, ax_ddm = plt.subplots(1, figsize=(10, 4))
plt.title('DDM simulation')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
contour = ax_ddm.imshow(ddm_sim,
cmap='jet',
extent=(delay_start, delay_end, doppler_end,
doppler_start),
aspect="auto")
cbar = fig_ddm.colorbar(contour, label='Power [Watt]')
T_noise_receiver = 225
k_b = 1.38e-23 # J/K
y_noise = 1 / sim_config.coherent_integration_time * k_b * T_noise_receiver
ddm_sim_snr = np.copy(10 * np.log10(np.abs(ddm_sim) / y_noise))
fig_ddm_snr, ax_ddm_snr = plt.subplots(1, figsize=(10, 4))
plt.title('DDM SNR simulation')
plt.xlabel('C/A chips')
plt.ylabel('Hz')
contour_snr = ax_ddm_snr.imshow(ddm_sim_snr,
cmap='jet',
extent=(delay_start, delay_end,
doppler_end, doppler_start),
aspect="auto")
cbar = fig_ddm_snr.colorbar(contour_snr, label='SNR [dB]')
plt.show()
