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processing.py
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processing.py
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#!python
# distutils: language = c++
# Script for radar signal processing
# This script requires that `numpy` and be installed within the Python
# environment you are running this script in.
# This file can be imported as a module and contains the following
# functions:
# * cal_range_profile - calculate range profile matrix
# * cal_range_doppler - range-Doppler processing
# * get_polar_image - convert cartesian coordinate to polar
# ----------
# RadarSimPy - A Radar Simulator Built with Python
# Copyright (C) 2018 - PRESENT Zhengyu Peng
# E-mail: [email protected]
# Website: https://zpeng.me
# ` `
# -:. -#:
# -//:. -###:
# -////:. -#####:
# -/:.://:. -###++##:
# .. `://:- -###+. :##:
# `:/+####+. :##:
# .::::::::/+###. :##:
# .////-----+##: `:###:
# `-//:. :##: `:###/.
# `-//:. :##:`:###/.
# `-//:+######/.
# `-/+####/.
# `+##+.
# :##:
# :##:
# :##:
# :##:
# :##:
# .+:
from warnings import warn
import numpy as np
from scipy.signal import convolve
from scipy import fft
from .tools import log_factorial
def range_fft(data, rwin=None, n=None):
"""
Calculate range profile matrix
:param numpy.3darray data:
Baseband data, ``[channels, pulses, adc_samples]``
:param numpy.1darray rwin:
Window for FFT, length should be equal to adc_samples. (default is
a square window)
:param int n:
FFT size, if n > adc_samples, zero-padding will be applied.
(default is None)
:return: A 3D array of range profile, ``[channels, pulses, range]``
:rtype: numpy.3darray
"""
shape = np.shape(data)
if rwin is None:
rwin = 1
else:
rwin = np.tile(rwin[np.newaxis, np.newaxis, ...],
(shape[0], shape[1], 1))
return fft.fft(data * rwin, n=n, axis=2)
def doppler_fft(data, dwin=None, n=None):
"""
Calculate range-Doppler matrix
:param numpy.3darray data:
Range profile matrix, ``[channels, pulses, adc_samples]``
:param numpy.1darray dwin:
Window for FFT, length should be equal to adc_samples. (default is
a square window)
:param int n:
FFT size, if n > adc_samples, zero-padding will be applied.
(default is None)
:return: A 3D array of range-Doppler map, ``[channels, Doppler, range]``
:rtype: numpy.3darray
"""
shape = np.shape(data)
if dwin is None:
dwin = 1
else:
dwin = np.tile(dwin[np.newaxis, ..., np.newaxis],
(shape[0], 1, shape[2]))
return fft.fft(data * dwin, n=n, axis=1)
def range_doppler_fft(data, rwin=None, dwin=None, rn=None, dn=None):
"""
Range-Doppler processing
:param numpy.3darray data:
Baseband data, ``[channels, pulses, adc_samples]``
:param numpy.1darray rwin:
Range window for FFT, length should be equal to adc_samples.
(default is a square window)
:param numpy.1darray dwin:
Doppler window for FFT, length should be equal to adc_samples.
(default is a square window)
:param int rn:
Range FFT size, if n > adc_samples, zero-padding will be applied.
(default is None)
:param int dn:
Doppler FFT size, if n > adc_samples, zero-padding will be applied.
(default is None)
:return: A 3D array of range-Doppler map, ``[channels, Doppler, range]``
:rtype: numpy.3darray
"""
return doppler_fft(range_fft(data, rwin=rwin, n=rn), dwin=dwin, n=dn)
def get_polar_image(image, range_bins, angle_bins, fov_deg):
"""
Convert cartesian coordinate to polar
:param numpy.2darray image:
Data with cartesian coordinate, [range, angle]
:param int range_bins:
Number of range bins
:param int angle_bins:
Number of angle bins
:param float fov_deg:
Field of view (deg)
:return: A 2D image with polar coordinate
:rtype: numpy.2darray
"""
angle_bin_res = fov_deg / angle_bins
latitude_bins = int(range_bins * np.sin(fov_deg / 360 * np.pi) + 1)
polar = np.zeros((range_bins, latitude_bins * 2), dtype=complex)
x = np.arange(1, range_bins, 1, dtype=int)
y = np.arange(0, latitude_bins * 2, 1, dtype=int)
X_data, Y_data = np.meshgrid(x, y)
b = 180 * np.arctan(
(Y_data - latitude_bins) /
X_data) / angle_bin_res / np.pi + fov_deg / angle_bin_res / 2
a = X_data / (np.cos((angle_bin_res * b - fov_deg / 2) / 180 * np.pi))
b = b.astype(int)
a = a.astype(int)
idx = np.where(
np.logical_and(
np.logical_and(np.less(b, angle_bins), np.greater_equal(b, 0)),
np.logical_and(np.less(a, range_bins), np.greater_equal(a, 0))))
b = b[idx]
a = a[idx]
xx = X_data[idx]
yy = Y_data[idx]
polar[xx, yy] = image[a, b]
return polar
def cfar_ca_1d(data, guard, trailing, pfa=1e-5, axis=0, offset=None):
"""
1-D Cell Averaging CFAR (CA-CFAR)
:param data:
Radar data
:type data: numpy.1darray or numpy.2darray
:param int guard:
Number of guard cells on one side, total guard cells are ``2*guard``
:param int trailing:
Number of trailing cells on one side, total trailing cells are
``2*trailing``
:param float pfa:
Probability of false alarm. ``default 1e-5``
:param int axis:
The axis to calculat CFAR. ``default 0``
:param float offset:
CFAR threshold offset. If offect is None, threshold offset is
``2*trailing(pfa^(-1/2/trailing)-1)``. ``default None``
:return: CFAR threshold. The dimension is the same as ``data``
:rtype: numpy.1darray or numpy.2darray
"""
data = np.abs(data)
data_shape = np.shape(data)
cfar = np.zeros_like(data)
if offset is None:
a = trailing*2*(pfa**(-1/(trailing*2))-1)
else:
a = offset
cfar_win = np.ones((guard+trailing)*2+1)
cfar_win[trailing:(trailing+guard*2+1)] = 0
cfar_win = cfar_win/np.sum(cfar_win)
if axis == 0:
if data.ndim == 1:
cfar = a*convolve(data, cfar_win, mode='same')
elif data.ndim == 2:
for idx in range(0, data_shape[1]):
cfar[:, idx] = a * \
convolve(data[:, idx], cfar_win, mode='same')
elif axis == 1:
for idx in range(0, data_shape[0]):
cfar[idx, :] = a*convolve(data[idx, :], cfar_win, mode='same')
return cfar
def cfar_ca_2d(data, guard, trailing, pfa=1e-5, offset=None):
"""
2-D Cell Averaging CFAR (CA-CFAR)
:param data:
Radar data
:type data: numpy.1darray or numpy.2darray
:param guard:
Number of guard cells on one side, total guard cells are ``2*guard``.
When ``guard`` is a list, ``guard[0]`` is for axis 0, and ``guard[1]``
is for axis 1. If ``guard`` is a number, axis 0 and axis 1 are the same
:type guard: int or list[int]
:param trailing:
Number of trailing cells on one side, total trailing cells are
``2*trailing``. When ``trailing`` is a list, ``trailing[0]`` is for
axis 0, and ``trailing[1]`` is for axis 1. If ``trailing`` is a number,
axis 0 and axis 1 are the same
:type trailing: int or list[int]
:param float pfa:
Probability of false alarm. ``default 1e-5``
:param float offset:
CFAR threshold offset. If offect is None, threshold offset is
``2*trailing(pfa^(-1/2/trailing)-1)``. ``default None``
:return: CFAR threshold. The dimension is the same as ``data``
:rtype: numpy.1darray or numpy.2darray
"""
data = np.abs(data)
guard = np.array(guard)
if guard.size == 1:
guard = np.tile(guard, 2)
trailing = np.array(trailing)
if trailing.size == 1:
trailing = np.tile(trailing, 2)
if offset is None:
tg_sum = trailing+guard
t_num = (2*tg_sum[0]+1)*(2*tg_sum[1]+1)
g_num = (2*guard[0]+1)*(2*guard[1]+1)
if t_num == g_num:
raise('No trailing bins!')
a = (t_num-g_num)*(pfa**(-1/(t_num-g_num))-1)
else:
a = offset
cfar_win = np.ones(((guard+trailing)*2+1))
cfar_win[trailing[0]:(trailing[0]+guard[0]*2+1),
trailing[1]:(trailing[1]+guard[1]*2+1)] = 0
cfar_win = cfar_win/np.sum(cfar_win)
return a*convolve(data, cfar_win, mode='same')
def os_cfar_threshold(k, n, pfa):
"""
Use Secant method to calculate OS-CFAR's threshold
:param int n:
Number of cells around CUT (cell under test) for calculating
:param int k:
Rank in the order
:param float pfa:
Probability of false alarm
:return: CFAR threshold
:rtype: float
*Reference*
Rohling, Hermann. "Radar CFAR thresholding in clutter and multiple target
situations." IEEE transactions on aerospace and electronic systems 4
(1983): 608-621.
"""
def fun(k, n, Tos, pfa):
return log_factorial(n)-log_factorial(n-k) - \
np.sum(np.log(np.arange(n, n-k, -1)+Tos))-np.log(pfa)
max_iter = 10000
t_max = 1e32
t_min = 1
for idx in range(0, max_iter):
m_n = t_max-fun(k, n, t_max, pfa)*(t_min-t_max) / \
(fun(k, n, t_min, pfa) -
fun(k, n, t_max, pfa))
f_m_n = fun(k, n, m_n, pfa)
if f_m_n == 0:
return m_n
elif np.abs(f_m_n) < 0.0001:
return m_n
elif fun(k, n, t_max, pfa)*f_m_n < 0:
t_max = t_max
t_min = m_n
elif fun(k, n, t_min, pfa)*f_m_n < 0:
t_max = m_n
t_min = t_min
else:
# print("Secant method fails.")
break
return None
def cfar_os_1d(
data,
guard,
trailing,
k,
pfa=1e-5,
axis=0,
offset=None):
"""
1-D Ordered Statistic CFAR (OS-CFAR)
For edge cells, use rollovered cells to fill the missing cells.
:param data:
Radar data
:type data: numpy.1darray or numpy.2darray
:param int guard:
Number of guard cells on one side, total guard cells are ``2*guard``
:param int trailing:
Number of trailing cells on one side, total trailing cells are
``2*trailing``
:param int k:
Rank in the order. ``k`` is usuall chosen to satisfy ``N/2 < k < N``.
Typically, ``k`` is on the order of ``0.75N``
:param float pfa:
Probability of false alarm. ``default 1e-5``
:param int axis:
The axis to calculat CFAR. ``default 0``
:param float offset:
CFAR threshold offset. If offect is None, threshold offset is
calculated from ``pfa``. ``default None``
:return: CFAR threshold. The dimension is the same as ``data``
:rtype: numpy.1darray or numpy.2darray
*Reference*
[1] H. Rohling, “Radar CFAR Thresholding in Clutter and Multiple Target
Situations,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-19, no. 4,
pp. 608-621, 1983.
"""
data = np.abs(data)
data_shape = np.shape(data)
cfar = np.zeros_like(data)
leading = trailing
# trailing = n-leading
if offset is None:
a = os_cfar_threshold(k, trailing*2, pfa)
else:
a = offset
if k < trailing or k > trailing*2:
warn('``k`` is usuall chosen to satisfy ``N/2 < k < N '
'(N = '+str(trailing*2)+')``. '
'Typically, ``k`` is on the order of ``0.75N``')
if axis == 0:
for idx in range(0, data_shape[0]):
win_idx = np.mod(
np.concatenate(
[np.arange(idx-leading-guard, idx-guard, 1),
np.arange(idx+1+guard, idx+1+trailing+guard, 1)]
), data_shape[0])
if data.ndim == 1:
samples = np.sort(data[win_idx.astype(int)])
cfar[idx] = a*samples[k]
elif data.ndim == 2:
samples = np.sort(data[win_idx.astype(int), :], axis=0)
cfar[idx, :] = a*samples[k, :]
elif axis == 1:
for idx in range(0, data_shape[1]):
win_idx = np.mod(
np.concatenate(
[np.arange(idx-leading-guard, idx-guard, 1),
np.arange(idx+1+guard, idx+1+trailing+guard, 1)]
), data_shape[1])
samples = np.sort(data[:, win_idx.astype(int)], axis=1)
cfar[:, idx] = a*samples[:, k]
return cfar
def cfar_os_2d(
data,
guard,
trailing,
k,
pfa=1e-5,
offset=None):
"""
2-D Ordered Statistic CFAR (OS-CFAR)
For edge cells, use rollovered cells to fill the missing cells.
:param data:
Radar data
:type data: numpy.1darray or numpy.2darray
:param guard:
Number of guard cells on one side, total guard cells are ``2*guard``.
When ``guard`` is a list, ``guard[0]`` is for axis 0, and ``guard[1]``
is for axis 1. If ``guard`` is a number, axis 0 and axis 1 are the same
:type guard: int or list[int]
:param trailing:
Number of trailing cells on one side, total trailing cells are
``2*trailing``. When ``trailing`` is a list, ``trailing[0]`` is for
axis 0, and ``trailing[1]`` is for axis 1. If ``trailing`` is a number,
axis 0 and axis 1 are the same
:type trailing: int or list[int]
:param int k:
Rank in the order. ``k`` is usuall chosen to satisfy ``N/2 < k < N``.
Typically, ``k`` is on the order of ``0.75N``
:param float pfa:
Probability of false alarm. ``default 1e-5``
:param float offset:
CFAR threshold offset. If offect is None, threshold offset is
calculated from ``pfa``. ``default None``
:return: CFAR threshold. The dimension is the same as ``data``
:rtype: numpy.1darray or numpy.2darray
*Reference*
[1] H. Rohling, “Radar CFAR Thresholding in Clutter and Multiple Target
Situations,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-19, no. 4,
pp. 608-621, 1983.
"""
data = np.abs(data)
data_shape = np.shape(data)
cfar = np.zeros_like(data)
guard = np.array(guard)
if guard.size == 1:
guard = np.tile(guard, 2)
trailing = np.array(trailing)
if trailing.size == 1:
trailing = np.tile(trailing, 2)
tg_sum = trailing+guard
if offset is None:
t_num = (2*tg_sum[0]+1)*(2*tg_sum[1]+1)
g_num = (2*guard[0]+1)*(2*guard[1]+1)
if t_num == g_num:
raise('No trailing bins!')
a = os_cfar_threshold(k, t_num-g_num, pfa)
else:
a = offset
if k < (t_num-g_num)/2 or k > t_num-g_num:
warn('``k`` is usuall chosen to satisfy ``N/2 < k < N '
'(N = '+str(t_num-g_num)+')``. '
'Typically, ``k`` is on the order of ``0.75N``')
cfar_win = np.ones((tg_sum*2+1), dtype=bool)
cfar_win[trailing[0]:(trailing[0]+guard[0]*2+1),
trailing[1]:(trailing[1]+guard[1]*2+1)] = False
for idx_0 in range(0, data_shape[0]):
for idx_1 in range(0, data_shape[1]):
win_idx_0 = np.mod(np.arange(idx_0-tg_sum[0],
idx_0+1+tg_sum[0],
1), data_shape[0])
win_idx_1 = np.mod(np.arange(idx_1-tg_sum[1],
idx_1+1+tg_sum[1],
1), data_shape[1])
x, y = np.meshgrid(win_idx_0, win_idx_1, indexing='ij')
sample_cube = data[x, y]
samples = np.sort(sample_cube[cfar_win].flatten())
cfar[idx_0, idx_1] = a*samples[k]
return cfar