#!/usr/bin/env python3 __doc__ = \ """ For each antenna i calculate the differences with the other antennas j, Do these sets of differences match upto an initial difference \Delta_{ii'}? """ from itertools import chain, combinations, product import numpy as np import matplotlib.pyplot as plt rng = np.random.default_rng() ns = 1e-9 # s km = 1e3 # m c_light = 3e8*ns # m/s 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.t = t0 self.name = name def __repr__(self): cls = self.__class__.__name__ return f'{cls}(x={self.x!r},y={self.y!r},z={self.z!r},t0={self.t!r},name={self.name!r})' 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 geometry_time(dist, x2=None, c_light=c_light): if x2 is not None: dist = distance(dist, x2) return dist/c_light 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 def antenna_triangles(antennas): return combinations(antennas, 3) def antenna_baselines(antennas): return combinations(antennas, 2) def add_spatial_time_delay(tx, antennas, time=geometry_time, t_scale=1): """ Modifies antennas inplace """ for ant in antennas: ant.t += time(tx, ant)/t_scale def random_antenna(N_ant=1, antenna_ranges=[10e3,10e3,10e3], max_clock_skew=1): antennas = [] for i in range(N_ant): loc = antenna_ranges*rng.random(3) if max_clock_skew is None: t0 = 0 else: t0 = rng.normal(0, max_clock_skew) ant = Antenna(name=i, x=loc[0], y=loc[1], z=loc[1], t0=t0) antennas.append(ant) return antennas def single_baseline_referenced_sigmas(tx, baseline, all_antennas, phase_func=None): N_ant = len(all_antennas) baseline_ts = np.array([b.t for b in baseline]) baseline_geo = np.array([geometry_time(tx,b) for b in baseline]) not_baseline = lambda ant: ant not in baseline sigmas = np.empty( (N_ant-2, 2) ) for j, ant in enumerate(filter(not_baseline, all_antennas)): t_diff = ant.t - baseline_ts geo_diff = geometry_time(tx, ant) - baseline_geo if phase_func is not None: sigmas[i] = phase_func(t_diff - geo_diff) else: sigmas[i] = t_diff - geo_diff return sigmas def reference_antenna_sigmas(tx, ref_ant, all_antennas, phase_func=None): N_ant = len(all_antennas) ref_geo = geometry_time(tx, ref_ant) sigmas = np.empty( (N_ant) ) for i, ant in enumerate(all_antennas): if False and ant is ref_ant: sigmas[i] = 0 t_diff = ant.t - ref_ant.t geo_diff = geometry_time(tx, ant) - ref_geo if phase_func is not None: sigmas[i] = phase_func(t_diff - geo_diff) else: sigmas[i] = t_diff - geo_diff return sigmas def all_sigmas_using_reference_antenna(tx, all_antennas, phase_func=None): N_ant = len(all_antennas) sigmas = np.empty( (N_ant,N_ant) ) for i, ant in enumerate(all_antennas): sigmas[i] = reference_antenna_sigmas(tx, ant, all_antennas, phase_func=phase_func) return sigmas def main(tx, antennas, spatial_unit=None, time_unit=None, ref_idx = [0, 1, -2, -1], plot_phase=False, remove_minimum=True, f_beacon=50e6, scatter_kwargs={}): # Use each baseline once as a reference # and loop over the remaining antennas N_ant = len(antennas) fig = None default_scatter_kwargs = {} #for i, baseline in enumerate(antenna_baselines(antennas)): if False: baseline = [antennas[0], antennas[1]] sigmas = single_baseline_referenced_sigmas(tx, baseline, antennas) print("Baseline {},{}".format(baseline[0].name, baseline[1].name)) print(sigmas) print(-1*np.diff(sigmas, axis=1)) print("Direct", np.diff([a.t for a in baseline])) print() if True: if plot_phase: phase_func = lambda t: phase_mod(2*np.pi* f_beacon * t) color_label='$\\varphi$' default_scatter_kwargs['cmap'] = 'Spectral_r' default_scatter_kwargs['vmin'] = -np.pi default_scatter_kwargs['vmax'] = +np.pi else: color_label='t' if time_unit is None else 't ['+time_unit+']' phase_func = None scatter_kwargs = { **default_scatter_kwargs, **scatter_kwargs } sigmas = all_sigmas_using_reference_antenna(tx, antennas, phase_func=phase_func) if remove_minimum: if True: # actually use the time diffs with the first ref ant # required for phase alignment mins = sigmas[0] else: mins = -1*np.min(sigmas, axis=-1) sigmas = sigmas + mins[:, np.newaxis] if plot_phase: # Redo the phase mod sigmas = phase_mod(sigmas) fig, axs = plt.subplots(2,2, sharex=True, sharey=True) title = "" if remove_minimum: title += '$\sigma_{0j}$ added' if remove_minimum and plot_phase: title += ', ' if plot_phase: t_scaler = 1 if time_unit == 'ns': t_scaler = 1e9 title += 'f= {:2.0f}MHz'.format(f_beacon*t_scaler/1e6) fig.suptitle(title) antenna_locs = list(zip(*[(ant.x, ant.y) for ant in antennas])) for i, ax in enumerate(axs.flat): ax.set_title("Ref Antenna: {}".format(ref_idx[i])) ax.set_xlabel('x' if spatial_unit is None else 'x [{}]'.format(spatial_unit)) ax.set_ylabel('y' if spatial_unit is None else 'y [{}]'.format(spatial_unit)) sc = ax.scatter(*antenna_locs, c=sigmas[ref_idx[i]], **scatter_kwargs) fig.colorbar(sc, ax=ax, label=color_label) ax.plot(antennas[ref_idx[i]].x, antennas[ref_idx[i]].y, 'rx') return fig, sigmas if __name__ == "__main__": from argparse import ArgumentParser from os import path rng = np.random.default_rng(1) parser = ArgumentParser(description=__doc__) parser.add_argument("fname", metavar="path/to/figure[/]", nargs="?", help="Location for generated figure, will append __file__ if a directory. If not supplied, figure is shown.") parser.add_argument('num_ant', help='Number of antennas to use', nargs='?', default=5, type=int) parser.add_argument('--remove-min', action='store_true') command_group = parser.add_mutually_exclusive_group(required=False) command_group.add_argument('--time', help='Calculate times (Default)', action='store_true') command_group.add_argument('--phase', help='Calculate wrapped phases', action='store_true') args = parser.parse_args() args.rm_minimum = True args.plot_phase = args.phase del args.time, args.phase if args.fname == 'none': args.fname = None if args.fname is not None: if path.isdir(args.fname): args.fname = path.join(args.fname, path.splitext(path.basename(__file__))[0]) # leave off extension if not path.splitext(args.fname)[1]: args.fname = [ args.fname+ext for ext in ['.pdf', '.png'] ] ###### antenna_ranges = np.array([10*km,10*km,5*km]) antenna_max_clock_skew = 100*ns/ns # 0.1 us f_beacon = 50e6*ns # 50 MHz tx = Antenna(name='tx', x=-300*km, y=200*km, z=0) antennas = random_antenna(args.num_ant, antenna_ranges, antenna_max_clock_skew) add_spatial_time_delay(tx, antennas) fig, sigmas = main(tx, antennas, spatial_unit='m', time_unit='ns', plot_phase=args.plot_phase, remove_minimum=args.rm_minimum, f_beacon=f_beacon) ###### Output if args.fname is not None: if isinstance(args.fname, str): args.fname = [args.fname] for fname in args.fname: plt.savefig(fname) else: plt.show()