def start(self):
plt.figure()
# simulate robot movement
N = 30
sensor = PosSensor1((0, 0), (2, .2), noise_std=self.R_std)
zs = np.array([np.array([sensor.read()]).T for _ in range(N)])
# run filter
robot_tracker = self.tracker1()
mu, cov, _, _ = robot_tracker.batch_filter(zs)
for x, P in zip(mu, cov):
# covariance of x and y
cov = np.array([[P[0, 0], P[2, 0]], [P[0, 2], P[2, 2]]])
mean = (x[0, 0], x[2, 0])
#print(mean)
#plot_covariance_ellipse(mean, cov=cov, fc='g', std=3, alpha=0.5)
#plot results
#zs *= .3048 # convert to meters
bp.plot_filter(mu[:, 0], mu[:, 2])
bp.plot_measurements(zs[:, 0], zs[:, 1])
plt.legend(loc=2)
plt.xlim((0, 70))
plt.show()
def plot_dog_track(xs, dog, measurement_var, process_var):
N = len(xs)
bp.plot_track(dog)
bp.plot_measurements(xs, label='Sensor')
bp.set_labels('variance = {}, process variance = {}'.format(
measurement_var, process_var), 'time', 'pos')
plt.ylim([0, N])
bp.show_legend()
plt.show()
def plot_track(ps,
actual,
zs,
cov,
std_scale=1,
plot_P=True,
y_lim=None,
dt=1.,
xlabel='time',
ylabel='position',
title='Kalman Filter'):
with interactive_plot():
count = len(zs)
zs = np.asarray(zs)
cov = np.asarray(cov)
std = std_scale * np.sqrt(cov[:, 0, 0])
std_top = np.minimum(actual + std, [count + 10])
std_btm = np.maximum(actual - std, [-50])
std_top = actual + std
std_btm = actual - std
bp.plot_track(actual, c='k')
bp.plot_measurements(range(1, count + 1), zs)
bp.plot_filter(range(1, count + 1), ps)
plt.plot(std_top, linestyle=':', color='k', lw=1, alpha=0.4)
plt.plot(std_btm, linestyle=':', color='k', lw=1, alpha=0.4)
plt.fill_between(range(len(std_top)),
std_top,
std_btm,
facecolor='yellow',
alpha=0.2,
interpolate=True)
plt.legend(loc=4)
plt.xlabel(xlabel)
plt.ylabel(ylabel)
if y_lim is not None:
plt.ylim(y_lim)
else:
plt.ylim((-50, count + 10))
plt.xlim((0, count))
plt.title(title)
plt.show()
if plot_P:
ax = plt.subplot(121)
ax.set_title("$\sigma^2_x$ (pos variance)")
plot_covariance(cov, (0, 0))
ax = plt.subplot(122)
ax.set_title("$\sigma^2_\dot{x}$ (vel variance)")
plot_covariance(cov, (1, 1))
plt.show()
def plot_dog_track(xs, dog, measurement_var, process_var):
N = len(xs)
bp.plot_track(dog)
bp.plot_measurements(xs, label='Sensor')
bp.set_labels(
'variance = {}, process variance = {}'.format(measurement_var,
process_var), 'time',
'pos')
plt.ylim([0, N])
bp.show_legend()
plt.show()
def plot_track_and_residuals(t, xs, z_xs, res):
plt.subplot(121)
if z_xs is not None:
bp.plot_measurements(t, z_xs, label='z')
bp.plot_filter(t, xs)
plt.legend(loc=2)
plt.xlabel('time (sec)')
plt.ylabel('X')
plt.title('estimates vs measurements')
plt.subplot(122)
# plot twice so it has the same color as the plot to the left!
plt.plot(t, res)
plt.plot(t, res)
plt.xlabel('time (sec)')
plt.ylabel('residual')
plt.title('residuals')
plt.show()
def plot_track(ps, actual, zs, cov, std_scale=1,
plot_P=True, y_lim=None, dt=1.,
xlabel='time', ylabel='position',
title='Kalman Filter'):
with interactive_plot():
count = len(zs)
zs = np.asarray(zs)
cov = np.asarray(cov)
std = std_scale*np.sqrt(cov[:,0,0])
std_top = np.minimum(actual+std, [count + 10])
std_btm = np.maximum(actual-std, [-50])
std_top = actual + std
std_btm = actual - std
bp.plot_track(actual,c='k')
bp.plot_measurements(range(1, count + 1), zs)
bp.plot_filter(range(1, count + 1), ps)
plt.plot(std_top, linestyle=':', color='k', lw=1, alpha=0.4)
plt.plot(std_btm, linestyle=':', color='k', lw=1, alpha=0.4)
plt.fill_between(range(len(std_top)), std_top, std_btm,
facecolor='yellow', alpha=0.2, interpolate=True)
plt.legend(loc=4)
plt.xlabel(xlabel)
plt.ylabel(ylabel)
if y_lim is not None:
plt.ylim(y_lim)
else:
plt.ylim((-50, count + 10))
plt.xlim((0,count))
plt.title(title)
plt.show()
if plot_P:
ax = plt.subplot(121)
ax.set_title("$\sigma^2_x$ (pos variance)")
plot_covariance(cov, (0, 0))
ax = plt.subplot(122)
ax.set_title("$\sigma^2_\dot{x}$ (vel variance)")
plot_covariance(cov, (1, 1))
plt.show()
def plot_track_ellipses(N, zs, ps, cov, title):
bp.plot_measurements(range(1,N + 1), zs)
plt.plot(range(1, N + 1), ps, c='b', lw=2, label='filter')
plt.legend(loc='best')
plt.title(title)
for i,p in enumerate(cov):
plot_covariance_ellipse(
(i+1, ps[i]), cov=p, variance=4,
axis_equal=False, ec='g', alpha=0.5)
if i == len(cov)-1:
s = ('$\sigma^2_{pos} = %.2f$' % p[0,0])
plt.text (20, 5, s, fontsize=18)
s = ('$\sigma^2_{vel} = %.2f$' % p[1, 1])
plt.text (20, 0, s, fontsize=18)
plt.xlim(-10, 80)
plt.gca().set_aspect('equal')
plt.show()
def plot_track_ellipses(N, zs, ps, cov, title):
bp.plot_measurements(range(1,N + 1), zs)
plt.plot(range(1, N + 1), ps, c='b', lw=2, label='filter')
plt.legend(loc='best')
plt.title(title)
for i,p in enumerate(cov):
plot_covariance_ellipse(
(i+1, ps[i]), cov=p, variance=4,
axis_equal=False, ec='g', alpha=0.5)
if i == len(cov)-1:
s = ('$\sigma^2_{pos} = %.2f$' % p[0,0])
plt.text (20, 5, s, fontsize=18)
s = ('$\sigma^2_{vel} = %.2f$' % p[1, 1])
plt.text (20, 0, s, fontsize=18)
plt.xlim(-10, 80)
plt.gca().set_aspect('equal')
plt.show()
def plot_g_h_results(measurements, filtered_data,
title='', z_label='Measurements',
**kwargs):
book_plots.plot_filter(filtered_data, **kwargs)
book_plots.plot_measurements(measurements, label=z_label)
plt.legend(loc=4)
plt.title(title)
plt.gca().set_xlim(left=0,right=len(measurements))
return
import time
if not interactive:
book_plots.plot_filter(filtered_data, **kwargs)
book_plots.plot_measurements(measurements, label=z_label)
book_plots.show_legend()
plt.title(title)
plt.gca().set_xlim(left=0,right=len(measurements))
else:
for i in range(2, len(measurements)):
book_plots.plot_filter(filtered_data, **kwargs)
book_plots.plot_measurements(measurements, label=z_label)
book_plots.show_legend()
plt.title(title)
plt.gca().set_xlim(left=0,right=len(measurements))
plt.gca().canvas.draw()
time.sleep(0.5)
def plot_gh_results(weights, estimates, predictions, time_step=0):
n = len(weights)
if time_step > 0:
rng = range(1, n + 1)
else:
rng = range(n, n + 1)
plt.xlim([-1, n + 1])
plt.ylim([156.0, 173])
act, = book_plots.plot_track([0, n], [160, 160 + n], c='k')
plt.gcf().canvas.draw()
for i in rng:
xs = list(range(i + 1))
#plt.cla()
pred, = book_plots.plot_track(xs[1:],
predictions[:i],
c='r',
marker='v')
plt.xlim([-1, n + 1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
scale, = book_plots.plot_measurements(xs[1:],
weights[:i],
color='k',
lines=False)
plt.xlim([-1, n + 1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
book_plots.plot_filter(xs[:i + 1], estimates[:i + 1], marker='o')
plt.xlim([-1, n + 1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
plt.legend([act, scale, pred],
['Actual Weight', 'Measurement', 'Predictions'],
loc=4)
book_plots.set_labels(x='day', y='weight (lbs)')
def plot_gh_results(weights, estimates, predictions, time_step=0):
n = len(weights)
if time_step > 0:
rng = range(1, n+1)
else:
rng = range(n, n+1)
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
act, = book_plots.plot_track([0, n], [160, 160+n], c='k')
plt.gcf().canvas.draw()
for i in rng:
xs = list(range(i+1))
#plt.cla()
pred, = book_plots.plot_track(xs[1:], predictions[:i], c='r', marker='v')
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
scale, = book_plots.plot_measurements(xs[1:], weights[:i], color='k', lines=False)
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
book_plots.plot_filter(xs[:i+1], estimates[:i+1], marker='o')
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
plt.gcf().canvas.draw()
time.sleep(time_step)
plt.legend([act, scale, pred], ['Actual Weight', 'Measurement', 'Predictions'], loc=4)
book_plots.set_labels(x='day', y='weight (lbs)')