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_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'):
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_gh_results(weights, estimates, predictions, actual, time_step=0):
n = len(weights)
if time_step > 0:
rng = range(1, n+1)
else:
rng = range(n, n+1)
xs = range(n+1)
book_plots.plot_measurements(xs[1:], weights, color='k', lines=False)
book_plots.plot_filter(xs, estimates, marker='o', label='Estimates')
book_plots.plot_track(xs[1:], predictions, c='r', marker='v', label='Predictions')
plt.plot([xs[0], xs[-1]], actual, c='k', lw=1, label='Actual')
plt.legend(loc=4)
book_plots.set_labels(x='day', y='weight (lbs)')
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
def plot_gh_results(weights, estimates, predictions, time_step=0):
plt.figure(figsize=(9, 4))
n = len(weights)
if time_step > 0:
rng = range(1, n + 1)
else:
rng = range(n, n + 1)
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))
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)
est, = 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, est, pred],
['Actual Weight', 'Measurement', 'Estimates', 'Predictions'],
loc=4)
book_plots.set_labels(x='day', y='weight (lbs)')
plt.xlim([-1, n + 1])
plt.ylim([156.0, 173])
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'):
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_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)
est, = 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, est, pred], ['Actual Weight', 'Measurement', 'Estimates', '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)
xs = range(n+1)
pred, = book_plots.plot_track(xs[1:], predictions, c='r', marker='v')
scale, = book_plots.plot_measurements(xs[1:], weights, color='k', lines=False)
est, = book_plots.plot_filter(xs, estimates, marker='o')
plt.legend([scale, est, pred], ['Measurement', 'Estimates', 'Predictions'], loc=4)
book_plots.set_labels(x='day', y='weight (lbs)')
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
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)
xs = range(n+1)
pred, = book_plots.plot_track(xs[1:], predictions, c='r', marker='v')
scale, = book_plots.plot_measurements(xs[1:], weights, color='k', lines=False)
est, = book_plots.plot_filter(xs, estimates, marker='o')
plt.legend([scale, est, pred], ['Measurement', 'Estimates', 'Predictions'], loc=4)
book_plots.set_labels(x='day', y='weight (lbs)')
plt.xlim([-1, n+1])
plt.ylim([156.0, 173])
def plot_radar(xs, track, time):
plt.figure()
bp.plot_track(time, track[:, 0])
bp.plot_filter(time, xs[:, 0])
plt.legend(loc=4)
plt.xlabel('time (sec)')
plt.ylabel('position (m)')
plt.figure()
bp.plot_track(time, track[:, 1])
bp.plot_filter(time, xs[:, 1])
plt.legend(loc=4)
plt.xlabel('time (sec)')
plt.ylabel('velocity (m/s)')
plt.figure()
bp.plot_track(time, track[:, 2])
bp.plot_filter(time, xs[:, 2])
plt.ylabel('altitude (m)')
plt.legend(loc=4)
plt.xlabel('time (sec)')
plt.ylim((900, 1600))
plt.show()
'data' contains the data(readings from the sensor) to be filtered.
'x0' is the initial value for our state variable
'dx' is the initial change rate for our state variable
'g' is the g-h's g scale factor
'h' is the g-h's h scale factor
'dt' is the length of the time step
"""
x = x0
meas = []
for z in data:
# predict
predict = x + dx * dt
# update
residual = z - predict
x = predict + g * residual
dx = dx + h * residual / dt
meas.append(x)
return np.array(meas)
%matplotlib inline
weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,
169.6, 167.4, 166.4, 171.0, 171.2, 172.6]
plt.figure(figsize=(16, 9))
book_plots.plot_track([0, 11], [160, 172], label='Actual weight')
data = g_h_filter(data=weights, x0=160., dx=1., g=6./10, h=2./3, dt=1.)
plot_g_h_results(weights, data)
