def GSF_linear_gaussian_models_simple_scenario():
arr = lambda scalar: np.array([[scalar]])
# Prior
x_prior = arr(0.5)
P_prior = arr(0.2)
p_prior_exact = GaussianMixture(Gaussian(x_prior, P_prior, weight=1))
p_prior_GSF = GaussianMixture(Gaussian(x_prior, P_prior, weight=1))
# Models
# - Motion
Q = arr(0.35)
F = arr(1)
# - Measurement
R = arr(0.2)
H = arr(1)
PD = 0.9
# - Clutter
lamb = 0.4
# GSF tuning params
Nmax = 5
tol_prune = 0.01 # or None
# Sensor
space = Space1D(-4, 4)
# Create measurement vector
Z1 = [-1.3, 1.7]
Z2 = [1.3]
Z3 = [-0.3, 2.3]
Z4 = [-2, 3]
Z5 = [2.6]
Z6 = [-3.5, 2.8]
Zs = [Z1, Z2, Z3, Z4, Z5, Z6]
# Plot settings
ax = plt.subplot()
res = 100
marker_size = 100
x_lim = [space.min, space.max]
# Compute exact posterior
for k, Z in enumerate(Zs, start=1):
print(f'Measurements: {Z}')
# Compute posterior
p_exact, p_pred_exact = exact_posterior_LG(p_prior_exact, Z, PD, lamb,
F, Q, H, R)
p_GSF, p_pred_GSF = GSF_LG(p_prior_GSF, Z, PD, lamb, F, Q, H, R, Nmax,
tol_prune)
# Number of hypotesis
print(f'Number of hypotesis, exact posterior: {p_exact.n_components}')
print(f'Number of hypotesis, GSF posterior: {p_GSF.n_components}')
# Plot
ax.clear()
ax.set(title=f'k = {k}', xlabel='x')
ax.axhline(0, color='gray', linewidth=0.5)
# - Predicted density according to GSF
plt1 = plot_gaussian_mixture_pdf(ax,
p_pred_GSF,
x_lim,
res=res,
color='r',
linestyle='--',
zorder=0)
# - Exact posterior density
plt2 = plot_gaussian_mixture_pdf(ax,
p_exact,
x_lim,
res=res,
color='k',
zorder=1)
# - Posterior density according to GSF
plt3 = plot_gaussian_mixture_pdf(ax,
p_GSF,
x_lim,
res=res,
color='orange',
linestyle='--',
marker='x',
zorder=2)
# - Measurements
plot_1D_measurements(ax,
Z,
color='b',
marker='*',
s=marker_size,
zorder=3)
# - Final details
ax.set_xlim([space.min, space.max])
ax.set_ylim([-0.05, 1.05])
ax.legend((plt1, plt2, plt3), ('pred', 'exact', 'GSF'))
plt.pause(0.0001)
p_prior_exact = p_exact
p_prior_GSF = p_GSF
input('Press to continue')
def PDA_linear_gaussian_models_simple_scenario():
arr = lambda scalar: np.array([[scalar]])
# Prior
x_prior = arr(0.5)
P_prior = arr(0.2)
p_prior_exact = Gaussian(x_prior, P_prior, weight=1)
p_prior_PDA = Gaussian(x_prior, P_prior)
# Models
# - Motion
Q = arr(0.35)
F = arr(1)
# - Measurement
R = arr(0.2)
H = arr(1)
PD = 0.9
# - Clutter
lamb = 0.4
# Sensor
space = Space1D(-4, 4)
# Create measurement vector
Z1 = [-1.3, 1.7]
Z2 = [1.3]
Z3 = [-0.3, 2.3]
Z4 = [-2, 3]
Z5 = [2.6]
Z6 = [-3.5, 2.8]
Zs = [Z1, Z2, Z3, Z4, Z5, Z6]
# Plot settings
ax = plt.subplot()
res = 100
x_lim = [space.min, space.max]
# Compute exact posterior
for k, Z in enumerate(Zs, start=1):
print(f'Measurements: {Z}')
# Compute posterior
p_exact, p_pred_exact = exact_posterior_LG(p_prior_exact, Z, PD, lamb,
F, Q, H, R)
p_PDA, p_pred_PDA = PDA_LG(p_prior_PDA, Z, PD, lamb, F, Q, H, R)
# Number of hypotesis
print(f'number of hypotesis: {p_exact.n_components}')
# Plot
ax.clear()
ax.set(title=f'k = {k}', xlabel='x')
ax.axhline(0, color='gray', linewidth=0.5)
# - Predicted density according to PDA
plt1 = plot_gaussian_pdf(ax,
p_pred_PDA,
x_lim,
res=res,
color='r',
linestyle='--',
zorder=0)
# - Exact posterior density
plt2 = plot_gaussian_mixture_pdf(ax,
p_exact,
x_lim,
res=res,
color='k',
zorder=1)
# - Posterior density according to PDA
plt3 = plot_gaussian_pdf(ax,
p_PDA,
x_lim,
res=res,
color='g',
marker='s',
zorder=2)
# - Hypotesis from PDA
marker_size = 100
ax.scatter(p_pred_PDA.x,
0,
color='b',
marker='o',
s=marker_size,
zorder=3)
x_axis = np.zeros(len(Z))
ax.scatter(Z, x_axis, color='b', marker='*', s=marker_size, zorder=3)
ax.set_xlim(x_lim)
ax.set_ylim([-0.05, 1.2])
ax.legend((plt1, plt2, plt3), ('pred', 'exact', 'PDA'))
p_prior_exact = p_exact
p_prior_PDA = p_PDA
plt.pause(0.0001)
input('Press to continue')