def test_simplex_sigma_points_1D():
""" tests passing 1D data into sigma_points"""
sp = SimplexSigmaPoints(1)
#ukf = UKF(dim_x=1, dim_z=1, dt=0.1, hx=None, fx=None, kappa=kappa)
Wm, Wc = sp.weights()
assert np.allclose(Wm, Wc, 1e-12)
assert len(Wm) == 2
mean = 5
cov = 9
Xi = sp.sigma_points(mean, cov)
xm, ucov = unscented_transform(Xi, Wm, Wc, 0)
# sum of weights*sigma points should be the original mean
m = 0.0
for x, w in zip(Xi, Wm):
m += x * w
assert abs(m - mean) < 1.e-12
assert abs(xm[0] - mean) < 1.e-12
assert abs(ucov[0, 0] - cov) < 1.e-12
assert Xi.shape == (2, 1)
def test_simplex_sigma_points_1D():
""" tests passing 1D data into sigma_points"""
sp = SimplexSigmaPoints(1)
#ukf = UKF(dim_x=1, dim_z=1, dt=0.1, hx=None, fx=None, kappa=kappa)
Wm, Wc = sp.weights()
assert np.allclose(Wm, Wc, 1e-12)
assert len(Wm) == 2
mean = 5
cov = 9
Xi = sp.sigma_points(mean, cov)
xm, ucov = unscented_transform(Xi, Wm, Wc, 0)
# sum of weights*sigma points should be the original mean
m = 0.0
for x, w in zip(Xi, Wm):
m += x*w
assert abs(m-mean) < 1.e-12
assert abs(xm[0] - mean) < 1.e-12
assert abs(ucov[0,0]-cov) < 1.e-12
assert Xi.shape == (2,1)
def test_sigma_plot():
""" Test to make sure sigma's correctly mirror the shape and orientation
of the covariance array."""
x = np.array([[1, 2]])
P = np.array([[2, 1.2], [1.2, 2]])
kappa = .1
# if kappa is larger, than points shoudld be closer together
sp0 = JulierSigmaPoints(n=2, kappa=kappa)
sp1 = JulierSigmaPoints(n=2, kappa=kappa * 1000)
sp2 = MerweScaledSigmaPoints(n=2, kappa=0, beta=2, alpha=1e-3)
sp3 = SimplexSigmaPoints(n=2)
# test __repr__ doesn't crash
str(sp0)
str(sp1)
str(sp2)
str(sp3)
w0, _ = sp0.weights()
w1, _ = sp1.weights()
w2, _ = sp2.weights()
w3, _ = sp3.weights()
Xi0 = sp0.sigma_points(x, P)
Xi1 = sp1.sigma_points(x, P)
Xi2 = sp2.sigma_points(x, P)
Xi3 = sp3.sigma_points(x, P)
assert max(Xi1[:, 0]) > max(Xi0[:, 0])
assert max(Xi1[:, 1]) > max(Xi0[:, 1])
if DO_PLOT:
plt.figure()
for i in range(Xi0.shape[0]):
plt.scatter((Xi0[i, 0] - x[0, 0]) * w0[i] + x[0, 0],
(Xi0[i, 1] - x[0, 1]) * w0[i] + x[0, 1],
color='blue',
label='Julier low $\kappa$')
for i in range(Xi1.shape[0]):
plt.scatter((Xi1[i, 0] - x[0, 0]) * w1[i] + x[0, 0],
(Xi1[i, 1] - x[0, 1]) * w1[i] + x[0, 1],
color='green',
label='Julier high $\kappa$')
# for i in range(Xi2.shape[0]):
# plt.scatter((Xi2[i, 0] - x[0, 0]) * w2[i] + x[0, 0],
# (Xi2[i, 1] - x[0, 1]) * w2[i] + x[0, 1],
# color='red')
for i in range(Xi3.shape[0]):
plt.scatter((Xi3[i, 0] - x[0, 0]) * w3[i] + x[0, 0],
(Xi3[i, 1] - x[0, 1]) * w3[i] + x[0, 1],
color='black',
label='Simplex')
stats.plot_covariance_ellipse([1, 2], P)
def test_sigma_plot():
""" Test to make sure sigma's correctly mirror the shape and orientation
of the covariance array."""
x = np.array([[1, 2]])
P = np.array([[2, 1.2],
[1.2, 2]])
kappa = .1
# if kappa is larger, than points shoudld be closer together
sp0 = JulierSigmaPoints(n=2, kappa=kappa)
sp1 = JulierSigmaPoints(n=2, kappa=kappa*1000)
sp2 = MerweScaledSigmaPoints(n=2, kappa=0, beta=2, alpha=1e-3)
sp3 = SimplexSigmaPoints(n=2)
w0, _ = sp0.weights()
w1, _ = sp1.weights()
w2, _ = sp2.weights()
w3, _ = sp3.weights()
Xi0 = sp0.sigma_points(x, P)
Xi1 = sp1.sigma_points(x, P)
Xi2 = sp2.sigma_points(x, P)
Xi3 = sp3.sigma_points(x, P)
assert max(Xi1[:,0]) > max(Xi0[:,0])
assert max(Xi1[:,1]) > max(Xi0[:,1])
if DO_PLOT:
plt.figure()
for i in range(Xi0.shape[0]):
plt.scatter((Xi0[i,0]-x[0, 0])*w0[i] + x[0, 0],
(Xi0[i,1]-x[0, 1])*w0[i] + x[0, 1],
color='blue', label='Julier low $\kappa$')
for i in range(Xi1.shape[0]):
plt.scatter((Xi1[i, 0]-x[0, 0]) * w1[i] + x[0,0],
(Xi1[i, 1]-x[0, 1]) * w1[i] + x[0,1],
color='green', label='Julier high $\kappa$')
# for i in range(Xi2.shape[0]):
# plt.scatter((Xi2[i, 0] - x[0, 0]) * w2[i] + x[0, 0],
# (Xi2[i, 1] - x[0, 1]) * w2[i] + x[0, 1],
# color='red')
for i in range(Xi3.shape[0]):
plt.scatter((Xi3[i, 0] - x[0, 0]) * w3[i] + x[0, 0],
(Xi3[i, 1] - x[0, 1]) * w3[i] + x[0, 1],
color='black', label='Simplex')
stats.plot_covariance_ellipse([1, 2], P)
def test_linear_2d_simplex():
""" should work like a linear KF if problem is linear """
def fx(x, dt):
F = np.array(
[[1, dt, 0, 0], [0, 1, 0, 0], [0, 0, 1, dt], [0, 0, 0, 1]],
dtype=float)
return np.dot(F, x)
def hx(x):
return np.array([x[0], x[2]])
dt = 0.1
points = SimplexSigmaPoints(n=4)
kf = UKF(dim_x=4, dim_z=2, dt=dt, fx=fx, hx=hx, points=points)
kf.x = np.array([-1., 1., -1., 1])
kf.P *= 0.0001
zs = []
for i in range(20):
z = np.array([i + randn() * 0.1, i + randn() * 0.1])
zs.append(z)
Ms, Ps = kf.batch_filter(zs)
smooth_x, _, _ = kf.rts_smoother(Ms, Ps, dt=dt)
if DO_PLOT:
zs = np.asarray(zs)
#plt.plot(zs[:,0])
plt.plot(Ms[:, 0])
plt.plot(smooth_x[:, 0], smooth_x[:, 2])
print(smooth_x)
def test_simplex_sigma_points_2D():
""" tests passing 1D data into sigma_points"""
sp = SimplexSigmaPoints(4)
Wm, Wc = sp.Wm, sp.Wc
assert np.allclose(Wm, Wc, 1e-12)
assert len(Wm) == 5
mean = np.array([-1, 2, 0, 5])
cov = np.eye(4)
cov[0, 1] = 0.5
cov[1, 0] = 0.5
cov[1, 1] = 5
cov[2, 2] = 3
Xi = sp.sigma_points(mean, cov)
xm, ucov = unscented_transform(Xi, Wm, Wc, 0)
assert np.allclose(xm, mean)
assert np.allclose(ucov, cov)
def test_simplex_sigma_points_2D():
""" tests passing 1D data into sigma_points"""
sp = SimplexSigmaPoints(4)
Wm, Wc = sp.Wm, sp.Wc
assert np.allclose(Wm, Wc, 1e-12)
assert len(Wm) == 5
mean = np.array([-1, 2, 0, 5])
cov1 = np.array([[1, 0.5], [0.5, 1]])
cov2 = np.array([[5, 0.5], [0.5, 3]])
cov = linalg.block_diag(cov1, cov2)
Xi = sp.sigma_points(mean, cov)
xm, ucov = unscented_transform(Xi, Wm, Wc)
assert np.allclose(xm, mean)
assert np.allclose(cov, ucov)