def build_ukf(x, P, std_r, std_b, dt=1.0):
'''
Build UKF.
x: initial state.
P: initial covariance matrix.
std_r: standard var. of laser measurement.
std_b: standard var. of IMU measurement.
dt: time interval.
Plus some defined functions as parameters.
returns ukf.
'''
# Calculate sigma points.
points = MerweScaledSigmaPoints(n=6, alpha=0.001, beta=2, kappa=-3, subtract=residual_x)
ukf = UKF(dim_x=6, dim_z=4, fx=move, hx=Hx, \
dt=dt, points=points, x_mean_fn=state_mean, \
z_mean_fn=z_mean, residual_x=residual_x, residual_z=residual_z)
ukf.x = np.array(x)
ukf.P = P
ukf.R = np.diag([std_r ** 2, std_r ** 2, std_b ** 2, std_b ** 2])
q1 = Q_discrete_white_noise(dim=2, dt=dt, var=1.0)
q2 = Q_discrete_white_noise(dim=2, dt=dt, var=1.0)
q3 = Q_discrete_white_noise(dim=2, dt=dt, var=3.05 * pow(10, -4))
ukf.Q = block_diag(q1, q2, q3)
# ukf.Q = np.eye(3) * 0.0001
return ukf
def unscented_kf(self, number=NUMBER):
global Time
P0 = np.diag([
3e-2, 3e-2, 3e-2, 3e-6, 3e-6, 3e-6, 3e-2, 3e-2, 3e-2, 3e-6, 3e-6,
3e-6
])
error = np.random.multivariate_normal(mean=np.zeros(12), cov=P0)
X0 = np.hstack((HPOP_1[0], HPOP_2[0])) + error
points = MerweScaledSigmaPoints(n=12, alpha=0.001, beta=2.0, kappa=-9)
ukf = UKF(dim_x=12,
dim_z=4,
fx=self.state_equation,
hx=self.measure_equation,
dt=STEP,
points=points)
ukf.x = X0
ukf.P = P0
ukf.R = Rk
ukf.Q = Qk
XF, XP = [X0], [X0]
print(error, "\n", Qk[0][0], "\n", Rk[0][0])
for i in range(1, number + 1):
ukf.predict()
Z = nav.measure_stk(i)
ukf.update(Z)
X_Up = ukf.x.copy()
XF.append(X_Up)
Time = Time + STEP
XF = np.array(XF)
return XF
def test_rts():
def fx(x, dt):
A = np.eye(3) + dt * np.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
f = np.dot(A, x)
return f
def hx(x):
return np.sqrt(x[0]**2 + x[2]**2)
dt = 0.05
sp = JulierSigmaPoints(n=3, kappa=1.)
kf = UKF(3, 1, dt, fx=fx, hx=hx, points=sp)
kf.Q *= 0.01
kf.R = 10
kf.x = np.array([0., 90., 1100.])
kf.P *= 100.
radar = RadarSim(dt)
t = np.arange(0, 20 + dt, dt)
n = len(t)
xs = np.zeros((n, 3))
random.seed(200)
rs = []
#xs = []
for i in range(len(t)):
r = radar.get_range()
#r = GetRadar(dt)
kf.predict()
kf.update(z=[r])
xs[i, :] = kf.x
rs.append(r)
kf.x = np.array([0., 90., 1100.])
kf.P = np.eye(3) * 100
M, P = kf.batch_filter(rs)
assert np.array_equal(M, xs), "Batch filter generated different output"
Qs = [kf.Q] * len(t)
M2, P2, K = kf.rts_smoother(Xs=M, Ps=P, Qs=Qs)
if DO_PLOT:
print(xs[:, 0].shape)
plt.figure()
plt.subplot(311)
plt.plot(t, xs[:, 0])
plt.plot(t, M2[:, 0], c='g')
plt.subplot(312)
plt.plot(t, xs[:, 1])
plt.plot(t, M2[:, 1], c='g')
plt.subplot(313)
plt.plot(t, xs[:, 2])
plt.plot(t, M2[:, 2], c='g')
def test_linear_1d():
""" should work like a linear KF if problem is linear """
def fx(x, dt):
F = np.array([[1., dt], [0, 1]])
return np.dot(F, x)
def hx(x):
return np.array([x[0]])
dt = 0.1
points = MerweScaledSigmaPoints(2, .1, 2., -1)
kf = UKF(dim_x=2, dim_z=1, dt=dt, fx=fx, hx=hx, points=points)
kf.x = np.array([1, 2])
kf.P = np.array([[1, 1.1], [1.1, 3]])
kf.R *= 0.05
kf.Q = np.array([[0., 0], [0., .001]])
z = np.array([2.])
kf.predict()
kf.update(z)
zs = []
for i in range(50):
z = np.array([i + randn() * 0.1])
zs.append(z)
kf.predict()
kf.update(z)
print('K', kf.K.T)
print('x', kf.x)
def build_ukf(x0=None, P0=None,
Q = None, R = None
):
# build ukf
if x0 is None:
x0 = np.zeros(6)
if P0 is None:
P0 = np.diag([1e-6,1e-6,1e-6, 1e-1, 1e-1, 1e-1])
if Q is None:
Q = np.diag([1e-4, 1e-4, 1e-2, 1e-1, 1e-1, 1e-1]) #xyhvw
if R is None:
R = np.diag([1e-1, 1e-1, 1e-1]) # xyh
#spts = MerweScaledSigmaPoints(6, 1e-3, 2, 3-6, subtract=ukf_residual)
spts = JulierSigmaPoints(6, 6-2, sqrt_method=np.linalg.cholesky, subtract=ukf_residual)
ukf = UKF(6, 3, (1.0 / 30.), # dt guess
ukf_hx, ukf_fx, spts,
x_mean_fn=ukf_mean,
z_mean_fn=ukf_mean,
residual_x=ukf_residual,
residual_z=ukf_residual)
ukf.x = x0.copy()
ukf.P = P0.copy()
ukf.Q = Q
ukf.R = R
return ukf
def ukf_process(x, P, sigma_range, sigma_bearing, dt=1.0):
""" construct Unscented Kalman Filter with the initial state x
and the initial covaiance matrix P
sigma_range: the std of laser range sensors
sigma_bearing: the std of IMU
"""
# construct the sigma points
points = MerweScaledSigmaPoints(n=3,
alpha=0.001,
beta=2,
kappa=0,
subtract=residual)
# build the UKF based on previous functions
ukf = UKF(dim_x=3,
dim_z=3,
fx=move,
hx=Hx,
dt=dt,
points=points,
x_mean_fn=state_mean,
z_mean_fn=z_mean,
residual_x=residual,
residual_z=residual)
# assign the parameters of ukf
ukf.x = np.array(x)
ukf.P = P
ukf.R = np.diag([sigma_range**2, sigma_range**2, sigma_bearing**2])
ukf.Q = np.eye(3) * 0.0001
return ukf
def create_ukf(cmds,
landmarks,
sigma_vel,
sigma_steer,
sigma_range,
sigma_bearing,
ellipse_step=1,
step=10):
points = MerweScaledSigmaPoints(n=3,
alpha=0.03,
beta=2.,
kappa=0,
subtract=residual_x,
sqrt_method=sqrt_func)
ukf = UKF(dim_x=3,
dim_z=2 * len(landmarks),
fx=move,
hx=Hx,
dt=dt,
points=points,
x_mean_fn=state_mean,
z_mean_fn=z_mean,
residual_x=residual_x,
residual_z=residual_h)
ukf.x = np.array([203.0, 1549.2, 1.34])
ukf.P = np.diag([100., 100., .5])
ukf.R = np.diag([sigma_range**2, sigma_bearing**2] * len(landmarks))
ukf.Q = np.diag([10.**2, 10.**2, 0.3**2])
return ukf
def run_localization(
cmds, landmarks, sigma_vel, sigma_steer, sigma_range,
sigma_bearing, ellipse_step=1, step=10):
plt.figure()
points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0,
subtract=residual_x)
ukf = UKF(dim_x=3, dim_z=2*len(landmarks), fx=fx, hx=Hx,
dt=dt, points=points, x_mean_fn=state_mean,
z_mean_fn=z_mean, residual_x=residual_x,
residual_z=residual_h)
ukf.x = np.array([2, 6, .3])
ukf.P = np.diag([.1, .1, .05])
ukf.R = np.diag([sigma_range**2,
sigma_bearing**2]*len(landmarks))
ukf.Q = np.eye(3)*0.0001
sim_pos = ukf.x.copy()
# plot landmarks
if len(landmarks) > 0:
plt.scatter(landmarks[:, 0], landmarks[:, 1],
marker='s', s=60)
track = []
for i, u in enumerate(cmds):
sim_pos = move(sim_pos, u, dt/step, wheelbase)
track.append(sim_pos)
if i % step == 0:
ukf.predict(fx_args=u)
if i % ellipse_step == 0:
plot_covariance_ellipse(
(ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,
facecolor='k', alpha=0.3)
x, y = sim_pos[0], sim_pos[1]
z = []
for lmark in landmarks:
dx, dy = lmark[0] - x, lmark[1] - y
d = sqrt(dx**2 + dy**2) + randn()*sigma_range
bearing = atan2(lmark[1] - y, lmark[0] - x)
a = (normalize_angle(bearing - sim_pos[2] +
randn()*sigma_bearing))
z.extend([d, a])
ukf.update(z, hx_args=(landmarks,))
if i % ellipse_step == 0:
plot_covariance_ellipse(
(ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,
facecolor='g', alpha=0.8)
track = np.array(track)
plt.plot(track[:, 0], track[:,1], color='k', lw=2)
plt.axis('equal')
plt.title("UKF Robot localization")
plt.show()
return ukf
def run_localization(
cmds, landmarks, sigma_vel, sigma_steer, sigma_range,
sigma_bearing, ellipse_step=1, step=10):
plt.figure()
points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0,
subtract=residual_x)
ukf = UKF(dim_x=3, dim_z=2*len(landmarks), fx=fx, hx=Hx,
dt=dt, points=points, x_mean_fn=state_mean,
z_mean_fn=z_mean, residual_x=residual_x,
residual_z=residual_h)
ukf.x = np.array([2, 6, .3])
ukf.P = np.diag([.1, .1, .05])
ukf.R = np.diag([sigma_range**2,
sigma_bearing**2]*len(landmarks))
ukf.Q = np.eye(3)*0.0001
sim_pos = ukf.x.copy()
# plot landmarks
if len(landmarks) > 0:
plt.scatter(landmarks[:, 0], landmarks[:, 1],
marker='s', s=60)
track = []
for i, u in enumerate(cmds):
sim_pos = move(sim_pos, u, dt/step, wheelbase)
track.append(sim_pos)
if i % step == 0:
ukf.predict(fx_args=u)
if i % ellipse_step == 0:
plot_covariance_ellipse(
(ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,
facecolor='k', alpha=0.3)
x, y = sim_pos[0], sim_pos[1]
z = []
for lmark in landmarks:
dx, dy = lmark[0] - x, lmark[1] - y
d = sqrt(dx**2 + dy**2) + randn()*sigma_range
bearing = atan2(lmark[1] - y, lmark[0] - x)
a = (normalize_angle(bearing - sim_pos[2] +
randn()*sigma_bearing))
z.extend([d, a])
ukf.update(z, hx_args=(landmarks,))
if i % ellipse_step == 0:
plot_covariance_ellipse(
(ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,
facecolor='g', alpha=0.8)
track = np.array(track)
plt.plot(track[:, 0], track[:,1], color='k', lw=2)
plt.axis('equal')
plt.title("UKF Robot localization")
plt.show()
return ukf
def myUKF(fx, hx, P, Q, R):
points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)
kf = UKF(4, 2, dt, fx=fx, hx=hx,
points=points) #(x_dimm, z_dimm,dt, hx, fx, sigmaPoints)
kf.P = P
kf.Q = Q
kf.R = R
kf.x = np.array([0., 90., 1100., 0.]) # initial gauss
return kf
def test_vhartman():
"""
Code provided by vhartman on github #172
https://github.com/rlabbe/filterpy/issues/172
"""
def fx(x, dt):
# state transition function - predict next state based
# on constant velocity model x = vt + x_0
F = np.array([[1.]], dtype=np.float32)
return np.dot(F, x)
def hx(x):
# measurement function - convert state into a measurement
# where measurements are [x_pos, y_pos]
return np.array([x[0]])
dt = 1.0
# create sigma points to use in the filter. This is standard for Gaussian processes
points = MerweScaledSigmaPoints(1, alpha=1, beta=2., kappa=0.1)
kf = UnscentedKalmanFilter(dim_x=1,
dim_z=1,
dt=dt,
fx=fx,
hx=hx,
points=points)
kf.x = np.array([0.]) # initial state
kf.P = np.array([[1]]) # initial uncertainty
kf.R = np.diag([1]) # 1 standard
kf.Q = np.diag([1]) # 1 standard
ekf = ExtendedKalmanFilter(dim_x=1, dim_z=1)
ekf.F = np.array([[1]])
ekf.x = np.array([0.]) # initial state
ekf.P = np.array([[1]]) # initial uncertainty
ekf.R = np.diag([1]) # 1 standard
ekf.Q = np.diag([1]) # 1 standard
np.random.seed(0)
zs = [[np.random.randn()] for i in range(50)] # measurements
for z in zs:
kf.predict()
ekf.predict()
assert np.allclose(ekf.P, kf.P)
assert np.allclose(ekf.x, kf.x)
kf.update(z)
ekf.update(z, lambda x: np.array([[1]]), hx)
assert np.allclose(ekf.P, kf.P)
assert np.allclose(ekf.x, kf.x)
def estimateUKF(camPoses):
points = MerweScaledSigmaPoints(3,.1,2.,0.)
filter = UKF(3,3,0,h, f, points, sqrt_fn=None, x_mean_fn=state_mean, z_mean_fn=state_mean, residual_x=residual, residual_z=residual)
filter.P = np.diag([0.04,0.04,0.003])
filter.Q = np.diag([(0.2)**2,(0.2)**2,(1*3.14/180)**2])
filter.R = np.diag([100,100,0.25])
Uposes = [[],[]]
for i in range(len(speed)):
x = filter.x
Uposes[0].append(x[0])
Uposes[1].append(x[1])
filter.predict(fx_args=[speed[i],angle[i]*0.01745])
filter.update(z = [camPoses[0][i],camPoses[1][i],camPoses[2][i]])
return Uposes
def create(self, pose, *args, **kwargs):
print 'CREATE!'
ukf = UKF(**self.ukf_args)
ukf._Q = self.Q.copy()
ukf.Q = self.Q.copy()
ukf.R = self.R.copy()
ukf.x = pose #np.zeros(5, dtype=np.float32)
#ukf.x[:3] = pose[:3]
ukf.P = self.P.copy()
# TODO : fill in more info, such as color(red/green/unknown), type(target/obs/unknown)
self.est[self.p_idx] = UKFEstimate(pose, *args, ukf=ukf, **kwargs)
self.p_idx += 1
def UKFinit():
global ukf
ukf_fuse = []
p_std_x, p_std_y = 0.2, 0.2
v_std_x, v_std_y = 0.01, 0.01
a_std_x, a_std_y = 0.01, 0.01
dt = 0.0125 #80HZ
sigmas = MerweScaledSigmaPoints(6, alpha=.1, beta=2., kappa=-1.0)
ukf = UKF(dim_x=6, dim_z=6, fx=f_cv, hx=h_cv, dt=dt, points=sigmas)
ukf.x = np.array([0., 0., 0., 0., 0., 0.])
ukf.R = np.diag([p_std_x, v_std_x, a_std_x, p_std_y, v_std_y, a_std_y])
ukf.Q[0:3, 0:3] = Q_discrete_white_noise(3, dt=dt, var=0.2)
ukf.Q[3:6, 3:6] = Q_discrete_white_noise(3, dt=dt, var=0.2)
ukf.P = np.diag([8, 2, 2, 5, 2, 2])
def UKFinit():
global ukf
ukf_fuse = []
std_y, std_z = 0.01, 0.01
vstd_y = 0.1
vstd_z = 0.1
dt = 0.005
sigmas = MerweScaledSigmaPoints(4, alpha=.1, beta=2., kappa=-1.0)
ukf = UKF(dim_x=4, dim_z=4, fx=f_cv, hx=h_cv, dt=dt, points=sigmas)
ukf.x = np.array([0., 0., 0., 0.])
ukf.R = np.diag([std_y, vstd_y, std_z, vstd_z])
ukf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.2)
ukf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.2)
ukf.P = np.diag([3**2, 0.5, 3**2, 0.5])
def UKFinit():
global ukf
p_std_x, p_std_y = 0.1, 0.1
v_std_x, v_std_y = 0.1, 0.1
dt = 0.0125 #80HZ
sigmas = MerweScaledSigmaPoints(4, alpha=.1, beta=2., kappa=-1.0)
ukf = UKF(dim_x=4, dim_z=4, fx=f_cv, hx=h_cv, dt=dt, points=sigmas)
ukf.x = np.array([0., 0., 0., 0.])
ukf.R = np.diag([p_std_x, v_std_x, p_std_y, v_std_y])
ukf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.2)
ukf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.2)
ukf.P = np.diag([8, 1.5 ,5, 1.5])
def test_rts():
def fx(x, dt):
A = np.eye(3) + dt * np.array ([[0, 1, 0],
[0, 0, 0],
[0, 0, 0]])
f = np.dot(A, x)
return f
def hx(x):
return np.sqrt (x[0]**2 + x[2]**2)
dt = 0.05
sp = JulierSigmaPoints(n=3, kappa=1.)
kf = UKF(3, 1, dt, fx=fx, hx=hx, points=sp)
kf.Q *= 0.01
kf.R = 10
kf.x = np.array([0., 90., 1100.])
kf.P *= 100.
radar = RadarSim(dt)
t = np.arange(0,20+dt, dt)
n = len(t)
xs = np.zeros((n,3))
random.seed(200)
rs = []
#xs = []
for i in range(len(t)):
r = radar.get_range()
#r = GetRadar(dt)
kf.predict()
kf.update(z=[r])
xs[i,:] = kf.x
rs.append(r)
kf.x = np.array([0., 90., 1100.])
kf.P = np.eye(3)*100
M, P = kf.batch_filter(rs)
assert np.array_equal(M, xs), "Batch filter generated different output"
Qs = [kf.Q]*len(t)
M2, P2, K = kf.rts_smoother(Xs=M, Ps=P, Qs=Qs)
def UKFinit():
global ukf
ukf_fuse = []
p_std_yaw = 0.004
v_std_yaw = 0.008
dt = 0.0125 #80HZ
sigmas = MerweScaledSigmaPoints(2, alpha=.1, beta=2., kappa=-1.0)
ukf = UKF(dim_x=2, dim_z=2, fx=f_cv, hx=h_cv, dt=dt, points=sigmas)
ukf.x = np.array([
0.,
0.,
])
ukf.R = np.diag([p_std_yaw, v_std_yaw])
ukf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.2)
ukf.P = np.diag([6.3, 1])
def ukf_process(x, P, sigma_range, sigma_bearing, dt=1.0):
points = MerweScaledSigmaPoints(n=3, alpha=0.001, beta=2, kappa=0,
subtract=residual)
# build the UKF based on previous functions
ukf = UKF(dim_x=3, dim_z=3, fx=move, hx=Hx,
dt=dt, points=points, x_mean_fn=state_mean,
z_mean_fn=z_mean, residual_x=residual,
residual_z=residual)
# assign the parameters of ukf
ukf.x = np.array(x)
ukf.P = P
ukf.R = np.diag([sigma_range**2, sigma_range**2, sigma_bearing**2])
ukf.Q = np.eye(3)*0.0001
return ukf
def Unscentedfilter(zs): # Filter function
points = MerweScaledSigmaPoints(2, alpha=.1, beta=2., kappa=1)
ukf = UnscentedKalmanFilter(dim_x=2,
dim_z=1,
fx=fx,
hx=hx,
points=points,
dt=dt)
ukf.Q = array(([50, 0], [0, 50]))
ukf.R = 100
ukf.P = eye(2) * 2
mu, cov = ukf.batch_filter(zs)
x, _, _ = ukf.rts_smoother(mu, cov)
return x[:, 0]
def UKFinit():
global ukf
ukf_fuse = []
p_std_x = rospy.get_param('~p_std_x',0.005)
v_std_x = rospy.get_param('~v_std_x',0.05)
p_std_y = rospy.get_param('~p_std_y',0.005)
v_std_y = rospy.get_param('~v_std_y',0.05)
dt = rospy.get_param('~dt',0.01) #100HZ
sigmas = MerweScaledSigmaPoints(4, alpha=.1, beta=2., kappa=-1.0)
ukf = UKF(dim_x=4, dim_z=4, fx=f_cv, hx=h_cv, dt=dt, points=sigmas)
ukf.x = np.array([0., 0., 0., 0.,])
ukf.R = np.diag([p_std_x, v_std_x, p_std_y, v_std_y])
ukf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=4.0)
ukf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=4.0)
ukf.P = np.diag([3, 1, 3, 1])
def test_1d():
def fx(x, dt):
F = np.array([[1., dt],
[0, 1]])
return np.dot(F, x)
def hx(x):
return np.array([[x[0]]])
ckf = CKF(dim_x=2, dim_z=1, dt=0.1, hx=hx, fx=fx)
ckf.x = np.array([[1.], [2.]])
ckf.P = np.array([[1, 1.1],
[1.1, 3]])
ckf.R = np.eye(1) * .05
ckf.Q = np.array([[0., 0], [0., .001]])
dt = 0.1
points = MerweScaledSigmaPoints(2, .1, 2., -1)
kf = UKF(dim_x=2, dim_z=1, dt=dt, fx=fx, hx=hx, points=points)
kf.x = np.array([1, 2])
kf.P = np.array([[1, 1.1],
[1.1, 3]])
kf.R *= 0.05
kf.Q = np.array([[0., 0], [0., .001]])
for i in range(50):
z = np.array([[i+randn()*0.1]])
#xx, pp, Sx = predict(f, x, P, Q)
#x, P = update(h, z, xx, pp, R)
ckf.predict()
ckf.update(z)
kf.predict()
kf.update(z[0])
assert abs(ckf.x[0] -kf.x[0]) < 1e-10
assert abs(ckf.x[1] -kf.x[1]) < 1e-10
plt.show()
def test_1d():
def fx(x, dt):
F = np.array([[1., dt],
[0, 1]])
return np.dot(F, x)
def hx(x):
return x[0:1]
ckf = CKF(dim_x=2, dim_z=1, dt=0.1, hx=hx, fx=fx)
ckf.x = np.array([[1.], [2.]])
ckf.P = np.array([[1, 1.1],
[1.1, 3]])
ckf.R = np.eye(1) * .05
ckf.Q = np.array([[0., 0], [0., .001]])
dt = 0.1
points = MerweScaledSigmaPoints(2, .1, 2., -1)
kf = UKF(dim_x=2, dim_z=1, dt=dt, fx=fx, hx=hx, points=points)
kf.x = np.array([1, 2])
kf.P = np.array([[1, 1.1],
[1.1, 3]])
kf.R *= 0.05
kf.Q = np.array([[0., 0], [0., .001]])
s = Saver(kf)
for i in range(50):
z = np.array([[i+randn()*0.1]])
ckf.predict()
ckf.update(z)
kf.predict()
kf.update(z[0])
assert abs(ckf.x[0] - kf.x[0]) < 1e-10
assert abs(ckf.x[1] - kf.x[1]) < 1e-10
s.save()
# test mahalanobis
a = np.zeros(kf.y.shape)
maha = scipy_mahalanobis(a, kf.y, kf.SI)
assert kf.mahalanobis == approx(maha)
s.to_array()
def test_ukf_ekf_comparison():
def fx(x, dt):
# state transition function - predict next state based
# on constant velocity model x = vt + x_0
F = np.array([[1.]], dtype=np.float32)
return np.dot(F, x)
def hx(x):
# measurement function - convert state into a measurement
# where measurements are [x_pos, y_pos]
return np.array([x[0]])
dt = 1.0
# create sigma points to use in the filter. This is standard for Gaussian processes
points = MerweScaledSigmaPoints(1, alpha=1, beta=2., kappa=0.1)
ukf = UnscentedKalmanFilter(dim_x=1,
dim_z=1,
dt=dt,
fx=fx,
hx=hx,
points=points)
ukf.x = np.array([0.]) # initial state
ukf.P = np.array([[1]]) # initial uncertainty
ukf.R = np.diag([1]) # 1 standard
ukf.Q = np.diag([1]) # 1 standard
ekf = ExtendedKalmanFilter(dim_x=1, dim_z=1)
ekf.F = np.array([[1]])
ekf.x = np.array([0.]) # initial state
ekf.P = np.array([[1]]) # initial uncertainty
ekf.R = np.diag([1]) # 1 standard
ekf.Q = np.diag([1]) # 1 standard
np.random.seed(0)
zs = [[np.random.randn()] for i in range(50)] # measurements
for z in zs:
ukf.predict()
ekf.predict()
assert np.allclose(ekf.P, ukf.P), 'ekf and ukf differ after prediction'
ukf.update(z)
ekf.update(z, lambda x: np.array([[1]]), hx)
assert np.allclose(ekf.P, ukf.P), 'ekf and ukf differ after update'
def smooth(data: ndarray, dt: float):
points = MerweScaledSigmaPoints(3, alpha=1e-3, beta=2.0, kappa=0)
noisy_kalman = UnscentedKalmanFilter(
dim_x=3,
dim_z=1,
dt=dt,
hx=state_to_measurement,
fx=state_transition,
points=points,
)
noisy_kalman.x = array([0, data[1], data[1] - data[0]], dtype="float32")
noisy_kalman.R *= 20**2 # sensor variance
noisy_kalman.P = diag([5**2, 5**2, 1**2]) # variance of the system
noisy_kalman.Q = Q_discrete_white_noise(3, dt=dt, var=0.05)
means, covariances = noisy_kalman.batch_filter(data)
means[:, 1][means[:, 1] < 0] = 0 # clip velocity
return means[:, 1]
def test_1d():
def fx(x, dt):
F = np.array([[1., dt], [0, 1]])
return np.dot(F, x)
def hx(x):
return x[0:1]
ckf = CKF(dim_x=2, dim_z=1, dt=0.1, hx=hx, fx=fx)
ckf.x = np.array([[1.], [2.]])
ckf.P = np.array([[1, 1.1], [1.1, 3]])
ckf.R = np.eye(1) * .05
ckf.Q = np.array([[0., 0], [0., .001]])
dt = 0.1
points = MerweScaledSigmaPoints(2, .1, 2., -1)
kf = UKF(dim_x=2, dim_z=1, dt=dt, fx=fx, hx=hx, points=points)
kf.x = np.array([1, 2])
kf.P = np.array([[1, 1.1], [1.1, 3]])
kf.R *= 0.05
kf.Q = np.array([[0., 0], [0., .001]])
s = Saver(kf)
for i in range(50):
z = np.array([[i + randn() * 0.1]])
ckf.predict()
ckf.update(z)
kf.predict()
kf.update(z[0])
assert abs(ckf.x[0] - kf.x[0]) < 1e-10
assert abs(ckf.x[1] - kf.x[1]) < 1e-10
s.save()
# test mahalanobis
a = np.zeros(kf.y.shape)
maha = scipy_mahalanobis(a, kf.y, kf.SI)
assert kf.mahalanobis == approx(maha)
s.to_array()
def test_1d():
def fx(x, dt):
F = np.array([[1., dt], [0, 1]])
return np.dot(F, x)
def hx(x):
return x[0:1]
ckf = CKF(dim_x=2, dim_z=1, dt=0.1, hx=hx, fx=fx)
ckf.x = np.array([[1.], [2.]])
ckf.P = np.array([[1, 1.1], [1.1, 3]])
ckf.R = np.eye(1) * .05
ckf.Q = np.array([[0., 0], [0., .001]])
dt = 0.1
points = MerweScaledSigmaPoints(2, .1, 2., -1)
kf = UKF(dim_x=2, dim_z=1, dt=dt, fx=fx, hx=hx, points=points)
kf.x = np.array([1, 2])
kf.P = np.array([[1, 1.1], [1.1, 3]])
kf.R *= 0.05
kf.Q = np.array([[0., 0], [0., .001]])
s = Saver(kf)
for i in range(50):
z = np.array([[i + randn() * 0.1]])
#xx, pp, Sx = predict(f, x, P, Q)
#x, P = update(h, z, xx, pp, R)
ckf.predict()
ckf.update(z)
kf.predict()
kf.update(z[0])
assert abs(ckf.x[0] - kf.x[0]) < 1e-10
assert abs(ckf.x[1] - kf.x[1]) < 1e-10
s.save()
s.to_array()
def test_linear_1d():
""" should work like a linear KF if problem is linear """
def fx(x, dt):
F = np.array([[1., dt],
[0, 1]], dtype=float)
return np.dot(F, x)
def hx(x):
return np.array([x[0]])
dt = 0.1
points = MerweScaledSigmaPoints(2, .1, 2., -1)
kf = UKF(dim_x=2, dim_z=1, dt=dt, fx=fx, hx=hx, points=points)
kf.x = np.array([1, 2])
kf.P = np.array([[1, 1.1],
[1.1, 3]])
kf.R *= 0.05
kf.Q = np.array([[0., 0], [0., .001]])
z = np.array([2.])
kf.predict()
kf.update(z)
zs = []
for i in range(50):
z = np.array([i+randn()*0.1])
zs.append(z)
kf.predict()
kf.update(z)
print('K', kf.K.T)
print('x', kf.x)
def estimateUKF(camPoses):
points = MerweScaledSigmaPoints(3, .1, 2., 0.)
filter = UKF(3,
3,
0,
h,
f,
points,
sqrt_fn=None,
x_mean_fn=state_mean,
z_mean_fn=state_mean,
residual_x=residual,
residual_z=residual)
filter.P = np.diag([0.04, 0.04, 0.003])
filter.Q = np.diag([(0.2)**2, (0.2)**2, (1 * 3.14 / 180)**2])
filter.R = np.diag([100, 100, 0.25])
Uposes = [[], []]
for i in range(len(speed)):
x = filter.x
Uposes[0].append(x[0])
Uposes[1].append(x[1])
filter.predict(fx_args=[speed[i], angle[i] * 0.01745])
filter.update(z=[camPoses[0][i], camPoses[1][i], camPoses[2][i]])
return Uposes
def ukf_filter_without_register(x, filt_times, filepath, measurement_raw,
timestamp_data):
measurement = copy.deepcopy(measurement_raw)
# In reverse Order
if filt_times % 2 == 0:
measurement = measurement[::-1, :]
timestamp_data = timestamp_data[::-1, :]
for i in range(1, measurement.shape[0]):
measurement[measurement.shape[0] - i,
0:3] = -measurement[measurement.shape[0] - i - 1, 0:3]
# measurement[i, 0:3] = -measurement[i, 0:3]
dt = 0.1
points = MerweScaledSigmaPoints(11, alpha=.1, beta=2., kappa=-1)
ukf = UKF(dim_x=11, dim_z=3, dt=dt, fx=ukf_f, hx=ukf_h, points=points)
ukf.x = x[0:11] # initial state
x_global = x[11:19]
ukf.P *= 0.2 # initial uncertainty
ukf.R = 1e-5 * np.diag(np.asarray([1, 1, 1]))
if filt_times == 1:
ukf.P = 1e-4 * np.diag(
np.asarray([0.0001, 0.0001, 1, 1, 1, 1, 10, 10, 1, 1, 1]))
ukf.Q = 1e-8 * np.diag(
np.asarray([0.0001, 0.0001, 1, 1, 1, 1, 10, 10, 1, 1, 1]))
else:
ukf.P = 1e-4 * np.diag(
np.asarray([0.001, 0.001, 0.001, 1, 1, 1, 10, 10, 1, 1, 1]))
ukf.Q = 1e-8 * np.diag(
np.asarray([0.001, 0.001, 0.001, 1, 1, 1, 10, 10, 1, 1, 1]))
# shrink_list = [3, 5, 7]
# shrink_index = bisect(shrink_list, filt_times)
# ukf.P[6:8,:] /= (10**shrink_index)
# ukf.Q[6:8,:] /= (10**shrink_index)
# P[8:11,:] = P[8:11,:]/(10**shrink_index)
# Q[8:11,:] = Q[8:11,:]/(10**shrink_index)
# P[3:7] = P[3:7]/(10**shrink_index)
# Q[3:7] = Q[3:7]/(10**shrink_index)
x_log = np.zeros((measurement.shape[0], 19))
x_log[0, 0:11] = ukf.x
x_log[0, 11:19] = x_global
for i in range(measurement.shape[0] - 1):
dtime = abs(timestamp_data[i + 1, 1] - timestamp_data[i, 1])
ukf.predict(dt=dtime)
# z_measure[3:7] = target_quat_raw
z_measure = measurement[i + 1, 3:7]
ukf, x_global, _ = ukf_update(ukf, z_measure, x_global)
x_global[0:4] = x_global[0:4] / np.linalg.norm(x_global[0:4])
x_global[4:8] = x_global[4:8] / np.linalg.norm(x_global[4:8])
x_log[i + 1, 0:11] = ukf.x
x_log[i + 1, 11:19] = x_global
np.savetxt(f"{filepath}ukf_log_all_{filt_times}.csv", x_log, delimiter=',')
x[0:11] = ukf.x
x[11:19] = x_global
return x
track_offset = 30230 #tracking log is ~29998 ms behind left gopro track_data_log_offset = track_offset + stereo_offset left_reader = lr.LogReader(l_logname,l_first_data_time_ms) right_reader = lr.LogReader(r_logname,r_first_data_time_ms) track = tr.TrackingReader(track_fname,right_reader,track_data_log_offset,F,30,1,vid_fname=vid_fname) pos_init = left_reader.get_ekf_loc_1d(START_TIME) vel_init = left_reader.get_ekf_vel(START_TIME) att_init = np.deg2rad(left_reader.get_ekf_att(START_TIME)) att_vel_init = np.zeros(3) state_init = np.hstack((pos_init,vel_init,att_init,att_vel_init)) ukf = UKF(dim_x=12, dim_z=15, dt=1.0/30, fx=fx, hx=hx) ukf.P = np.diag([5,5,2, 2,2,2, .017,.017,.017, .1,.1,.1]) ukf.x = state_init ukf.Q = np.diag([.5,.5,.5, .5,.5,.5, .1,.1,.1, .1,.1,.1]) T = np.array([16.878, -7.1368, 0]) #Translation vector joining two inertial frames time = np.arange(START_TIME,END_TIME,dt) print time.shape,time[0],time[-1] d = np.linspace(20,40,time.shape[0]) zs = np.zeros((time.shape[0],15)) Rs = np.zeros((time.shape[0],15,15)) means = np.zeros((time.shape[0],12)) covs = np.zeros((time.shape[0],12,12)) cam_locs = np.zeros((time.shape[0],3)) ekf_locs = np.zeros((time.shape[0],3))
range_std = 5 # meters
elevation_angle_std = math.radians(0.5)
ac_pos = (0., 1000.)
ac_vel = (100., 0.)
radar_pos = (0., 0.)
h_radar.radar_pos = radar_pos
points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)
kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)
kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)
kf.Q[2, 2] = 0.1
kf.R = np.diag([range_std**2, elevation_angle_std**2])
kf.x = np.array([0., 90., 1100.])
kf.P = np.diag([300**2, 30**2, 150**2])
#randn.seed(200)
pos = (0, 0)
radar = RadarStation(pos, range_std, elevation_angle_std)
ac = ACSim(ac_pos, (100, 0), 0.02)
time = np.arange(0, 360 + dt, dt)
xs = []
for _ in time:
ac.update(dt)
r = radar.noisy_reading(ac.pos)
kf.predict()
kf.update([r[0], r[1]])
xs.append(kf.x)
plot_radar(xs, time)
dt = 20 # ms
points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=1.)
ukf = UKF(testx.shape[0],
testy.shape[0],
dt,
fx=f_force,
hx=h_forceToNeural,
points=points) #(x_dimm, z_dimm,dt, hx, fx, sigmaPoints)
ukf.x = [0.05, 0, 0] # initial gauss
# Optimize : P
fstd = 0.5
ratestd = 0.01
yankstd = 0.001
P = np.diag([fstd**2, ratestd**2, yankstd**2])
ukf.P = P
ukf.Q = Q
ukf.R = R
predict, fvar = [], []
for t in np.arange(target.shape[0]):
ukf.predict()
ukf.update(testy[:, t])
fvar.append(ukf.P[0, 0])
predict.append(ukf.x[0]) #(f,f',f'')
criterion = nn.MSELoss()
mse_loss = criterion(torch.from_numpy(np.asarray(predict)),
torch.from_numpy(np.asarray(target)))
figname = plot_dir + "ukfResult"
def two_radar_constalt():
dt = 0.05
def hx(x):
r1, b1 = hx.R1.reading_of((x[0], x[2]))
r2, b2 = hx.R2.reading_of((x[0], x[2]))
return array([r1, b1, r2, b2])
pass
def fx(x, dt):
x_est = x.copy()
x_est[0] += x[1] * dt
return x_est
vx = 100 / 1000 # meters/sec
vz = 0.0
f = UKF(dim_x=3, dim_z=4, dt=dt, hx=hx, fx=fx, kappa=0)
aircraft = ACSim((0, 1), (vx * dt, vz * dt), 0.00)
range_std = 1 / 1000.0
bearing_std = 1 / 1000000.0
R1 = RadarStation((0, 0), range_std, bearing_std)
R2 = RadarStation((60, 0), range_std, bearing_std)
hx.R1 = R1
hx.R2 = R2
f.x = array([aircraft.pos[0], vx, aircraft.pos[1]])
f.R = np.diag([range_std ** 2, bearing_std ** 2, range_std ** 2, bearing_std ** 2])
q = Q_discrete_white_noise(2, var=0.0002, dt=dt)
# q = np.array([[0,0],[0,0.0002]])
f.Q[0:2, 0:2] = q
f.Q[2, 2] = 0.0002
f.P = np.diag([0.1, 0.01, 0.1]) * 0.1
track = []
zs = []
for i in range(int(500 / dt)):
pos = aircraft.update()
r1, b1 = R1.noisy_reading(pos)
r2, b2 = R2.noisy_reading(pos)
z = np.array([r1, b1, r2, b2])
zs.append(z)
track.append(pos.copy())
zs = asarray(zs)
xs, Ps = f.batch_filter(zs)
ms, _, _ = f.rts_smoother(xs, Ps)
track = asarray(track)
time = np.arange(0, len(xs) * dt, dt)
plt.figure()
plt.subplot(311)
plt.plot(time, track[:, 0])
plt.plot(time, xs[:, 0])
plt.legend(loc=4)
plt.xlabel("time (sec)")
plt.ylabel("x position (m)")
plt.subplot(312)
plt.plot(time, xs[:, 1] * 1000, label="UKF")
plt.plot(time, ms[:, 1] * 1000, label="RTS")
plt.legend(loc=4)
plt.xlabel("time (sec)")
plt.ylabel("velocity (m/s)")
plt.subplot(313)
plt.plot(time, xs[:, 2] * 1000, label="UKF")
plt.plot(time, ms[:, 2] * 1000, label="RTS")
plt.legend(loc=4)
plt.xlabel("time (sec)")
plt.ylabel("altitude (m)")
plt.ylim([900, 1100])
for z in zs[:10]:
p = R1.z_to_x(z[0], z[1])
# plt.scatter(p[0], p[1], marker='+', c='k')
p = R2.z_to_x(z[2], z[3])
# plt.scatter(p[0], p[1], marker='+', c='b')
plt.show()
def track_head(camera_matrix, markerss, world_markers):
M = camera_matrix
f_x, c_x = M[0, 0], M[0, -1]
f_y, c_y = M[1, 1], M[1, -1]
h = 1
w = 16 / 9
dt = 1 / 30 # TODO: Use the actual timestamps
pos = np.array([0.0, 0.0, -2.0])
rot = np.array([0.0, 0.0, 0.0])
dpos = np.array([0.0, 0.0, 0.0])
drot = np.array([0.0, 0.0, 0.0])
state = np.array([
pos,
rot,
#dpos, drot
])
state_shape = state.shape
M = np.prod(state_shape)
points = JulierSigmaPoints(M)
def project(state, world_positions):
return project_plane_markers(world_positions,
state.reshape(state_shape)).reshape(-1)
kf = UnscentedKalmanFilter(
dt=dt,
dim_x=M,
dim_z=len(world_markers) * 2,
points=points,
#fx=lambda X, dt: predict_state(X.reshape(4, -1), dt).reshape(-1),
fx=lambda x, dt: x,
hx=project,
)
z_dim = 2 # This changes according to the measurement
kf.P = np.eye(M) * 0.3
kf.x = state.reshape(-1).copy() # Initial state guess
z_var = 0.05**2
kf.R = z_var # Observation variance
dpos_var = 0.01**2 * dt
drot_var = np.radians(1.0)**2 * dt
#kf.Q = np.diag([0]*3 + [0]*3 + [dpos_var]*3 + [drot_var]*3)
kf.Q = np.diag([dpos_var] * 3 + [drot_var] * 3)
all_world_positions = []
for w in world_markers.values():
for v in w:
all_world_positions.append(v)
all_world_positions = np.array(all_world_positions)
for row in markerss:
markers = row['markers']
world_positions = []
screen_positions = []
for m in markers:
try:
world = world_markers[str(m['id'])]
except KeyError:
continue
if m['id_confidence'] < 0.7: continue
for w, s in zip(world, m['verts']):
world_positions.append(w)
screen_positions.append(s)
world_positions = np.array(world_positions).reshape(-1, 2)
screen_positions = np.array(screen_positions).reshape(-1, 2)
screen_positions[:, 0] -= c_x
screen_positions[:, 0] /= f_x
screen_positions[:, 1] -= c_y
screen_positions[:, 1] /= -f_y
kf.predict()
if len(world_positions) >= 0:
measurement = screen_positions.reshape(-1)
kf.update(measurement,
R=np.diag([z_var] * len(measurement)),
world_positions=world_positions)
yield kf.x.copy(), kf.P.copy()
def test_rts():
def fx(x, dt):
A = np.eye(3) + dt * np.array ([[0, 1, 0],
[0, 0, 0],
[0, 0, 0]])
f = np.dot(A, x)
return f
def hx(x):
return np.sqrt (x[0]**2 + x[2]**2)
dt = 0.05
kf = UKF(3, 1, dt, fx=fx, hx=hx, kappa=1.)
kf.Q *= 0.01
kf.R = 10
kf.x = np.array([0., 90., 1100.])
kf.P *= 100.
radar = RadarSim(dt)
t = np.arange(0,20+dt, dt)
n = len(t)
xs = np.zeros((n,3))
random.seed(200)
rs = []
#xs = []
for i in range(len(t)):
r = radar.get_range()
#r = GetRadar(dt)
kf.predict()
kf.update(z=[r])
xs[i,:] = kf.x
rs.append(r)
kf.x = np.array([0., 90., 1100.])
kf.P = np.eye(3)*100
M, P = kf.batch_filter(rs)
assert np.array_equal(M, xs), "Batch filter generated different output"
Qs = [kf.Q]*len(t)
M2, P2, K = kf.rts_smoother(Xs=M, Ps=P, Qs=Qs)
if DO_PLOT:
print(xs[:,0].shape)
plt.figure()
plt.subplot(311)
plt.plot(t, xs[:,0])
plt.plot(t, M2[:,0], c='g')
plt.subplot(312)
plt.plot(t, xs[:,1])
plt.plot(t, M2[:,1], c='g')
plt.subplot(313)
plt.plot(t, xs[:,2])
plt.plot(t, M2[:,2], c='g')
def two_radar_constvel():
dt = 5
def hx(x):
r1, b1 = hx.R1.reading_of((x[0], x[2]))
r2, b2 = hx.R2.reading_of((x[0], x[2]))
return array([r1, b1, r2, b2])
pass
def fx(x, dt):
x_est = x.copy()
x_est[0] += x[1] * dt
x_est[2] += x[3] * dt
return x_est
f = UKF(dim_x=4, dim_z=4, dt=dt, hx=hx, fx=fx, kappa=0)
aircraft = ACSim((100, 100), (0.1 * dt, 0.02 * dt), 0.002)
range_std = 0.2
bearing_std = radians(0.5)
R1 = RadarStation((0, 0), range_std, bearing_std)
R2 = RadarStation((200, 0), range_std, bearing_std)
hx.R1 = R1
hx.R2 = R2
f.x = array([100, 0.1, 100, 0.02])
f.R = np.diag([range_std ** 2, bearing_std ** 2, range_std ** 2, bearing_std ** 2])
q = Q_discrete_white_noise(2, var=0.002, dt=dt)
# q = np.array([[0,0],[0,0.0002]])
f.Q[0:2, 0:2] = q
f.Q[2:4, 2:4] = q
f.P = np.diag([0.1, 0.01, 0.1, 0.01])
track = []
zs = []
for i in range(int(300 / dt)):
pos = aircraft.update()
r1, b1 = R1.noisy_reading(pos)
r2, b2 = R2.noisy_reading(pos)
z = np.array([r1, b1, r2, b2])
zs.append(z)
track.append(pos.copy())
zs = asarray(zs)
xs, Ps, Pxz = f.batch_filter(zs)
ms, _, _ = f.rts_smoother2(xs, Ps, Pxz)
track = asarray(track)
time = np.arange(0, len(xs) * dt, dt)
plt.figure()
plt.subplot(411)
plt.plot(time, track[:, 0])
plt.plot(time, xs[:, 0])
plt.legend(loc=4)
plt.xlabel("time (sec)")
plt.ylabel("x position (m)")
plt.subplot(412)
plt.plot(time, track[:, 1])
plt.plot(time, xs[:, 2])
plt.legend(loc=4)
plt.xlabel("time (sec)")
plt.ylabel("y position (m)")
plt.subplot(413)
plt.plot(time, xs[:, 1])
plt.plot(time, ms[:, 1])
plt.legend(loc=4)
plt.ylim([0, 0.2])
plt.xlabel("time (sec)")
plt.ylabel("x velocity (m/s)")
plt.subplot(414)
plt.plot(time, xs[:, 3])
plt.plot(time, ms[:, 3])
plt.ylabel("y velocity (m/s)")
plt.legend(loc=4)
plt.xlabel("time (sec)")
plt.show()
def test_fixed_lag():
def fx(x, dt):
A = np.eye(3) + dt * np.array ([[0, 1, 0],
[0, 0, 0],
[0, 0, 0]])
f = np.dot(A, x)
return f
def hx(x):
return np.sqrt (x[0]**2 + x[2]**2)
dt = 0.05
kf = UKF(3, 1, dt, fx=fx, hx=hx, kappa=0.)
kf.Q *= 0.01
kf.R = 10
kf.x = np.array([0., 90., 1100.])
kf.P *= 1.
radar = RadarSim(dt)
t = np.arange(0,20+dt, dt)
n = len(t)
xs = np.zeros((n,3))
random.seed(200)
rs = []
#xs = []
M = []
P = []
N =10
flxs = []
for i in range(len(t)):
r = radar.get_range()
#r = GetRadar(dt)
kf.predict()
kf.update(z=[r])
xs[i,:] = kf.x
flxs.append(kf.x)
rs.append(r)
M.append(kf.x)
P.append(kf.P)
print(i)
#print(i, np.asarray(flxs)[:,0])
if i == 20 and len(M) >= N:
try:
M2, P2, K = kf.rts_smoother(Xs=np.asarray(M)[-N:], Ps=np.asarray(P)[-N:])
flxs[-N:] = M2
#flxs[-N:] = [20]*N
except:
print('except', i)
#P[-N:] = P2
kf.x = np.array([0., 90., 1100.])
kf.P = np.eye(3)*100
M, P = kf.batch_filter(rs)
Qs = [kf.Q]*len(t)
M2, P2, K = kf.rts_smoother(Xs=M, Ps=P, Qs=Qs)
flxs = np.asarray(flxs)
print(xs[:,0].shape)
plt.figure()
plt.subplot(311)
plt.plot(t, xs[:,0])
plt.plot(t, flxs[:,0], c='r')
plt.plot(t, M2[:,0], c='g')
plt.subplot(312)
plt.plot(t, xs[:,1])
plt.plot(t, flxs[:,1], c='r')
plt.plot(t, M2[:,1], c='g')
plt.subplot(313)
plt.plot(t, xs[:,2])
plt.plot(t, flxs[:,2], c='r')
plt.plot(t, M2[:,2], c='g')
def test_fixed_lag():
def fx(x, dt):
A = np.eye(3) + dt * np.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
f = np.dot(A, x)
return f
def hx(x):
return np.sqrt(x[0]**2 + x[2]**2)
dt = 0.05
sp = JulierSigmaPoints(n=3, kappa=0)
kf = UKF(3, 1, dt, fx=fx, hx=hx, points=sp)
kf.Q *= 0.01
kf.R = 10
kf.x = np.array([0., 90., 1100.])
kf.P *= 1.
radar = RadarSim(dt)
t = np.arange(0, 20 + dt, dt)
n = len(t)
xs = np.zeros((n, 3))
random.seed(200)
rs = []
#xs = []
M = []
P = []
N = 10
flxs = []
for i in range(len(t)):
r = radar.get_range()
#r = GetRadar(dt)
kf.predict()
kf.update(z=[r])
xs[i, :] = kf.x
flxs.append(kf.x)
rs.append(r)
M.append(kf.x)
P.append(kf.P)
print(i)
#print(i, np.asarray(flxs)[:,0])
if i == 20 and len(M) >= N:
try:
M2, P2, K = kf.rts_smoother(Xs=np.asarray(M)[-N:],
Ps=np.asarray(P)[-N:])
flxs[-N:] = M2
#flxs[-N:] = [20]*N
except:
print('except', i)
#P[-N:] = P2
kf.x = np.array([0., 90., 1100.])
kf.P = np.eye(3) * 100
M, P = kf.batch_filter(rs)
Qs = [kf.Q] * len(t)
M2, P2, K = kf.rts_smoother(Xs=M, Ps=P, Qs=Qs)
flxs = np.asarray(flxs)
print(xs[:, 0].shape)
plt.figure()
plt.subplot(311)
plt.plot(t, xs[:, 0])
plt.plot(t, flxs[:, 0], c='r')
plt.plot(t, M2[:, 0], c='g')
plt.subplot(312)
plt.plot(t, xs[:, 1])
plt.plot(t, flxs[:, 1], c='r')
plt.plot(t, M2[:, 1], c='g')
plt.subplot(313)
plt.plot(t, xs[:, 2])
plt.plot(t, flxs[:, 2], c='r')
plt.plot(t, M2[:, 2], c='g')
#m = array([[5., 10], [10, 5]])
sigma_r = .3
sigma_h = .1#radians(.5)#np.radians(1)
#sigma_steer = radians(10)
dt = 0.1
wheelbase = 0.5
points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2, kappa=0, subtract=residual_x)
#points = JulierSigmaPoints(n=3, kappa=3)
ukf= UKF(dim_x=3, dim_z=2*len(m), fx=fx, hx=Hx, dt=dt, points=points,
x_mean_fn=state_mean, z_mean_fn=z_mean,
residual_x=residual_x, residual_z=residual_h)
ukf.x = array([2, 6, .3])
ukf.P = np.diag([.1, .1, .05])
ukf.R = np.diag([sigma_r**2, sigma_h**2]* len(m))
ukf.Q =np.eye(3)*.00001
u = array([1.1, 0.])
xp = ukf.x.copy()
plt.cla()
plt.scatter(m[:, 0], m[:, 1])
cmds = [[v, .0] for v in np.linspace(0.001, 1.1, 30)]
cmds.extend([cmds[-1]]*50)
""" takes a state variable and returns the measurement that would
correspond to that state.
"""
px = landmark[0]
py = landmark[1]
dist = np.sqrt((px - x[0])**2 + (py - x[1])**2)
Hx = array([dist, atan2(py - x[1], px - x[0]) - x[2]])
return Hx
points = MerweScaledSigmaPoints(n=3, alpha=1.e-3, beta=2, kappa=0)
ukf= UKF(dim_x=3, dim_z=2, fx=fx, hx=Hx, dt=dt, points=points,
x_mean_fn=state_mean, z_mean_fn=z_mean,
residual_x=residual_x, residual_z=residual_h)
ukf.x = array([2, 6, .3])
ukf.P = np.diag([.1, .1, .2])
ukf.R = np.diag([sigma_r**2, sigma_h**2])
ukf.Q = np.zeros((3,3))
u = array([1.1, .01])
xp = ukf.x.copy()
plt.figure()
plt.scatter(m[:, 0], m[:, 1])
for i in range(200):
xp = move(xp, u, dt/10., wheelbase) # simulate robot
plt.plot(xp[0], xp[1], ',', color='g')
def create_ukf(vehicle, landmarks, P0, Q, dt, extents):
def f(x, dt, u=np.zeros(2), extents=extents):
vehicle.x = x.copy()
print(u, dt)
vehicle.move(u=u, dt=dt, extents=extents)
return vehicle.x
def h(x, landmark=None):
assert landmark is not None
hx = np.empty(2)
lx, ly = landmark
hx[0] = np.sqrt((lx - x[0])**2 + (ly - x[1])**2)
hx[1] = np.arctan2(ly - x[1], lx - x[0])
return hx
def residual_h(z, h):
"""Subtract [range, bearing] vectors, accounting for angle"""
y = z - h
y[1] = mpi_to_pi(y[1])
wrap(y, extents)
return y
def residual_x(xa, xb):
"""Subtract [x, y, phi] vectors, accounting for angle"""
dx = xa - xb
dx[2] = mpi_to_pi(dx[2])
wrap(dx, extents)
return dx
def state_mean(sigmas, w_m):
x = np.empty(3)
# This is a hack (and not a very good one) to handle periodic boundary
# crossings. Seems to help a little.
std = np.std(sigmas[:, :2])
if std > (extents[1] - extents[0]) / 4:
x[:2] = sigmas[0, :2]
else:
x[0] = np.dot(sigmas[:, 0], w_m)
x[1] = np.dot(sigmas[:, 1], w_m)
sum_sin = np.dot(np.sin(sigmas[:, 2]), w_m)
sum_cos = np.dot(np.cos(sigmas[:, 2]), w_m)
x[2] = np.arctan2(sum_sin, sum_cos)
wrap(x, extents)
return x
def z_mean(sigmas, w_m):
z_count = sigmas.shape[1]
x = np.zeros(z_count)
for z in range(0, z_count, 2):
sum_sin = np.dot(np.sin(sigmas[:, z + 1]), w_m)
sum_cos = np.dot(np.cos(sigmas[:, z + 1]), w_m)
x[z] = np.dot(sigmas[:, z], w_m)
x[z + 1] = np.arctan2(sum_sin, sum_cos)
return x
points = MerweScaledSigmaPoints(n=3,
alpha=1e-3,
beta=2,
kappa=0,
subtract=residual_x)
ukf = UKF(
dim_x=3,
dim_z=2,
fx=f,
hx=h,
dt=dt,
points=points,
x_mean_fn=state_mean,
z_mean_fn=z_mean,
residual_x=residual_x,
residual_z=residual_h,
)
ukf.x = vehicle.x.copy()
ukf.P = P0.copy()
ukf.Q = Q
# This large scale factor is theoretically unjustified.
# TODO: without it, the sim crashes. Figure this out!
ukf.R = 1e5 * np.diag([vehicle.range_sigma**2, vehicle.bearing_sigma**2])
# ukf.R = np.diag([vehicle.range_sigma**2, vehicle.bearing_sigma**2])
return ukf
return x
def residual(a, b):
y = a - b
y[2] = normalize_angle(y[2])
return y
def f(x,dt,u):
"""Estimate the non-linear state of the system"""
#print ((u[0]/self.L)*math.tan(u[1]))
return np.array([x[0]+u[0]*math.cos(x[2]),
x[1]+u[0]*math.sin(x[2]),
x[2]+((u[0]/1)*math.tan(u[1]))])
def h(z):
return z
points = MerweScaledSigmaPoints(3,.001,2.,0.)
filter = UKF(3,3,0,h, f, points, sqrt_fn=None, x_mean_fn=state_mean, z_mean_fn=state_mean, residual_x=residual, residual_z=residual)
filter.P = np.diag([0.04,0.04,1])
filter.Q = np.diag([(0.2)**2,(0.2)**2,(1*3.14/180)**2])
filter.R = np.diag([100,100,0.25])
robot = vehicle.Vehicle(1,50) #create a robot
robot.setOdometry(True) #configure its odometer
robot.setOdometryVariance([0.2,1])
speed,angle = [],[]
for a in xrange(4): #create a retangular path
for i in xrange(400):
angle.append(0)
for i in xrange(9):
angle.append(10)
for i in xrange(len(angle)): #set the speed to a constant along the path
speed.append(1)
def register_and_filter_once(x, filt_times):
start_frame = 48
end_frame = 12
skip = 1
filepath = "./20210312_3axis/"
pose_data = np.genfromtxt(f'{filepath}point_cloud_pose.txt', delimiter=',')
timestamp_data = np.genfromtxt(f'{filepath}timestamp.txt', delimiter=',')
pose_data = pose_data[start_frame:-end_frame:skip, :]
measurement_data = np.genfromtxt(f'{filepath}registration_measurement.csv',
delimiter=',')
measurement_data = measurement_data[::skip, :]
pose_data[:, 6:10] = measurement_data[::skip, 3:7]
timestamp_data = timestamp_data[start_frame:-end_frame:skip, :]
pose_data = continous_quat(pose_data)
# filepath = "./test_pointcloud/"
# pose_data = np.genfromtxt(f'{filepath}blensor_data_csv.txt', delimiter=',')
# pose_data = np.concatenate((np.zeros((pose_data.shape[0],6)), pose_data), axis=1)
# arange_data = np.arange(pose_data.shape[0]).reshape((pose_data.shape[0],1))
# timestamp_data = np.concatenate((arange_data, arange_data*0.05), axis=1)
# pose_data = pose_data[::skip,:]
# timestamp_data = timestamp_data[::skip,:]
quat0_inv = quat_inv(pose_data[0, 6:10])
for i in range(pose_data.shape[0]):
pose_data[i, 6:10] = quaternion_mul_num(pose_data[i, 6:10], quat0_inv)
# In reverse Order
if filt_times % 2 == 0:
pose_data = pose_data[::-1, :]
timestamp_data = timestamp_data[::-1, :]
measurement_data[:, 0:3] = -measurement_data[::-1, 0:3]
source_quat_zero_raw = pose_data[0, 6:10]
R = 1e-6 * np.diag(np.asarray([1, 1, 1]))
P = 1e-4 * np.diag(
np.asarray([0.001, 0.001, 0.001, 1, 1, 1, 10, 10, 1, 1, 1]))
Q = 1e-8 * np.diag(
np.asarray([0.001, 0.001, 0.001, 1, 1, 1, 10, 10, 1, 1, 1]))
# shrink_list = [3, 5, 7]
# shrink_index = bisect(shrink_list, filt_times)
# P[7:9,:] = P[7:9,:]/(10**shrink_index)
# Q[7:9,:] = Q[7:9,:]/(10**shrink_index)
# P[0:6]*=skip**2
# Q[0:6]*=skip**2
P[0:3] *= 1000
Q[0:3] *= 1000
x_log = np.zeros((pose_data.shape[0], 19))
x_log[0, :] = x
#UKF setting
points = MerweScaledSigmaPoints(11, alpha=.1, beta=2., kappa=-1)
ukf = UKF(dim_x=11, dim_z=3, dt=0.1, fx=ukf_f, hx=ukf_h, points=points)
ukf.x = x[0:11] # initial state
ukf.P = P
ukf.Q = Q
ukf.R = R
x_global = x[11:19]
# w_body = np.zeros((pose_data.shape[0]-1, 3))
# for i in range(w_body.shape[0]):
# w_body[i, :] = get_w_in_body_frame(pose_data[i,6:10], pose_data[i+1,6:10], timestamp_data[i+1, 1] - timestamp_data[i, 1])
source_s_root = 1
now_quat = source_quat_zero_raw
register_log = np.zeros((pose_data.shape[0], 4))
dq_real_log = np.zeros((pose_data.shape[0] - 1, 4))
dq_correct_log = np.zeros((pose_data.shape[0] - 1, 4))
register_log[0, :] = now_quat
loop_start_R = Rotation.from_quat(to_scalar_last(now_quat))
loop_angle_log = np.zeros((pose_data.shape[0], ))
for i in range(pose_data.shape[0] - 1):
source_quat_raw = pose_data[i, 6:10]
target_quat_raw = pose_data[i + 1, 6:10]
source_quat = np.zeros((4, ))
target_quat = np.zeros((4, ))
source_quat[3] = source_quat_raw[0]
source_quat[0:3] = source_quat_raw[1:4]
target_quat[3] = target_quat_raw[0]
target_quat[0:3] = target_quat_raw[1:4]
sourceR = Rotation.from_quat(source_quat)
targetR = Rotation.from_quat(target_quat)
nowR_from_loop_start = targetR * loop_start_R.inv()
nowR_from_loop_start_angle = np.linalg.norm(
nowR_from_loop_start.as_rotvec())
loop_angle_log[i] = nowR_from_loop_start_angle
dR_real = targetR * sourceR.inv()
dq_real = to_scalar_first(dR_real.as_quat())
dq_real_log[i, :] = dq_real
dtime = abs(timestamp_data[i + 1, 1] - timestamp_data[i, 1])
# x_predict, P = ekf_predict(x, P, Q, dtime)
x_predict, P = mekf_predict(x, P, Q, dtime)
# ukf.predict(dt=dtime)
# point to plane ICP
dq_estimate = dR_real.as_quat()
if dq_estimate[3] > 0.5:
dq_estimate = dq_estimate
else:
dq_estimate = -dq_estimate
z_measure = np.zeros((7, ))
z_measure[0:3] = dq_estimate[0:3]
# z_measure[3:7] = quaternion_mul_num(to_scalar_first(dq_estimate), now_quat)
z_measure[3:7] = target_quat_raw
# x_correct, P, z_correct = ekf_update(x, x_predict, P, z_measure, R, dtime)
x_correct, P, z_correct = mekf_update(x_predict, P,
measurement_data[i + 1,
0:3], R, dtime)
# ukf, x_global, _ = ukf_update(ukf, z_measure[3:7], x_global)
# dq_correct = np.asarray([z_correct[0],z_correct[1],z_correct[2],1])
# dR_correct = Rotation.from_quat(dq_correct/np.linalg.norm(dq_correct))
x_correct = mekf_normalize_state(x_correct)
x_log[i + 1, :] = x_correct
x = x_correct
# x_global[0:4] = x_global[0:4]/np.linalg.norm(x_global[0:4])
# x_global[4:8] = x_global[4:8]/np.linalg.norm(x_global[4:8])
# x_log[i+1,0:11] = ukf.x
# x_log[i+1,11:19] = x_global
# now_quat = quaternion_mul_num(to_scalar_first(dq_correct), now_quat)
# now_quat = z_correct[3:7]
# register_log[i+1, :] = now_quat
# dq_correct_log[i,:] = to_scalar_first(dq_correct)
np.savetxt(f"{filepath}mekf_log_ground_truth_{filt_times}.csv",
x_log,
delimiter=',')
# x[0:11] = ukf.x
# x[11:19] = x_global
return x
