def test_circle():
def hx(x):
return np.array([x[0], x[3]])
F = np.array([[1., 1., .5, 0., 0., 0.],
[0., 1., 1., 0., 0., 0.],
[0., 0., 1., 0., 0., 0.],
[0., 0., 0., 1., 1., .5],
[0., 0., 0., 0., 1., 1.],
[0., 0., 0., 0., 0., 1.]])
def fx(x, dt):
return np.dot(F, x)
x = np.array([50., 0., 0, 0, .0, 0.])
P = np.eye(6)* 100.
f = EnKF(x=x, P=P, dim_z=2, dt=1., N=30, hx=hx, fx=fx)
std_noise = .1
f.R *= std_noise**2
f.Q[0:3, 0:3] = Q_discrete_white_noise(3, 1., .001)
f.Q[3:6, 3:6] = Q_discrete_white_noise(3, 1., .001)
measurements = []
results = []
zs = []
for t in range (0,300):
a = t / 300000
x = cos(a) * 50.
y = sin(a) * 50.
# create measurement = t plus white noise
z = np.array([x,y])
zs.append(z)
f.predict()
f.update(z)
# save data
results.append (f.x)
measurements.append(z)
results = np.asarray(results)
measurements = np.asarray(measurements)
def test_circle():
def hx(x):
return np.array([x[0], x[3]])
F = np.array([[1., 1., .5, 0., 0., 0.],
[0., 1., 1., 0., 0., 0.],
[0., 0., 1., 0., 0., 0.],
[0., 0., 0., 1., 1., .5],
[0., 0., 0., 0., 1., 1.],
[0., 0., 0., 0., 0., 1.]])
def fx(x, dt):
return np.dot(F, x)
x = np.array([50., 0., 0, 0, .0, 0.])
P = np.eye(6)* 100.
f = EnKF(x=x, P=P, dim_z=2, dt=1., N=30, hx=hx, fx=fx)
std_noise = .1
f.R *= std_noise**2
f.Q[0:3, 0:3] = Q_discrete_white_noise(3, 1., .001)
f.Q[3:6, 3:6] = Q_discrete_white_noise(3, 1., .001)
measurements = []
results = []
zs = []
for t in range (0,300):
a = t / 300000
x = cos(a) * 50.
y = sin(a) * 50.
# create measurement = t plus white noise
z = np.array([x,y])
zs.append(z)
f.predict()
f.update(z)
# save data
results.append (f.x)
measurements.append(z)
#test that __repr__ doesn't assert
str(f)
results = np.asarray(results)
measurements = np.asarray(measurements)
if DO_PLOT:
plt.plot(results[:,0], results[:,2], label='EnKF')
plt.plot(measurements[:,0], measurements[:,1], c='r', label='z')
#plt.plot (results-ps, c='k',linestyle='--', label='3$\sigma$')
#plt.plot(results+ps, c='k', linestyle='--')
plt.legend(loc='best')
plt.axis('equal')
def test_1d_const_vel():
def hx(x):
return np.array([x[0]])
F = np.array([[1., 1.],[0., 1.]])
def fx(x, dt):
return np.dot(F, x)
x = np.array([0., 1.])
P = np.eye(2)* 100.
f = EnKF(x=x, P=P, dim_z=1, dt=1., N=8, hx=hx, fx=fx)
std_noise = 10.
f.R *= std_noise**2
f.Q = Q_discrete_white_noise(2, 1., .001)
measurements = []
results = []
ps = []
zs = []
s = Saver(f)
for t in range (0,100):
# create measurement = t plus white noise
z = t + randn()*std_noise
zs.append(z)
f.predict()
f.update(np.asarray([z]))
# save data
results.append (f.x[0])
measurements.append(z)
ps.append(3*(f.P[0,0]**.5))
s.save()
s.to_array()
results = np.asarray(results)
ps = np.asarray(ps)
if DO_PLOT:
plt.plot(results, label='EnKF')
plt.plot(measurements, c='r', label='z')
plt.plot (results-ps, c='k',linestyle='--', label='3$\sigma$')
plt.plot(results+ps, c='k', linestyle='--')
plt.legend(loc='best')
#print(ps)
return f
def test_1d_const_vel():
def hx(x):
return np.array([x[0]])
F = np.array([[1., 1.],[0., 1.]])
def fx(x, dt):
return np.dot(F, x)
x = np.array([0., 1.])
P = np.eye(2)* 100.
f = EnKF(x=x, P=P, dim_z=1, dt=1., N=8, hx=hx, fx=fx)
std_noise = 10.
f.R *= std_noise**2
f.Q = Q_discrete_white_noise(2, 1., .001)
measurements = []
results = []
ps = []
zs = []
for t in range (0,100):
# create measurement = t plus white noise
z = t + randn()*std_noise
zs.append(z)
f.predict()
f.update(np.asarray([z]))
# save data
results.append (f.x[0])
measurements.append(z)
ps.append(3*(f.P[0,0]**.5))
results = np.asarray(results)
ps = np.asarray(ps)
def kalman():
filter = KalmanFilter(dim_x=2, dim_z=1)
x = array([0., 1.])
P = eye(2) * 100.
enf = EnsembleKalmanFilter(x=x, P=P, dim_z=1, dt=1., N=20, hx=hx, fx=fx)
measurements = []
results = []
ps = []
kf_results = []
for i in range(len(data)):
z = data.iloc[i].as_array()
enf.predict()
enf.update(asarray([z]))
filter.predict()
filter.update(asarray([[z]]))
results.append (enf.x[0])
kf_results.append (kf.x[0,0])
measurements.append(z)
ps.append(3*(enf.P[0,0]**.5))
results = asarray(results)
ps = asarray(ps)
#模型
def fx(x, dt):
return state[time]
#观测噪声的标准差
std_noise = 1
#初值
x = np.array([state[0]])
#状态协方差矩阵初始化
P = np.eye(1)
#ensemble kalman filter
enkf = EnKF(x=x, P=P, dim_z=1, dt=0.1, N=5, hx=hx, fx=fx)
#观测噪声
enkf.R *= std_noise**2
#系统噪声
enkf.Q = np.eye(1) * 1
filter_result = []
#方便写fx
global time
time = 0
#运行
for i in range(0, state.shape[0]):
m = measurements[i]
dim_z = 0
for element in H:
if element != 0:
dim_z += 1
##
##
##
# Define EnKF
#xTrue = np.array(h_iTrue)
#xTrue1 = np.array(h_iTrue1)
x = np.array(h_i)
u = np.array(u_i)
P = np.eye(nodesInZ * numberOfGrids) * stdState * stdState
f = EnKF(x=x, u=u, P=P, dim_z=dim_z, N=N)
f.R *= std_noise_R**2
f.Q *= std_noise_Q**2
ensemble = f.initialize(x=x, P=P)
# Generating lists for data collection and for plots
thetaList = []
ThetaListOne = []
ThetaListAll = []
ThetaU = []
ThetaUR = []
ThetaListMeanU = []
measurementListTPlot = []
measurementListTCal = []
measurementListF = []
# x1 = x[0]
# x2 = x[1]
# if x1 < 0: # Water levels in both tanks cannot be negative
# x1 = 0
# if x2 < 0:
# x2 = 0
# x1_p = ((-dt*cv1)/A)*math.sqrt(x1) + x1 + (dt/A)*u + randn()*processNoise
# x2_p = ((dt*cv1)/A)*math.sqrt(x1) - ((dt*cv2)/A)*math.sqrt(x2) + x2 + randn()*processNoise
# return [x1_p, x2_p]
# Define EnKF
#x = np.array(h_i)
#u = np.array(qi_i)
#P = np.eye(2) * stateCov
f = EnKF(x=x, u=u, P=P, dim_z=dim_z, dt=dt, N=N,
hx=hx, fx=fx)
f.R *= std_noise ** 2
f.Q *= std_noise ** 2
# Generating lists for data collection and for plots
prediction1 = [x[0]]
prediction2 = [x[1]]
# Prediction using the model
for i in range(timeSpan):
x_p = f.predict()
prediction1.append(x_p[0])
prediction2.append(x_p[1])
time = []
xx = (np.linspace(0, n - 1, n))
yy = (np.linspace(0, m - 1, m))
X, Y = np.meshgrid(xx, yy)
xxa = X.copy()
xa = np.array([xxa[:, i] for i in range(0, xxa.shape[1])]).flatten()
yya = Y.copy()
ya = np.array([yya[:, i] for i in range(0, yya.shape[1])]).flatten()
# Kalman filter
for i in range(1, npd):
F = np.array([[1., 0.], [0., 1.]])
zz = fval[:][i]
x = np.array([1., 0.])
P = np.eye(2) * 100.
enf = EnKF(x=x, P=P, dim_z=1, dt=1., N=5, hx=hx, fx=fx)
std_noise = 1e-6
enf.R *= std_noise**2
enf.Q = Q_discrete_white_noise(2, std_noise, std_noise)
results = np.zeros((1, tt)).T
for t in range(0, tt):
# create measurement = t plus white noise
z = zz[t] + randn() * std_noise
enf.predict()
enf.update(np.asarray([z]))
# save data
if zz[t] > 1e-12:
results[t] = enf.x[0]
