kopia lustrzana https://github.com/gabrielegilardi/SignalFilters
184 wiersze
4.4 KiB
Python
184 wiersze
4.4 KiB
Python
|
|
# import numpy as np
|
|
|
|
# measurements = np.array([5., 6., 7., 9., 10.])
|
|
# motion = np.array([1., 1., 2., 1., 1.])
|
|
# measurement_sigma = 4.
|
|
# motion_sigma = 2.
|
|
# mu = 0.
|
|
# sigma = 1000.
|
|
|
|
# # Measurement
|
|
# def Update( mean1, var1, mean2, var2 ):
|
|
# mean = (var2*mean1 + var1*mean2) / (var1 + var2)
|
|
# var = 1.0 / (1.0/var1 + 1.0/var2)
|
|
# return [mean, var]
|
|
|
|
# # Motion
|
|
# def Predict( mean1, var1, U, varU ):
|
|
# mean = mean1 + U
|
|
# var = var1 + varU
|
|
# return [mean, var]
|
|
|
|
# for n in range(len(measurements)):
|
|
# [mu, sigma] = Update(mu, sigma, measurements[n], measurement_sigma)
|
|
# print('Update : ', n, [mu, sigma])
|
|
# [mu, sigma] = Predict(mu, sigma, motion[n],motion_sigma)
|
|
# print('Predict: ', n, [mu, sigma])
|
|
|
|
# print(' ')
|
|
# print(Update(1,1,3,1))
|
|
|
|
# -------------------------------------------------------
|
|
|
|
import numpy as np
|
|
|
|
measurements = [ 1., 2., 3. ]
|
|
dt = 1.
|
|
|
|
# Initial state (location and velocity)
|
|
x = np.array([[ 0. ],
|
|
[ 0. ]])
|
|
# Initial uncertainty
|
|
P = np.array([[ 1000., 0. ],
|
|
[ 0., 1000. ]])
|
|
# External motion
|
|
U = np.array([[ 0. ],
|
|
[ 0. ]])
|
|
# Next state function
|
|
F = np.array([[ 1., dt ],
|
|
[ 0., 1. ]])
|
|
# Measurement function
|
|
H = np.array([[ 1., 0. ]])
|
|
# Measurement uncertainty
|
|
R = np.array([[ 1. ]])
|
|
# Identity matrix
|
|
I = np.eye(2)
|
|
|
|
|
|
def filter(x, P):
|
|
|
|
step = 0
|
|
for z in (measurements):
|
|
step += 1
|
|
print("step = ", step, " meas. = ", z)
|
|
|
|
# Measurement
|
|
Htra = H.T
|
|
S = H.dot(P.dot(Htra)) + R
|
|
Sinv = np.linalg.inv(S)
|
|
K = P.dot(Htra.dot(Sinv))
|
|
y = z - H.dot(x)
|
|
xp = x +K.dot(y)
|
|
Pp = P - K.dot(H.dot(P))
|
|
|
|
# Prediction
|
|
x = F.dot(xp) + U
|
|
Ftra = F.T
|
|
P = F.dot(Pp.dot(Ftra))
|
|
|
|
print('x =')
|
|
print(x)
|
|
print('P =')
|
|
print(P)
|
|
|
|
filter(x, P)
|
|
|
|
# # -------------------------------------------------------
|
|
|
|
# import numpy as np
|
|
|
|
# # x0 = 4.
|
|
# # y0 = 12.
|
|
# # measurements = np.array([[ 5., 10. ],
|
|
# # [ 6., 8. ],
|
|
# # [ 7., 6. ],
|
|
# # [ 8., 4. ],
|
|
# # [ 9., 2. ],
|
|
# # [ 10., 0. ]])
|
|
# # x0 = -4.
|
|
# # y0 = 8.
|
|
# # measurements = np.array([[ 1., 4. ],
|
|
# # [ 6., 0. ],
|
|
# # [ 11., -4. ],
|
|
# # [ 16., -8. ]])
|
|
# # x0 = 1.
|
|
# # y0 = 19.
|
|
# # measurements = np.array([[ 1., 17. ],
|
|
# # [ 1., 15. ],
|
|
# # [ 1., 13. ],
|
|
# # [ 1., 11. ]])
|
|
# x0 = 1.
|
|
# y0 = 19.
|
|
# measurements = np.array([[ 2., 17. ],
|
|
# [ 0., 15. ],
|
|
# [ 2., 13. ],
|
|
# [ 0., 11. ]])
|
|
# # Time step
|
|
# dt = 0.1
|
|
# # Initial state (location and velocity)
|
|
# x = np.array([[ x0 ],
|
|
# [ y0 ],
|
|
# [ 0. ],
|
|
# [ 0. ]])
|
|
# # Initial uncertainty
|
|
# P = np.array([[ 0., 0., 0., 0. ],
|
|
# [ 0., 0., 0., 0. ],
|
|
# [ 0., 0., 1000., 0. ],
|
|
# [ 0., 0., 0., 1000. ]])
|
|
# # External motion
|
|
# U = np.array([[ 0. ],
|
|
# [ 0. ],
|
|
# [ 0. ],
|
|
# [ 0. ]])
|
|
# # Next state function
|
|
# F = np.array([[ 1., 0., dt, 0. ],
|
|
# [ 0., 1., 0., dt ],
|
|
# [ 0., 0., 1., 0. ],
|
|
# [ 0., 0., 0., 1. ]])
|
|
# # Measurement function
|
|
# H = np.array([[ 1., 0., 0., 0. ],
|
|
# [ 0., 1., 0., 0. ]])
|
|
# # Measurement uncertainty
|
|
# R = np.array([[ 0.1, 0. ],
|
|
# [ 0. , 0.1 ]])
|
|
# # Measurement vector
|
|
# z = np.zeros((2,1))
|
|
|
|
|
|
# def filter(x, P):
|
|
|
|
# for n in range(len(measurements)):
|
|
|
|
# z[0][0] = measurements[n][0]
|
|
# z[1][0] = measurements[n][1]
|
|
|
|
# # Prediction
|
|
# xp = F.dot(x) + U
|
|
# Ftra = F.T
|
|
# Pp = F.dot(P.dot(Ftra))
|
|
|
|
# # Measurement
|
|
# Htra = H.T
|
|
# S = H.dot(Pp.dot(Htra)) + R
|
|
# Sinv = np.linalg.inv(S)
|
|
# K = Pp.dot(Htra.dot(Sinv))
|
|
# y = z - H.dot(xp)
|
|
# x = xp +K.dot(y)
|
|
# P = Pp - K.dot(H.dot(Pp))
|
|
# # print(z)
|
|
# # print('x = ')
|
|
# # print(x)
|
|
# # print('P = ')
|
|
# # print(P)
|
|
# # print(' ')
|
|
|
|
# return x, P
|
|
|
|
|
|
# x_final, P_final = filter(x, P)
|
|
# print('x = ')
|
|
# print(x_final)
|
|
# print('P = ')
|
|
# print(P_final)
|