kopia lustrzana https://github.com/gabrielegilardi/SignalFilters
save work
Gabriele Gilardi
rodzic
8d18544acd
commit
1f8e47a34f
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@ -0,0 +1,183 @@
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# import numpy as np
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# measurements = np.array([5., 6., 7., 9., 10.])
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# motion = np.array([1., 1., 2., 1., 1.])
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# measurement_sigma = 4.
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# motion_sigma = 2.
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# mu = 0.
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# sigma = 1000.
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# # Measurement
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# def Update( mean1, var1, mean2, var2 ):
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# mean = (var2*mean1 + var1*mean2) / (var1 + var2)
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# var = 1.0 / (1.0/var1 + 1.0/var2)
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# return [mean, var]
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# # Motion
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# def Predict( mean1, var1, U, varU ):
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# mean = mean1 + U
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# var = var1 + varU
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# return [mean, var]
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# for n in range(len(measurements)):
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# [mu, sigma] = Update(mu, sigma, measurements[n], measurement_sigma)
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# print('Update : ', n, [mu, sigma])
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# [mu, sigma] = Predict(mu, sigma, motion[n],motion_sigma)
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# print('Predict: ', n, [mu, sigma])
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# print(' ')
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# print(Update(1,1,3,1))
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# -------------------------------------------------------
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import numpy as np
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measurements = [ 1., 2., 3. ]
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dt = 1.
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# Initial state (location and velocity)
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x = np.array([[ 0. ],
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[ 0. ]])
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# Initial uncertainty
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P = np.array([[ 1000., 0. ],
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[ 0., 1000. ]])
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# External motion
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U = np.array([[ 0. ],
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[ 0. ]])
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# Next state function
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F = np.array([[ 1., dt ],
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[ 0., 1. ]])
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# Measurement function
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H = np.array([[ 1., 0. ]])
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# Measurement uncertainty
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R = np.array([[ 1. ]])
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# Identity matrix
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I = np.eye(2)
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def filter(x, P):
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step = 0
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for z in (measurements):
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step += 1
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print("step = ", step, " meas. = ", z)
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# Measurement
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Htra = H.T
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S = H.dot(P.dot(Htra)) + R
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Sinv = np.linalg.inv(S)
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K = P.dot(Htra.dot(Sinv))
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y = z - H.dot(x)
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xp = x +K.dot(y)
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Pp = P - K.dot(H.dot(P))
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# Prediction
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x = F.dot(xp) + U
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Ftra = F.T
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P = F.dot(Pp.dot(Ftra))
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print('x =')
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print(x)
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print('P =')
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print(P)
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filter(x, P)
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# # -------------------------------------------------------
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# import numpy as np
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# # x0 = 4.
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# # y0 = 12.
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# # measurements = np.array([[ 5., 10. ],
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# # [ 6., 8. ],
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# # [ 7., 6. ],
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# # [ 8., 4. ],
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# # [ 9., 2. ],
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# # [ 10., 0. ]])
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# # x0 = -4.
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# # y0 = 8.
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# # measurements = np.array([[ 1., 4. ],
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# # [ 6., 0. ],
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# # [ 11., -4. ],
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# # [ 16., -8. ]])
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# # x0 = 1.
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# # y0 = 19.
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# # measurements = np.array([[ 1., 17. ],
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# # [ 1., 15. ],
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# # [ 1., 13. ],
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# # [ 1., 11. ]])
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# x0 = 1.
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# y0 = 19.
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# measurements = np.array([[ 2., 17. ],
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# [ 0., 15. ],
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# [ 2., 13. ],
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# [ 0., 11. ]])
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# # Time step
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# dt = 0.1
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# # Initial state (location and velocity)
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# x = np.array([[ x0 ],
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# [ y0 ],
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# [ 0. ],
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# [ 0. ]])
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# # Initial uncertainty
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# P = np.array([[ 0., 0., 0., 0. ],
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# [ 0., 0., 0., 0. ],
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# [ 0., 0., 1000., 0. ],
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# [ 0., 0., 0., 1000. ]])
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# # External motion
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# U = np.array([[ 0. ],
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# [ 0. ],
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# [ 0. ],
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# [ 0. ]])
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# # Next state function
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# F = np.array([[ 1., 0., dt, 0. ],
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# [ 0., 1., 0., dt ],
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# [ 0., 0., 1., 0. ],
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# [ 0., 0., 0., 1. ]])
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# # Measurement function
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# H = np.array([[ 1., 0., 0., 0. ],
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# [ 0., 1., 0., 0. ]])
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# # Measurement uncertainty
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# R = np.array([[ 0.1, 0. ],
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# [ 0. , 0.1 ]])
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# # Measurement vector
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# z = np.zeros((2,1))
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# def filter(x, P):
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# for n in range(len(measurements)):
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# z[0][0] = measurements[n][0]
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# z[1][0] = measurements[n][1]
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# # Prediction
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# xp = F.dot(x) + U
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# Ftra = F.T
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# Pp = F.dot(P.dot(Ftra))
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# # Measurement
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# Htra = H.T
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# S = H.dot(Pp.dot(Htra)) + R
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# Sinv = np.linalg.inv(S)
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# K = Pp.dot(Htra.dot(Sinv))
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# y = z - H.dot(xp)
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# x = xp +K.dot(y)
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# P = Pp - K.dot(H.dot(Pp))
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# # print(z)
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# # print('x = ')
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# # print(x)
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# # print('P = ')
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# # print(P)
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# # print(' ')
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# return x, P
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# x_final, P_final = filter(x, P)
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# print('x = ')
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# print(x_final)
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# print('P = ')
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# print(P_final)
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@ -1,178 +1,67 @@
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"""
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- generalize to N and M
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M = 1
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N = 2
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"""
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import numpy as np
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measurements = np.array([5., 6., 7., 9., 10.])
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motion = np.array([1., 1., 2., 1., 1.])
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measurement_sigma = 4.
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motion_sigma = 2.
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mu = 0.
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sigma = 1000.
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# Measurement
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def Update( mean1, var1, mean2, var2 ):
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mean = (var2*mean1 + var1*mean2) / (var1 + var2)
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var = 1.0 / (1.0/var1 + 1.0/var2)
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return [mean, var]
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# Motion
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def Predict( mean1, var1, U, varU ):
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mean = mean1 + U
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var = var1 + varU
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return [mean, var]
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for n in range(len(measurements)):
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[mu, sigma] = Update(mu, sigma, measurements[n], measurement_sigma)
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print('Update : ', n, [mu, sigma])
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[mu, sigma] = Predict(mu, sigma, motion[n],motion_sigma)
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print('Predict: ', n, [mu, sigma])
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print(' ')
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print(Update(1,1,3,1))
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# -------------------------------------------------------
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import numpy as np
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measurements = [ 1., 2., 3. ]
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dt = 1.
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# Initial state (location and velocity)
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measurements = np.array([ 1., 2., 3., 4., 5., 6., 7., 8, 9, 10])
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# State vector
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# (N, 1)
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x = np.array([[ 0. ],
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[ 0. ]])
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# Initial uncertainty
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# Prediction uncertainty (covariance matrix of x)
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# (N, N)
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P = np.array([[ 1000., 0. ],
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[ 0., 1000. ]])
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# External motion
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# (N, 1)
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U = np.array([[ 0. ],
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[ 0. ]])
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# Next state function
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# Update matrix (state transition matrix)
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# (N, N)
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F = np.array([[ 1., dt ],
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[ 0., 1. ]])
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# Measurement function
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H = np.array([[ 1., 0. ]])
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# Measurement uncertainty
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R = np.array([[ 1. ]])
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# Identity matrix
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I = np.eye(2)
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# Measurement function (extraction matrix)
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# (M, N)
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H = np.array([[ 1., 0. ]])
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# Measurement uncertainty/noise (covariance matrix of z)
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# (M, M)
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R = np.array([[ 1. ]])
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# z = measurament vector
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# (M, 1)
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def filter(x, P):
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for z in (measurements):
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step = 0
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for z in (measurements):
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step += 1
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print("step = ", step, " meas. = ", z)
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# Measurement
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Htra = H.T
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S = H.dot(P.dot(Htra)) + R
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Sinv = np.linalg.inv(S)
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K = P.dot(Htra.dot(Sinv))
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y = z - H.dot(x)
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xp = x +K.dot(y)
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Pp = P - K.dot(H.dot(P))
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S = H @ P @ H.T + R # (M, M)
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K = P @ H.T @ np.linalg.inv(S) # (N, M)
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y = z - H @ x
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xp = x + K @ y
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Pp = P - K @ H @ P
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# Prediction
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x = F.dot(xp) + U
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Ftra = F.T
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P = F.dot(Pp.dot(Ftra))
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x = F @ xp + U
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P = F @ Pp @ F.T
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print('x = ',x)
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print('P = ',P)
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print('x =')
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print(x)
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print('P =')
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print(P)
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filter(x, P)
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# -------------------------------------------------------
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import numpy as np
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# x0 = 4.
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# y0 = 12.
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# measurements = np.array([[ 5., 10. ],
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# [ 6., 8. ],
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# [ 7., 6. ],
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# [ 8., 4. ],
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# [ 9., 2. ],
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# [ 10., 0. ]])
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# x0 = -4.
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# y0 = 8.
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# measurements = np.array([[ 1., 4. ],
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# [ 6., 0. ],
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# [ 11., -4. ],
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# [ 16., -8. ]])
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# x0 = 1.
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# y0 = 19.
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# measurements = np.array([[ 1., 17. ],
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# [ 1., 15. ],
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# [ 1., 13. ],
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# [ 1., 11. ]])
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x0 = 1.
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y0 = 19.
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measurements = np.array([[ 2., 17. ],
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[ 0., 15. ],
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[ 2., 13. ],
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[ 0., 11. ]])
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# Time step
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dt = 0.1
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# Initial state (location and velocity)
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x = np.array([[ x0 ],
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[ y0 ],
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[ 0. ],
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[ 0. ]])
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# Initial uncertainty
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P = np.array([[ 0., 0., 0., 0. ],
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[ 0., 0., 0., 0. ],
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[ 0., 0., 1000., 0. ],
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[ 0., 0., 0., 1000. ]])
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# External motion
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U = np.array([[ 0. ],
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[ 0. ],
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[ 0. ],
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[ 0. ]])
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# Next state function
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F = np.array([[ 1., 0., dt, 0. ],
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[ 0., 1., 0., dt ],
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[ 0., 0., 1., 0. ],
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[ 0., 0., 0., 1. ]])
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# Measurement function
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H = np.array([[ 1., 0., 0., 0. ],
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[ 0., 1., 0., 0. ]])
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# Measurement uncertainty
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R = np.array([[ 0.1, 0. ],
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[ 0. , 0.1 ]])
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# Measurement vector
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z = np.zeros((2,1))
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def filter(x, P):
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for n in range(len(measurements)):
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z[0][0] = measurements[n][0]
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z[1][0] = measurements[n][1]
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# Prediction
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xp = F.dot(x) + U
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Ftra = F.T
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Pp = F.dot(P.dot(Ftra))
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# Measurement
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Htra = H.T
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S = H.dot(Pp.dot(Htra)) + R
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Sinv = np.linalg.inv(S)
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K = Pp.dot(Htra.dot(Sinv))
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y = z - H.dot(xp)
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x = xp +K.dot(y)
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P = Pp - K.dot(H.dot(Pp))
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# print(z)
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# print('x = ')
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# print(x)
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# print('P = ')
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# print(P)
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# print(' ')
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return x, P
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x_final, P_final = filter(x, P)
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print('x = ')
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print(x_final)
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print('P = ')
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print(P_final)
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@ -25,7 +25,6 @@ Notes:
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- non filtered data are set equal to the original input, i.e.
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Y[0:idx-1,:] = X[0:idx-1,:]
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Filters:
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Generic b,a Generic case
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