1d_kf_compare.ipynb

Kernel: Unknown Kernel

Compare 1d kalman filter with full kalman filter with only 1 observed state variable.

from __future__ import division
import numpy as np

def predict(pos, variance, movement, movement_variance):
    return (pos + movement, variance + movement_variance)
    
def update(mean, variance, measurement, measurement_variance):
    return multiply(mean, variance, measurement, measurement_variance)
    
def multiply(mu1, var1, mu2, var2):
    mean = (var1*mu2 + var2*mu1) / (var1+var2)
    variance = 1 / (1/var1 + 1/var2)
    return (mean, variance)

%matplotlib inline
from numpy.random import randn
import numpy as np
from filterpy.kalman import KalmanFilter
from filterpy.leastsq import LeastSquaresFilter
import matplotlib.pyplot as plt
import matplotlib.pylab as pylab

pylab.rcParams['figure.figsize'] = (16.0, 16.0)

lsq = LeastSquaresFilter(dt=1, order=2, noise_variance = 5)

f = KalmanFilter(dim_x=1, dim_z=1, dim_u=1)
f.P = 500
f.H = np.array([[1.]])
f.F = np.array([[1.]])
f.B = np.array([[1.]])
f.Q = 3
f.R = 5

pos = (0., 500.)
print (pos)
plt.figure()
for i in range(50):
    z = i + randn()
    pos = update(pos[0], pos[1], z, 5)
    x = lsq(z)
    f.update(z)
    
    plt.scatter(i, pos[0], c='b')
    plt.scatter(i, x, c='g')
    plt.scatter(i, f.x[0,0], c='r')
    
    assert abs(pos[0]- f.x[0,0]) < 1.e-12
    
    pos = predict(pos[0], pos[1], 1., 3.)
    f.predict(u=1)
    
plt.show()

(0.0, 500.0)

%matplotlib inline
from numpy.random import randn
import numpy as np
from filterpy.kalman import KalmanFilter
from filterpy.leastsq import LeastSquaresFilter
import matplotlib.pyplot as plt
import matplotlib.pylab as pylab

pylab.rcParams['figure.figsize'] = (16.0, 16.0)

lsq = LeastSquaresFilter(dt=1, order=2, noise_variance = 5)

f = KalmanFilter(dim_x=1, dim_z=1, dim_u=1)
f.P = 500
f.H = np.array([[1.]])
f.F = np.array([[1.]])
f.B = np.array([[1.]])
f.Q = .02
f.R = 5

kxs = []
lxs = []
kKs = []
lKs = []
zs = []

for i in range(500):
    z = i + randn()*5
    zs.append(z)

    lsq(z)
    f.update(z)
    
    kxs.append(f.x[0,0])
    lxs.append(lsq.x)
    
    kKs.append(f.K[0,0])
    lKs.append(lsq.K2)

    f.predict(u=1)
    
    
plt.figure()
plt.plot (kxs, c='b')
plt.plot (lxs, c='g')
plt.plot (zs, c='r')

plt.figure()
plt.plot (kKs, c='b')
plt.plot (lKs, c='r')
    
plt.show()

print(lKs[-1])
print(kKs[-1])

0.00014299687477634373
0.0612771680782

# pos,vel filter

%matplotlib inline
from numpy.random import randn
import numpy as np
from filterpy.kalman import KalmanFilter
from filterpy.leastsq import LeastSquaresFilter
import matplotlib.pyplot as plt
import matplotlib.pylab as pylab

pylab.rcParams['figure.figsize'] = (16.0, 16.0)

lsq = LeastSquaresFilter(dt=1, order=2, noise_variance = 5)

f = KalmanFilter(dim_x=2, dim_z=1, dim_u=0)
f.P *= 500
f.F = np.array([[1., 1.],
                [0., 1.]])
f.H = np.array([[1., 0.]])
f.Q *= .001
f.R *= 5

kxs = []
lxs = []
kKs = []
lKs = []
zs = []

for i in range(100):
    z = i + randn()*5
    zs.append(z)

    lsq(z)
    f.update(z)
    
    kxs.append(f.x[0,0])
    lxs.append(lsq.x)
    
    kKs.append(f.K[0,0])
    lKs.append(lsq.K2)

    f.predict(u=1)
    
    
plt.figure()
plt.plot (kxs, c='b')
plt.plot (lxs, c='g')
plt.plot (zs, c='r')

plt.figure()
plt.plot (kKs, c='b')
plt.plot (lKs, c='r')
    
plt.show()

#print(f.K)

[[ 0.15538196]
 [ 0.01299707]]

#testing a constant K gain filter implementation

from numpy import dot
class kf(object):
    
    def __init__ (self):
        self.H  = 1
        self.x  = 0
        self.y = 0
        self.F  = 1
        self.B  = 0
        self.K  = 1
        
    
    def update(self, Z):
        self.y = Z - dot(self.H, self.x)
        
        # x = x + Ky
        # predict new x with residual scaled by the kalman gain
        self.x = self.x + dot(self.K, self.y)


    def predict(self, u=0):
        # x = Fx + Bu
        self._x = dot(self.F, self.x) + dot(self.B, u)  
        
        
k = kf()
k.x = np.array([[1., 0.]]).T
k.F = np.array([[1., 1.],
                [0., 1.]])
k.H = np.array([[1., 0.]])
k.K = np.array([[0.15538196, 0.01299707]]).T
lsq = LeastSquaresFilter(dt=1, order=2, noise_variance = 5)


kxs = []
lxs = []
zs = []
for i in range(1,100):
    z = i + randn()*5
    zs.append(z)

    lsq(z)
    k.predict()
    k.update(z)
    
    kxs.append(k.x[0,0])
    lxs.append(lsq.x)
    
plt.figure()
plt.plot (kxs, c='b')
plt.plot (lxs, c='g')
plt.plot (zs, c='r')
plt.show()