我一直在实现一个卡尔曼滤波器来搜索二维数据集中的异常值，这与我在这里找到的优秀帖子非常相似。作为下一步，我想预测置信区间（例如，地板和天花板值的95％置信度），以预测下一个值将落在哪里。因此，除了下面的线条之外，我还想能够生成另外两条线，表示下一个值将在地板以下或天花板以上的95％置信度。
我假设我将使用由卡尔曼滤波器生成的每个预测返回的不确定性协方差矩阵（P），但我不确定是否正确。任何指导或如何执行此操作的参考都将不胜感激！ Python中的kalman 2d滤波器 上述帖子中的代码会随时间生成一组测量值，并使用卡尔曼滤波器平滑结果。
我假设我将使用由卡尔曼滤波器生成的每个预测返回的不确定性协方差矩阵（P），但我不确定是否正确。任何指导或如何执行此操作的参考都将不胜感激！ Python中的kalman 2d滤波器 上述帖子中的代码会随时间生成一组测量值，并使用卡尔曼滤波器平滑结果。
import numpy as np
import matplotlib.pyplot as plt
def kalman_xy(x, P, measurement, R,
motion = np.matrix('0. 0. 0. 0.').T,
Q = np.matrix(np.eye(4))):
"""
Parameters:
x: initial state 4-tuple of location and velocity: (x0, x1, x0_dot, x1_dot)
P: initial uncertainty convariance matrix
measurement: observed position
R: measurement noise
motion: external motion added to state vector x
Q: motion noise (same shape as P)
"""
return kalman(x, P, measurement, R, motion, Q,
F = np.matrix('''
1. 0. 1. 0.;
0. 1. 0. 1.;
0. 0. 1. 0.;
0. 0. 0. 1.
'''),
H = np.matrix('''
1. 0. 0. 0.;
0. 1. 0. 0.'''))
def kalman(x, P, measurement, R, motion, Q, F, H):
'''
Parameters:
x: initial state
P: initial uncertainty convariance matrix
measurement: observed position (same shape as H*x)
R: measurement noise (same shape as H)
motion: external motion added to state vector x
Q: motion noise (same shape as P)
F: next state function: x_prime = F*x
H: measurement function: position = H*x
Return: the updated and predicted new values for (x, P)
See also http://en.wikipedia.org/wiki/Kalman_filter
This version of kalman can be applied to many different situations by
appropriately defining F and H
'''
# UPDATE x, P based on measurement m
# distance between measured and current position-belief
y = np.matrix(measurement).T - H * x
S = H * P * H.T + R # residual convariance
K = P * H.T * S.I # Kalman gain
x = x + K*y
I = np.matrix(np.eye(F.shape[0])) # identity matrix
P = (I - K*H)*P
# PREDICT x, P based on motion
x = F*x + motion
P = F*P*F.T + Q
return x, P
def demo_kalman_xy():
x = np.matrix('0. 0. 0. 0.').T
P = np.matrix(np.eye(4))*1000 # initial uncertainty
N = 20
true_x = np.linspace(0.0, 10.0, N)
true_y = true_x**2
observed_x = true_x + 0.05*np.random.random(N)*true_x
observed_y = true_y + 0.05*np.random.random(N)*true_y
plt.plot(observed_x, observed_y, 'ro')
result = []
R = 0.01**2
for meas in zip(observed_x, observed_y):
x, P = kalman_xy(x, P, meas, R)
result.append((x[:2]).tolist())
kalman_x, kalman_y = zip(*result)
plt.plot(kalman_x, kalman_y, 'g-')
plt.show()
demo_kalman_xy()