用Pykalman的EM算法

Question

我试图用Pykalman实现卡尔曼滤波器的simpel应用程序，但是在Pykalman软件包中的EM算法的估计步骤上，我得到了一个错误。

它是一个简单的线性回归与时变系数，根据模拟数据.下面的代码模拟数据并启动卡尔曼滤波，但是当我尝试根据观测值估计参数时，使用kf.em(Data)，它返回错误：ValueError: object arrays are not supported。

我是不是对pykalman**?**做错了什么？

模型和下面的完整代码。错误发生在代码的最后一行。

模型(小图像)

对问题的描述

模型的状态空间表示

全码

import pandas as pd
import scipy as sp
import numpy as np

import matplotlib.pyplot as plt
import pylab as pl
from pykalman import KalmanFilter

# generates the data
Data = pd.DataFrame(columns=['NoiseAR','NoiseReg', 'x', 'beta', 'y'], index=range(1000))
Data['NoiseAR'] = np.random.normal(loc=0.0, scale=1.0, size=1000)
Data['NoiseReg'] = np.random.normal(loc=0.0, scale=1.0, size=1000)

for i in range(1000):
    if i==0:
        Data.loc[i, 'x'] = Data.loc[i, 'NoiseAR']
    else:
        Data.loc[i, 'x'] = 0.95*Data.loc[i-1, 'x'] + Data.loc[i, 'NoiseAR']

for i in range(1000):
    Data.loc[i, 'beta'] = np.sin(np.radians(i))

Data['y'] = Data['x']*Data['beta'] + Data['NoiseReg']

# set up the kalman filter
F = [1.]
H = Data['x'].values.reshape(1000,1,1)
Q = [2.]
R = [2.]

init_state_mean = [0.]
init_state_cov = [2.]

kf = KalmanFilter(
    transition_matrices=F, 
    observation_matrices=H, 
    transition_covariance=Q, 
    observation_covariance=R, 
    initial_state_mean=init_state_mean, 
    initial_state_covariance=init_state_cov, 
    em_vars=['transition_covariance', 'observation_covariance', 'initial_state_mean', 'initial_state_covariance']
)

# estimate the parameters from em_vars using the EM algorithm
kf = kf.em(Data['y'].values)

Answer 1

我想明白了！Data['y'].values是一个带有dtype=object的numpy数组。我所要做的就是使用.astype(float)更改数组的类型以浮动。这必须对pykalman的卡尔曼滤波对象进行处理，所以我还必须改变H矩阵的类型。

希望这对将来的人有帮助！

最后的工作代码如下所示：

import pandas as pd
import scipy as sp
import numpy as np
import matplotlib.pyplot as plt
import pylab as pl
from pykalman import KalmanFilter

Data = pd.DataFrame(columns=['NoiseAR','NoiseReg', 'x', 'beta', 'y'], index=range(1000))

Data['NoiseAR'] = np.random.normal(loc=0.0, scale=1.0, size=1000)
Data['NoiseReg'] = np.random.normal(loc=0.0, scale=1.0, size=1000)
plt.plot(Data[['NoiseAR','NoiseReg']])
plt.show()

for i in range(1000):
    if i == 0:
        Data.loc[i, 'x'] = Data.loc[i, 'NoiseAR']
    else:
        Data.loc[i, 'x'] = 0.95 * Data.loc[i - 1, 'x'] + Data.loc[i, 'NoiseAR']

plt.plot(Data['x'])
plt.show()

for i in range(1000):
    Data.loc[i, 'beta'] = np.sin(np.radians(i))

plt.plot(Data['beta'])
plt.show()

Data['y'] = Data['x']*Data['beta'] + Data['NoiseReg']

plt.plot(Data[['x', 'y']])
plt.show()

F = [1.]
H = Data['x'].values.reshape(1000,1,1).astype(float)
Q = [2.]
R = [2.]

init_state_mean = [0.]
init_state_cov = [2.]

kf = KalmanFilter(
    transition_matrices=F,
    observation_matrices=H,
    transition_covariance=Q,
    observation_covariance=R,
    initial_state_mean=init_state_mean,
    initial_state_covariance=init_state_cov,
    em_vars=['transition_covariance', 'observation_covariance', 'initial_state_mean', 'initial_state_covariance']
)

kf = kf.em(Data['y'].values.astype(float))

filtered_state_estimates = kf.filter(Data['y'].values.astype(float))[0]
smoothed_state_estimates = kf.smooth(Data['y'].values.astype(float))[0]

pl.figure(figsize=(10, 6))
lines_true = pl.plot(Data['beta'].values, linestyle='-', color='b')
lines_filt = pl.plot(filtered_state_estimates, linestyle='--', color='g')
lines_smooth = pl.plot(smoothed_state_estimates, linestyle='-.', color='r')
pl.legend(
    (lines_true[0], lines_filt[0], lines_smooth[0]),
    ('true', 'filtered', 'smoothed')
)
pl.xlabel('time')
pl.ylabel('state')

pl.show()