notebook.community

Edit and run



In [1]:

    
%matplotlib inline



In [2]:

    
import os, sys
sys.path.append(os.path.abspath('../../main/python'))

import datetime as dt

import numpy as np
import numpy.testing as npt
import matplotlib.pyplot as plt

from thalesians.tsa.distrs import NormalDistr as N
import thalesians.tsa.filtering as filtering
import thalesians.tsa.filtering.kalman as kalman
import thalesians.tsa.filtering.lineargaussian as lineargaussian
import thalesians.tsa.filtering.particle as particle
import thalesians.tsa.filtering.visual as visual
import thalesians.tsa.numpyutils as npu
import thalesians.tsa.processes as proc
import thalesians.tsa.randomness as rnd
import thalesians.tsa.simulation as sim



In [3]:

    
X = proc.GeometricBrownianMotion()
x0 = .3



In [4]:

    
rnd.random_state(np.random.RandomState(seed=42), force=True)
em = sim.EulerMaruyama(process=X, initial_value=x0, times=sim.xtimes(start=0., stop=1., step=1E-3))
df = sim.run(em)
plt.plot(df);



In [5]:

    
t0 = 0.
kf = filtering.kalman.KalmanFilter(t0, state_distr=N(mean=x0, cov=2.5), process=X, approximate_distr=True)



In [6]:

    
observable = kf.create_observable(lineargaussian.LinearGaussianObsModel.create(1.), X)



In [7]:

    
run_df = filtering.run(observable=observable, obss=0, df=df, return_df=True)



In [8]:

    
run_df.df









    Out[8]:







  
    
      
      time
      filter_name
      filter_type
      observable_name
      accepted
      obs_mean
      obs_cov
      predicted_obs_mean
      predicted_obs_cov
      cross_cov
      innov_mean
      innov_cov
      prior_state_mean
      prior_state_cov
      posterior_state_mean
      posterior_state_cov
      true_value
      log_likelihood
      gain
    
  
  
    
      0
      0.000
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      None
      None
      NaN
      NaN
      NaN
      NaN
      NaN
      NaN
      NaN
      0.300000
      2.500000
      0.300000
      2.500000
      None
      NaN
      None
    
    
      1
      0.000
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.300000
      0.0
      0.300000
      2.500000
      2.500000
      0.000000
      2.500000
      0.300000
      2.500000
      0.300000
      2.500000
      None
      -1.377084
      [[1.0]]
    
    
      2
      0.001
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.304712
      0.0
      0.300000
      0.000090
      0.000090
      0.004712
      0.000090
      0.300000
      0.000090
      0.300000
      0.000090
      None
      3.615361
      [[1.0]]
    
    
      3
      0.002
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.303380
      0.0
      0.304712
      0.000093
      0.000093
      -0.001332
      0.000093
      0.304712
      0.000093
      0.304712
      0.000093
      None
      3.713523
      [[1.0]]
    
    
      4
      0.003
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.309594
      0.0
      0.303380
      0.000092
      0.000092
      0.006214
      0.000092
      0.303380
      0.000092
      0.303380
      0.000092
      None
      3.517813
      [[0.9999999999999999]]
    
    
      5
      0.004
      KalmanFilter_2228659095872
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      KalmanObservable_2228659093912
      True
      0.324504
      0.0
      0.309594
      0.000096
      0.000096
      0.014911
      0.000096
      0.309594
      0.000096
      0.309594
      0.000096
      None
      2.547953
      [[1.0]]
    
    
      6
      0.005
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.322102
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      0.324504
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      0.000105
      -0.002403
      0.000105
      0.324504
      0.000105
      0.324504
      0.000105
      None
      3.632745
      [[1.0]]
    
    
      7
      0.006
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.319717
      0.0
      0.322102
      0.000104
      0.000104
      -0.002385
      0.000104
      0.322102
      0.000104
      0.322102
      0.000104
      None
      3.640181
      [[1.0]]
    
    
      8
      0.007
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.335683
      0.0
      0.319717
      0.000102
      0.000102
      0.015966
      0.000102
      0.319717
      0.000102
      0.319717
      0.000102
      None
      2.428676
      [[1.0]]
    
    
      9
      0.008
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.343830
      0.0
      0.335683
      0.000113
      0.000113
      0.008146
      0.000113
      0.335683
      0.000113
      0.335683
      0.000113
      None
      3.331946
      [[0.9999999999999999]]
    
    
      10
      0.009
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.338725
      0.0
      0.343830
      0.000118
      0.000118
      -0.005105
      0.000118
      0.343830
      0.000118
      0.343830
      0.000118
      None
      3.492150
      [[1.0]]
    
    
      11
      0.010
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.344537
      0.0
      0.338725
      0.000115
      0.000115
      0.005812
      0.000115
      0.338725
      0.000115
      0.338725
      0.000115
      None
      3.470143
      [[1.0]]
    
    
      12
      0.011
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
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      0.339488
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      0.000119
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      0.000119
      0.344537
      0.000119
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      3.492919
      [[1.0]]
    
    
      13
      0.012
      KalmanFilter_2228659095872
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      KalmanObservable_2228659093912
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      0.000115
      -0.005000
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      0.339488
      0.000115
      0.339488
      0.000115
      None
      3.506609
      [[1.0]]
    
    
      14
      0.013
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.337047
      0.0
      0.334488
      0.000112
      0.000112
      0.002559
      0.000112
      0.334488
      0.000112
      0.334488
      0.000112
      None
      3.600586
      [[1.0]]
    
    
      15
      0.014
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.316655
      0.0
      0.337047
      0.000114
      0.000114
      -0.020392
      0.000114
      0.337047
      0.000114
      0.337047
      0.000114
      None
      1.792816
      [[1.0]]
    
    
      16
      0.015
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.299382
      0.0
      0.316655
      0.000100
      0.000100
      -0.017272
      0.000100
      0.316655
      0.000100
      0.316655
      0.000100
      None
      2.197705
      [[0.9999999999999999]]
    
    
      17
      0.016
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.294059
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      0.000090
      0.000090
      -0.005323
      0.000090
      0.299382
      0.000090
      0.299382
      0.000090
      None
      3.582719
      [[1.0]]
    
    
      18
      0.017
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
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      0.000087
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      0.294059
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      [[1.0]]
    
    
      19
      0.018
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
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      0.000081
      None
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      [[1.0]]
    
    
      20
      0.019
      KalmanFilter_2228659095872
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      KalmanObservable_2228659093912
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      [[1.0]]
    
    
      21
      0.020
      KalmanFilter_2228659095872
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      KalmanObservable_2228659093912
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      0.000078
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      [[1.0]]
    
    
      22
      0.021
      KalmanFilter_2228659095872
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      [[1.0]]
    
    
      23
      0.022
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
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      0.279108
      0.000078
      0.279108
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      None
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      [[1.0]]
    
    
      24
      0.023
      KalmanFilter_2228659095872
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      0.000592
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      [[1.0]]
    
    
      25
      0.024
      KalmanFilter_2228659095872
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      26
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      KalmanFilter_2228659095872
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      27
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      KalmanFilter_2228659095872
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      [[1.0]]
    
    
      28
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      KalmanFilter_2228659095872
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      29
      0.028
      KalmanFilter_2228659095872
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      0.000064
      None
      3.842380
      [[1.0]]
    
    
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
      ...
    
    
      971
      0.970
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
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      972
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      KalmanFilter_2228659095872
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      973
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      KalmanFilter_2228659095872
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      974
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      975
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      976
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      977
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      [[1.0]]
    
    
      978
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      979
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      980
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      [[1.0]]
    
    
      981
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      KalmanFilter_2228659095872
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      0.000117
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      [[1.0]]
    
    
      982
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      983
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      984
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      KalmanFilter_2228659095872
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      [[1.0]]
    
    
      985
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      KalmanFilter_2228659095872
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      KalmanObservable_2228659093912
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      -0.000531
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      None
      3.577128
      [[1.0]]
    
    
      986
      0.985
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.351621
      0.0
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      0.000124
      0.000124
      -0.000040
      0.000124
      0.351661
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      0.000124
      None
      3.579769
      [[1.0]]
    
    
      987
      0.986
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.338741
      0.0
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      0.000124
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      0.000124
      None
      2.909321
      [[1.0]]
    
    
      988
      0.987
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.354845
      0.0
      0.338741
      0.000115
      0.000115
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      0.000115
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      0.338741
      0.000115
      None
      2.487670
      [[0.9999999999999999]]
    
    
      989
      0.988
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.364690
      0.0
      0.354845
      0.000126
      0.000126
      0.009845
      0.000126
      0.354845
      0.000126
      0.354845
      0.000126
      None
      3.186072
      [[1.0]]
    
    
      990
      0.989
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.362142
      0.0
      0.364690
      0.000133
      0.000133
      -0.002548
      0.000133
      0.364690
      0.000133
      0.364690
      0.000133
      None
      3.518995
      [[1.0]]
    
    
      991
      0.990
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.362450
      0.0
      0.362142
      0.000131
      0.000131
      0.000308
      0.000131
      0.362142
      0.000131
      0.362142
      0.000131
      None
      3.550046
      [[1.0]]
    
    
      992
      0.991
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.364838
      0.0
      0.362450
      0.000131
      0.000131
      0.002388
      0.000131
      0.362450
      0.000131
      0.362450
      0.000131
      None
      3.527857
      [[1.0]]
    
    
      993
      0.992
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.341283
      0.0
      0.364838
      0.000133
      0.000133
      -0.023556
      0.000133
      0.364838
      0.000133
      0.364838
      0.000133
      None
      1.459691
      [[1.0]]
    
    
      994
      0.993
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.338615
      0.0
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      0.000117
      0.000117
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      0.000117
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      0.000117
      None
      3.579200
      [[1.0]]
    
    
      995
      0.994
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.331312
      0.0
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      0.000115
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      0.000115
      0.338615
      0.000115
      0.338615
      0.000115
      None
      3.385146
      [[1.0]]
    
    
      996
      0.995
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.320818
      0.0
      0.331312
      0.000110
      0.000110
      -0.010494
      0.000110
      0.331312
      0.000110
      0.331312
      0.000110
      None
      3.138012
      [[0.9999999999999999]]
    
    
      997
      0.996
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.317967
      0.0
      0.320818
      0.000103
      0.000103
      -0.002852
      0.000103
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      0.000103
      0.320818
      0.000103
      None
      3.632080
      [[1.0]]
    
    
      998
      0.997
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.336042
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      0.000101
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      None
      2.065468
      [[1.0]]
    
    
      999
      0.998
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.342852
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      None
      3.419970
      [[1.0]]
    
    
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      0.999
      KalmanFilter_2228659095872
      <class 'thalesians.tsa.filtering.kalman.Kalman...
      KalmanObservable_2228659093912
      True
      0.336660
      0.0
      0.342852
      0.000118
      0.000118
      -0.006193
      0.000118
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      0.342852
      0.000118
      None
      3.442104
      [[0.9999999999999999]]
    
  

1001 rows × 19 columns



In [9]:

    
sp = visual.StatePlot(plot_obs_results=False)
sp.process_run_df(run_df.df)
sp.ax.set_ylim((0., .45));



In [10]:

    
pf = filtering.particle.ParticleFilter(t0, state_distr=N(mean=x0, cov=2.5), process=X)



In [11]:

    
observable = pf.create_observable(particle.ParticleFilterObsModel.create(1.), X)



In [12]:

    
pf.predict(0.0001)



In [13]:

    
pf.mean









    Out[13]:





array([0.41408505])



In [14]:

    
pf.var









    Out[14]:





array([2.48376226])



In [15]:

    
pf.time









    Out[15]:





0.0001

	time	filter_name	filter_type	observable_name	accepted	obs_mean	obs_cov	predicted_obs_mean	predicted_obs_cov	cross_cov	innov_mean	innov_cov	prior_state_mean	prior_state_cov	posterior_state_mean	posterior_state_cov	true_value	log_likelihood	gain
0	0.000	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	None	None	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0.300000	2.500000	0.300000	2.500000	None	NaN	None
1	0.000	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.300000	0.0	0.300000	2.500000	2.500000	0.000000	2.500000	0.300000	2.500000	0.300000	2.500000	None	-1.377084	[[1.0]]
2	0.001	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.304712	0.0	0.300000	0.000090	0.000090	0.004712	0.000090	0.300000	0.000090	0.300000	0.000090	None	3.615361	[[1.0]]
3	0.002	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.303380	0.0	0.304712	0.000093	0.000093	-0.001332	0.000093	0.304712	0.000093	0.304712	0.000093	None	3.713523	[[1.0]]
4	0.003	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.309594	0.0	0.303380	0.000092	0.000092	0.006214	0.000092	0.303380	0.000092	0.303380	0.000092	None	3.517813	[[0.9999999999999999]]
5	0.004	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.324504	0.0	0.309594	0.000096	0.000096	0.014911	0.000096	0.309594	0.000096	0.309594	0.000096	None	2.547953	[[1.0]]
6	0.005	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.322102	0.0	0.324504	0.000105	0.000105	-0.002403	0.000105	0.324504	0.000105	0.324504	0.000105	None	3.632745	[[1.0]]
7	0.006	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.319717	0.0	0.322102	0.000104	0.000104	-0.002385	0.000104	0.322102	0.000104	0.322102	0.000104	None	3.640181	[[1.0]]
8	0.007	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.335683	0.0	0.319717	0.000102	0.000102	0.015966	0.000102	0.319717	0.000102	0.319717	0.000102	None	2.428676	[[1.0]]
9	0.008	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.343830	0.0	0.335683	0.000113	0.000113	0.008146	0.000113	0.335683	0.000113	0.335683	0.000113	None	3.331946	[[0.9999999999999999]]
10	0.009	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.338725	0.0	0.343830	0.000118	0.000118	-0.005105	0.000118	0.343830	0.000118	0.343830	0.000118	None	3.492150	[[1.0]]
11	0.010	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.344537	0.0	0.338725	0.000115	0.000115	0.005812	0.000115	0.338725	0.000115	0.338725	0.000115	None	3.470143	[[1.0]]
12	0.011	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.339488	0.0	0.344537	0.000119	0.000119	-0.005049	0.000119	0.344537	0.000119	0.344537	0.000119	None	3.492919	[[1.0]]
13	0.012	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.334488	0.0	0.339488	0.000115	0.000115	-0.005000	0.000115	0.339488	0.000115	0.339488	0.000115	None	3.506609	[[1.0]]
14	0.013	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.337047	0.0	0.334488	0.000112	0.000112	0.002559	0.000112	0.334488	0.000112	0.334488	0.000112	None	3.600586	[[1.0]]
15	0.014	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.316655	0.0	0.337047	0.000114	0.000114	-0.020392	0.000114	0.337047	0.000114	0.337047	0.000114	None	1.792816	[[1.0]]
16	0.015	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.299382	0.0	0.316655	0.000100	0.000100	-0.017272	0.000100	0.316655	0.000100	0.316655	0.000100	None	2.197705	[[0.9999999999999999]]
17	0.016	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.294059	0.0	0.299382	0.000090	0.000090	-0.005323	0.000090	0.299382	0.000090	0.299382	0.000090	None	3.582719	[[1.0]]
18	0.017	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.284641	0.0	0.294059	0.000087	0.000087	-0.009418	0.000087	0.294059	0.000087	0.294059	0.000087	None	3.246007	[[1.0]]
19	0.018	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.287469	0.0	0.284641	0.000081	0.000081	0.002829	0.000081	0.284641	0.000081	0.284641	0.000081	None	3.741866	[[1.0]]
20	0.019	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.279215	0.0	0.287469	0.000083	0.000083	-0.008254	0.000083	0.287469	0.000083	0.287469	0.000083	None	3.369281	[[1.0]]
21	0.020	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.266745	0.0	0.279215	0.000078	0.000078	-0.012470	0.000078	0.279215	0.000078	0.279215	0.000078	None	2.813661	[[1.0]]
22	0.021	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.279108	0.0	0.266745	0.000071	0.000071	0.012363	0.000071	0.266745	0.000071	0.266745	0.000071	None	2.782626	[[1.0]]
23	0.022	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.277115	0.0	0.279108	0.000078	0.000078	-0.001993	0.000078	0.279108	0.000078	0.279108	0.000078	None	3.785371	[[1.0]]
24	0.023	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.277707	0.0	0.277115	0.000077	0.000077	0.000592	0.000077	0.277115	0.000077	0.277115	0.000077	None	3.815733	[[1.0]]
25	0.024	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.265195	0.0	0.277707	0.000077	0.000077	-0.012512	0.000077	0.277707	0.000077	0.277707	0.000077	None	2.801432	[[1.0]]
26	0.025	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.260630	0.0	0.265195	0.000070	0.000070	-0.004565	0.000070	0.265195	0.000070	0.265195	0.000070	None	3.713877	[[1.0]]
27	0.026	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.261544	0.0	0.260630	0.000068	0.000068	0.000914	0.000068	0.260630	0.000068	0.260630	0.000068	None	3.873195	[[1.0]]
28	0.027	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.252024	0.0	0.261544	0.000068	0.000068	-0.009520	0.000068	0.261544	0.000068	0.261544	0.000068	None	3.213781	[[0.9999999999999999]]
29	0.028	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.255018	0.0	0.252024	0.000064	0.000064	0.002994	0.000064	0.252024	0.000064	0.252024	0.000064	None	3.842380	[[1.0]]
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
971	0.970	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.431501	0.0	0.451949	0.000204	0.000204	-0.020448	0.000204	0.451949	0.000204	0.451949	0.000204	None	2.305827	[[0.9999999999999999]]
972	0.971	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.433249	0.0	0.431501	0.000186	0.000186	0.001748	0.000186	0.431501	0.000186	0.431501	0.000186	None	3.366973	[[1.0]]
973	0.972	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.423918	0.0	0.433249	0.000188	0.000188	-0.009331	0.000188	0.433249	0.000188	0.433249	0.000188	None	3.139332	[[1.0]]
974	0.973	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.435187	0.0	0.423918	0.000180	0.000180	0.011269	0.000180	0.423918	0.000180	0.423918	0.000180	None	3.039740	[[1.0]]
975	0.974	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.426206	0.0	0.435187	0.000189	0.000189	-0.008981	0.000189	0.435187	0.000189	0.435187	0.000189	None	3.153815	[[1.0]]
976	0.975	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.420193	0.0	0.426206	0.000182	0.000182	-0.006014	0.000182	0.426206	0.000182	0.426206	0.000182	None	3.288031	[[1.0]]
977	0.976	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.395085	0.0	0.420193	0.000177	0.000177	-0.025108	0.000177	0.420193	0.000177	0.420193	0.000177	None	1.617442	[[1.0]]
978	0.977	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.389434	0.0	0.395085	0.000156	0.000156	-0.005651	0.000156	0.395085	0.000156	0.395085	0.000156	None	3.361104	[[1.0]]
979	0.978	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.359584	0.0	0.389434	0.000152	0.000152	-0.029850	0.000152	0.389434	0.000152	0.389434	0.000152	None	0.541623	[[1.0]]
980	0.979	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.341573	0.0	0.359584	0.000129	0.000129	-0.018011	0.000129	0.359584	0.000129	0.359584	0.000129	None	2.303750	[[1.0]]
981	0.980	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.349787	0.0	0.341573	0.000117	0.000117	0.008214	0.000117	0.341573	0.000117	0.341573	0.000117	None	3.319911	[[1.0]]
982	0.981	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.358479	0.0	0.349787	0.000122	0.000122	0.008692	0.000122	0.349787	0.000122	0.349787	0.000122	None	3.276534	[[1.0]]
983	0.982	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.363302	0.0	0.358479	0.000129	0.000129	0.004823	0.000129	0.358479	0.000129	0.358479	0.000129	None	3.470113	[[1.0]]
984	0.983	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.352193	0.0	0.363302	0.000132	0.000132	-0.011109	0.000132	0.363302	0.000132	0.363302	0.000132	None	3.079923	[[1.0]]
985	0.984	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.351661	0.0	0.352193	0.000124	0.000124	-0.000531	0.000124	0.352193	0.000124	0.352193	0.000124	None	3.577128	[[1.0]]
986	0.985	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.351621	0.0	0.351661	0.000124	0.000124	-0.000040	0.000124	0.351661	0.000124	0.351661	0.000124	None	3.579769	[[1.0]]
987	0.986	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.338741	0.0	0.351621	0.000124	0.000124	-0.012880	0.000124	0.351621	0.000124	0.351621	0.000124	None	2.909321	[[1.0]]
988	0.987	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.354845	0.0	0.338741	0.000115	0.000115	0.016104	0.000115	0.338741	0.000115	0.338741	0.000115	None	2.487670	[[0.9999999999999999]]
989	0.988	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.364690	0.0	0.354845	0.000126	0.000126	0.009845	0.000126	0.354845	0.000126	0.354845	0.000126	None	3.186072	[[1.0]]
990	0.989	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.362142	0.0	0.364690	0.000133	0.000133	-0.002548	0.000133	0.364690	0.000133	0.364690	0.000133	None	3.518995	[[1.0]]
991	0.990	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.362450	0.0	0.362142	0.000131	0.000131	0.000308	0.000131	0.362142	0.000131	0.362142	0.000131	None	3.550046	[[1.0]]
992	0.991	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.364838	0.0	0.362450	0.000131	0.000131	0.002388	0.000131	0.362450	0.000131	0.362450	0.000131	None	3.527857	[[1.0]]
993	0.992	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.341283	0.0	0.364838	0.000133	0.000133	-0.023556	0.000133	0.364838	0.000133	0.364838	0.000133	None	1.459691	[[1.0]]
994	0.993	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.338615	0.0	0.341283	0.000117	0.000117	-0.002668	0.000117	0.341283	0.000117	0.341283	0.000117	None	3.579200	[[1.0]]
995	0.994	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.331312	0.0	0.338615	0.000115	0.000115	-0.007303	0.000115	0.338615	0.000115	0.338615	0.000115	None	3.385146	[[1.0]]
996	0.995	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.320818	0.0	0.331312	0.000110	0.000110	-0.010494	0.000110	0.331312	0.000110	0.331312	0.000110	None	3.138012	[[0.9999999999999999]]
997	0.996	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.317967	0.0	0.320818	0.000103	0.000103	-0.002852	0.000103	0.320818	0.000103	0.320818	0.000103	None	3.632080	[[1.0]]
998	0.997	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.336042	0.0	0.317967	0.000101	0.000101	0.018076	0.000101	0.317967	0.000101	0.317967	0.000101	None	2.065468	[[1.0]]
999	0.998	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.342852	0.0	0.336042	0.000113	0.000113	0.006810	0.000113	0.336042	0.000113	0.336042	0.000113	None	3.419970	[[1.0]]
1000	0.999	KalmanFilter_2228659095872	<class 'thalesians.tsa.filtering.kalman.Kalman...	KalmanObservable_2228659093912	True	0.336660	0.0	0.342852	0.000118	0.000118	-0.006193	0.000118	0.342852	0.000118	0.342852	0.000118	None	3.442104	[[0.9999999999999999]]