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test_kalman_filter.py
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test_kalman_filter.py
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import numpy as np
from src.kalman_filter import (
kalman_updates_sequence_univariate,
kalman_update_multivariate,
kalman_update_multivariate_reannotated,
kalman_updates_sequence_multivariate,
)
def esme_kalman_input_output():
"""
Example from:
http://bilgin.esme.org/BitsAndBytes/KalmanFilterforDummies
Kalman Filter For Dummies
Bilgin Esme
March 2009
"""
x_input = [0.] # state vector with initial state at zero
p_input = [1.] # state variance vector with initial state at one
r_input = 0.1 # standard deviation of measurement noise
z_input = [0.39, 0.50, 0.48, 0.29, 0.25, 0.32, 0.34, 0.48, 0.41, 0.45]
x_output = [
x_input[0],
0.355, 0.424, 0.442, 0.405, 0.375,
0.366, 0.362, 0.377, 0.380, 0.387]
p_output = [
p_input[0],
0.091, 0.048, 0.032, 0.024, 0.020,
0.016, 0.014, 0.012, 0.011, 0.010]
return x_input, p_input, r_input, z_input, x_output, p_output
def test_esme_example_univariate():
"""
Test Esme example data with univariate Kalman filter
"""
x, p, r, z, correct_x, correct_p = esme_kalman_input_output()
result_x, result_p = kalman_updates_sequence_univariate(x, p, z, r)
assert all([e[0] == round(e[1], 3) for e in zip(correct_x, result_x)])
assert all([e[0] == round(e[1], 3) for e in zip(correct_p, result_p)])
def test_esme_example_multivariate():
"""
Test Esme example data with multivariate Kalman filter
"""
x0, p0, r, z, correct_x, correct_p = esme_kalman_input_output()
result_x, result_p = kalman_updates_sequence_multivariate(
x0=np.array(np.array(x0[0]).reshape(1, 1)),
P0=np.array(np.array(p0[0]).reshape(1, 1)),
F=np.array([1.]).reshape(1, 1),
Q=np.array([0.]).reshape(1, 1),
B=np.array([0.]).reshape(1, 1),
u=np.array([0.]).reshape(1, 1),
H=np.array([1.]).reshape(1, 1),
R=np.array(r).reshape(1, 1),
z_vec=z,
kalman_function=kalman_update_multivariate)
assert all([e[0] == np.round(e[1], 3)[0][0] for e in zip(correct_x, result_x)])
assert all([e[0] == np.round(e[1], 3)[0][0] for e in zip(correct_p, result_p)])
def test_esme_example_multivariate_reannotated():
"""
Test Esme example data with multivariate Kalman filter
"""
x0, p0, r, z, correct_x, correct_p = esme_kalman_input_output()
result_x, result_p = kalman_updates_sequence_multivariate(
x0=np.array(np.array(x0[0]).reshape(1, 1)),
P0=np.array(np.array(p0[0]).reshape(1, 1)),
F=np.array([1.]).reshape(1, 1),
Q=np.array([0.]).reshape(1, 1),
B=np.array([0.]).reshape(1, 1),
u=np.array([0.]).reshape(1, 1),
H=np.array([1.]).reshape(1, 1),
R=np.array(r).reshape(1, 1),
z_vec=z,
kalman_function=kalman_update_multivariate_reannotated)
assert all([e[0] == np.round(e[1], 3)[0][0] for e in zip(correct_x, result_x)])
assert all([e[0] == np.round(e[1], 3)[0][0] for e in zip(correct_p, result_p)])
def labbe_chapter_6_kalman_input_output_01():
"""
Example from:
https://rlabbe.github.io/Kalman-and-Bayesian-Filters-in-Python/
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
Kalman and Bayesian Filters in Python
Roger R Labbe Jr
May 23, 2020
Chapter 6 Multivariate Kalman Filters
6.12 Adjusting the Filter
PDF version, page 217-218:
https://drive.google.com/open?id=0By_SW19c1BfhSVFzNHc0SjduNzg
"""
# trk = [
# 0.941, 1.639, 2.385, 3.456, 4.307, 5.385, 6.391,
# 7.467, 8.464, 9.358, 10.234, 11.271, 12.223, 13.132,
# 13.931, 14.893, 15.549, 16.601, 17.672, 18.672, 19.628,
# 20.364, 21.571, 22.658, 23.541, 24.682, 25.629, 26.69 ,
# 27.601, 28.631, 29.572, 30.566, 31.278, 32.182, 33.256,
# 34.164, 35.11 , 35.954, 36.578, 37.676, 38.65 , 39.766,
# 40.709, 41.903, 42.837, 43.891, 44.92 , 45.674, 46.728,
# 47.894]
x_input = [0., 0.]
# unclear whether this is intended initialization of P, because it comes
# from an earlier, completed filtering run, but it is the one that is
# input into the example
p_input = np.array([[2.222, 0.279], [0.279, 0.075]])
r_input = 225
q_input = 200
z_input = [
0.097, 26.243, -10.241, -15.223, -9.328, 39.768, -10.378,
-1.475, 26.089, 9.494, 7.888, -3.561, 8.68 , -4.682,
11.629, 48.364, 17.24 , 36.996, 5.009, 26.808, 31.193,
46.332, 16.536, 23.378, 24.856, 18.966, 24.512, 45.866,
35.227, 0.752, 27.587, 35.456, 31.972, 10.59 , 44.285,
46.8 , 36.107, 59.722, 35.206, 7.174, 37.491, 58.49 ,
19.941, 60.171, 48.101, 52.385, 66.021, 61.287, 43.471,
12.74 ]
x_output = np.array([
x_input,
[ 0.018, 0.035],
[ 17.095, 14.066],
[ 0.83 , -5.591],
[-12.43 , -10.508],
[-12.912, -3.996],
[ 25.001, 23.25 ],
[ 4.861, -4.931],
[ -1.11 , -5.607],
[ 17.563, 10.16 ],
[ 14.231, 1.399],
[ 9.9 , -2.322],
[ -0.666, -7.676],
[ 4.256, 0.505],
[ -2.228, -4.033],
[ 6.98 , 4.565],
[ 38.795, 22.261],
[ 28.627, 1.202],
[ 35.133, 4.647],
[ 14.045, -12.065],
[ 20.356, -0.132],
[ 28.342, 5.14 ],
[ 42.992, 11.316],
[ 26.352, -6.838],
[ 22.373, -4.982],
[ 22.917, -1.394],
[ 19.63 , -2.623],
[ 22.562, 0.984],
[ 40.065, 11.712],
[ 39.528, 3.757],
[ 11.805, -16.685],
[ 19.149, -1.081],
[ 30.938, 7.276],
[ 33.594, 4.276],
[ 17.68 , -8.835],
[ 35.075, 8.199],
[ 45.884, 9.894],
[ 41.219, 0.44 ],
[ 55.027, 9.121],
[ 42.728, -4.789],
[ 15.169, -19.575],
[ 26.603, 0.562],
[ 50.349, 15.617],
[ 31.902, -6.504],
[ 51.134, 10.209],
[ 51.542, 3.844],
[ 53.165, 2.402],
[ 63.304, 7.426],
[ 63.741, 2.887],
[ 49.489, -8.243],
[ 20.148, -21.944]])
p_output = np.array([
p_input,
[[ 42.8 , 81.264],
[ 81.264, 163.83 ]],
[[146.409, 120.539],
[120.539, 178.953]],
[[164.835, 106.824],
[106.824, 189.286]],
[[164.93 , 105.752],
[105.752, 203.11 ]],
[[165.758, 107.653],
[107.653, 207.487]],
[[166.376, 108.166],
[108.166, 207.915]],
[[166.516, 108.151],
[108.151, 207.916]],
[[166.524, 108.134],
[108.134, 207.956]],
[[166.525, 108.138],
[108.138, 207.978]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]],
[[166.527, 108.141],
[108.141, 207.982]]])
return x_input, p_input, r_input, q_input, z_input, x_output, p_output
def labbe_chapter_6_kalman_input_output_02():
"""
Example from:
https://rlabbe.github.io/Kalman-and-Bayesian-Filters-in-Python/
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
Kalman and Bayesian Filters in Python
Roger R Labbe Jr
May 23, 2020
Chapter 6 Multivariate Kalman Filters
6.12 Adjusting the Filter
PDF version, page 217-218:
https://drive.google.com/open?id=0By_SW19c1BfhSVFzNHc0SjduNzg
"""
# trk = [
# 0.941, 1.639, 2.385, 3.456, 4.307, 5.385, 6.391,
# 7.467, 8.464, 9.358, 10.234, 11.271, 12.223, 13.132,
# 13.931, 14.893, 15.549, 16.601, 17.672, 18.672, 19.628,
# 20.364, 21.571, 22.658, 23.541, 24.682, 25.629, 26.69 ,
# 27.601, 28.631, 29.572, 30.566, 31.278, 32.182, 33.256,
# 34.164, 35.11 , 35.954, 36.578, 37.676, 38.65 , 39.766,
# 40.709, 41.903, 42.837, 43.891, 44.92 , 45.674, 46.728,
# 47.894]
x_input = [0., 0.]
# unclear whether this is intended initialization of P, because it comes
# from an earlier, completed filtering run, but it is the one that is
# input into the example
p_input = np.array([[2.222, 0.279], [0.279, 0.075]])
r_input = 225
q_input = 0.02
z_input = [
0.097, 26.243, -10.241, -15.223, -9.328, 39.768, -10.378,
-1.475, 26.089, 9.494, 7.888, -3.561, 8.68 , -4.682,
11.629, 48.364, 17.24 , 36.996, 5.009, 26.808, 31.193,
46.332, 16.536, 23.378, 24.856, 18.966, 24.512, 45.866,
35.227, 0.752, 27.587, 35.456, 31.972, 10.59 , 44.285,
46.8 , 36.107, 59.722, 35.206, 7.174, 37.491, 58.49 ,
19.941, 60.171, 48.101, 52.385, 66.021, 61.287, 43.471,
12.74 ]
x_output = np.array([
x_input,
[ 0.001, 0. ],
[ 0.419, 0.053],
[ 0.257, 0.026],
[-0.105, -0.021],
[-0.411, -0.055],
[ 1.045, 0.117],
[ 0.644, 0.061],
[ 0.59 , 0.049],
[ 2.183, 0.204],
[ 2.876, 0.251],
[ 3.492, 0.285],
[ 3.159, 0.23 ],
[ 3.871, 0.271],
[ 3.281, 0.199],
[ 4.321, 0.267],
[ 9.309, 0.638],
[10.763, 0.701],
[14.405, 0.922],
[14.111, 0.832],
[16.367, 0.935],
[18.994, 1.056],
[23.283, 1.284],
[23.571, 1.214],
[24.61 , 1.202],
[25.693, 1.194],
[25.892, 1.126],
[26.702, 1.104],
[30.083, 1.259],
[31.833, 1.293],
[29.037, 1.015],
[29.741, 0.994],
[31.332, 1.035],
[32.316, 1.031],
[30.468, 0.836],
[32.947, 0.947],
[35.53 , 1.059],
[36.527, 1.054],
[40.39 , 1.246],
[40.82 , 1.19 ],
[37.585, 0.888],
[38.348, 0.879],
[41.678, 1.047],
[39.824, 0.848],
[43.157, 1.019],
[44.676, 1.053],
[46.579, 1.111],
[50.03 , 1.272],
[52.578, 1.359],
[52.599, 1.267],
[48.607, 0.906]])
p_output = np.array([
p_input,
[[ 2.824, 0.359],
[ 0.359, 0.094]],
[[ 3.583, 0.456],
[ 0.456, 0.113]],
[[ 4.52 , 0.567],
[ 0.567, 0.132]],
[[ 5.646, 0.691],
[ 0.691, 0.15 ]],
[[ 6.961, 0.824],
[ 0.824, 0.166]],
[[ 8.451, 0.963],
[ 0.963, 0.182]],
[[10.091, 1.104],
[ 1.104, 0.196]],
[[11.841, 1.241],
[ 1.241, 0.209]],
[[13.656, 1.372],
[ 1.372, 0.22 ]],
[[15.48 , 1.492],
[ 1.492, 0.23 ]],
[[17.264, 1.599],
[ 1.599, 0.237]],
[[18.959, 1.69 ],
[ 1.69 , 0.244]],
[[20.528, 1.767],
[ 1.767, 0.248]],
[[21.943, 1.827],
[ 1.827, 0.252]],
[[23.19 , 1.874],
[ 1.874, 0.254]],
[[24.264, 1.908],
[ 1.908, 0.256]],
[[25.171, 1.931],
[ 1.931, 0.258]],
[[25.92 , 1.945],
[ 1.945, 0.259]],
[[26.528, 1.953],
[ 1.953, 0.259]],
[[27.013, 1.955],
[ 1.955, 0.26 ]],
[[27.392, 1.955],
[ 1.955, 0.261]],
[[27.683, 1.952],
[ 1.952, 0.261]],
[[27.903, 1.947],
[ 1.947, 0.262]],
[[28.065, 1.943],
[ 1.943, 0.263]],
[[28.183, 1.938],
[ 1.938, 0.264]],
[[28.267, 1.934],
[ 1.934, 0.265]],
[[28.326, 1.931],
[ 1.931, 0.266]],
[[28.367, 1.929],
[ 1.929, 0.267]],
[[28.396, 1.928],
[ 1.928, 0.268]],
[[28.416, 1.927],
[ 1.927, 0.269]],
[[28.432, 1.928],
[ 1.928, 0.27 ]],
[[28.446, 1.929],
[ 1.929, 0.271]],
[[28.459, 1.931],
[ 1.931, 0.272]],
[[28.473, 1.933],
[ 1.933, 0.273]],
[[28.488, 1.936],
[ 1.936, 0.274]],
[[28.504, 1.939],
[ 1.939, 0.275]],
[[28.522, 1.942],
[ 1.942, 0.276]],
[[28.541, 1.946],
[ 1.946, 0.277]],
[[28.562, 1.949],
[ 1.949, 0.277]],
[[28.583, 1.952],
[ 1.952, 0.278]],
[[28.605, 1.956],
[ 1.956, 0.279]],
[[28.627, 1.959],
[ 1.959, 0.279]],
[[28.648, 1.962],
[ 1.962, 0.279]],
[[28.669, 1.964],
[ 1.964, 0.28 ]],
[[28.69 , 1.967],
[ 1.967, 0.28 ]],
[[28.709, 1.969],
[ 1.969, 0.28 ]],
[[28.727, 1.971],
[ 1.971, 0.281]],
[[28.744, 1.972],
[ 1.972, 0.281]],
[[28.759, 1.974],
[ 1.974, 0.281]],
[[28.774, 1.975],
[ 1.975, 0.281]]])
return x_input, p_input, r_input, q_input, z_input, x_output, p_output
def test_labbe_chapter_6_example_1_multivariate():
"""
Test Labbe Chapter 6 example #1 data with multivariate Kalman filter
"""
x0, p0, r, q, z, correct_x, correct_p = (
labbe_chapter_6_kalman_input_output_01())
result_x, result_p = kalman_updates_sequence_multivariate(
x0=np.array(np.array(x0).reshape(2, 1)),
P0=p0,
F=np.array([[1., 1.], [0., 1.]]),
Q=np.array([[50., 100.], [100., q]]),
B=np.array([0.]).reshape(1, 1),
u=np.array([0.]).reshape(1, 1),
H=np.array([1., 0.]).reshape(1, 2),
R=np.array(r).reshape(1, 1),
z_vec=z,
kalman_function=kalman_update_multivariate)
result_x_arr = np.stack(result_x).reshape(-1, 2)
assert np.allclose(result_x_arr, correct_x, atol=1e-3)
result_p_arr = np.stack(result_p)
assert np.allclose(result_p_arr, correct_p, atol=1e-3)
def test_labbe_chapter_6_example_2_multivariate():
"""
Test Labbe Chapter 6 example #2 data with multivariate Kalman filter
"""
x0, p0, r, q, z, correct_x, correct_p = (
labbe_chapter_6_kalman_input_output_02())
result_x, result_p = kalman_updates_sequence_multivariate(
x0=np.array(np.array(x0).reshape(2, 1)),
P0=p0,
F=np.array([[1., 1.], [0., 1.]]),
Q=np.array([[0.005, 0.01], [0.01, q]]),
B=np.array([0.]).reshape(1, 1),
u=np.array([0.]).reshape(1, 1),
H=np.array([1., 0.]).reshape(1, 2),
R=np.array(r).reshape(1, 1),
z_vec=z,
kalman_function=kalman_update_multivariate)
result_x_arr = np.stack(result_x).reshape(-1, 2)
assert np.allclose(result_x_arr, correct_x, atol=1e-2)
result_p_arr = np.stack(result_p)
assert np.allclose(result_p_arr, correct_p, atol=1e-1)
def test_labbe_chapter_6_example_1_multivariate_reannotated():
"""
Test Labbe Chapter 6 example #1 data with multivariate Kalman filter
"""
x0, p0, r, q, z, correct_x, correct_p = (
labbe_chapter_6_kalman_input_output_01())
result_x, result_p = kalman_updates_sequence_multivariate(
x0=np.array(np.array(x0).reshape(2, 1)),
P0=p0,
F=np.array([[1., 1.], [0., 1.]]),
Q=np.array([[50., 100.], [100., q]]),
B=np.array([0.]).reshape(1, 1),
u=np.array([0.]).reshape(1, 1),
H=np.array([1., 0.]).reshape(1, 2),
R=np.array(r).reshape(1, 1),
z_vec=z,
kalman_function=kalman_update_multivariate_reannotated)
result_x_arr = np.stack(result_x).reshape(-1, 2)
assert np.allclose(result_x_arr, correct_x, atol=1e-3)
result_p_arr = np.stack(result_p)
assert np.allclose(result_p_arr, correct_p, atol=1e-3)
def test_labbe_chapter_6_example_2_multivariate_reannotated():
"""
Test Labbe Chapter 6 example #2 data with multivariate Kalman filter
"""
x0, p0, r, q, z, correct_x, correct_p = (
labbe_chapter_6_kalman_input_output_02())
result_x, result_p = kalman_updates_sequence_multivariate(
x0=np.array(np.array(x0).reshape(2, 1)),
P0=p0,
F=np.array([[1., 1.], [0., 1.]]),
Q=np.array([[0.005, 0.01], [0.01, q]]),
B=np.array([0.]).reshape(1, 1),
u=np.array([0.]).reshape(1, 1),
H=np.array([1., 0.]).reshape(1, 2),
R=np.array(r).reshape(1, 1),
z_vec=z,
kalman_function=kalman_update_multivariate_reannotated)
result_x_arr = np.stack(result_x).reshape(-1, 2)
assert np.allclose(result_x_arr, correct_x, atol=1e-2)
result_p_arr = np.stack(result_p)
assert np.allclose(result_p_arr, correct_p, atol=1e-1)