Filters with Constant Gains¶
In [1]:
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
In [2]:
from filters.ghk import GFilter
from filters.ghk import GHFilter
from filters.ghk import print_steps
from plots.plot_gh import plot_gh_compar_data
from plots.plot_gh import plot_gh_compar_param
from simulators.datagen import gen_cvca
g-h Filter¶
In [3]:
heights = pd.read_csv("data/heights.csv", header=None).to_numpy().flatten()
heights
Out[3]:
array([158. , 164.2, 160.3, 159.9, 162.1, 164.6, 169.6, 167.4, 166.4,
171. , 171.2, 172.6])
Predict With Constant Steps¶
In [4]:
init_estimate = 160.0
time_step = 1
gain_scale = 1
gf = GFilter(x0=init_estimate, dx=time_step, dt=1, g=gain_scale)
ests, preds = gf.batch_filter(heights, save_preds=True)
print_steps(ests[:, 0], preds)
previous x: 160.00, current x: 158.00, predicted x̂: 161.00 previous x: 158.00, current x: 164.20, predicted x̂: 159.00 previous x: 164.20, current x: 160.30, predicted x̂: 165.20 previous x: 160.30, current x: 159.90, predicted x̂: 161.30 previous x: 159.90, current x: 162.10, predicted x̂: 160.90 previous x: 162.10, current x: 164.60, predicted x̂: 163.10 previous x: 164.60, current x: 169.60, predicted x̂: 165.60 previous x: 169.60, current x: 167.40, predicted x̂: 170.60 previous x: 167.40, current x: 166.40, predicted x̂: 168.40 previous x: 166.40, current x: 171.00, predicted x̂: 167.40 previous x: 171.00, current x: 171.20, predicted x̂: 172.00 previous x: 171.20, current x: 172.60, predicted x̂: 172.20
In [5]:
init_estimates = [160] * 2
gain_rates = [1, -1]
gain_scales = [4.0 / 10] * 2
filters = []
for x0, dx, g in zip(init_estimates, gain_rates, gain_scales):
gf = GFilter(x0=x0, dx=dx, dt=1, g=g)
filters.append(gf)
_, axes = plt.subplots(2, 1, figsize=(8, 4), constrained_layout=True)
plot_gh_compar_param(
axes,
heights,
filters=filters,
x0s=init_estimates,
vary_obj="dx",
show_preds=True,
combined=False,
)
# plt.savefig("../images/gh-cv.png")
Predict With Changing Steps¶
In [6]:
init_estimate = 160.0
time_step = 1
gain_scale = 1
height_scale = 4.0 / 10
ghf = GHFilter(x0=init_estimate, dx=time_step, dt=1, g=gain_scale, h=height_scale)
ests, preds = ghf.batch_filter(heights, save_preds=True)
print_steps(ests[:, 0], preds)
previous x: 160.00, current x: 158.00, predicted x̂: 161.00 previous x: 158.00, current x: 164.20, predicted x̂: 157.80 previous x: 164.20, current x: 160.30, predicted x̂: 166.56 previous x: 160.30, current x: 159.90, predicted x̂: 160.16 previous x: 159.90, current x: 162.10, predicted x̂: 159.65 previous x: 162.10, current x: 164.60, predicted x̂: 162.83 previous x: 164.60, current x: 169.60, predicted x̂: 166.04 previous x: 169.60, current x: 167.40, predicted x̂: 172.46 previous x: 167.40, current x: 166.40, predicted x̂: 168.24 previous x: 166.40, current x: 171.00, predicted x̂: 166.50 previous x: 171.00, current x: 171.20, predicted x̂: 172.90 previous x: 171.20, current x: 172.60, predicted x̂: 172.42
In [7]:
height = [160.0] * 2
gain_rates = [1, -1]
gain_scales = [1.0 / 3] * 2
height_scales = [4.0 / 10] * 2
filters = []
for x0, dx, g, h in zip(init_estimates, gain_rates, gain_scales, height_scales):
ghf = GHFilter(x0=x0, dx=dx, dt=1, g=g, h=h)
filters.append(ghf)
_, axes = plt.subplots(2, 1, figsize=(8, 4), constrained_layout=True)
plot_gh_compar_param(
axes,
heights,
filters=filters,
x0s=init_estimates,
vary_obj="dx",
show_preds=True,
combined=False,
)
Varying Noise¶
In [8]:
xs1, zs1 = gen_cvca(num=100, x0=5, dx=2, R=100)
xs2, zs2 = gen_cvca(num=100, x0=5, dx=2, R=100 * 2)
ghf = GHFilter(x0=5.0, dx=2.0, dt=1.0, g=0.2, h=0.02)
_, axes = plt.subplots(2, 1, figsize=(8, 4), constrained_layout=True)
plot_gh_compar_data(axes, data_ls=[zs1, zs2], filt=ghf, x0=5.0, show_preds=True)
Varying g¶
In [9]:
xs, zs = gen_cvca(num=50, x0=5.0, dx=5.0, R=50)
starts = [0] * 3
dxs = [1] * 3
gs = [0.1, 0.4, 0.8]
hs = [0.01] * 3
filters = []
for x0, dx, g, h in zip(starts, dxs, gs, hs):
ghf = GHFilter(x0=x0, dx=dx, dt=1, g=g, h=h)
filters.append(ghf)
_, ax = plt.subplots(figsize=(8, 4))
plot_gh_compar_param(ax, data=zs, filters=filters, x0s=starts, vary_obj="g")
# plt.savefig('../images/gh-g.png')
In [10]:
zs = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
zs.extend(14 for _ in range(50))
zs = np.array(zs)
starts = [4] * 3
dxs = [1] * 3
gs = [0.1, 0.4, 0.8]
hs = [0.01] * 3
filters = []
for x0, dx, g, h in zip(starts, dxs, gs, hs):
ghf = GHFilter(x0=x0, dx=dx, dt=1, g=g, h=h)
filters.append(ghf)
_, ax = plt.subplots(figsize=(8, 4))
plot_gh_compar_param(ax, data=zs, filters=filters, x0s=starts, vary_obj="g")
# plt.savefig("../images/gh-g.png")
Varying h¶
In [11]:
zs = np.linspace(0, 10, 50)
starts = [0] * 3
dxs = [2] * 3
gs = [0.2] * 3
hs = [0.05, 0.1, 0.2]
filters = []
for x0, dx, g, h in zip(starts, dxs, gs, hs):
ghf = GHFilter(x0=x0, dx=dx, dt=1, g=g, h=h)
filters.append(ghf)
_, ax = plt.subplots(figsize=(8, 4))
plot_gh_compar_param(ax, data=zs, filters=filters, x0s=starts, vary_obj="h")
# plt.savefig("../images/gh-h.png")
In [12]:
data = pd.read_csv("data/demo.csv", header=None).to_numpy().flatten()
data
Out[12]:
array([ 5, 6, 7, 8, 9, 9, 9, 9, 9, 10, 11, 12, 13, 14, 15, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16, 16])
In [13]:
starts = [4] * 4
dxs = [1] * 4
gs = [0.1, 1, 2, 0.01]
hs = [2, 1, 0.1, 0.01]
filters = []
for x0, dx, g, h in zip(starts, dxs, gs, hs):
ghf = GHFilter(x0=x0, dx=dx, dt=1, g=g, h=h)
filters.append(ghf)
_, ax = plt.subplots(figsize=(8, 4))
plot_gh_compar_param(ax, data=data, filters=filters, x0s=starts, vary_obj="gh")
# plt.savefig("../images/gh-gh.png")
Dependent Data¶
In [14]:
x0 = 23 * 1000
dx = 15
xs, zs = gen_cvca(100, x0, dx, dt=1, R=500)
starts = [x0] * 3
dxs = [dx] * 3
gs = [0.01, 0.2]
hs = [0.001, 0.001]
filters = []
for x0, dx, g, h in zip(starts, dxs, gs, hs):
ghf = GHFilter(x0=x0, dx=dx, dt=1, g=g, h=h)
filters.append(ghf)
_, ax = plt.subplots(figsize=(8, 4))
plot_gh_compar_param(ax, data=zs, filters=filters, x0s=starts, vary_obj="gh")
In [15]:
x0 = 23 * 1000
dx = 15
x, zs = gen_cvca(100, x0, dx, ddx=0.2, dt=1, R=500)
starts = [x0] * 3
dxs = [dx] * 3
gs = [0.01, 0.2, 0.01]
hs = [0.001, 0.001, 0.01]
filters = []
for x0, dx, g, h in zip(starts, dxs, gs, hs):
ghf = GHFilter(x0=x0, dx=dx, dt=1, g=g, h=h)
filters.append(ghf)
_, ax = plt.subplots(figsize=(8, 4))
plot_gh_compar_param(ax, data=zs, filters=filters, x0s=starts, vary_obj="gh")
