def process(data_file, error_apriori, units):
'''
Given a .csv data file in the format of (time, x, y, z) applies both filters, generates a filtered.csv data
file, prints out the final keplerian elements computed from both Lamberts and Interpolation and finally plots
the initial, filtered data set and the final orbit.
Args:
data_file (string): The name of the .csv file containing the positional data
error_apriori (float): apriori estimation of the measurements error in km
Returns:
Runs the whole process of the program
'''
# First read the csv file called "orbit" with the positional data
print("Imported file format is:",
read_data.detect_file_format(data_file)["file"])
print("")
data = read_data.load_data(data_file)
if (units == 'm'):
# Transform m to km
data[:, 1:4] = data[:, 1:4] / 1000
print(
"***********Choose filter(s) in desired order of application***********"
)
print(
"(SPACE to toggle, UP/DOWN to navigate, RIGHT/LEFT to select/deselect and ENTER to submit)"
)
print(
"*if nothing is selected, Triple Moving Average followed by Savitzky Golay will be applied"
)
questions = [
inquirer.Checkbox(
'filter',
message="Select filter(s)",
choices=[
'None', 'Savitzky Golay Filter',
'Triple Moving Average Filter', 'Wiener Filter'
],
),
]
choices = inquirer.prompt(questions)
data_after_filter = data
if (len(choices['filter']) == 0):
print("Applying Triple Moving Average followed by Savitzky Golay...")
# Apply the Triple moving average filter with window = 3
data_after_filter = triple_moving_average.generate_filtered_data(
data_after_filter, 3)
# Use the golay_window.py script to find the window for the Savitzky Golay filter based on the error you input
window = golay_window.window(error_apriori, data_after_filter)
polyorder = 3
if polyorder < window:
# Apply the Savitzky Golay filter with window = window (51 for example_data/orbit.csv) and polynomial order = 3
data_after_filter = sav_golay.golay(data_after_filter, window,
polyorder)
else:
for index, choice in enumerate(choices['filter']):
if (choice == 'None'):
print("Using the original data...")
# no filter is applied
data_after_filter = data_after_filter
elif (choice == 'Savitzky Golay Filter'):
print("Applying Savitzky Golay Filter...")
# Use the golay_window.py script to find the window for the Savitzky Golay filter
# based on the error you input
window = golay_window.window(error_apriori, data_after_filter)
polyorder = 3
if polyorder < window:
# Apply the Savitzky Golay filter with window = window (51 for example_data/orbit.csv) and polynomial order = 3
data_after_filter = sav_golay.golay(
data_after_filter, window, polyorder)
elif (choice == 'Wiener Filter'):
print("Applying Wiener Filter...")
# Apply the Wiener filter
data_after_filter = wiener.wiener_new(data_after_filter, 3)
else:
print("Applying Triple Moving Average Filter...")
# Apply the Triple moving average filter with window = 3
data_after_filter = triple_moving_average.generate_filtered_data(
data_after_filter, 3)
# Compute the residuals between filtered data and initial data and then the sum and mean values of each axis
res = data_after_filter[:, 1:4] - data[:, 1:4]
sums = np.sum(res, axis=0)
print("\nDisplaying the sum of the residuals for each axis")
print(sums, "\n")
means = np.mean(res, axis=0)
print("Displaying the mean of the residuals for each axis")
print(means, "\n")
# Save the filtered data into a new csv called "filtered"
np.savetxt("filtered.csv", data_after_filter, delimiter=",")
print("***********Choose Method(s) for Orbit Determination***********")
print(
"(SPACE to toggle, UP/DOWN to navigate, RIGHT/LEFT to select/deselect and ENTER to submit)"
)
print(
"*if nothing is selected, Cubic Spline Interpolation will be used for Orbit Determination"
)
questions = [
inquirer.Checkbox(
'method',
message="Select Method(s)",
choices=[
'Lamberts Kalman', 'Cubic Spline Interpolation',
'Ellipse Best Fit', 'Gibbs 3 Vector', 'Gauss 3 Vector',
'MCMC (exp.)'
],
),
]
choices = inquirer.prompt(questions)
kep_elements = {}
if (len(choices['method']) == 0):
# Apply the interpolation method
kep_inter = interpolation.main(data_after_filter)
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_inter = lamberts_kalman.kalman(kep_inter, 0.01**2)
kep_final_inter = np.transpose(kep_final_inter)
kep_final_inter = np.resize(kep_final_inter, ((7, 1)))
kep_final_inter[6, 0] = sgp4.rev_per_day(kep_final_inter[0, 0])
kep_elements['Cubic Spline Interpolation'] = kep_final_inter
else:
for index, choice in enumerate(choices['method']):
if (choice == 'Lamberts Kalman'):
# Apply Lambert Kalman method for the filtered data set
#previously, all data...
#kep_lamb = lamberts_kalman.create_kep(data_after_filter)
# only three (3) observations from half an orbit.
# also just two (2) observations are fine for lamberts.
data = np.array([
data_after_filter[:, :][0],
data_after_filter[:, :][len(data_after_filter) // 2],
data_after_filter[:, :][-1]
])
kep_lamb = lamberts_kalman.create_kep(data)
# Determination of orbit period
semimajor_axis = kep_lamb[0][0]
timestamps = data_after_filter[:, 0]
index = get_timestamp_index_by_orbitperiod(
semimajor_axis, timestamps)
# enough data for half orbit
data = np.array([
data_after_filter[:, :][0],
data_after_filter[:, :][index // 2],
data_after_filter[:, :][index]
])
kep_lamb = lamberts_kalman.create_kep(data)
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_lamb = lamberts_kalman.kalman(kep_lamb, 0.01**2)
kep_final_lamb = np.transpose(kep_final_lamb)
kep_final_lamb = np.resize(kep_final_lamb, ((7, 1)))
kep_final_lamb[6, 0] = sgp4.rev_per_day(kep_final_lamb[0, 0])
kep_elements['Lamberts Kalman'] = kep_final_lamb
elif (choice == 'Cubic Spline Interpolation'):
# Apply the interpolation method
kep_inter = interpolation.main(data_after_filter)
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_inter = lamberts_kalman.kalman(kep_inter, 0.01**2)
kep_final_inter = np.transpose(kep_final_inter)
kep_final_inter = np.resize(kep_final_inter, ((7, 1)))
kep_final_inter[6, 0] = sgp4.rev_per_day(kep_final_inter[0, 0])
kep_elements['Cubic Spline Interpolation'] = kep_final_inter
elif (choice == 'Ellipse Best Fit'):
# Apply the ellipse best fit method
kep_ellip = ellipse_fit.determine_kep(data_after_filter[:,
1:])[0]
kep_final_ellip = np.transpose(kep_ellip)
kep_final_ellip = np.resize(kep_final_ellip, ((7, 1)))
kep_final_ellip[6, 0] = sgp4.rev_per_day(kep_final_ellip[0, 0])
kep_elements['Ellipse Best Fit'] = kep_final_ellip
elif (choice == 'Gibbs 3 Vector'):
# Apply the Gibbs method
# first only with first, middle and last measurement
R = np.array([
data_after_filter[:, 1:][0],
data_after_filter[:, 1:][len(data_after_filter) // 2],
data_after_filter[:, 1:][-1]
])
kep_gibbs = gibbs_method.gibbs_get_kep(R)
# Determination of orbit period
semimajor_axis = kep_gibbs[0][0]
timestamps = data_after_filter[:, 0]
index = get_timestamp_index_by_orbitperiod(
semimajor_axis, timestamps)
# enough data for half orbit
R = np.array([
data_after_filter[:, 1:][0],
data_after_filter[:, 1:][index // 2],
data_after_filter[:, 1:][index]
])
kep_gibbs = gibbs_method.gibbs_get_kep(R)
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_gibbs = lamberts_kalman.kalman(kep_gibbs, 0.01**2)
kep_final_gibbs = np.transpose(kep_final_gibbs)
kep_final_gibbs = np.resize(kep_final_gibbs, ((7, 1)))
kep_final_gibbs[6, 0] = sgp4.rev_per_day(kep_final_gibbs[0, 0])
kep_elements['Gibbs 3 Vector'] = kep_final_gibbs
elif (choice == 'Gauss 3 Vector'):
# Apply the Gauss method
# first only with first, middle and last measurement
R = np.array([
data_after_filter[:, 1:][0],
data_after_filter[:, 1:][len(data_after_filter) // 2],
data_after_filter[:, 1:][-1]
])
t1 = data_after_filter[:, 0][0]
t2 = data_after_filter[:, 0][len(data_after_filter) // 2]
t3 = data_after_filter[:, 0][-1]
v2 = gauss_method.gauss_method_get_velocity(
R[0], R[1], R[2], t1, t2, t3)
# Determination of orbit period
semimajor_axis = oe.semimajor_axis(R[0], v2)
timestamps = data_after_filter[:, 0]
index = get_timestamp_index_by_orbitperiod(
semimajor_axis, timestamps)
# enough data for half orbit
R = np.array([
data_after_filter[:, 1:][0],
data_after_filter[:, 1:][index // 2],
data_after_filter[:, 1:][index]
])
t1 = data_after_filter[:, 0][0]
t2 = data_after_filter[:, 0][index // 2]
t3 = data_after_filter[:, 0][index]
v2 = gauss_method.gauss_method_get_velocity(
R[0], R[1], R[2], t1, t2, t3)
semimajor_axis = oe.semimajor_axis(R[0], v2)
ecc = oe.eccentricity_v(R[1], v2)
ecc = np.linalg.norm(ecc)
inc = oe.inclination(R[1], v2) * 180.0 / np.pi
AoP = oe.AoP(R[1], v2) * 180.0 / np.pi
raan = oe.raan(R[1], v2) * 180.0 / np.pi
true_anomaly = oe.true_anomaly(R[1], v2) * 180.0 / np.pi
T_orbitperiod = oe.T_orbitperiod(semimajor_axis=semimajor_axis)
n_mean_motion_perday = oe.n_mean_motion_perday(T_orbitperiod)
kep_gauss = np.array([[
semimajor_axis, ecc, inc, AoP, raan, true_anomaly,
n_mean_motion_perday
]])
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_gauss = lamberts_kalman.kalman(kep_gauss, 0.01**2)
kep_final_gauss = np.transpose(kep_final_gauss)
kep_final_gauss = np.resize(kep_final_gauss, ((7, 1)))
kep_final_gauss[6, 0] = sgp4.rev_per_day(kep_final_gauss[0, 0])
kep_elements['Gauss 3 Vector'] = kep_final_gauss
else:
# apply mcmc method, a real optimizer
# all data
timestamps = data_after_filter[:, 0]
R = np.array(data_after_filter[:, 1:])
# all data can make the MCMC very slow. so we just pick a few in random, but in order.
timestamps_short = []
R_short = []
if len(timestamps) > 25:
print(
"Too many positions for MCMC. Just 25 positons are selected"
)
# pick randomly, but in order and no duplicates
l = list(
np.linspace(0,
len(timestamps) - 1,
num=len(timestamps)))
select_index = sorted(random.sample(list(l)[1:-1], k=23))
print(select_index)
timestamps_short.append(timestamps[0])
R_short.append(R[0])
for select in range(len(select_index)):
timestamps_short.append(timestamps[int(
select_index[select])])
R_short.append(R[int(select_index[select])])
timestamps_short.append(timestamps[-1])
R_short.append(R[-1])
else:
timestamps_short = timestamps
R_short = R
parameters = with_mcmc.fromposition(timestamps_short, R_short)
r_a = parameters["r_a"]
r_p = parameters["r_p"]
AoP = parameters["AoP"]
inc = parameters["inc"]
raan = parameters["raan"]
tp = parameters["tp"]
semimajor_axis = (r_p + r_a) / 2.0
ecc = (r_a - r_p) / (r_a + r_p)
T_orbitperiod = oe.T_orbitperiod(semimajor_axis=semimajor_axis)
true_anomaly = tp / T_orbitperiod * 360.0
n_mean_motion_perday = oe.n_mean_motion_perday(T_orbitperiod)
kep_mcmc = np.array([[
semimajor_axis, ecc, inc, AoP, raan, true_anomaly,
n_mean_motion_perday
]])
kep_elements['MCMC (exp.)'] = kep_mcmc
kep_final = np.zeros((7, len(kep_elements)))
order = []
for index, key in enumerate(kep_elements):
kep_final[:, index] = np.ravel(kep_elements[key])
order.append(str(key))
# Print the final orbital elements for all solutions
kep_elements = [
"Semi major axis (a)(km)", "Eccentricity (e)", "Inclination (i)(deg)",
"Argument of perigee (ω)(deg)",
"Right acension of ascending node (Ω)(deg)", "True anomaly (v)(deg)",
"Frequency (f)(rev/day)"
]
for i in range(0, len(order)):
print("\n******************Output for %s Method******************\n" %
order[i])
for j in range(0, 7):
print("%s: %.16f" % (kep_elements[j], kep_final[j, i]))
print("\nShow plots? [y/n]")
user_input = input()
if (user_input == "y" or user_input == "Y"):
for j in range(0, len(order)):
# Plot the initial data set, the filtered data set and the final orbit
# First we transform the set of keplerian elements into a state vector
state = kep_state.kep_state(np.resize(kep_final[:, j], (7, 1)))
# Then we produce more state vectors at varius times using a Runge Kutta algorithm
keep_state = np.zeros((6, 150))
ti = 0.0
tf = 1.0
t_hold = np.zeros((150, 1))
x = state
h = 0.1
tetol = 1e-04
for i in range(0, 150):
keep_state[:,
i] = np.ravel(rkf78.rkf78(6, ti, tf, h, tetol, x))
t_hold[i, 0] = tf
tf = tf + 1
positions = keep_state[0:3, :]
## Finally we plot the graph
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = plt.axes(projection='3d')
ax.plot(data[:, 1],
data[:, 2],
data[:, 3],
".",
label='Initial data ')
ax.plot(data_after_filter[:, 1],
data_after_filter[:, 2],
data_after_filter[:, 3],
"k",
linestyle='-',
label='Filtered data')
ax.plot(positions[0, :],
positions[1, :],
positions[2, :],
"r-",
label='Orbit after %s method' % order[j])
ax.legend()
ax.can_zoom()
ax.set_xlabel('x (km)')
ax.set_ylabel('y (km)')
ax.set_zlabel('z (km)')
plt.show()
def process(data_file, error_apriori, units):
'''
Given a .csv data file in the format of (time, x, y, z) applies both filters, generates a filtered.csv data
file, prints out the final keplerian elements computed from both Lamberts and Interpolation and finally plots
the initial, filtered data set and the final orbit.
Args:
data_file (string): The name of the .csv file containing the positional data
error_apriori (float): apriori estimation of the measurements error in km
Returns:
Runs the whole process of the program
'''
# First read the csv file called "orbit" with the positional data
data = read_data.load_data(data_file)
if(units == 'm'):
# Transform m to km
data[:, 1:4] = data[:, 1:4] / 1000
print("***********Choose filter(s) in desired order of application***********")
print("(SPACE to toggle, UP/DOWN to navigate, RIGHT/LEFT to select/deselect and ENTER to submit)")
print("*if nothing is selected, Triple Moving Average followed by Savitzky Golay will be applied")
questions = [
inquirer.Checkbox('filter',
message="Select filter(s)",
choices=['None', 'Savitzky Golay Filter', 'Triple Moving Average Filter','Wiener Filter'],
),
]
choices = inquirer.prompt(questions)
data_after_filter = data
if(len(choices['filter']) == 0):
print("Applying Triple Moving Average followed by Savitzky Golay...")
# Apply the Triple moving average filter with window = 3
data_after_filter = triple_moving_average.generate_filtered_data(data_after_filter, 3)
# Use the golay_window.py script to find the window for the Savitzky Golay filter based on the error you input
window = golay_window.window(error_apriori, data_after_filter)
# Apply the Savitzky Golay filter with window = window (51 for orbit.csv) and polynomial order = 3
data_after_filter = sav_golay.golay(data_after_filter, window, 3)
else:
for index, choice in enumerate(choices['filter']):
if(choice == 'None'):
print("Using the original data...")
# no filter is applied
data_after_filter = data_after_filter
elif (choice == 'Savitzky Golay Filter'):
print("Applying Savitzky Golay Filter...")
# Use the golay_window.py script to find the window for the Savitzky Golay filter
# based on the error you input
window = golay_window.window(error_apriori, data_after_filter)
# Apply the Savitzky Golay filter with window = window (51 for orbit.csv) and polynomial order = 3
data_after_filter = sav_golay.golay(data_after_filter, window, 3)
elif(choice == 'Wiener Filter'):
print("Applying Wiener Filter...")
# Apply the Wiener filter
data_after_filter = wiener.wiener_new(data_after_filter, 3)
else:
print("Applying Triple Moving Average Filter...")
# Apply the Triple moving average filter with window = 3
data_after_filter = triple_moving_average.generate_filtered_data(data_after_filter, 3)
# Compute the residuals between filtered data and initial data and then the sum and mean values of each axis
res = data_after_filter[:, 1:4] - data[:, 1:4]
sums = np.sum(res, axis = 0)
print("\nDisplaying the sum of the residuals for each axis")
print(sums, "\n")
means = np.mean(res, axis = 0)
print("Displaying the mean of the residuals for each axis")
print(means, "\n")
# Save the filtered data into a new csv called "filtered"
np.savetxt("filtered.csv", data_after_filter, delimiter = ",")
print("***********Choose Method(s) for Orbit Determination***********")
print("(SPACE to toggle, UP/DOWN to navigate, RIGHT/LEFT to select/deselect and ENTER to submit)")
print("*if nothing is selected, Cubic Spline Interpolation will be used for Orbit Determination")
questions = [
inquirer.Checkbox('method',
message="Select Method(s)",
choices=['Lamberts Kalman', 'Cubic Spline Interpolation', 'Ellipse Best Fit', 'Gibbs 3 Vector'],
),
]
choices = inquirer.prompt(questions)
kep_elements = {}
if(len(choices['method']) == 0):
# Apply the interpolation method
kep_inter = interpolation.main(data_after_filter)
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_inter = lamberts_kalman.kalman(kep_inter, 0.01 ** 2)
kep_final_inter = np.transpose(kep_final_inter)
kep_final_inter = np.resize(kep_final_inter, ((7, 1)))
kep_final_inter[6, 0] = sgp4.rev_per_day(kep_final_inter[0, 0])
kep_elements['Cubic Spline Interpolation'] = kep_final_inter
else:
for index, choice in enumerate(choices['method']):
if(choice == 'Lamberts Kalman'):
# Apply Lambert Kalman method for the filtered data set
#previously, all data...
#kep_lamb = lamberts_kalman.create_kep(data_after_filter)
# only three (3) observations from half an orbit.
# also just two (2) observations are fine for lamberts.
data = np.array([data_after_filter[:, :][0],
data_after_filter[:, :][len(data_after_filter) // 2],
data_after_filter[:, :][-1]])
kep_lamb = lamberts_kalman.create_kep(data)
# Determination of orbit period
semimajor_axis = kep_lamb[0][0]
T_orbitperiod = oe.T_orbitperiod(semimajor_axis=semimajor_axis)
timestamps = data_after_filter[:, 0]
runtime = np.subtract(timestamps, np.min(timestamps))
index = np.argmax(runtime >= T_orbitperiod // 2) - 1 # only half orbit is good for Gibbs method
if index < 2:
# in case there are not enough points to have the result at index point at 2
# or the argmax search does not find anything and sets index = 0.
index = len(timestamps) - 1
# enough data for half orbit
data = np.array([data_after_filter[:, :][0],
data_after_filter[:, :][index // 2],
data_after_filter[:, :][index]])
kep_lamb = lamberts_kalman.create_kep(data)
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_lamb = lamberts_kalman.kalman(kep_lamb, 0.01 ** 2)
kep_final_lamb = np.transpose(kep_final_lamb)
kep_final_lamb = np.resize(kep_final_lamb, ((7, 1)))
kep_final_lamb[6, 0] = sgp4.rev_per_day(kep_final_lamb[0, 0])
kep_elements['Lamberts Kalman'] = kep_final_lamb
elif(choice == 'Cubic Spline Interpolation'):
# Apply the interpolation method
kep_inter = interpolation.main(data_after_filter)
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_inter = lamberts_kalman.kalman(kep_inter, 0.01 ** 2)
kep_final_inter = np.transpose(kep_final_inter)
kep_final_inter = np.resize(kep_final_inter, ((7, 1)))
kep_final_inter[6, 0] = sgp4.rev_per_day(kep_final_inter[0, 0])
kep_elements['Cubic Spline Interpolation'] = kep_final_inter
elif(choice == 'Ellipse Best Fit'):
# Apply the ellipse best fit method
kep_ellip = ellipse_fit.determine_kep(data_after_filter[:, 1:])[0]
kep_final_ellip = np.transpose(kep_ellip)
kep_final_ellip = np.resize(kep_final_ellip, ((7, 1)))
kep_final_ellip[6, 0] = sgp4.rev_per_day(kep_final_ellip[0, 0])
kep_elements['Ellipse Best Fit'] = kep_final_ellip
else:
# Apply the Gibbs method
# first only with first, middle and last measurement
R = np.array([data_after_filter[:, 1:][0],
data_after_filter[:, 1:][len(data_after_filter) // 2],
data_after_filter[:, 1:][-1]])
kep_gibbs = gibbs_method.gibbs_get_kep(R)
# Determination of orbit period
semimajor_axis = kep_gibbs[0][0]
T_orbitperiod = oe.T_orbitperiod(semimajor_axis=semimajor_axis)
timestamps = data_after_filter[:, 0]
runtime = np.subtract(timestamps, np.min(timestamps))
index = np.argmax(runtime >= T_orbitperiod // 2) - 1 # only half orbit is good for Gibbs method
if index < 2:
# in case there are not enough points to have the result at index point at 2
# or the argmax search does not find anything and sets index = 0.
index = len(timestamps) - 1
# enough data for half orbit
R = np.array([data_after_filter[:, 1:][0],
data_after_filter[:, 1:][index // 2],
data_after_filter[:, 1:][index]])
kep_gibbs = gibbs_method.gibbs_get_kep(R)
# Apply Kalman filters to find the best approximation of the keplerian elements for all solutions
# We set an estimate of measurement variance R = 0.01 ** 2
kep_final_gibbs = lamberts_kalman.kalman(kep_gibbs, 0.01 ** 2)
kep_final_gibbs = np.transpose(kep_final_gibbs)
kep_final_gibbs = np.resize(kep_final_gibbs, ((7, 1)))
kep_final_gibbs[6, 0] = sgp4.rev_per_day(kep_final_gibbs[0, 0])
kep_elements['Gibbs 3 Vector'] = kep_final_gibbs
kep_final = np.zeros((7, len(kep_elements)))
order = []
for index, key in enumerate(kep_elements):
kep_final[:, index] = np.ravel(kep_elements[key])
order.append(str(key))
# Print the final orbital elements for all solutions
kep_elements = ["Semi major axis (a)(km)", "Eccentricity (e)", "Inclination (i)(deg)",
"Argument of perigee (ω)(deg)", "Right acension of ascending node (Ω)(deg)",
"True anomaly (v)(deg)", "Frequency (f)(rev/day)"]
for i in range(0, len(order)):
print("\n******************Output for %s Method******************\n" % order[i])
for j in range(0, 7):
print("%s: %.16f" % (kep_elements[j], kep_final[j, i]))
print("\nShow plots? [y/n]")
user_input = input()
if(user_input == "y" or user_input == "Y"):
for j in range(0, len(order)):
# Plot the initial data set, the filtered data set and the final orbit
# First we transform the set of keplerian elements into a state vector
state = kep_state.kep_state(np.resize(kep_final[:, j], (7, 1)))
# Then we produce more state vectors at varius times using a Runge Kutta algorithm
keep_state = np.zeros((6, 150))
ti = 0.0
tf = 1.0
t_hold = np.zeros((150, 1))
x = state
h = 0.1
tetol = 1e-04
for i in range(0, 150):
keep_state[:, i] = np.ravel(rkf78.rkf78(6, ti, tf, h, tetol, x))
t_hold[i, 0] = tf
tf = tf + 1
positions = keep_state[0:3, :]
## Finally we plot the graph
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection = '3d')
ax.plot(data[:, 1], data[:, 2], data[:, 3], ".", label = 'Initial data ')
ax.plot(data_after_filter[:, 1], data_after_filter[:, 2], data_after_filter[:, 3], "k", linestyle = '-',
label = 'Filtered data')
ax.plot(positions[0, :], positions[1, :], positions[2, :], "r-", label = 'Orbit after %s method' % order[j])
ax.legend()
ax.can_zoom()
ax.set_xlabel('x (km)')
ax.set_ylabel('y (km)')
ax.set_zlabel('z (km)')
plt.show()
def read(data_file):
#global data
data = read_data.load_data(data_file)
data[:, 1:4] = data[:, 1:4] / 1000
data_after_filter = wiener.wiener_new(data, 3)
return data_after_filter