def temp_model(state_grid, obs_grid, source_terms, params):
source_grid, source_weights = source_terms[0], source_terms[1]
# Unpack params: V, W, prior_guess, prior_var
obs_noise, move_noise = params[0], params[1]
prior_guess, prior_var = params[2], params[3]
N, p, q = state_grid[0].size, obs_grid[0].size, source_grid[0].size
dx = state_grid[0][1] - state_grid[0][0]
# Define relevant parameters
k, rho, c_p = 0.026, 1.2, 0.001 # The standard properties of air
alpha = k / (rho * c_p)
dt = 0.1 * dx**2 / (2 * alpha)
lam, gamma = alpha * dt / (dx**2), dt / (rho * c_p)
# Construct G, F, and Q
G = heat_eq_state_mat(state_grid, dx, lam)
F = heat_eq_obs_mat(obs_grid, state_grid, dx)
Q = heat_eq_source_mat(source_terms, state_grid, gamma)
# Construct W and V
W = np.identity(N) * move_noise
V = np.identity(p) * obs_noise
# Construct m and C
m = np.array([prior_guess] * N)
C = np.identity(N) * prior_var
# Create and return model
model = kf.DLM([G, W], [F, V], [m, C], Q)
return model
def default_model():
# Create default model
V, W = 0.5, 0.01
W = np.array([[W]])
space_params = [np.array([[1]]), np.array([[V]])]
state_params = [np.array([[1]]), W]
prior = [np.array([[0]]), np.array([[1]])]
model = kf.DLM(state_params, space_params, prior)
return model
def default_RWWN_model():
# Create default model
# Random walk with noise
V, W = 0.5, 0.1
obs_params = [np.array([1]), np.array([[V]])]
state_params = [np.array([1]), np.array([[W]])]
prior = [np.array([80]), np.array([[1]])]
source = np.array([0])
model = kf.DLM(state_params, obs_params, prior, source)
return model
def default_RWWN_vel_model():
# Create default model
# Random walk with noise and time-varying velocity
V, W_x, W_v = 10, 0.1, 0.5
prior_x, prior_v = 80, 1
prior_x_var, prior_v_var = 1, 1
obs_params = [np.array([[1, 0]]), np.array([[V]])]
state_params = [np.array([[1, 1], [0, 1]]), np.array([[W_x, 0], [0, W_v]])]
prior = [np.array([prior_x, prior_v]), np.array([[prior_x_var, 0], [0, prior_v_var]])]
model = kf.DLM(state_params, obs_params, prior, np.array([0, 0]))
return model
def target_model(params):
# Parmaters: gamma, var_Y, var_x, var_v, prior_mean, prior_var_x, prior_var_v
gamma = params[0]
var_Y = params[1]
var_x, var_v = params[2], params[3]
prior_mean, prior_var_x, prior_var_v = params[4], params[5], params[6]
I_2 = np.identity(2)
Zero_2 = np.zeros((2, 2))
top = np.concatenate((I_2, I_2), axis=1)
bottom = np.concatenate((Zero_2, np.array([[1, -gamma], [-gamma, 1]])),
axis=1)
G = np.concatenate((top, bottom))
F = np.concatenate((I_2, Zero_2), axis=1)
top = np.concatenate((var_x * I_2, Zero_2), axis=1)
bottom = np.concatenate((Zero_2, var_v * I_2), axis=1)
W = np.concatenate((top, bottom))
V = var_Y * I_2
top = np.concatenate((prior_var_x * I_2, Zero_2), axis=1)
bottom = np.concatenate((Zero_2, prior_var_v * I_2), axis=1)
prior_var = np.concatenate((top, bottom))
model = kf.DLM([G, W], [F, V], [prior_mean, prior_var],
np.array([0, 0, 0, 0]))
return model
import kalman_filter as kf
import plotting as pl
active = True
while active:
default = input('Use default simulation parameters? Y/N: ')
if default != 'Y':
params = [0.0] * 5
params[0] = float(input('Enter state (movement) variance: '))
params[1] = float(input('Enter space (obervational) variance: '))
init = float(input('Enter initial state value: '))
params[2] = float(input('Enter prior mean: '))
params[3] = float(input('Enter prior variance: '))
obs_params = [np.array([1]), np.array([[params[1]]])]
state_params = [np.array([1]), np.array([[params[0]]])]
prior = [np.array([params[2]]), np.array([[params[3]]])]
source = np.array([0])
model = kf.DLM(state_params, obs_params, prior, source)
else:
model = ex.default_RWWN_model()
init = 80
length = int(input('Enter length of simulation: '))
print('Simulating data...')
theta, Y = model.simulate(length, np.array([init]))
print('Applying filter to simulated data...')
fit_values, fit_var = model.kfilter(Y[::, 0])
print('Plotting results...')
pl.one_d_kalman_plot(theta, Y, fit_values, fit_var)
again = input('Run program again? Y/N: ')
if again != 'Y':
break
# Write option to enter parameters
default = input('Use default simulation parameters? Y/N: ')
if default != 'Y':
params = [0] * 4
init_temp = float(input('Enter initial temperature: '))
init = np.array([init_temp] * N)
params[0] = float(input('Enter temperature movement variance: '))
params[1] = float(input('Enter observational variance: '))
params[2] = float(input('Enter prior guess of overall temperature: '))
params[3] = float(input('Enter prior variance: '))
else:
params = ex.default_Heat_params()
init = np.array([70] * N)
sim_model = tg.temp_model(state_grid, obs_grid, source_terms, params)
source_in_filter = input(
'Allow Kalman filter to know about the sources/sinks? Y/N: ')
if source_in_filter != 'Y':
pred_model = kf.DLM(sim_model.state_params, sim_model.space_params,
sim_model.filter_params, np.array([0] * N))
else:
pred_model = sim_model
length = int(input('Enter desired number of frames to simulate: '))
print('Simulating data...')
theta, Y = sim_model.simulate(length, init)
print('Filtering simulated data...')
fit_values, fit_var = pred_model.kfilter(Y)
print('Constructing animations...')
anim.animate_heat_eqn_wrapper(state_grid, obs_grid, theta, fit_values, Y)
again = input('Run program again? Y/N: ')
if again != 'Y':
break
W_v = float(input('Enter state velocity variance: '))
V = float(input('Enter space (obervational) variance: '))
init[0] = float(input('Enter initial position: '))
init[1] = float(input('Enter initial velocity: '))
prior_x = float(input('Enter prior guess for position: '))
prior_v = float(input('Enter prior guess for velocity: '))
prior_x_var = float(input('Enter prior position variance: '))
prior_v_var = float(input('Enter prior velocity variance: '))
obs_params = [np.array([[1, 0]]), np.array([[V]])]
state_params = [
np.array([[1, 1], [0, 1]]),
np.array([[W_x, 0], [0, W_v]])
]
prior = [
np.array([prior_x, prior_v]),
np.array([[prior_x_var, 0], [0, prior_v_var]])
]
model = kf.DLM(state_params, obs_params, prior, np.array([0, 0]))
else:
model = ex.default_RWWN_vel_model()
init = [80, 1]
length = int(input('Enter length of simulation: '))
print('Simulating data...')
theta, Y = model.simulate(length, np.array([init]))
print('Applying filter to simulated data...')
fit_values, fit_var = model.kfilter(Y[::, 0])
print('Plotting results...')
pl.one_d_kalman_plot(theta, Y, fit_values, fit_var)
again = input('Run program again? Y/N: ')
if again != 'Y':
break