def kalman_filter(self, observ):
"""Kalman filter using the model on a set of observations"""
# Get system matrices
F = self.transition_matrix()
Q = self.transition_covariance()
H = self.observation_matrix()
R = self.observation_covariance()
# Initialise arrays of Gaussian densities and (log-)likelihood
num_time_instants = len(observ)
flt = GaussianDensityTimeSeries(num_time_instants, self.ds)
prd = GaussianDensityTimeSeries(num_time_instants, self.ds)
lhood = 0
# Loop through time instants
for kk in range(num_time_instants):
# Prediction
if kk > 0:
prd_kk = kal.predict(flt.get_instant(kk-1), F, Q)
else:
prd_kk = self.initial_state_prior
prd.set_instant(kk, prd_kk)
# Correction - handles misisng data indicated by NaNs
y = observ[kk]
if not np.any(np.isnan(y)):
# Nothing missing - full update
flt_kk,innov = kal.correct(prd.get_instant(kk), y, H, R)
lhood = lhood + mvn.logpdf(observ[kk], innov.mn, innov.vr)
elif np.all(np.isnan(y)):
# All missing - no update
flt_kk = prd_kk
else:
# Partially missing - delete missing elements
missing = np.where( np.isnan(y) )
yp = np.delete(y, missing, axis=0)
Hp = np.delete(H, missing, axis=0)
Rp = np.delete(np.delete(R, missing, axis=0), missing, axis=1)
flt_kk,innov = kal.correct(prd.get_instant(kk), yp, Hp, Rp)
lhood = lhood + mvn.logpdf(yp, innov.mn, innov.vr)
flt.set_instant(kk, flt_kk)
return flt, prd, lhood
def rts_smoother(self, flt, prd):
"""Rauch-Tung-Striebel smooth using the model"""
# Get system matrices
F = self.transition_matrix()
# Initialise arrays of Gaussian densities and (log-)likelihood
num_time_instants = flt.num_time_instants
smt = GaussianDensityTimeSeries(num_time_instants, self.ds)
# Loop through time instants
for kk in reversed(range(num_time_instants)):
# RTS update
if kk < num_time_instants-1:
smt_kk = kal.update(flt.get_instant(kk),
smt.get_instant(kk+1), prd.get_instant(kk+1), F)
else:
smt_kk = flt.get_instant(kk)
smt.set_instant(kk, smt_kk)
return smt
def rts_smoother(self, flt, prd):
"""Rauch-Tung-Striebel smooth using the model"""
# Get system matrices
F = self.transition_matrix()
# Initialise arrays of Gaussian densities and (log-)likelihood
num_time_instants = flt.num_time_instants
smt = GaussianDensityTimeSeries(num_time_instants, self.ds)
# Loop through time instants
for kk in reversed(range(num_time_instants)):
# RTS update
if kk < num_time_instants - 1:
smt_kk = kal.update(flt.get_instant(kk),
smt.get_instant(kk + 1),
prd.get_instant(kk + 1), F)
else:
smt_kk = flt.get_instant(kk)
smt.set_instant(kk, smt_kk)
return smt
def kalman_filter(self, observ):
"""Kalman filter using the model on a set of observations"""
# Get system matrices
F = self.transition_matrix()
Q = self.transition_covariance()
H = self.observation_matrix()
R = self.observation_covariance()
# Initialise arrays of Gaussian densities and (log-)likelihood
num_time_instants = len(observ)
flt = GaussianDensityTimeSeries(num_time_instants, self.ds)
prd = GaussianDensityTimeSeries(num_time_instants, self.ds)
lhood = 0
# Loop through time instants
for kk in range(num_time_instants):
# Prediction
if kk > 0:
prd_kk = kal.predict(flt.get_instant(kk - 1), F, Q)
else:
prd_kk = self.initial_state_prior
prd.set_instant(kk, prd_kk)
# Correction - handles misisng data indicated by NaNs
y = observ[kk]
if not np.any(np.isnan(y)):
# Nothing missing - full update
flt_kk, innov = kal.correct(prd.get_instant(kk), y, H, R)
lhood = lhood + mvn.logpdf(observ[kk], innov.mn, innov.vr)
elif np.all(np.isnan(y)):
# All missing - no update
flt_kk = prd_kk
else:
# Partially missing - delete missing elements
missing = np.where(np.isnan(y))
yp = np.delete(y, missing, axis=0)
Hp = np.delete(H, missing, axis=0)
Rp = np.delete(np.delete(R, missing, axis=0), missing, axis=1)
flt_kk, innov = kal.correct(prd.get_instant(kk), yp, Hp, Rp)
lhood = lhood + mvn.logpdf(yp, innov.mn, innov.vr)
flt.set_instant(kk, flt_kk)
return flt, prd, lhood
