def test_skew_list(self):
"""
Test formation of skew symmetric matrix from 1D list input
"""
rho = [1, 2, 3]
rho_x_expected = np.array([[0, -rho[2], rho[1]], [rho[2], 0, -rho[0]],
[-rho[1], rho[0], 0]])
np.testing.assert_almost_equal(rho_x_expected, navpy.skew(rho))
def test_skew_matrix(self):
"""
Test formation of skew symmetric matrix from matrix input
"""
rho = np.matrix([1, 2, 3])
rho_x_expected = np.array([[ 0 , -rho[0,2], rho[0,1]],
[ rho[0,2], 0 , -rho[0,0]],
[-rho[0,1], rho[0,0], 0 ]])
np.testing.assert_almost_equal(rho_x_expected, navpy.skew(rho))
def test_skew_list(self):
"""
Test formation of skew symmetric matrix from 1D list input
"""
rho = [1, 2, 3]
rho_x_expected = np.array([[ 0 , -rho[2], rho[1]],
[ rho[2], 0 , -rho[0]],
[-rho[1], rho[0], 0 ]])
np.testing.assert_almost_equal(rho_x_expected, navpy.skew(rho))
def test_skew_matrix(self):
"""
Test formation of skew symmetric matrix from matrix input
"""
rho = np.matrix([1, 2, 3])
rho_x_expected = np.array([[0, -rho[0, 2], rho[0, 1]],
[rho[0, 2], 0, -rho[0, 0]],
[-rho[0, 1], rho[0, 0], 0]])
np.testing.assert_almost_equal(rho_x_expected, navpy.skew(rho))
def update(self, imu, gps, verbose=True):
# Check for validity of GNSS at this time
self.tcpu = imu.time
self.tow = gps.tow
# Test 1: navValid flag and the data is indeed new (new Time of Week)
# Execute Measurement Update if this is true and Test 2 passes
NEW_GNSS_FLAG = ((gps.valid == 0) &
(abs(self.tow - self.last_tow) > 1e-3))
# Test 2: Check if the delta time of the Time of Week and the
# CPU time are consistent
# If this fails, re-initialize the filter. There must have been a glitch
if NEW_GNSS_FLAG:
#print self.tcpu, self.last_tcpu, self.tcpu-self.last_tcpu
#print self.tow, self.last_tow, self.tow-self.last_tow
if abs((self.tcpu - self.last_tcpu) -
(self.tow - self.last_tow)) > 0.5:
self.TU_COUNT = 0
self.NAV_INIT = False
if verbose:
print("Time Sync Error -- Request reinitialization")
# Record the tow and tcpu at this new update
self.last_tow = self.tow
self.last_tcpu = self.tcpu
# Different subroutine executed in the filter
if not self.NAV_INIT:
if not self.IMU_CAL_INIT:
# SUBROUTINE: IMU CALIBRATION,
# This only happens first time round on the ground. Inflight
# reinitialization is not the same.
self.estAB[:] = [0, 0, 0]
if self.very_first_time:
self.very_first_time = False
self.estGB[:] = [imu.p, imu.q, imu.r]
self.phi = 0
self.theta = 0
else:
self.estGB[:] = self.last_estGB[:]*self.TU_COUNT \
+ [imu.p, imu.q, imu.r]
# Simple AHRS values
self.phi = self.phi*self.TU_COUNT \
+ np.arctan2(-imu.ay, -imu.az)
self.theta = self.theta*self.TU_COUNT \
+ np.arctan2(imu.ax, np.sqrt(imu.ay**2+imu.az**2))
self.phi /= (self.TU_COUNT + 1)
self.theta /= (self.TU_COUNT + 1)
self.estGB[:] /= (self.TU_COUNT + 1)
self.estATT[0], self.estATT[1:] = navpy.angle2quat(
0, self.theta, self.phi)
"""
print("t = %7.3f, Gyro Bias Value: [%6.2f, %6.2f, %6.2f] deg/sec" %\
(imu.time, np.rad2deg(self.estGB[0]), np.rad2deg(self.estGB[1]), np.rad2deg(self.estGB[2]) ))
print("t = %7.3f, phi = %6.2f, theta = %6.2f" % (imu.time,np.rad2deg(self.phi),np.rad2deg(self.theta)) )
"""
self.TU_COUNT += 1
if self.TU_COUNT >= 35:
self.TU_COUNT = 0
self.IMU_CAL_INIT = True
if verbose:
print("t = %7.3f, IMU Calibrated!" % (imu.time))
del (self.phi)
del (self.theta)
else:
if not NEW_GNSS_FLAG:
# SUBROUTINE 1: BACKUP NAVIGATION or IN-FLIGHT INITIALIZATION
# >>>> AHRS CODE GOES HERE
self.estATT[:] = self.last_estATT[:] # This should be some backup nav mode
# <<<<
# When still there is no GNSS signal, continue propagating bias
self.estAB[:] = self.last_estAB[:]
self.estGB[:] = self.last_estGB[:]
else:
# When there is GNSS fix available, initialize all the states
# and renew covariance
self.estPOS[:] = [gps.lat, gps.lon, gps.alt]
self.estVEL[:] = [gps.vn, gps.ve, gps.vd]
self.estATT[:] = self.last_estATT[:]
#self.estATT[0], self.estATT[1:] = navpy.angle2quat(flight_data.psi[i],flight_data.theta[i],flight_data.phi[i])
self.estAB[:] = self.last_estAB[:]
self.estGB[:] = self.last_estGB[:]
self.init_covariance()
#idx_init.append(i)
self.NAV_INIT = True
if verbose:
print("t = %7.3f, Filter (Re-)initialized" %
(imu.time))
elif self.NAV_INIT:
# SUBROUTINE 2: MAIN FILTER ALGORITHM, INS + GNSS
# ==== Time-Update ====
dt = imu.time - self.last_imu.time
q0, qvec = self.last_estATT[0], self.last_estATT[1:4]
C_B2N = navpy.quat2dcm(q0, qvec).T
# 0. Data Acquisition
f_b=np.array([0.5*(self.last_imu.ax+imu.ax)-self.last_estAB[0],\
0.5*(self.last_imu.ay+imu.ay)-self.last_estAB[1],\
0.5*(self.last_imu.az+imu.az)-self.last_estAB[2]])
om_ib=np.array([0.5*(self.last_imu.p+imu.p)-self.last_estGB[0],\
0.5*(self.last_imu.q+imu.q)-self.last_estGB[1],\
0.5*(self.last_imu.r+imu.r)-self.last_estGB[2]])
# 1. Attitude Update
# --> Need to compensate for navrate and earthrate
dqvec = 0.5 * om_ib * dt
self.estATT[0], self.estATT[1:4] = navpy.qmult(
q0, qvec, 1.0, dqvec)
self.estATT[0] /= np.sqrt(self.estATT[0]**2 \
+ la.norm(self.estATT[1:4])**2)
self.estATT[1:4] /= np.sqrt(self.estATT[0]**2 \
+ la.norm(self.estATT[1:4])**2)
# 2. Velocity Update
# --> Need to compensate for coriolis effect
g = np.array([0, 0, 9.81])
f0, fvec = navpy.qmult(q0, qvec, 0, f_b)
f_n0, f_nvec = navpy.qmult(f0, fvec, q0, -qvec)
self.estVEL[:] = self.last_estVEL[:] + (f_nvec + g) * dt
# 3. Position Update
dPOS = navpy.llarate(self.last_estVEL[0], self.last_estVEL[1],
self.last_estVEL[2], self.last_estPOS[0],
self.last_estPOS[2])
dPOS *= dt
self.estPOS[:] = self.last_estPOS[:] + dPOS
# 4. Biases are constant
self.estAB[:] = self.last_estAB[:]
self.estGB[:] = self.last_estGB[:]
# 5. Jacobian
pos2pos = np.zeros((3, 3))
pos2gs = np.eye(3)
pos2att = np.zeros((3, 3))
pos2acc = np.zeros((3, 3))
pos2gyr = np.zeros((3, 3))
gs2pos = np.zeros((3, 3))
gs2pos[2, 2] = -2 * 9.81 / wgs84.R0
gs2gs = np.zeros((3, 3))
gs2att = -2 * C_B2N.dot(navpy.skew(f_b))
gs2acc = -C_B2N
gs2gyr = np.zeros((3, 3))
att2pos = np.zeros((3, 3))
att2gs = np.zeros((3, 3))
att2att = -navpy.skew(om_ib)
att2acc = np.zeros((3, 3))
att2gyr = -0.5 * np.eye(3)
F = np.zeros((15, 15))
F[0:3, 0:3] = pos2pos
F[0:3, 3:6] = pos2gs
F[0:3, 6:9] = pos2att
F[0:3, 9:12] = pos2acc
F[0:3, 12:15] = pos2gyr
F[3:6, 0:3] = gs2pos
F[3:6, 3:6] = gs2gs
F[3:6, 6:9] = gs2att
F[3:6, 9:12] = gs2acc
F[3:6, 12:15] = gs2gyr
F[6:9, 0:3] = att2pos
F[6:9, 3:6] = att2gs
F[6:9, 6:9] = att2att
F[6:9, 9:12] = att2acc
F[6:9, 12:15] = att2gyr
F[9:12, 9:12] = -1.0 / self.tau_a * np.eye(3)
F[12:15, 12:15] = -1.0 / self.tau_g * np.eye(3)
PHI = np.eye(15) + F * dt
# 6. Process Noise
G = np.zeros((15, 12))
G[3:6, 0:3] = -C_B2N
G[6:9, 3:6] = att2gyr
G[9:12, 6:9] = np.eye(3)
G[12:15, 9:12] = np.eye(3)
Q = G.dot(self.Rw.dot(G.T)) * dt
# 7. Covariance Update
self.P = PHI.dot(self.P.dot(PHI.T)) + Q
self.TU_COUNT += 1
if self.TU_COUNT >= 500:
# Request reinitialization after 12 seconds of no GNSS updates
self.TU_COUNT = 0
self.NAV_INIT = False
if NEW_GNSS_FLAG:
# ==== Measurement-Update ====
# 0. Get measurement and make innovations
ecef_ref = navpy.lla2ecef(self.estPOS[0], self.estPOS[1], 0)
ins_ecef = navpy.lla2ecef(self.estPOS[0], self.estPOS[1],
self.estPOS[2])
gnss_ecef = navpy.lla2ecef(gps.lat, gps.lon, gps.alt)
ins_ned = navpy.ecef2ned(ins_ecef - ecef_ref, self.estPOS[0],
self.estPOS[1], self.estPOS[2])
gnss_ned = navpy.ecef2ned(gnss_ecef - ecef_ref, self.estPOS[0],
self.estPOS[1], self.estPOS[2])
dpos = gnss_ned - ins_ned
gnss_vel = np.array([gps.vn, gps.ve, gps.vd])
dvel = gnss_vel - self.estVEL[:]
dy = np.hstack((dpos, dvel))
self.stateInnov[:] = dy
# 1. Kalman Gain
K = self.P.dot(self.H.T)
K = K.dot(la.inv(self.H.dot(self.P.dot(self.H.T)) + self.R))
# 2. Covariance Update
ImKH = np.eye(15) - K.dot(self.H)
KRKt = K.dot(self.R.dot(K.T))
self.P = ImKH.dot(self.P.dot(ImKH.T)) + KRKt
# 3. State Update
dx = K.dot(dy)
Rew, Rns = navpy.earthrad(self.estPOS[0])
self.estPOS[2] -= dx[2]
self.estPOS[0] += np.rad2deg(dx[0] / (Rew + self.estPOS[2]))
self.estPOS[1] += np.rad2deg(
dx[1] / (Rns + self.estPOS[2]) /
np.cos(np.deg2rad(self.estPOS[0])))
self.estVEL[:] += dx[3:6]
self.estATT[0], self.estATT[1:4] = navpy.qmult(
self.estATT[0], self.estATT[1:4], 1, dx[6:9])
self.estATT[0] /= np.sqrt(self.estATT[0]**2 \
+ la.norm(self.estATT[1:4])**2)
self.estATT[1:4] /= np.sqrt(self.estATT[0]**2 \
+ la.norm(self.estATT[1:4])**2)
self.estAB[:] += dx[9:12]
self.estGB[:] += dx[12:15]
if verbose:
print("t = %7.3f, GNSS Update, self.TU_COUNT = %d" %\
(gps.time, self.TU_COUNT) )
self.TU_COUNT = 0
self.last_estPOS[:] = self.estPOS[:]
self.last_estVEL[:] = self.estVEL[:]
self.last_estATT[:] = self.estATT[:]
self.last_estAB[:] = self.estAB[:]
self.last_estGB[:] = self.estGB[:]
else:
# SUBROUTINE 3: e.g. BACKUP NAVIGATION MODE
pass
self.last_imu = imu
self.last_gps = gps
result = INSGPS(self.NAV_INIT, imu.time, self.estPOS, self.estVEL,
self.estATT, self.estAB, self.estGB, self.P,
self.stateInnov)
return result
def update(self, imu, gps, verbose=True):
# Check for validity of GNSS at this time
self.tcpu = imu.time
self.tow = gps.tow
# Test 1: navValid flag and the data is indeed new (new Time of Week)
# Execute Measurement Update if this is true and Test 2 passes
NEW_GNSS_FLAG = ((gps.valid==0) & (abs(self.tow-self.last_tow) > 1e-3))
# Test 2: Check if the delta time of the Time of Week and the
# CPU time are consistent
# If this fails, re-initialize the filter. There must have been a glitch
if NEW_GNSS_FLAG:
#print self.tcpu, self.last_tcpu, self.tcpu-self.last_tcpu
#print self.tow, self.last_tow, self.tow-self.last_tow
if abs((self.tcpu-self.last_tcpu) - (self.tow-self.last_tow)) > 0.5:
self.TU_COUNT = 0
self.NAV_INIT = False
if verbose:
print("Time Sync Error -- Request reinitialization")
# Record the tow and tcpu at this new update
self.last_tow = self.tow
self.last_tcpu = self.tcpu
# Different subroutine executed in the filter
if not self.NAV_INIT:
if not self.IMU_CAL_INIT:
# SUBROUTINE: IMU CALIBRATION,
# This only happens first time round on the ground. Inflight
# reinitialization is not the same.
self.estAB[:] = [0,0,0]
if self.very_first_time:
self.very_first_time = False
self.estGB[:] = [imu.p, imu.q, imu.r]
self.phi = 0
self.theta = 0
else:
self.estGB[:] = self.last_estGB[:]*self.TU_COUNT \
+ [imu.p, imu.q, imu.r]
# Simple AHRS values
self.phi = self.phi*self.TU_COUNT \
+ np.arctan2(-imu.ay, -imu.az)
self.theta = self.theta*self.TU_COUNT \
+ np.arctan2(imu.ax, np.sqrt(imu.ay**2+imu.az**2))
self.phi /= (self.TU_COUNT + 1)
self.theta /= (self.TU_COUNT + 1)
self.estGB[:] /= (self.TU_COUNT + 1)
self.estATT[0], self.estATT[1:] = navpy.angle2quat(0, self.theta, self.phi)
"""
print("t = %7.3f, Gyro Bias Value: [%6.2f, %6.2f, %6.2f] deg/sec" %\
(imu.time, np.rad2deg(self.estGB[0]), np.rad2deg(self.estGB[1]), np.rad2deg(self.estGB[2]) ))
print("t = %7.3f, phi = %6.2f, theta = %6.2f" % (imu.time,np.rad2deg(self.phi),np.rad2deg(self.theta)) )
"""
self.TU_COUNT += 1
if self.TU_COUNT >= 35:
self.TU_COUNT = 0
self.IMU_CAL_INIT = True
if verbose:
print("t = %7.3f, IMU Calibrated!" % (imu.time))
del(self.phi)
del(self.theta)
else:
if not NEW_GNSS_FLAG:
# SUBROUTINE 1: BACKUP NAVIGATION or IN-FLIGHT INITIALIZATION
# >>>> AHRS CODE GOES HERE
self.estATT[:] = self.last_estATT[:] # This should be some backup nav mode
# <<<<
# When still there is no GNSS signal, continue propagating bias
self.estAB[:] = self.last_estAB[:]
self.estGB[:] = self.last_estGB[:]
else:
# When there is GNSS fix available, initialize all the states
# and renew covariance
self.estPOS[:] = [gps.lat, gps.lon, gps.alt]
self.estVEL[:] = [gps.vn, gps.ve, gps.vd]
self.estATT[:] = self.last_estATT[:]
#self.estATT[0], self.estATT[1:] = navpy.angle2quat(flight_data.psi[i],flight_data.theta[i],flight_data.phi[i])
self.estAB[:] = self.last_estAB[:]
self.estGB[:] = self.last_estGB[:]
self.init_covariance()
#idx_init.append(i)
self.NAV_INIT = True
if verbose:
print("t = %7.3f, Filter (Re-)initialized" % (imu.time) )
elif self.NAV_INIT:
# SUBROUTINE 2: MAIN FILTER ALGORITHM, INS + GNSS
# ==== Time-Update ====
dt = imu.time - self.last_imu.time
q0, qvec = self.last_estATT[0], self.last_estATT[1:4]
C_B2N = navpy.quat2dcm(q0,qvec).T
# 0. Data Acquisition
f_b=np.array([0.5*(self.last_imu.ax+imu.ax)-self.last_estAB[0],\
0.5*(self.last_imu.ay+imu.ay)-self.last_estAB[1],\
0.5*(self.last_imu.az+imu.az)-self.last_estAB[2]])
om_ib=np.array([0.5*(self.last_imu.p+imu.p)-self.last_estGB[0],\
0.5*(self.last_imu.q+imu.q)-self.last_estGB[1],\
0.5*(self.last_imu.r+imu.r)-self.last_estGB[2]])
# 1. Attitude Update
# --> Need to compensate for navrate and earthrate
dqvec = 0.5*om_ib*dt
self.estATT[0], self.estATT[1:4] = navpy.qmult(q0,qvec,1.0,dqvec)
self.estATT[0] /= np.sqrt(self.estATT[0]**2 \
+ la.norm(self.estATT[1:4])**2)
self.estATT[1:4] /= np.sqrt(self.estATT[0]**2 \
+ la.norm(self.estATT[1:4])**2)
# 2. Velocity Update
# --> Need to compensate for coriolis effect
g = np.array([0,0,9.81])
f0, fvec = navpy.qmult(q0,qvec,0,f_b)
f_n0,f_nvec = navpy.qmult(f0,fvec,q0,-qvec)
self.estVEL[:] = self.last_estVEL[:] + (f_nvec+g)*dt
# 3. Position Update
dPOS = navpy.llarate(self.last_estVEL[0], self.last_estVEL[1],
self.last_estVEL[2], self.last_estPOS[0],
self.last_estPOS[2])
dPOS *= dt
self.estPOS[:] = self.last_estPOS[:] + dPOS
# 4. Biases are constant
self.estAB[:] = self.last_estAB[:]
self.estGB[:] = self.last_estGB[:]
# 5. Jacobian
pos2pos = np.zeros((3,3))
pos2gs = np.eye(3)
pos2att = np.zeros((3,3))
pos2acc = np.zeros((3,3))
pos2gyr = np.zeros((3,3))
gs2pos = np.zeros((3,3))
gs2pos[2,2] = -2*9.81/wgs84.R0
gs2gs = np.zeros((3,3))
gs2att = -2*C_B2N.dot(navpy.skew(f_b))
gs2acc = -C_B2N
gs2gyr = np.zeros((3,3))
att2pos = np.zeros((3,3))
att2gs = np.zeros((3,3))
att2att = -navpy.skew(om_ib)
att2acc = np.zeros((3,3))
att2gyr = -0.5*np.eye(3)
F = np.zeros((15,15))
F[0:3,0:3] = pos2pos
F[0:3,3:6] = pos2gs
F[0:3,6:9] = pos2att
F[0:3,9:12] = pos2acc
F[0:3,12:15] = pos2gyr
F[3:6,0:3] = gs2pos
F[3:6,3:6] = gs2gs
F[3:6,6:9] = gs2att
F[3:6,9:12] = gs2acc
F[3:6,12:15] = gs2gyr
F[6:9,0:3] = att2pos
F[6:9,3:6] = att2gs
F[6:9,6:9] = att2att
F[6:9,9:12] = att2acc
F[6:9,12:15] = att2gyr
F[9:12,9:12] = -1.0/self.tau_a*np.eye(3)
F[12:15,12:15] = -1.0/self.tau_g*np.eye(3)
PHI = np.eye(15) + F*dt
# 6. Process Noise
G = np.zeros((15,12))
G[3:6,0:3] = -C_B2N
G[6:9,3:6] = att2gyr
G[9:12,6:9] = np.eye(3)
G[12:15,9:12] = np.eye(3)
Q = G.dot(self.Rw.dot(G.T))*dt
# 7. Covariance Update
self.P = PHI.dot(self.P.dot(PHI.T)) + Q
self.TU_COUNT += 1
if self.TU_COUNT >= 500:
# Request reinitialization after 12 seconds of no GNSS updates
self.TU_COUNT = 0
self.NAV_INIT = False
if NEW_GNSS_FLAG:
# ==== Measurement-Update ====
# 0. Get measurement and make innovations
ecef_ref = navpy.lla2ecef(self.estPOS[0], self.estPOS[1], 0)
ins_ecef = navpy.lla2ecef(self.estPOS[0], self.estPOS[1],
self.estPOS[2])
gnss_ecef = navpy.lla2ecef(gps.lat, gps.lon, gps.alt)
ins_ned = navpy.ecef2ned(ins_ecef-ecef_ref, self.estPOS[0],
self.estPOS[1], self.estPOS[2])
gnss_ned = navpy.ecef2ned(gnss_ecef-ecef_ref, self.estPOS[0],
self.estPOS[1], self.estPOS[2])
dpos = gnss_ned - ins_ned
gnss_vel = np.array([gps.vn, gps.ve, gps.vd])
dvel = gnss_vel - self.estVEL[:]
dy = np.hstack((dpos, dvel))
self.stateInnov[:] = dy
# 1. Kalman Gain
K = self.P.dot(self.H.T)
K = K.dot( la.inv(self.H.dot(self.P.dot(self.H.T)) + self.R) )
# 2. Covariance Update
ImKH = np.eye(15) - K.dot(self.H)
KRKt = K.dot(self.R.dot(K.T))
self.P = ImKH.dot(self.P.dot(ImKH.T)) + KRKt
# 3. State Update
dx = K.dot(dy)
Rew, Rns = navpy.earthrad(self.estPOS[0])
self.estPOS[2] -= dx[2]
self.estPOS[0] += np.rad2deg(dx[0]/(Rew + self.estPOS[2]))
self.estPOS[1] += np.rad2deg(dx[1]/(Rns + self.estPOS[2])/np.cos(np.deg2rad(self.estPOS[0])))
self.estVEL[:] += dx[3:6]
self.estATT[0], self.estATT[1:4] = navpy.qmult(self.estATT[0], self.estATT[1:4], 1, dx[6:9])
self.estATT[0] /= np.sqrt(self.estATT[0]**2 \
+ la.norm(self.estATT[1:4])**2)
self.estATT[1:4] /= np.sqrt(self.estATT[0]**2 \
+ la.norm(self.estATT[1:4])**2)
self.estAB[:] += dx[9:12]
self.estGB[:] += dx[12:15]
if verbose:
print("t = %7.3f, GNSS Update, self.TU_COUNT = %d" %\
(gps.time, self.TU_COUNT) )
self.TU_COUNT = 0
self.last_estPOS[:] = self.estPOS[:]
self.last_estVEL[:] = self.estVEL[:]
self.last_estATT[:] = self.estATT[:]
self.last_estAB[:] = self.estAB[:]
self.last_estGB[:] = self.estGB[:]
else:
# SUBROUTINE 3: e.g. BACKUP NAVIGATION MODE
pass
self.last_imu = imu
self.last_gps = gps
result = INSGPS( self.NAV_INIT, imu.time, self.estPOS, self.estVEL,
self.estATT, self.estAB, self.estGB,
self.P, self.stateInnov )
return result