def maha_test(self, x, P, kind, z, R, extra_args=[], maha_thresh=0.95):
# init vars
z = z.reshape((-1, 1))
h = np.zeros(z.shape, dtype=np.float64)
H = np.zeros((z.shape[0], self.dim_x), dtype=np.float64)
# C functions
self.hs[kind](x, extra_args, h)
self.Hs[kind](x, extra_args, H)
# y is the "loss"
y = z - h
# if using eskf
H_mod = np.zeros((x.shape[0], P.shape[0]), dtype=np.float64)
self.H_mod(x, H_mod)
H = H.dot(H_mod)
a = np.linalg.inv(H.dot(P).dot(H.T) + R)
maha_dist = y.T.dot(a.dot(y))
if maha_dist > chi2_ppf(maha_thresh, y.shape[0]):
return False
else:
return True
def _update_python(self, x, P, kind, z, R, extra_args=[]):
# init vars
z = z.reshape((-1, 1))
h = np.zeros(z.shape, dtype=np.float64)
H = np.zeros((z.shape[0], self.dim_x), dtype=np.float64)
# C functions
self.hs[kind](x, extra_args, h)
self.Hs[kind](x, extra_args, H)
# y is the "loss"
y = z - h
# *** same above this line ***
if self.msckf and kind in self.Hes:
# Do some algebraic magic to decorrelate
He = np.zeros((z.shape[0], len(extra_args)), dtype=np.float64)
self.Hes[kind](x, extra_args, He)
# TODO: Don't call a function here, do projection locally
A = null(He.T)
y = A.T.dot(y)
H = A.T.dot(H)
R = A.T.dot(R.dot(A))
# TODO If nullspace isn't the dimension we want
if A.shape[1] + He.shape[1] != A.shape[0]:
print(
'Warning: null space projection failed, measurement ignored'
)
return x, P, np.zeros(A.shape[0] - He.shape[1])
# if using eskf
H_mod = np.zeros((x.shape[0], P.shape[0]), dtype=np.float64)
self.H_mod(x, H_mod)
H = H.dot(H_mod)
# Do mahalobis distance test
# currently just runs on msckf observations
# could run on anything if needed
if self.msckf and kind in self.maha_test_kinds:
a = np.linalg.inv(H.dot(P).dot(H.T) + R)
maha_dist = y.T.dot(a.dot(y))
if maha_dist > chi2_ppf(0.95, y.shape[0]):
R = 10e16 * R
# *** same below this line ***
# Outlier resilient weighting as described in:
# "A Kalman Filter for Robust Outlier Detection - Jo-Anne Ting, ..."
weight = 1 # (1.5)/(1 + np.sum(y**2)/np.sum(R))
S = dot(dot(H, P), H.T) + R / weight
K = solve(S, dot(H, P.T)).T
I_KH = np.eye(P.shape[0]) - dot(K, H)
# update actual state
delta_x = dot(K, y)
P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
# inject observed error into state
x_new = np.zeros(x.shape, dtype=np.float64)
self.err_function(x, delta_x, x_new)
return x_new, P, y.flatten()
def gen_code(name,
f_sym,
dt_sym,
x_sym,
obs_eqs,
dim_x,
dim_err,
eskf_params=None,
msckf_params=None,
maha_test_kinds=[]):
# optional state transition matrix, H modifier
# and err_function if an error-state kalman filter (ESKF)
# is desired. Best described in "Quaternion kinematics
# for the error-state Kalman filter" by Joan Sola
if eskf_params:
err_eqs = eskf_params[0]
inv_err_eqs = eskf_params[1]
H_mod_sym = eskf_params[2]
f_err_sym = eskf_params[3]
x_err_sym = eskf_params[4]
else:
nom_x = sp.MatrixSymbol('nom_x', dim_x, 1)
true_x = sp.MatrixSymbol('true_x', dim_x, 1)
delta_x = sp.MatrixSymbol('delta_x', dim_x, 1)
err_function_sym = sp.Matrix(nom_x + delta_x)
inv_err_function_sym = sp.Matrix(true_x - nom_x)
err_eqs = [err_function_sym, nom_x, delta_x]
inv_err_eqs = [inv_err_function_sym, nom_x, true_x]
H_mod_sym = sp.Matrix(np.eye(dim_x))
f_err_sym = f_sym
x_err_sym = x_sym
# This configures the multi-state augmentation
# needed for EKF-SLAM with MSCKF (Mourikis et al 2007)
if msckf_params:
msckf = True
dim_main = msckf_params[0] # size of the main state
dim_augment = msckf_params[1] # size of one augment state chunk
dim_main_err = msckf_params[2]
dim_augment_err = msckf_params[3]
N = msckf_params[4]
feature_track_kinds = msckf_params[5]
assert dim_main + dim_augment * N == dim_x
assert dim_main_err + dim_augment_err * N == dim_err
else:
msckf = False
dim_main = dim_x
dim_augment = 0
dim_main_err = dim_err
dim_augment_err = 0
N = 0
# linearize with jacobians
F_sym = f_err_sym.jacobian(x_err_sym)
if eskf_params:
for sym in x_err_sym:
F_sym = F_sym.subs(sym, 0)
assert dt_sym in F_sym.free_symbols
for i in range(len(obs_eqs)):
obs_eqs[i].append(obs_eqs[i][0].jacobian(x_sym))
if msckf and obs_eqs[i][1] in feature_track_kinds:
obs_eqs[i].append(obs_eqs[i][0].jacobian(obs_eqs[i][2]))
else:
obs_eqs[i].append(None)
# collect sympy functions
sympy_functions = []
# error functions
sympy_functions.append(('err_fun', err_eqs[0], [err_eqs[1], err_eqs[2]]))
sympy_functions.append(
('inv_err_fun', inv_err_eqs[0], [inv_err_eqs[1], inv_err_eqs[2]]))
# H modifier for ESKF updates
sympy_functions.append(('H_mod_fun', H_mod_sym, [x_sym]))
# state propagation function
sympy_functions.append(('f_fun', f_sym, [x_sym, dt_sym]))
sympy_functions.append(('F_fun', F_sym, [x_sym, dt_sym]))
# observation functions
for h_sym, kind, ea_sym, H_sym, He_sym in obs_eqs:
sympy_functions.append(('h_%d' % kind, h_sym, [x_sym, ea_sym]))
sympy_functions.append(('H_%d' % kind, H_sym, [x_sym, ea_sym]))
if msckf and kind in feature_track_kinds:
sympy_functions.append(('He_%d' % kind, He_sym, [x_sym, ea_sym]))
# Generate and wrap all th c code
header, code = sympy_into_c(sympy_functions)
extra_header = "#define DIM %d\n" % dim_x
extra_header += "#define EDIM %d\n" % dim_err
extra_header += "#define MEDIM %d\n" % dim_main_err
extra_header += "typedef void (*Hfun)(double *, double *, double *);\n"
extra_header += "\nvoid predict(double *x, double *P, double *Q, double dt);"
extra_post = ""
for h_sym, kind, ea_sym, H_sym, He_sym in obs_eqs:
if msckf and kind in feature_track_kinds:
He_str = 'He_%d' % kind
# ea_dim = ea_sym.shape[0]
else:
He_str = 'NULL'
# ea_dim = 1 # not really dim of ea but makes c function work
maha_thresh = chi2_ppf(0.95, int(
h_sym.shape[0])) # mahalanobis distance for outlier detection
maha_test = kind in maha_test_kinds
extra_post += """
void update_%d(double *in_x, double *in_P, double *in_z, double *in_R, double *in_ea) {
update<%d,%d,%d>(in_x, in_P, h_%d, H_%d, %s, in_z, in_R, in_ea, MAHA_THRESH_%d);
}
""" % (kind, h_sym.shape[0], 3, maha_test, kind, kind, He_str, kind)
extra_header += "\nconst static double MAHA_THRESH_%d = %f;" % (
kind, maha_thresh)
extra_header += "\nvoid update_%d(double *, double *, double *, double *, double *);" % kind
code += '\nextern "C"{\n' + extra_header + "\n}\n"
code += "\n" + open(os.path.join(TEMPLATE_DIR, "ekf_c.c")).read()
code += '\nextern "C"{\n' + extra_post + "\n}\n"
header += "\n" + extra_header
write_code(name, code, header)