def update_landmark(particle, landmark, measurement):
""" update the mean and covariance of a landmark
uses the Extended Kalman Filter (EKF) to update the existing
landmark's mean (x, y) and covariance according to the new measurement
args:
particle: the particle to update
landmark: the old_landmark to update, ((x, y), covariance)
measurement: the new measurement to `landmark`,
in the form of (distance, bearing)
returns:
None
"""
robot_x, robot_y, robot_theta = particle.robot_position
distance, bearing = measurement
landmark_pos = landmark[0]
oldCovariance = landmark[1]
landmark_x = landmark_pos[0]
landmark_y = landmark_pos[1]
x_dif = landmark_x - robot_x
y_dif = landmark_y - robot_y
# calculate the predicted measurement using landmark and robot posistions
m_r = math.sqrt(x_dif * x_dif + y_dif * y_dif)
m_phi = math.atan2(y_dif, x_dif)
predicted_measurement = (m_r, m_phi)
jacobian = utils.calculate_jacobian((robot_x, robot_y), (landmark_x, landmark_y))
Q = utils.compute_measurement_covariance(jacobian, oldCovariance, sigma_observation)
K = utils.compute_kalman_gain(jacobian, oldCovariance, Q)
new_landmark = utils.compute_new_landmark(measurement, predicted_measurement, K, landmark_pos)
new_cov = utils.compute_new_covariance(K, jacobian, oldCovariance)
# remove the landmark from the particle's list of landmarks then change landmark and add it back
particle.landmarks.remove(landmark)
landmark = (new_landmark, new_cov)
particle.landmarks.append(landmark)
def update_map(particle, measurements):
""" associates new measurements with old landmarks
given a list of measurements to landmarks, determine whether a
landmark is a new landmark or a re-observed landmark. If it is
a new one, call add_landmark(). If it is an existing landmark,
call update_landmark(), and update the weight.
traditionally done maximizing the likelihood of observation at
that particular correspondance
args:
particle: the particle to perform the data association on
measurements: a list of (distance, bearing) where a landmark was observed
returns:
index pairs? none if not matched
"""
# retrieve the newly sampled robot pos
robot_x, robot_y, robot_theta = particle.robot_position
# some measurements were [] so need to loop through and only work with the valid ones
valid_measurements = []
for m in measurements:
if len(m) > 0:
valid_measurements.append(m)
weight_as_log_sum = 0
# loop through non-empty measurements to find the best landmark and best probability
for measurement in valid_measurements:
best_landmark = None
best_prob = 0
for landmark in particle.landmarks:
landmark_pos = landmark[0]
oldCovariance = landmark[1]
landmark_x, landmark_y = landmark_pos
x_dif = landmark_x - robot_x
y_dif = landmark_y - robot_y
m_r = math.sqrt(x_dif * x_dif + y_dif * y_dif)
m_phi = math.atan2(y_dif, x_dif) - robot_theta
# calculate where the landmark should be
predicted_measurement = (m_r, m_phi)
jacobian = utils.calculate_jacobian((robot_x, robot_y), (landmark_x, landmark_y))
Q = utils.compute_measurement_covariance(jacobian, oldCovariance, sigma_observation)
likelihood = utils.calculate_likelihood_probability(measurement, predicted_measurement, Q)
if likelihood > best_prob:
best_prob = likelihood
best_landmark = landmark
# if the landmark is likely to be a new landmark then add it
if best_prob < prob_threshold:
add_landmark(particle, measurement)
weight_as_log_sum += np.log(prob_threshold)
# otherwise if it is likely the same as an observed landmark, update it
else:
update_landmark(particle, best_landmark, measurement)
weight_as_log_sum += np.log(best_prob)
# update the particles weight, will take e^weight later
particle.weight = weight_as_log_sum
