def calculate_jacobian(self, x_state):
"""
Todo:
* Calculate a Jacobian here.
"""
Hj = Matrix([[]])
Hj.zero(3, 4)
#recover state parameters
px = x_state.value[0][0]
py = x_state.value[1][0]
vx = x_state.value[2][0]
vy = x_state.value[3][0]
#pre-compute a set of terms to avoid repeated calculation
c1 = px * px + py * py
c2 = sqrt(c1)
c3 = (c1 * c2)
#check division by zero
if (abs(c1) < 0.0001):
print("CalculateJacobian () - Error - Division by Zero")
return Hj
#compute the Jacobian matrix
Hj = Matrix([[(px / c2), (py / c2), 0, 0],
[-(py / c1), (px / c1), 0, 0],
[
py * (vx * py - vy * px) / c3,
px * (px * vy - py * vx) / c3, px / c2, py / c2
]])
return Hj
def calculate_rmse(self, estimations, ground_truth):
"""
Todo:
* Calculate the RMSE here.
"""
rmse = Matrix([[]])
rmse.zero(4, 1)
# check the validity of the following inputs:
# * the estimation vector size should not be zero
# * the estimation vector size should equal ground truth vector size
if len(estimations) != len(ground_truth) or not estimations:
print("Invalid estimation or ground_truth data")
return rmse
#accumulate squared residuals
for i in range(len(estimations)):
residual = estimations[i] - ground_truth[i]
#coefficient-wise multiplication
residual = residual.cwise_product(residual)
rmse += residual
#calculate the mean
rmse.value = [[i[0] / len(estimations)] for i in rmse.value]
#calculate the squared root
rmse.value = [[sqrt(i[0])] for i in rmse.value]
#return the result
return rmse
def test_calculate_jacobian_returns0_if_px_and_py_is0(self):
state = Matrix([[]])
state.zero(4, 1)
expected_Hj = Matrix([[]])
expected_Hj.zero(3, 4)
Hj = self._tools.calculate_jacobian(state)
self.assertEqual(Hj.value, expected_Hj.value,
"Jacobian should be 0 when px and py is 0.")
def test_calculate_rmse_returns0_if_estimations_size_is0(self):
estimations = []
ground_truth = []
expected_rmse = Matrix([[]])
expected_rmse.zero(4, 1)
rmse = self._tools.calculate_rmse(estimations, ground_truth)
self.assertEqual(rmse.value, expected_rmse.value,
"RMSE should be 0 when estimation size is 0.")
def test_calculate_rmse_returns0_if_estimations_size_differ(self):
estimations = [Matrix([[1], [1], [0.2], [0.1]])]
ground_truth = [
Matrix([[1.1], [1.1], [0.3], [0.2]]),
Matrix([[2.1], [2.1], [0.4], [0.3]])
]
expected_rmse = Matrix([[]])
expected_rmse.zero(4, 1)
rmse = self._tools.calculate_rmse(estimations, ground_truth)
self.assertEqual(rmse.value, expected_rmse.value,
"RMSE should be 0 when estimation size differs.")
def __init__(self, ekf, tools):
"""Constructor"""
#: obj`KalmanFilter`: Kalman Filter update and prediction math lives in here.
self._ekf = ekf
#: obj`Tools`: tool object used to compute Jacobian and RMSE
self._tools = tools
#: bool: check whether the tracking toolbox was initialized or not (first measurement)
self._is_initialized = False
#: long: previous timestamp
self._previous_timestamp = 0
#initializing matrices
self._R_laser = Matrix([[]])
self._R_radar = Matrix([[]])
self._H_laser_ = Matrix([[]])
self._Hj = Matrix([[]])
self._Hj.zero(3, 4)
#measurement covariance matrix - laser
self._R_laser = Matrix([[0.0225, 0], [0, 0.0225]])
#measurement covariance matrix - radar
self._R_radar = Matrix([[0.09, 0, 0], [0, 0.0009, 0], [0, 0, 0.09]])
"""
Todo:
* Finish initializing the FusionEKF.
* Set the process and measurement noises
"""
#initialize variables and matrices (x, F, H_laser, H_jacobian, P, etc.)
#create a 4D state vector, we don't know yet the values of the x state
x_in = Matrix([[]])
x_in.zero(4, 1)
#state covariance matrix P
P_in = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1000, 0],
[0, 0, 0, 1000]])
#measurement matrix
self._H_laser = Matrix([[1, 0, 0, 0],
[0, 1, 0, 0]]) # From Lesson 5 Section 10.
#the initial transition matrix F_
F_in = Matrix([[1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0], [0, 0, 0, 1]])
Q_in = Matrix([[]])
Q_in.zero(4, 4)
self._ekf.init(x_in, P_in, F_in, self._H_laser, self._R_laser, Q_in)
class FusionEKF:
def __init__(self, ekf, tools):
"""Constructor"""
#: obj`KalmanFilter`: Kalman Filter update and prediction math lives in here.
self._ekf = ekf
#: obj`Tools`: tool object used to compute Jacobian and RMSE
self._tools = tools
#: bool: check whether the tracking toolbox was initialized or not (first measurement)
self._is_initialized = False
#: long: previous timestamp
self._previous_timestamp = 0
#initializing matrices
self._R_laser = Matrix([[]])
self._R_radar = Matrix([[]])
self._H_laser_ = Matrix([[]])
self._Hj = Matrix([[]])
self._Hj.zero(3, 4)
#measurement covariance matrix - laser
self._R_laser = Matrix([[0.0225, 0], [0, 0.0225]])
#measurement covariance matrix - radar
self._R_radar = Matrix([[0.09, 0, 0], [0, 0.0009, 0], [0, 0, 0.09]])
"""
Todo:
* Finish initializing the FusionEKF.
* Set the process and measurement noises
"""
#initialize variables and matrices (x, F, H_laser, H_jacobian, P, etc.)
#create a 4D state vector, we don't know yet the values of the x state
x_in = Matrix([[]])
x_in.zero(4, 1)
#state covariance matrix P
P_in = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1000, 0],
[0, 0, 0, 1000]])
#measurement matrix
self._H_laser = Matrix([[1, 0, 0, 0],
[0, 1, 0, 0]]) # From Lesson 5 Section 10.
#the initial transition matrix F_
F_in = Matrix([[1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0], [0, 0, 0, 1]])
Q_in = Matrix([[]])
Q_in.zero(4, 4)
self._ekf.init(x_in, P_in, F_in, self._H_laser, self._R_laser, Q_in)
def process_measurement(self, measurement_pack):
"""Run the whole flow of the Kalman Filter from here."""
"""
Initialization
"""
if not self._is_initialized:
"""
Todo:
* Initialize the state ekf_.x_ with the first measurement.
* Create the covariance matrix.
You'll need to convert radar from polar to cartesian coordinates.
"""
# first measurement
print("EKF: ")
self._ekf._x = Matrix([[1], [1], [1], [1]])
#initialize the Kalman filter position vector with the first sensor measurements
if measurement_pack._sensor_type == MeasurementPackage.SensorType.RADAR:
"""
Convert radar from polar to cartesian coordinates and initialize state.
"""
ro = measurement_pack._raw_measurements.value[0][0]
theta = measurement_pack._raw_measurements.value[1][0]
self._ekf._x = Matrix([[ro * cos(theta)], [ro * sin(theta)],
[0], [0]])
elif measurement_pack._sensor_type == MeasurementPackage.SensorType.LASER:
"""
Initialize state.
"""
#set the state with the initial location and zero velocity
self._ekf._x = Matrix([
measurement_pack._raw_measurements.value[0],
measurement_pack._raw_measurements.value[1], [0], [0]
])
self._previous_timestamp = measurement_pack._timestamp
# done initializing, no need to predict or update
self._is_initialized = True
return
"""
Prediction
"""
"""
Todo:
* Update the state transition matrix F according to the new elapsed time.
Time is measured in seconds.
Todo:
* Update the process noise covariance matrix.
Use noise_ax = 9 and noise_ay = 9 for your Q matrix.
"""
# modify the F and Q matrices prior to the prediction step based on the
# elapsed time between measurements
# compute the time elapsed between the current and previous measurements
dt = (measurement_pack._timestamp -
self._previous_timestamp) / 1000000.0 #dt - expressed in seconds
self._previous_timestamp = measurement_pack._timestamp
dt_2 = dt * dt
dt_3 = dt_2 * dt
dt_4 = dt_3 * dt
#Modify the F matrix so that the time is integrated
#Lesson 5 Section 8
self._ekf._F.value[0][2] = dt
self._ekf._F.value[1][3] = dt
#acceleration noise components
noise_ax = 9
noise_ay = 9
#set the process covariance matrix Q
#Lesson 5 Section 9
self._ekf._Q = Matrix(
[[dt_4 / 4 * noise_ax, 0, dt_3 / 2 * noise_ax, 0],
[0, dt_4 / 4 * noise_ay, 0, dt_3 / 2 * noise_ay],
[dt_3 / 2 * noise_ax, 0, dt_2 * noise_ax, 0],
[0, dt_3 / 2 * noise_ay, 0, dt_2 * noise_ay]])
self._ekf.predict()
"""
Update
"""
"""
Todo:
* Use the sensor type to perform the update step.
* Update the state and covariance matrices.
"""
if measurement_pack._sensor_type == MeasurementPackage.SensorType.RADAR:
# Radar updates
#set ekf_.H_ by setting to Hj which is the calculated the jacobian
#set ekf_.R_ by just using R_radar_
self._Hj = self._tools.calculate_jacobian(self._ekf._x)
self._ekf._H = self._Hj
self._ekf._R = self._R_radar
self._ekf.update_ekf(measurement_pack._raw_measurements)
else:
# Laser updates
#set ekf_.H_ by just using H_laser_
#set ekf_.R_ by just using R_laser_
self._ekf._H = self._H_laser
self._ekf._R = self._R_laser
self._ekf.update(measurement_pack._raw_measurements)
# print the output
print("x_ = ", self._ekf._x)
print("P_ = ", self._ekf._P)