-
-
Notifications
You must be signed in to change notification settings - Fork 6.7k
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
New script: 'ekf_with_velocity_correction.py'
- Loading branch information
1 parent
97ad5df
commit 7f07f89
Showing
2 changed files
with
232 additions
and
41 deletions.
There are no files selected for viewing
198 changes: 198 additions & 0 deletions
198
Localization/extended_kalman_filter/ekf_with_velocity_correction.py
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,198 @@ | ||
| """ | ||
| Extended kalman filter (EKF) localization with velocity correction sample | ||
| author: Atsushi Sakai (@Atsushi_twi) | ||
| modified by: Ryohei Sasaki (@rsasaki0109) | ||
| """ | ||
| import sys | ||
| import pathlib | ||
|
|
||
| sys.path.append(str(pathlib.Path(__file__).parent.parent.parent)) | ||
|
|
||
| import math | ||
| import matplotlib.pyplot as plt | ||
| import numpy as np | ||
|
|
||
| from utils.plot import plot_covariance_ellipse | ||
|
|
||
| # Covariance for EKF simulation | ||
| Q = np.diag([ | ||
| 0.1, # variance of location on x-axis | ||
| 0.1, # variance of location on y-axis | ||
| np.deg2rad(1.0), # variance of yaw angle | ||
| 0.4, # variance of velocity | ||
| 0.1 # variance of scale factor | ||
| ]) ** 2 # predict state covariance | ||
| R = np.diag([0.1, 0.1]) ** 2 # Observation x,y position covariance | ||
|
|
||
| # Simulation parameter | ||
| INPUT_NOISE = np.diag([0.1, np.deg2rad(5.0)]) ** 2 | ||
| GPS_NOISE = np.diag([0.05, 0.05]) ** 2 | ||
|
|
||
| DT = 0.1 # time tick [s] | ||
| SIM_TIME = 50.0 # simulation time [s] | ||
|
|
||
| show_animation = True | ||
|
|
||
|
|
||
| def calc_input(): | ||
| v = 1.0 # [m/s] | ||
| yawrate = 0.1 # [rad/s] | ||
| u = np.array([[v], [yawrate]]) | ||
| return u | ||
|
|
||
|
|
||
| def observation(xTrue, xd, u): | ||
| xTrue = motion_model(xTrue, u) | ||
|
|
||
| # add noise to gps x-y | ||
| z = observation_model(xTrue) + GPS_NOISE @ np.random.randn(2, 1) | ||
|
|
||
| # add noise to input | ||
| ud = u + INPUT_NOISE @ np.random.randn(2, 1) | ||
|
|
||
| xd = motion_model(xd, ud) | ||
|
|
||
| return xTrue, z, xd, ud | ||
|
|
||
|
|
||
| def motion_model(x, u): | ||
| F = np.array([[1.0, 0, 0, 0, 0], | ||
| [0, 1.0, 0, 0, 0], | ||
| [0, 0, 1.0, 0, 0], | ||
| [0, 0, 0, 0, 0], | ||
| [0, 0, 0, 0, 1.0]]) | ||
|
|
||
| B = np.array([[DT * math.cos(x[2, 0]) * x[4, 0], 0], | ||
| [DT * math.sin(x[2, 0]) * x[4, 0], 0], | ||
| [0.0, DT], | ||
| [1.0, 0.0], | ||
| [0.0, 0.0]]) | ||
|
|
||
| x = F @ x + B @ u | ||
|
|
||
| return x | ||
|
|
||
|
|
||
| def observation_model(x): | ||
| H = np.array([ | ||
| [1, 0, 0, 0, 0], | ||
| [0, 1, 0, 0, 0] | ||
| ]) | ||
| z = H @ x | ||
|
|
||
| return z | ||
|
|
||
|
|
||
| def jacob_f(x, u): | ||
| """ | ||
| Jacobian of Motion Model | ||
| motion model | ||
| x_{t+1} = x_t+v*s*dt*cos(yaw) | ||
| y_{t+1} = y_t+v*s*dt*sin(yaw) | ||
| yaw_{t+1} = yaw_t+omega*dt | ||
| v_{t+1} = v{t} | ||
| s_{t+1} = s{t} | ||
| so | ||
| dx/dyaw = -v*dt*sin(yaw) | ||
| dx/dv = dt*cos(yaw) | ||
| dx/ds = dt*v*cos(yaw) | ||
| dy/dyaw = v*dt*cos(yaw) | ||
| dy/dv = dt*sin(yaw) | ||
| dy/ds = dt*v*sin(yaw) | ||
| """ | ||
| yaw = x[2, 0] | ||
| v = u[0, 0] | ||
| s = x[4, 0] | ||
| jF = np.array([ | ||
| [1.0, 0.0, -DT * v * s * math.sin(yaw), DT * s * math.cos(yaw), DT * v * math.cos(yaw)], | ||
| [0.0, 1.0, DT * v * s * math.cos(yaw), DT * s * math.sin(yaw), DT * v * math.sin(yaw)], | ||
| [0.0, 0.0, 1.0, 0.0, 0.0], | ||
| [0.0, 0.0, 0.0, 1.0, 0.0], | ||
| [0.0, 0.0, 0.0, 0.0, 1.0]]) | ||
| return jF | ||
|
|
||
|
|
||
| def jacob_h(): | ||
| jH = np.array([[1, 0, 0, 0, 0], | ||
| [0, 1, 0, 0, 0]]) | ||
| return jH | ||
|
|
||
|
|
||
| def ekf_estimation(xEst, PEst, z, u): | ||
| # Predict | ||
| xPred = motion_model(xEst, u) | ||
| jF = jacob_f(xEst, u) | ||
| PPred = jF @ PEst @ jF.T + Q | ||
|
|
||
| # Update | ||
| jH = jacob_h() | ||
| zPred = observation_model(xPred) | ||
| y = z - zPred | ||
| S = jH @ PPred @ jH.T + R | ||
| K = PPred @ jH.T @ np.linalg.inv(S) | ||
| xEst = xPred + K @ y | ||
| PEst = (np.eye(len(xEst)) - K @ jH) @ PPred | ||
| return xEst, PEst | ||
|
|
||
|
|
||
| def main(): | ||
| print(__file__ + " start!!") | ||
|
|
||
| time = 0.0 | ||
|
|
||
| # State Vector [x y yaw v s]' | ||
| xEst = np.zeros((5, 1)) | ||
| xEst[4, 0] = 1.0 # Initial scale factor | ||
| xTrue = np.zeros((5, 1)) | ||
| true_scale_factor = 0.9 # True scale factor | ||
| xTrue[4, 0] = true_scale_factor | ||
| PEst = np.eye(5) | ||
|
|
||
| xDR = np.zeros((5, 1)) # Dead reckoning | ||
|
|
||
| # history | ||
| hxEst = xEst | ||
| hxTrue = xTrue | ||
| hxDR = xTrue | ||
| hz = np.zeros((2, 1)) | ||
|
|
||
| while SIM_TIME >= time: | ||
| time += DT | ||
| u = calc_input() | ||
|
|
||
| xTrue, z, xDR, ud = observation(xTrue, xDR, u) | ||
|
|
||
| xEst, PEst = ekf_estimation(xEst, PEst, z, ud) | ||
|
|
||
| # store data history | ||
| hxEst = np.hstack((hxEst, xEst)) | ||
| hxDR = np.hstack((hxDR, xDR)) | ||
| hxTrue = np.hstack((hxTrue, xTrue)) | ||
| hz = np.hstack((hz, z)) | ||
| estimated_scale_factor = hxEst[4, -1] | ||
| if show_animation: | ||
| plt.cla() | ||
| # for stopping simulation with the esc key. | ||
| plt.gcf().canvas.mpl_connect('key_release_event', | ||
| lambda event: [exit(0) if event.key == 'escape' else None]) | ||
| plt.plot(hz[0, :], hz[1, :], ".g") | ||
| plt.plot(hxTrue[0, :].flatten(), | ||
| hxTrue[1, :].flatten(), "-b") | ||
| plt.plot(hxDR[0, :].flatten(), | ||
| hxDR[1, :].flatten(), "-k") | ||
| plt.plot(hxEst[0, :].flatten(), | ||
| hxEst[1, :].flatten(), "-r") | ||
| plt.text(0.45, 0.85, f"True Velocity Scale Factor: {true_scale_factor:.2f}", ha='left', va='top', transform=plt.gca().transAxes) | ||
| plt.text(0.45, 0.95, f"Estimated Velocity Scale Factor: {estimated_scale_factor:.2f}", ha='left', va='top', transform=plt.gca().transAxes) | ||
| plot_covariance_ellipse(xEst[0, 0], xEst[1, 0], PEst) | ||
| plt.axis("equal") | ||
| plt.grid(True) | ||
| plt.pause(0.001) | ||
|
|
||
|
|
||
| if __name__ == '__main__': | ||
| main() |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters