Lidar & Radar Fusion with EKF and UKF

• EKF: Multi-Sensor Fusion: LiDAR and Radar fusion based on EKF
• UKF: Multi-Sensor Fusion: LiDAR and Radar fusion based on UKF

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[TOC]

Introduction

This is an Kalman Filter (EKF & UKF) implementation in C++ for fusing lidar and radar sensor measurements.

In this case, we have two 'noisy' sensors:

• A lidar sensor that measures our position in cartesian-coordinates (x, y)
• A radar sensor that measures our position and relative velocity (the velocity within line of sight) in polar coordinates (rho, phi, drho)

EKF

We want to predict our position, and how fast we are going in what direction at any point in time:

• the position and velocity of the system in cartesian coordinates: (x, y, vx, vy)

• We are assuming a constant velocity model (CV) for this particular system

Note:

• The measurement covariance matrices lidar_R and radar_R are hard-coded in src/fusionekf.cpp.
• The initial state covariance matrix P is hard-coded in src/fusionekf.cpp.
• The process 2d noise ax and ay used to update the process covariance matrix Q is hard-coded in include/fusionekf.h.

UKF

• In essence we want to get: the position of the system in cartesian coordinates, the velocity magnitude, the yaw angle in radians, and yaw rate in radians per second (x, y, v, yaw, yawrate)

• We are assuming a constant turn/yaw rate and velocity magnitude model (CRTV) for this particular system

• Compared with an EKF with a constant velocity model, RMSE should be lower for the UKF especially for velocity. The CTRV model is more precise than a constant velocity model. And UKF is also known for handling non-linear equations better than EKF.

Build

make build & cd build
cmake .. & make -j3

Run

EKF

• run with datafile (data-1, data-2)

  ./extended_kf ../data/data-1.txt output.txt

• Please use the following format for your input file

  L(for lidar) m_x m_y t r_x r_y r_vx r_vy
  R(for radar) m_rho m_phi m_drho t r_px r_py r_vx r_vy
  
  Where:
  (m_x, m_y) - measurements by the lidar
  (m_rho, m_phi, m_drho) - measurements by the radar in polar coordinates
  (t) - timestamp in unix/epoch time the measurements were taken
  (r_x, r_y, r_vx, r_vy) - the real ground truth state of the system
  
  Example:
  R 8.60363 0.0290616 -2.99903  1477010443399637  8.6 0.25  -3.00029  0
  L 8.45  0.25  1477010443349642  8.45  0.25  -3.00027  0
  

• The program outputs the predictions in the following format on the output file path you specified

  p_x p_y p_vx p_vy m_x m_y r_px r_py r_vx r_vy
  
  Where:
  (p_x, p_y, p_vx, p_vy) - the predicted state of the system by FusionEKF
  (m_x, m_y) - the position value as measured by the sensor converted to cartesian coordinates
  (r_x, r_y, r_vx, r_vy) - the real ground truth state of the system
  
  Example:
  4.53271 0.279 -0.842172 53.1339 4.29136 0.215312  2.28434 0.226323
  43.2222 2.65959 0.931181  23.2469 4.29136 0.215312  2.28434 0.226323
  

• draw the position data from output.txt

  • input data-1.txt

    

  • input data-2.txt

    

UKF

• run with datafile (data-3)

  ./unscented_kf ../data/data-3.txt out-3.txt

• Please use the following format for your input file

  L(for lidar) m_x m_y t r_x r_y r_vx r_vy, r_yaw, r_yawrate
  R(for radar) m_rho m_phi m_drho t r_px r_py r_vx r_vy, r_yaw, r_yawrate
  
  Where:
  (m_x, m_y) - measurements by the lidar
  (m_rho, m_phi, m_drho) - measurements by the radar in polar coordinates
  (t) - timestamp in unix/epoch time the measurements were taken
  (r_x, r_y, r_vx, r_vy, r_yaw, r_yawrate) - the real ground truth state of the system
  
  Example:
  L 3.122427e-01  5.803398e-01  1477010443000000  6.000000e-01  6.000000e-01  5.199937e+00  0 0 6.911322e-03
  R 1.014892e+00  5.543292e-01  4.892807e+00  1477010443050000  8.599968e-01  6.000449e-01  5.199747e+00  1.796856e-03  3.455661e-04  1.382155e-02
  

• The program outputs the predictions in the following format on the output file path you specified

  time_stamp  px_state  py_state  v_state yaw_angle_state yaw_rate_state  sensor_type NIS px_measured py_measured px_ground_truth py_ground_truth vx_ground_truth vy_ground_truth
  1477010443000000  0.312243  0.58034 0 0 0 lidar 2.32384e-319  0.312243  0.58034 0.6 0.6 0 0
  1477010443050000  0.735335  0.629467  7.20389 9.78669e-18 5.42626e-17 radar 74.6701 0.862916  0.534212  0.859997  0.600045  0.000345533 4.77611e-06
  ...
  

Ref

EKF

• based on mithi/fusion-ekf, and its related python code is mithi/fusion-ekf-python

  • Sensor Fusion and Object Tracking using an Extended Kalman Filter Algorithm — Part 1

  • Sensor Fusion and Object Tracking using an Extended Kalman Filter Algorithm — Part 2

• udacity/CarND-Extended-Kalman-Filter-Project: Self-Driving Car Nanodegree Program Starter Code for the Extended Kalman Filter Project

• Sensor Fusion (towardsautonomy)

UKF

• mithi/fusion-ukf
• udacity/CarND-Unscented-Kalman-Filter-Project: Unscented Kalman Filter Project Starter Code
• udacity/CarND-Catch-Run-Away-Car-UKF (Deprecated): Run Away Robot with Unscented Kalman Filter Bonus Challenge Starter Code