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This is an extended Kalman Filter implementation in C++ for fusing lidar and radar sensor measurements. A Kalman filter can be used anywhere where you have uncertain information about some dynamic system, and you want to make an educated guess about what the system is going to do next.

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)

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

  • In essence: the position and velocity of the system in cartesian coordinates: (x, y, vx, vy)
  • NOTE: We are assuming a constant velocity model (CV) for this particular system

This extended kalman filter does just that.

Table of Contents

  • Dependencies
  • Basic Usage
  • Notes


This project was tested on a Macbook Pro with Mac0S Sierra 10.12.4 with the following:

  • cmake version 3.7.2
  • GNU Make 4.2.1
  • gcc GNU 6.3.0

Here's a sample recipe:

  • Install xcode and xcode command line tools, if you haven't yet
$ xcode-select --install
  • Install homebrew if you haven't yet
$ ruby -e "$(curl -fsSL"
  • Install make
$ brew install homebrew/dupes/make --with-default-names
  • Install cmake
$ brew install cmake
  • Check if you have the correct version or higher
$ gcc-6 --version
$ make --version
$ cmake --version

Basic Usage

  • Clone this repository
$ git clone
  • Go inside the build folder and compile:
$ cd build
$ CC=gcc-6 cmake .. && make
  • To execute inside the build folder use the following format:
$ ./ExtendedKF ../data/data-1.txt ../data/out-1.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

(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

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

(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

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
  • The measurement covariance matrices lidar_R and radar_R are hard-coded in line 16-21 of src/fusionekf.cpp. Change and recompile as necessary.
  • The initial state covariance matrix P is hard-coded in line 36-39 of src/fusionekf.cpp. Change and recompile as necessary.
  • The process 2d noise ax and ay used to update the process covariance matrix Q is hard-coded in line 17-18 of headers/fusionekf.h. Change and recompile as necessary.


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