Extended Kalman Filter Project

Disclaimer: The code in this repository is derived from the Extended Kalman Filter project of Udacity. If you like it feel free to support it in the above link!

Description

We implement an Extended Kalman Filter (EKF) to estimate the state of a moving car given noisy LiDAR and RADAR measurements. The equations of motions are assumed as follows:

px[k+1] = px[k+1] + vx[k] * dt + wpx[k]
py[k+1] = py[k+1] + vy[k] * dt + wpy[k]
vx[k+1] = vx[k] + wvx[k]
vy[k+1] = vy[k] + wvy[k]

i.e., a linear system, where px and py denote the position of the car along the x and y axes, and vx and vy the corresponding velocities. The quantity w is assumed to be Gaussian white noise. The fusion of the two types of measurements is performed as follows:

• when the incoming measurement is from the LiDAR, its output is y[k] = (px[k], py[k]), which is a linear function of the state and, hence, we use a regular Kalman Filter prediction and update step.
• when the incoming measurement is from the RADAR, its output is y[k] = (sqrt(px[k]^2+py[k]^2), atan(py[k]/px[k]), (px[k]vx[k]+py[k]vy[y])/sqrt(px[k]^2+py[k]^2)), which is a non-linear function of the state and, hence, we use an Extended Kalman Filter prediction and update step.

Dependencies

1. Udacity's Term 2 Simulator.
2. uWebSocketIO, which can be installed using the provided bash scripts by Udacity for either Linux or Mac systems.
3. Eigen template library for linear algebra.
4. cmake >= 3.5
5. make >= 4.1 (Linux, Mac)
6. gcc/g++ >= 5.4

Build and run

Once the dependencies are installed, the main program is built and run as follows:

mkdir build
cd build
cmake ..
make
./ExtendedKF

If successful the output should be:

Listening to port 4567
Connected!!!

Then, one just opens the simulator and executes a test run.

For more details on how main.cpp uses uWebSocketIO to communicate with the simulator is as follows see the original Udacity repository.