Assuming that a robot has been kidnapped and transported to a new location! Luckily it has a map of this location, a (noisy) GPS estimate of its initial location, and lots of (noisy) sensor and control data.
In this project, I implemented a 2D particle filter in C++. The particle filter was given a map and some initial localization information (analogous to what a GPS would provide).
At each time step the filter also got observation and control data.

The full demos are available at https://youtu.be/oEYFJUF8AYY

The Particle Filters flowchart:

Particle filters algorithm consists of four main steps:

1. Initialisation step: At the initialization step I estimated the car's position based on the GPS input. The subsequent steps in the process will refine this estimate to localize our vehicle. I set num_particles to 1000 (the value could be changed in line #37 in file src/particle_filter.cpp).

2. Prediction step: During the prediction step I added the control input (yaw rate & velocity) for all particles.
   The equations for updating x, y and the yaw angle when the yaw rate is not equal to zero:

3. Update step: During the update step, I updated our particle weights using map landmark positions and feature measurements.
   
   There are three sub-steps in the update step:

   • Transformation: Transforming the car’s measurements from its local car coordinate system to the map’s coordinate system.
   • Association: Matching landmark measurement to object in the map landmarks (Finding nearest neighbor)
   • Update Weights: Calculating the product of each measurement’s Multivariate-Gaussian probability density.

4. Resample step: During resampling I resampled num_particles times drawing a particle i (i is the particle index) proportional to its weight . Resampling wheel method was used at this step.

The Particle Filters pseudo code:

The directory structure of this repository is as follows:

${ROOT}
├──build.sh
├──clean.sh
├──CMakeLists.txt
├──README.md
├──run.sh
├──data/
    ├──map_data.txt
├──src/
    ├──helper_functions.h
    ├──main.cpp
    ├──map.h
    ├──particle_filter.cpp
    ├──particle_filter.h

1. Download the Term 2 Simulator here.

2. Install uWebSocketIO:
   This repository includes two files that can be used to set up and install uWebSocketIO for either Linux or Mac systems. For windows you can use either Docker, VMware, or even Windows 10 Bash on Ubuntu
   You can execute the install-ubuntu.sh to install uWebSocketIO.

3. Once the install for uWebSocketIO is complete, the main program can be built and ran by doing the following from the project top directory.

mkdir build
cd build
cmake ..
make
./particle_filter

Alternatively some scripts have been included to streamline this process, these can be leveraged by executing the following in the top directory of the project:

./clean.sh
./build.sh
./run.sh

map_data.txt includes the position of landmarks (in meters) on an arbitrary Cartesian coordinate system. Each row has three columns

• x position
• y position
• landmark id

Input values provided by the simulator to the C++ program

• Sense noisy position data from the simulator: "sense_x", "sense_y", "sense_theta"

• Get the previous velocity and yaw rate to predict the particle's transitioned state: "previous_velocity", "previous_yawrate"

• Receive noisy observation data from the simulator, in a respective list of x/y values: "sense_observations_x", "sense_observations_y"

Output values provided by the C++ program to the simulator

• Best particle values used for calculating the error evaluation: "best_particle_x", "best_particle_y", "best_particle_theta"

• Optional message data used for debugging particle's sensing and associations for respective (x,y) sensed positions ID label

  • "best_particle_associations": for respective (x,y) sensed positions

  • "best_particle_sense_x": list of sensed x positions

  • "best_particle_sense_y": list of sensed y positions

1. Accuracy: The particle filter should localize vehicle position and yaw to within the values specified in the parameters max_translation_error and max_yaw_error

2. Performance: The particle filter should complete execution within the time of 100 seconds.

Finally, the simulator output says:

Success! Your particle filter passed!