void ParticleFilter::init(double x, double y, double theta, double std[]) {

  // Set the number of particles
  num_particles = 100;

  // Declare the random generator
  default_random_engine gen;

  // Extract the standard deviations for x, y, and theta
  double std_x = std[0];
  double std_y = std[1];
  double std_theta = std[2];

  // Creates normal distributions for x, y and theta.
  normal_distribution<double> dist_x(x, std_x);
  normal_distribution<double> dist_y(y, std_y);
  normal_distribution<double> dist_theta(theta, std_theta);

  // Create the vector to contain the `num_particles` particles
  particles = vector<Particle>(num_particles);

  // Create the vector to contain the weight for each particle
  weights = vector<double>(num_particles);

  // Loop over the particle vector and initialize each particle with the initial (x,y,theta) position
  // passed in the arguments with added Gaussian noise and weight 1
  for (int i = 0; i < num_particles; i++) {

    particles[i].id = i; // Set this particle's ID
    particles[i].x = dist_x(gen); // Generate a random value from `dist_x` to set as this particle's x position
    particles[i].y = dist_y(gen); // Generate a random value from `dist_y` to set as this particle's y position
    particles[i].theta = dist_theta(gen); // Generate a random value from `dist_theta` to set as this particle's orientation theta
    particles[i].weight = 1.0; // Set the initial weight for all particles to 1

  }

  is_initialized = true;

}