Filter, i would like to understand it as estimator. It is also comprised of posterior sense and motion prediction same as histogram and Kalman filters.

the difference is that particle filter starts with thousands of uniform particle guesses, and then after round of sensing/motion, reduced to an accurate particle/location. And there is resampling step, in codes as follows to ensure the particles with higher weight have more probabilities being chosen.

A particle filter can be thought of as an estimator, encompassing two principal stages: posterior estimation and motion prediction, similar to histogram and Kalman filters.

Distinctively, a particle filter initiates with a broad set of uniformly distributed particle hypotheses. These are progressively refined through successive cycles of sensing and motion updates, leading the particles to converge on the most probable state or location.

A crucial aspect of this procedure is the resampling step. As demonstrated in the implementation, this step ensures that particles with higher weights, representing a higher likelihood of accuracy, are selected with a higher probability for the next round of estimation.

def resample(particles, weights):

    # Number of particles

    N = len(particles)

    # Resampling wheel algorithm

    new_particles = []

    index = int(np.random.random() * N)

    beta = 0.0

    mw = max(weights)

    for _ in range(N):

        beta += np.random.random() * 2.0 * mw

        while beta > weights[index]:

            beta -= weights[index]

            index = (index + 1) % N

        new_particles.append(particles[index])

    return new_particles

  

# Let's test this with a simple example

particles = ['p1', 'p2', 'p3', 'p4', 'p5']  # replace with your actual particles

weights = [0.1, 0.2, 0.4, 0.15, 0.15]  # replace with your actual weights

  

resampled_particles = resample(particles, weights)

print(resampled_particles)