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Assignment 1 - Part 2: Particle Filter Localisation
Introduction
Almost all of the probabilistic Localisation algorithms are based on the Bayes filter. In
Tutorial 1-1 we solved the localisation problem in a 1-dimensional (discrete) environment
using the discrete Bayes filter. In reality we need to localise our robot in a 2D or 3D
continuous space. Unfortunately in these cases we are not able to implement the exact
Bayes filter (e.g., due to the non-linearity of our measurement functions). Therefore we have
to approximate the Bayes filter.
Table 1: Properties of localisation algorithms
State Space Belief Final Solution
Histogram Filter discrete multi-modal approximate
Extended Kalman Filter continuous uni-modal approximate
Particle Filter discrete? multi-modal approximate
In Table 1 we have listed a number of popular localisation algorithms. For example in
Histogram filter we discretize the space; i.e., we approximate the continuous space by a set
of discrete “cells” (similar to what you did in Tutorial 1-1). In Extended Kalman filter
(EKF) we linearise the non-linear models; i.e., we approximate the non-linear models with
linear models.
In Particle filter localisation (also known as Monte Carlo Localization, or MCL) we use
random samples (also called particles) to represent our belief about the robot pose (i.e.,
position and orientation). Each particle is a potential robot pose (a guess); e.g., in 2D
environments, each particle has three fields: x, y (position) and θ (orientation).
In this assignment you implement 2D MCL, the most successful localization algorithm!