An RFS ‘Brute Force’ Formulation for Bayesian SLAM

Introduction

The feature-based (FB) SLAM scenario is a vehicle moving through an environment represented by an unknown number of features. The classical problem definition is one of “a state estimation problem involving a variable number of dimensions” [28]. The SLAM problem requires a robot to navigate in an unknown environment and use its suite of on board sensors to both construct a map and localise itself within that map without the use of any a priori information. Often, in the planar navigation context, a vehicle is assumed to acquire measurements of its surrounding environment using on board range-bearing measuring sensors. This requires joint estimates of the three dimensional robot pose (Cartesian x and y coordinates, as well as the heading angle θ), the number of features in the map as well as their two dimensional Euclidean coordinates. For a real world application, this should be performed incrementally as the robot manoeuvres about the environment. As the robot motion introduces error, coupled with a feature sensing error, both localisation and mapping must be performed simultaneously [8]. As mentioned in Chapter 2, for any given sensor, an FB decision is subject to detection and data association uncertainty, spurious measurements and measurement noise, as well as bias.