A random set formulation for Bayesian SLAM

Abstract

This paper presents an alternative formulation for the Bayesian feature-based simultaneous localisation and mapping (SLAM) problem, using a random finite set approach. For a feature based map, SLAM requires the joint estimation of the vehicle location and the map. The map itself involves the joint estimation of both the number of features and their states (typically in a 2D Euclidean space), as an a priori unknown map is completely unknown in both landmark location and number. In most feature based SLAM algorithms, so-called 'feature management' algorithms as well as data association hypotheses along with extended Kalman filters are used to generate the joint posterior estimate. This paper, however, presents a recursive filtering algorithm which jointly propagates both the estimate of the number of landmarks, their corresponding states, and the vehicle pose state, without the need for explicit feature management and data association algorithms.Using a finite set-valued joint vehicle-map state and setvalued measurements, the first order statistic of the set, called the intensity, is propagated via the probability hypothesis density (PHD) filter, from which estimates of the map and vehicle can be jointly extracted. Assuming a mildly nonlinear Gaussian system, an extended-Kalman Gaussian Mixture implementation of the recursion is then tested for both featurebased robotic mapping (known location) and SLAM. Results from the experiments show promising performance for the proposed SLAM framework, especially in environments of high spurious measurements.

Single cluster PHD SLAM: Application to autonomous underwater vehicles using stereo vision

“…The reader is referred to the work of Mullane et al [9], [10] and Lee, Clark & Salvi [12], [13] for an in-depth treatment of the PHD-based SLAM methods. Additionally, the reader is referred to the works of Mahler, B.-N. Vo, B.-T. Vo, Ristic and Clark [7], [15]- [21] for further information on PHD filters.…”

Road Intensity Based Mapping Using Radar Measurements With a Probability Hypothesis Density Filter

“…given the x and y-coordinates of the Gaussian components, and expressed in the vehicle's coordinate frame E. Furthermore, assume that the left and right edge of the road are approximately parallel and that they can be modeled using at most K polynomials (22). The polynomials only differ by the lateral distances a…”

“…are derived by using the road border model (22) and the parametersθ (1) andθ (2) , respectively. The coordinates form the mean values of the position of the Gaussian components on the road edges according to…”

“…To describe the map by a continuous surface distinguishes our method from the other mapping approaches mentioned above. An approach to make use of the PHD filter to solve the related SLAM problem is presented in [22]. In contrast to the intensity based map, the map in [22] is represented by a finite set of map features, which are extracted from the intensity density.…”

Rao-Blackwellised PHD SLAM

“…The proposed Bayesian FB-SLAM framework allows for the joint, on-line estimation of the vehicle trajectory, the feature locations and the number of features in the map. Preliminary studies using 'brute force' implementations can be found in [10], [11], [12]. In this paper, a tractable first order solution, coined the PHD-SLAM filter, is derived, which jointly propagates the posterior PHD or intensity function of the map and the posterior distribution of the trajectory of the vehicle.…”