Global localization in SLAM in bilinear time

In this paper we study the global localization problem in SLAM: the determination of the vehicle location in a previously mapped environment with no other prior information. We show that, using a grid sampling representation of the configuration space, it is possible to evaluate all vehicle location hypotheses in the environment (up to a certain resolution) with a computational cost that is bilinear: linear both in the number of map features and in the number of sensor measurements. We propose a pairing-driven algorithm that considers only individual measurement-feature pairings and thus, in contrast with current correspondence space algorithms, it avoids searching in the exponential correspondence space. It uses a voting strategy that accumulates evidence for each vehicle location hypothesis, assuring robustness to noise in the sensor measurements and environment models. The general nature of the proposed strategy allows the consideration of different types of features and sensor measurements. Using the popular Victoria Park dataset, we compare its performance with location-driven algorithms where the solution space is usually randomly sampled. We show that the proposed pairing-driven technique is computationally more efficient in proportion to the density of features in the environment.