Posterior representation with a multi-modal likelihood using the gaussian sum filter for localization in a known map

A Gaussian sum filter (GSF) with component extended Kalman filters (EKF) is proposed as an approach to localizing an autonomous vehicle in an urban environment with limited GPS availability. The GSF uses vehicle-relative vision-based measurements of known map features coupled with inertial navigation solutions to accomplish localization in the absence of GPS. The vision-based measurements have multimodal measurement likelihood functions that are well represented as weighted sums of Gaussian densities. The GSF is used because of its ability to represent the posterior distribution of the vehicle pose with better efficiency (fewer terms, less computational complexity) than a corresponding bootstrap particle filter with various numbers of particles because of the interaction with measurement hypothesis tests. The expectation-maximization algorithm is used off line to determine the representational efficiency of the particle filter in terms of an effective number of Gaussian densities. In comparison, the GSF, which uses an iterative condensation procedure after each iteration of the filter to maintain real-time capabilities, is shown through a series of in-depth empirical studies to more accurately maintain a representation of the posterior distribution than the particle filter using 37 min of recorded data from Cornell University's autonomous vehicle driven in an urban environment, including a 32 min GPS blackout. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.