Toward AUV Survey Design for Optimal Coverage and Localization Using the Cramer Rao Lower Bound

Abstract

This paper discusses an approach to using the Cramer Rao Lower Bound (CRLB) as a trajectory design tool for autonomous underwater vehicle (AUV) visual navigation. We begin with a discussion of Fisher Information as a measure of the lower bound of uncertainty in a simultaneous localization and mapping (SLAM) pose-graph. Treating the AUV trajectory as an non-random parameter, the Fisher information is calculated from the CRLB derivation, and depends only upon path geometry and sensor noise. The effect of the trajectory design parameters are evaluated by calculating the CRLB with different parameter sets. Next, optimal survey parameters are selected to improve the overall coverage rate while maintaining an acceptable level of localization precision for a fixed number of pose samples. The utility of the CRLB as a design tool in pre-planning an AUV survey is demonstrated using a synthetic data set for a boustrophedon survey. In this demonstration, we compare the CRLB of the improved survey plan with that of an actual previous hull-inspection survey plan of the USS Saratoga. Survey optimality is evaluated by measuring the overall coverage area and CRLB localization precision for a fixed number of nodes in the graph. We also examine how to exploit prior knowledge of environmental feature distribution in the survey plan.