On the Observability and Observability Analysis of SLAM

Simultaneous localization and mapping problem for mobile robots has received considerable attention over the last decade. The widely used formulation of the SLAM problem has been the augmented state approach in an estimation theoretic framework. Although, many related issues of SLAM such as computational complexity, loop closing and data association have received much attention, the observability issue has largely remained ignored. System observability is an important aspect in any state estimation problem. Observability analysis provides for understanding of the fundamental limits of the solution obtainable, regardless of process and measurement noises. The standard world-centric SLAM formulation is a highly non-linear system. Thus the direct use of linear observability tools and criteria in the analysis of its observability yields incorrect and inconsistent results. In this paper an appropriate method of analysis of the observability of non-linear systems is applied to investigate the properties of the standard SLAM formulation. Contrary to popular belief, it is shown through theoretical analysis that the standard 2D planar world-centric SLAM formulation involving odometry inputs for robot speed and heading, and range/bearing measurements to features in the environment is unobservable. It is also shown that for the system to be observable, it requires at least two absolutely known feature point positions, thus questioning the very meaning implied by SLAM. The analytical results thus established are verified through simulations.