On the nonlinear observability and the information form of the SLAM problem

The theory of nonlinear observability is an important tool available for the assessment of highly nonlinear estimation problems such as simultaneous localization and mapping (SLAM). It is shown that all the estimated landmarks must be observed and at least two a priori known landmarks be observed for the nonlinear observability of single vehicle SLAM when estimating any number of unknown landmark locations. The relationship between the information form of SLAM and the nonlinear observability is established. It is shown that when the nonlinear observability conditions are satisfied the single vehicle SLAM problem can in theory be initialized with infinitely large initial uncertainties. Simulations and experiments are also provided to substantiate the theoretical results.