The Effects of Partial Observability When Building Fully Correlated Maps

This paper presents an analysis of the fully correlated approach to the simultaneous localization and map building (SLAM) problem from a control systems theory point of view, both for linear and nonlinear vehicle models. We show how partial observability hinders full reconstructibility of the state space, making the final map estimate dependent on the initial observations. Nevertheless, marginal filter stability guarantees convergence of the state error covariance to a positive semidefinite covariance matrix. By characterizing the form of the total Fisher information, we are able to determine the unobservable state space directions. Moreover, we give a closed-form expression that links the amount of reconstruction error to the number of landmarks used. The analysis allows the formulation of measurement models that make SLAM observable.