On the observability of path constrained vehicle localisation

Reliable and robust localisation is an important prerequisite in the synthesis of driver assistance systems and intelligent vehicles deployable in complex environments. In the past many strategies have been proposed and implemented for vehicle localisation. In particular, estimation theoretic techniques aided by a priori information constitute a useful class of localisation algorithms. This a priori information used is usually feature maps and/or road maps. However, what is often neglected is rigorous theoretical investigations and treatment of issues of observability of the formulations and their implications. Observability is an important aspect of any state estimation problem as this determines the existence and the nature of solution. In the case of vehicle localisation, analysis of observability is not straightforward due to the non-linear and coupled nature of the problem. The few published work uses linearised models and applies standard linear observability analysis. The results hence derived are incomplete and inconsistent at best. In this paper, an appropriate method of observability analysis is used to elicit observability properties of vehicle localisation problem and demonstrates its application to path constrained vehicle localisation. The theoretical results derived are validated through simulations. Further the results of theoretical analysis are shown to provide insights into the synthesis of more theoretically correct and accurate vehicle localisation algorithms and their eventual realisation