Covariance analysis of spatial and temporal effects of collaborative navigation

Collaborative navigation is an emerging network technology by which a group of mobile users, each being a node of an ad hoc wireless network, attempt to improve their navigation performance. Each node in the network has a means of its own for navigation, e.g., using an integrated INS/GPS system. However, individual navigation performance is rather limited due to inertial sensor drifts when GPS signal is lost for instance. By exchanging navigation states and in particular obtaining relative measurements (range, range rate, or angular) via radio communications, the distributed nodes in the network collaborate and serve as reference beacons or anchors to one another. In this paper, we investigate spatial and temporal effects of collaborative navigation on navigation performance improvement. Indeed, the improvement in navigation performance is affected by the number of collaborating nodes and inter-node measurement quality in relation to the uncertainty of individual navigation states (spatial effect). Navigation errors after inter-node measurement exchanges become correlated, which limits further reduction in errors by subsequent measurements (temporal effect). Scenarios with simple measurement models and fusion rules are used to illustrate the spatial and temporal effects of collaborative navigation via covariance analysis and computer simulations. Understanding of such fundamental effects provides practical guidelines for optimal design of communication protocols and estimation algorithms.