Split Covariance Intersection with Correlated Components for Distributed Estimation

This paper introduces a new conservative fusion method to exploit the correlated components within the estimation errors. Fusion is the process of combining multiple estimates of a given state to produce a new estimate with a smaller MSE. To perform the optimal linear fusion, the (centralized) covariance associated with the errors of all estimates is required. If it is partially unknown, the optimal fusion cannot be computed. Instead, a solution is to perform a conservative fusion. A conservative fusion provides a gain and a bound on the resulting MSE matrix which guarantees that the error is not underestimated. A well-known conservative fusion is the Covariance Intersection fusion. It has been modified to exploit the uncorrelated components within the errors. In this paper, it is further extended to exploit the correlated components as well. The resulting fusion is integrated into standard distributed algorithms where it allows exploiting the process noise observed by all agents. The improvement is confirmed by simulations.

Pseudorange Rigidity and Solvability of Cooperative GNSS Positioning

Global Navigation Satellite Systems (GNSS) are a widely used technology for positioning and navigation. GNSS positioning relies on pseudorange measurements from satellites to receivers. A pseudorange is the apparent distance between two agents deduced from the time-of-flight of a signal sent from one agent to the other. Because of the lack of synchronization between the agents' clocks, it is a biased version of their distance. This paper introduces a new rigidity theory adapted to pseudorange measurements. The peculiarity of pseudoranges is that they are asymmetrical measurements. Therefore, unlike other usual rigidities, the graphs of pseudorange frameworks are directed. In this paper, pseudorange rigidity is proved to be a generic property of the underlying undirected graph of constraints. The main result is a characterization of rigid pseudorange graphs as combinations of rigid distance graphs and connected graphs. This new theory is adapted for GNSS. It provides new insights into the minimum number of satellites needed to locate a receiver, and is applied to the localization of GNSS cooperative networks of receivers. The interests of asymmetrical constraints in the context of formation control are also discussed.