Sensor Graphs for Guaranteed Cooperative Localization Performance

Abstract

A group of mobile robots can localize cooperatively, using relative position and absolute orientation measurements, fused through an extended Kalman filter (ekf).The topology of the graph of relative measurements is known to affect the steady state value of the position error covariance matrix. Classes of sensor graphs are identified, for which tight bounds for the trace of the covariance matrix can be obtained based on the algebraic properties of the underlying relative measurement graph. The string and the star graph topologies are considered, and the explicit form of the eigenvalues of error covariance matrix is given. More general sensor graph topologies are considered as combinations of the string and star topologies, when additional edges are added. It is demonstrated how the addition of edges increases the trace of the steady state value of the position error covariance matrix, and the theoretical predictions are verified through simulation analysis.

Distributed state estimation for linear multi-agent systems with time-varying measurement topology

“…To avoid those pitfalls, the aim of decentralized solutions is to break down the problem in several parts, leaving each agent in the formation with the responsibility of performing a subset of the computations, relying on limited information and communication with other vehicles in the formation. On the subject of decentralized and distributed state estimation, interesting approaches can be found in works such as Barooah (2007), Sousa, Oliveira, and Gaspar (2009), and Yuan and Tanner (2010). The closely related area of distributed control has also seen a wealth of relevant solutions, such as those in Chen, Wen, Liu, and Wang (2014), Fax (2002), and Tanner and Christodoulakis (2007), and recent work on the subject of quadratic invariance has offered optimal solutions for certain classes of measurement topologies, see e.g.…”

GAS decentralized navigation filters in a continuous-discrete fixed topology framework

“…[6] and [21]. On the subject of decentralized state estimation, interesting approaches can be found in [17], [22], and [2]. The closely related area of decentralized control has also seen a wealth of relevant solutions, such as in [10] and [18].…”