Sensor Graphs for Guaranteed Cooperative Localization Performance

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.