An analytical solution for the complete sensor network attitude estimation problem

Sensor network attitude estimation problem consists in retrieving the attitude of each multi-axis sensor of a distributed network knowing some relative attitudes between pairs of sensors. The attitude of a sensor is its orientation in an absolute axis system. We present an analytical method for solving the sensor network attitude problem using quaternion formalism which allows to apply tools from linear algebra. The proposed algorithm allows to solve the problem when all of the pairwise relative attitudes are known. A complete characterization of the algorithm is established: spatial complexity, time complexity and robustness. The performance of our algorithm is illustrated by numerical simulations and by real experiments.

► A method for identifying all relative orientations of a set of sensors is proposed.
► Torgerson's algorithm is generalized and extended to a quaternionic framework.
► Error bounds and robustness are studied by using matrix perturbation theory.
► Simulation results and an application on experimental data are presented.