We consider the design of a pair of moving sensors trajectories for the purpose of optimally localizing a stationary emitter based on time-difference-of-arrival measurements. The localization error covariance matrix is predicted by the Cramér-Rao bound. As an optimization criterion for the localization error, we propose the maximization of the smallest eigenvalue of the Fisher information matrix that is associated with the major principle axis of the confidence ellipsoid. We establish the path design problem under a set of constraints rising from speed, maneuvering, safety, and no-fly zones limitations. We propose a solution based on a nonconvex alternating direction method of multipliers. We examine the results of the algorithm for the case of a pair of sensor against the basin hopping global optimizer with impressive results.
- Time difference of arrival (TDOA)
- alternating direction method of multipliers (ADMM)
- augmented Lagrangian method (ALM)
- majorization-minimization (MM) algorithm
- semi-definite programming (SDP)
- semi-definite relaxation (SDR)