We consider the design of a single moving sensor trajectory for the purpose of optimally localizing a stationary emitter based on time-of-arrival measurements, which are deteriorated by oscillator instability. The localization error covariance matrix is predicted by the Cramér-Rao bound. In order to optimize the localization, we propose the minimization of the largest eigenvalue of the bound matrix, or, equivalently, the maximization of the smallest eigenvalue of the associated Fisher information matrix. Two different cases are discussed. In the first case, a pre-mission path design is considered where the path is optimized for locating an emitter in the vicinity of a postulated location. In the second case, the path is designed in real time, as the sensor moves, using measurements collected online. Using robust optimization methods, the best next way-point is chosen, considering the uncertainty in the emitter location. Constraints rising from speed and maneuvering limitations, and restricted regions are treated. Since these optimization problems are non-convex, we use semi-definite relaxation. We demonstrate that in many scenarios, the proposed algorithms yield near optimal results.
- Convex optimization
- Cramér-Rao lower bound
- Semi-definite programming (SDP)
- Semi-definite relaxation (SDR)
- Time of arrival (TOA)