Noncausal Trajectory Optimization for Real-Time Range-Only Target Localization by multiple UAVs

This study proposes a new method namely noncausal trajectory optimization which is developed to obtain superior performance in range-only (i.e. distance and received signal strength based) target localization by multiple unmanned aerial vehicles (UAVs). Noncausal trajectory optimization suggests to optimize the next waypoint considering not only the past waypoints already visited but also the future remaining trajectory of the UAV. Therefore, based on the analogy of noncausal filters in signal processing, the new proposed method is named as “noncausal trajectory optimization”. In the previous literature, because only the past trajectory is taken into account, the UAVs are mostly suggested to make circular or spiral motions around the target. However, this study suggests that the UAV must create a linear trajectory as much as possible when total travel length is shorter than initial distance to the target. For a single UAV, this study proves that the ideal direction of this linear path is only the function of the ratio of the total length of trajectory over the initial distance to the target. To prove this, the summation operators in Fisher information matrices (FIM) are converted to line integrals and then D-optimality criterion is applied. Next, noncausal trajectory optimization is introduced which is dedicated to obtain a higher final localization capability by sacrificing immediate or early advantages. Then, noncausal joint trajectory optimization for multiple UAVs is illustrated. Finally, trajectory optimization for moving target as well as three dimensional trajectory optimization are discussed. Monte Carlo simulations showed that the proposed optimization method obtains a higher final accuracy level compared to the ordinary trajectory optimization.