Optimal Configuration and Path Planning for UAV Swarms Using a Novel Localization Approach

Weijia Wang, Peng Bai, Hao Li, Xiaolong Liang
2018 Applied Sciences  
In localization estimation systems, it is well known that the sensor-emitter geometry can seriously impact the accuracy of the location estimate. In this paper, time-difference-of-arrival (TDOA) localization is applied to locate the emitter using unmanned aerial vehicle (UAV) swarms equipped with TDOA-based sensors. Different from existing studies where the variance of measurement noises is assumed to be independent and changeless, we consider a more realistic model where the variance is
more » ... emitter distance-dependent. First, the measurements model and variance model based on signal-to-noise ratio (SNR) are considered. Then the Cramer-Rao low bound (CRLB) is calculated and the optimal configuration is analyzed via the distance rule and angle rule. The sensor management problem of optimizing UAVs trajectories is studied by generating a sequence of waypoints based on CRLB. Simulation results show that path optimization enhances the localization accuracy and stability. 2 of 17 heterogeneous sensor network. Francisco et al. [4] applied a multi-objective optimization in sensor placement. Kim et al. [12] studied the optimal configuration of sensors with the assumption that the emitter was located far from the sensors, while the sensors were relatively close to each other. In recent years, more realistic distance-dependent noise for TOA and AOA measurements was also considered [4, 13, 14] . In this paper, the CRLB in TDOA localization with distance-dependent noise is calculated in both static and movable scenarios; the distance rule and angle rule of the optimal configuration are extracted, which can provide guidance in optimal sensor-emitter geometries. The application of unmanned aerial vehicle (UAV) swarms can provide unique platforms for TDOA localization. Their characteristics of flexible movement and cooperation enable them to rapidly change current geometries to achieve higher location accuracy [15, 16] . Therefore, the sensor management of real-time UAV path optimization has been a heated research issue in recent years [17] . Frew [18] presented the signal strength measurement to control the UAVs movement. Soltanizadeh et al. applied the determinant of Fisher information matrix (FIM) as the control objective function in RSS localization. Wang [19] investigated UAV path planning for tracking a target using bearing-only sensors. Alomari et al. [20] provided a path planning algorithm based on the dynamic fuzzy-logic method for a movable anchor node. Kaune [21, 22] preliminarily considered the path optimization method when there was only one sensor moving platform during TDOA localization. In this paper, UAVs' trajectories are optimized by generating a sequence of waypoints based on CRLB. The CRLB of TDOA location is not only taken as a performance estimator but also as the rule of UAV path optimization. The emitter position is solved by combining the SDP methods and an extended Kalman filter (EKF) estimator. Meanwhile, the constraints of UAV swarms are considered, such as motion and communication constraints. Therefore, the real-time path planning of UAVs is converted to nonlinear optimization with constraints. The interior penalty function method is adopted to convert the nonlinear optimization to simple unconstrained optimization so as to get the flight path of each UAV for the next time. The rest of the paper is structured as follows. Section 2 introduces the TDOA measurement model and distance-dependent noise model. In Section 3, the optimal configuration is analyzed in both static and movable emitter scenarios based on the CRLB. Section 4 presents the optimal UAV path optimization method. Simulations and conclusions are given in Sections 5 and 6, respectively. Problem Formulation Measurement Model Consider that M time-synchronized UAVs are applied to receive the emitted signals and measure the TOAs with the state vector of each UAV χ i (k) = (x i (k), y i (k)) T , i = 1, 2, · · · M. Let x t = (x t , y t ) ∈ R 2 be the location of an unknown emitter. The TDOA measurement can be obtained by the difference between any two TOA measurements, eliminating the unknown time of emission. By multiplication of the TDOA measurements by the electromagnetic wave transmission speed, the measurement function in the range domain is obtained:
doi:10.3390/app8061001 fatcat:puimgb4gh5dhlp342jwxdijoqm