# Optimal Configuration and Path Planning for UAV Swarms Using a Novel Localization Approach
## 1 Introduction  
Passive localization of an emitter from its radio frequency (RF) transmissions has many applications such as search and rescue, electronic surveillance, cognitive radio networks, and wireless sensor networks. The receiving platform can employ sensors measuring angle of arrival (AOA) [1], time difference of arrival (TDOA) [2], and received signal strength (RSS) [3]. TDOA measurements construct a time difference observation equation by measuring the time difference of the emitter signal arriving at different sensors. Therefore, each time difference, corresponding to one hyperboloid, and the emitter can be obtained from two or more hyperbolas. With its high accuracy and simplicity, the TDOA localization technique is widely applied [4]. The equations of the TDOA technique are quadratic and the goal is to find the position of an emitter by solving a set of nonlinear equations obtained from TDOA measurements. The TDOA measurements can be calculated by a simple closed form, e.g., spherical intersection (SX) and spherical interpolation (SI) [5], which usually uses nonlinear least-square solutions. Furthermore, the maximum likelihood method, like the Chan algorithm, was also proposed in [6] and semidefinite programming (SDP) methods in [7]. It is well known that location accuracy depends not only on the localization algorithm but also on the sensor-emitter geometry. Therefore, the selection of an optimal configuration can further improve the location accuracy. [PERSON] et al. [8] initially performed a theoretical analysis of the sensor-emitter geometry based on CRLB with uncorrelated TDOA measurements. [PERSON] [9] discussed optimal sensor deployment considering the correlated TDOA measurement, which makes the configuration rule more applicable. [PERSON] et al. [10; 11] formulated an optimal configuration in centralized and decentralized types of TDOA localization and further research focused on theheterogeneous sensor network. [PERSON] et al. [4] applied a multi-objective optimization in sensor placement. [PERSON] 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]. [PERSON] [18] presented the signal strength measurement to control the UAVs movement. [PERSON] et al. applied the determinant of Fisher information matrix (FIM) as the control objective function in RSS localization. [PERSON] [19] investigated UAV path planning for tracking a target using bearing-only sensors. [PERSON] et al. [20] provided a path planning algorithm based on the dynamic fuzzy-logic method for a movable anchor node. [PERSON] [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.