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Unmanned Aerial Vehicles (UAVs) localization has become crucial in recent years, mainly for navigation or self-positioning and for UAV based security monitoring and surveillance. In this paper, azimuth and elevation radio positioning of UAVs are considered. The localization is based on multiple differential phase-of-arrival measures exploiting a 3-Axial Uniform Linear Array of antennas. An ad hoc particle filtering algorithm is applied to improve the positioning performance using a dynamic motion model. A novel adaptive algorithm, namely, Particles Swarm Adaptive Scattering (PSAS), is proposed to increment the algorithm stability and precision. To assess performance a Confined Area Random Aerial Trajectory Emulator (CARATE) algorithm has been developed to generate actual paths of flying UAVs. The algorithm performance is compared with the baseline method and with the average trajectory Cramér Rao lower bound to show the effectiveness of the proposed algorithm.

Unmanned Aerial Vehicles (UAVs) are attracting considerable attention since they can be used for a number of consumer, industrial, and military applications ranging, for instance, from sport video making to environmental monitoring and parcel delivery [

In this paper, a radio localization approach is considered and it is based on azimuth and elevation positioning using a transmitting source as a reference. Azimuth and elevation are determined by processing with particle filtering (PF) the signals that impinge on a 3-Axial Uniform Linear Array (3A-ULA). The 3A-ULA can be mounted either on a ground base station or on the UAVs. In the first case, namely, Ground-Localization Scenario (GL-S), the base station passively eavesdrops the signals emitted by the UAVs to determine their angular coordinates. In the latter case, namely, Self-Localization Scenario (SL-S), the ground node acts as a radio anchor allowing UAVs self-localization. The system can be used in a standalone way or to complement existing GNSS/inertial or inertial sensors employing data fusion techniques [

In Section

In order to quantify the performance of the proposed tracking algorithm an emulator for the UAV behaviours is specifically developed in Section

Finally, in Section

A system that determines the position of flying UAVs through the analysis of a signal impinging on the 3 branches of a 3A-ULA is considered.

The GL-S is built as follows. UAVs send narrow band radio signals that are captured by a ground base station equipped with a 3A-ULA. The radio signals are properly frequency/time duplexed to allow multiple UAVs tracking. The ground node can then compute locally the UAVs azimuth and elevation coordinates [

The SL-S is analogously arranged. Each 3A-ULA is mounted on the UAVs so that the ground device takes the role of a radio beacon anchor [

The 3A-ULA is constituted, for each one of the 3 branches, by

The signal model considered in the following describes for simplicity the scenario with only one UAV; this assumption can be easily extended to a multi-UAVs application. Both GL-S and SL-S scenarios, due to symmetry, can be modelled in the same way. Hence, in general, the downconverted signal received by the

Considering the scenario where the transmitted signals carry also information, the component

In this model, the presence of multipath propagation is not considered; a line of sight environment is assumed. This can hold true when the ground and UAV antennas have a wide vertical lobe, respectively, directed upward and downward.

A radio source moving in the 3D Cartesian space is considered. Its angular spherical coordinates

In [

The estimations computed in (

In this section, the application of the PF algorithms [

The relations (

For notational simplicity, both

PF has been chosen because of its simplicity and versatility. PF algorithms are a numeric implementation of Bayesian estimation [

As shown in (

Particles weights

The PF estimation

The parameter

The value of

Considering the spreading variable

For these reasons in this paper a novel algorithm that manages the dynamic evolution of

The distance metric

The value of

To assess performance of BM and PF algorithms estimations and to evaluate the effects of different parameters on the estimation process, it is necessary to emulate UAVs trajectories using a proper coordinates evolution algorithm. Herein, a possible trajectory generation method is proposed.

The proposed algorithm, named Confined Area Random Aerial Trajectory Emulator (CARATE), generates iteratively a 3D path obtained from a variable length previous history of the trajectory and a tunable set of random variables. CARATE is specifically designed to emulate UAVs trajectories inside a limited flight area, in the GL-S, around the receiving array. Thus, the generated trajectories allow testing the tracking algorithms for a broad range of arrival angles. An UAV located far from the receiving array instead would be localized using a limited range of angles. The Cartesian position

Diagram of CARATE components for variable

Example of UAV 3D trajectory generated with CARATE.

The CARATE algorithm, as visible in the sample path in Figure

In statistics the Cramér-Rao Lower Bound (CRLB) expresses the lowest value of the Root Mean Square Error (RMSE) of an optimal estimator given a certain set of data [

Now, we define

To calculate the CRLB it is necessary to evaluate the log-likelihood

The performance of the PF algorithm is now assessed. A comparison with the BM estimation introduced in Section

Analogously, with the purpose to allow a performance comparison with the CRLB, we define the average trajectory CRLB (AT-CRLB), as

The default parameters for the performance evaluation are (a) angles

In Figure

We now consider the performance as a function of the signal-to-noise ratio

AT-RMSE for different

AT-RMSE for different normalized 3A-ULA interantenna distance

Now, the behaviour of the AT-RMSE for the BM and PF algorithms is analysed varying the normalized interantenna distance

We have discussed the application of an appropriately designed PF algorithm for self-localization (SL-S) and ground localization (GL-S) of UAVs using a 3A-ULA of antennas, showing an overall increase of performance with respect to the BM. A novel algorithm to manage the amplitude of the particle swarm, namely, Particles Swarm Adaptive Scattering (PSAS), has been developed and tested, showing a further increase of precision. A complete, fully adjustable, and effective 3D UAVs trajectory emulator, namely, CARATE, has been proposed and used to assess performance. Strong impairing effects like Doppler spread, phase offset, and phase noise have been considered in the performance evaluation. The effects on the proposed localization algorithm of the PF model parameters as well as the SNR and the 3A-ULA characteristics have been studied. Numerical results show that the proposed PF algorithm is able of dynamically track the UAVs angular position better that the BM. A critical point of this approach is that, similarly to PSAS behaviour, a dynamic calibration procedure has to be implemented to optimize the PF parameters. Future work will also investigate the integration of ranging algorithms like Received Signal Strength Estimation (RSSE) and ToA to PF to provide full 3D localization.

The authors declare that they have no competing interests.