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This article considers the problem of estimating the trajectory of a ballistic target in the reentry phase using 2-D measurements (azimuth and elevation angles) from a moving passive sensor. Previous works investigated the estimation problem of an object in the thrusting and initial ballistic phase from a single fixed passive sensor. This article shows that the 3-D trajectory in the reentry phase can be obtained by estimating the target's state at the end of the observation interval. The 7-d motion parameter vector (velocity azimuth angle, velocity elevation angle, drag coefficient, target speed, and 3-D position) is estimated by the maximum likelihood (ML) estimator with numerical search. Then we can predict the future position at an arbitrary time and the impact point of the target. The observability of the system for a sensor on a fast aircraft moving with constant velocity or maneuvering is verified via the invertibility of the Fisher information matrix. This is a major extension of the applicability of the recent observability proof for a stationary passive sensor observing a target in a gravitational field. The Cramer–Rao lower bound for the estimated parameters is evaluated and it shows that the estimates are statistically efficient. The angle estimation performance for the ML estimator is also compared with that of the polynomial fitting method. Simulation results illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the three-dimensional (3D) trajectory optimization problem for unmanned aerial vehicle (UAV) aided wireless communication. Existing works mainly rely on the kinematic equations for UAV’s mobility modeling, while its dynamic equations are usually missing. As a result, the planned UAV trajectories are piece-wise line segments in general, which may be difficult to implement in practice. By leveraging the concept of state-space model, a control-based UAV trajectory design is proposed in this paper, which takes into account both of the UAV’s kinematic equations and the dynamic equations. Consequently, smooth trajectories that are amenable to practical implementation can be obtained. Moreover, the UAV’s controller design is achieved along with the trajectory optimization, where practical roll angle and pitch angle constraints are considered. Furthermore, a new energy consumption model is derived for quad-rotor UAVs, which is based on the voltage and current flows of the electric motors and thus captures both the consumed energy for motion and the energy conversion efficiency of the motors. Numerical results are provided to validate the derived energy consumption model and show the effectiveness of our proposed algorithms. [ABSTRACT FROM AUTHOR]

3D human trajectory reconstruction in an indoor scene is critical in various applications, such as indoor navigation and human activity recognition. This task is challenging due to occlusion and clutters of indoor scenes, flexible human body joints, and severe lack of relevant datasets. Although several methods have been proposed to reconstruct a 3D human trajectory, they either can recover only 2D positions or require human initiative cooperation. In this paper, we propose a novel framework for 3D human trajectory reconstruction in an indoor scene using monocular surveillance videos and static point clouds without any initiative cooperation. The proposed framework consists of three modules: 3D pose estimation, depth regression, and trajectory reconstruction. We first estimate 3D pose from videos. Especially, we reconstruct a half-body 3D pose to deal with the occlusion problem. Then, we propose a depth regression approach to iteratively regress the depth of a 3D pose. Unlike data-driven approaches, our depth regression approach does not require training data and can be integrated into any 3D pose model. Finally, we exploit the geometric constraints from the point cloud to optimize the 3D trajectory. We evaluated the 3D pose estimation and depth regression modules on the H3.6M datasets. Due to the lack of evaluation datasets, we also built a trajectory dataset to evaluate the trajectory reconstruction performance. Empirical evaluation shows that our framework achieves accurate trajectory reconstruction results on real-world videos. [ABSTRACT FROM AUTHOR]

Indoor location-based services have become more and more important due to their potential applications in a wide range of personalized services in recent years. The accuracy of smartphone based 3D indoor localization is subjected to the poor performance of low-cost sensors and limited coverage of location sources. In order to solve these problems, this paper proposes a precise 3D indoor localization and trajectory optimization framework that uses the combination of sparse Wi-Fi Fine Time Measurement (FTM) anchors and built-in sensors (3D-LOWS). The inertial navigation system (INS) mechanization, multi-level constraints and observed values are integrated by the adaptive unscented Kalman filter to eliminate effects of cumulative error, indoor magnetic interference, and diversity of handheld modes. The Wi-Fi based ranging and landmark detection information is used to provide an accurate absolute reference to the built-in sensors based method. In addition, this paper proposes and evaluates two different trajectory optimization algorithms and compares the improved localization performance. The comprehensive experiments indicate that the proposed 3D-LOWS is proved to achieve accurate and stable 3D indoor positioning and trajectory optimization performance under complex indoor environments using sparse wireless stations. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) is a viable solution to remotely charge several energy receivers (ERs) in areas with intermittent access to a source of energy. However, given the limited available energy in the on-board battery of the UAV, which is mainly required to suffice propulsion energy consumption, the UAV struggles to roam seamlessly for long intervals. A key challenge is thus to efficiently use the limited battery energy, and accordingly prolong the UAV’s endurance, via controlling the underlying associated parameters such as cruising velocity. To further extend the battery lifetime, the UAV can also harness other sources of sustainable energy, such as sunlight, via solar energy harvesting. This paper studies a UAV-enabled WPT system, where a rotary-wing UAV transfers radio frequency (RF) wireless energy to several ERs at known locations. To offer uninterrupted seamless service, the UAV also harvests solar energy using solar panels. Considering the propulsion energy consumption of the UAV, we maximize the minimum average power received among all ERs over a finite cycle duration by jointly optimizing the UAV’s time allocation between harvesting and charging, flight trajectory as well as velocity, and transmit power allocation. Due to the non-convexity of the problem, we utilize the block coordinate descent (BCD) and successive convex approximation (SCA) methods. Numerical results show that the proposed solution outperforms benchmark schemes. [ABSTRACT FROM AUTHOR]

We investigate a transmission mechanism aiming to improve the data rate between a base station (BS) and a user equipment (UE) through deploying multiple relaying UAVs. We consider the effect of interference incurred by another established communication network, which makes our problem challenging and different from the state of the art. We aim to design the 3D trajectories and power allocation for the UAVs to maximize the data flow of the network while keeping the interference on the existing communication network below a threshold. We utilize the mobility feature of the UAVs to evade the (un)-intended interference caused by (un)-intentional interferers. To this end, we propose an alternating-maximization approach to jointly obtain the 3D trajectories and the UAVs transmission powers. We handle the 3D trajectory design by resorting to spectral graph theory and subsequently address the power allocation through convex optimization techniques. We also approach the problem from the intentional interferer’s perspective where smart jammers chase the UAVs to effectively degrade the data flow of the network. We also extend our work to the case for multiple UEs. Finally, we demonstrate the efficacy of our proposed method through extensive simulations. [ABSTRACT FROM AUTHOR]

Despite the wide utilization of unmanned aerial vehicles (UAVs), UAV communications are susceptible to eavesdropping due to air-ground line-of-sight channels. Intelligent reflecting surface (IRS) is capable of reconfiguring the propagation environment, and thus is an attractive solution for integrating with UAV to facilitate the security in wireless networks. In this paper, we investigate the secure transmission design for an IRS-assisted UAV network in the presence of an eavesdropper. With the aim at maximizing the average secrecy rate, the trajectory of UAV, the transmit beamforming, and the phase shift of IRS are jointly optimized. To address this sophisticated problem, we decompose it into three sub-problems and resort to an iterative algorithm to solve them alternately. First, we derive the closed-form solution to the active beamforming. Then, with the optimal transmit beamforming, the passive beamforming optimization problem of fractional programming is transformed into corresponding parametric sub-problems. Moreover, the successive convex approximation is applied to deal with the non-convex UAV trajectory optimization problem by reformulating a convex problem which serves as a lower bound for the original one. Simulation results validate the effectiveness of the proposed scheme and the performance improvement achieved by the joint trajectory and beamforming design. [ABSTRACT FROM AUTHOR]

Recent advances in trajectory replanning have enabled quadrotor to navigate autonomously in unknown environments. However, high-speed navigation still remains a significant challenge. Given very limited time, existing methods have no strong guarantee on the feasibility or quality of the solutions. Moreover, most methods do not consider environment perception, which is the key bottleneck to fast flight. In this article, we present RAPTOR, a robust and perception-aware replanning framework to support fast and safe flight, which addresses these issues systematically. A path-guided optimization approach that incorporates multiple topological paths is devised, to ensure finding feasible and high-quality trajectories in very limited time. We also introduce two perception-aware planning approaches to actively observe and avoid unknown obstacles. A risk-aware trajectory refinement ensures that unknown obstacles which may endanger the quadrotor can be observed earlier and avoid in time. The motion of yaw angle is planned to actively explore the surrounding space that is relevant for safe navigation. The proposed methods are tested extensively through benchmark comparisons and challenging indoor and outdoor aggressive flights. We release our implementation as an open-source package1 for the community. [ABSTRACT FROM AUTHOR]

The performance optimization of UAV communication systems requires the joint design of UAV trajectory and communication efficiently. To tackle the challenge of infinite design variables arising from the continuous-time UAV trajectory optimization, a commonly adopted approach in the existing literature is by approximating the UAV trajectory with piecewise-linear path segments connected via a finite number of waypoints in three-dimensional (3D) space. However, this approach may still incur prohibitive computational complexity in practice when the UAV flight period/distance becomes long, as the distance between consecutive waypoints needs to be kept sufficiently small to retain high approximation accuracy. To resolve this fundamental issue, we propose in this paper a new and general framework for UAV trajectory and communication co-design with flexible number of waypoint optimization variables (called designable waypoints) or their sub-path representations. First, we propose a flexible path discretization scheme that optimizes only a number of selected waypoints (designable waypoints) along the UAV path for complexity reduction, while all the designable and non-designable waypoints are used in calculating the approximated communication utility along the UAV trajectory for ensuring high trajectory discretization accuracy. Next, we propose a novel path compression scheme, which treats the UAV trajectory as a signal and compresses its path representation based on the basis decomposition. Specifically, the UAV 3D path is first decomposed into three one-dimensional (1D) sub-paths and each sub-path is then approximated by superimposing a number of selected basis paths (which are generally less than the number of designable waypoints) weighted by their corresponding path coefficients, thus further reducing the path design complexity. Finally, we provide a case study on UAV trajectory design for aerial data harvesting from distributed sensors, and numerically show that the proposed flexible path discretization and path compression schemes can significantly reduce the UAV trajectory design complexity yet achieve favorable rate performance as compared to conventional path/time discretization schemes. [ABSTRACT FROM AUTHOR]

In this letter, we investigate an unmanned aerial vehicle (UAV) enabled wireless powered communication network (WPCN), in which the UAV first employs the radio frequency (RF) signal to power ground users, and then the users communicate with the UAV by using the harvested energy. The sum rate maximization problem in WPCN suffers doubly near-far effect caused by the double signal propagation loss in both the energy harvesting and communication stage. It is generally believed that this effect can be alleviated by integrating UAV into WPCN, thanks to its flexible deployment. However, due to the lack of analytical solution in state-of-art research, it is still unclear how to quantify the advantage that the mobility of UAV brings to migrating the doubly near-far effect. To address this issue, by showing that the optimal UAV trajectory has a multi-location hovering structure, we first derive the closed-form optimal solution of resource allocation, as a function of the UAV hovering location for downlink wireless power transfer (WPT). We then prove that the UAV in our case only needs to hover at a single location for WPT. More importantly, it is explicitly shown that the doubly near far effect can be alleviated into near-far effect. Simulation results validate our analysis. [ABSTRACT FROM AUTHOR]

Autonomous tracking of suspicious unmanned aerial vehicles (UAVs) by legitimate monitoring UAVs (or monitors) can be crucial to public safety and security. It is non-trivial to optimize the trajectory of a monitor while conceiving its monitoring intention, due to typically non-convex propulsion and thrust power functions. This article presents a novel framework to jointly optimize the propulsion and thrust powers, as well as the 3D trajectory of a solar-powered monitor which conducts covert, video-based, UAV-on-UAV tracking and surveillance. A multi-objective problem is formulated to minimize the energy consumption of the monitor and maximize a weighted sum of distance keeping and altitude changing, which measures the disguising of the monitor. Based on the practical power models of the UAV propulsion, thrust and hovering, and the model of the harvested solar power, the problem is non-convex and intangible for existing solvers. We convexify the propulsion power by variable substitution, and linearize the solar power. With successive convex approximation, the resultant problem is then transformed with tightened constraints and efficiently solved by the proximal difference-of-convex algorithm with extrapolation in polynomial time. The proposed scheme can be also applied online. Extensive simulations corroborate the merits of the scheme, as compared to baseline schemes with partial or no disguising. [ABSTRACT FROM AUTHOR]

This letter considers a solar-powered unmanned aerial vehicle (UAV) system, where the UAV collects data from Internet of Things Devices (IoTDs) on the ground while also charging them using laser charging technology. Both the linear and nonlinear laser charging models are considered. We aim to maximize the residual energy of the UAV while satisfying the requirements of IoTDs by jointly optimizing the three-dimensional (3D) trajectory of UAV and scheduling for IoTDs. The optimization problem is formulated as a mixed integer non-convex problem which is difficult to solve in general. We apply the successive convex approximation and block coordinate descent algorithm to address this problem successfully. Simulation results verify the effectiveness of our algorithm compared with two benchmark methods. [ABSTRACT FROM AUTHOR]

This paper considers secure communications for an underlay cognitive radio network (CRN) in the presence of an external eavesdropper (Eve). The secrecy performance of CRNs is usually limited by the primary receiver's interference power constraint. To overcome this issue, we propose to use an unmanned aerial vehicle (UAV) as a friendly jammer to interfere Eve in decoding the confidential message from the secondary transmitter. Our goal is to jointly optimize the transmit power and UAV's trajectory in the three-dimensional space to maximize the average achievable secrecy rate of the secondary system. The formulated optimization problem is nonconvex due to the non-convexity of the objective and non-convexity of constraints, which is very challenging to solve. To obtain a suboptimal but efficient solution to the design problem, we first transform it into a more tractable form and then develop an iterative algorithm for its solution by leveraging the inner approximation (IA) framework. Combining tools from IA framework and S-procedure, we further extend the proposed algorithm to a more realistic scenario, where the imperfect location information of ground nodes (including Eve, secondary receiver and primary receiver) is considered, resulting in the average worst-case secrecy rate. Extensive numerical results are provided to demonstrate the merits of the proposed algorithms over existing approaches. [ABSTRACT FROM AUTHOR]

This paper considers an unmanned aerial vehicle (UAV)-aided millimeter Wave (mmWave) multiple-input-multiple-output (MIMO) non-orthogonal multiple access (NOMA) system, where a UAV serves as a flying base station (BS) to provide wireless access services to a set of Internet of Things (IoT) devices in different clusters. We aim to maximize the downlink sum rate by jointly optimizing the three-dimensional (3D) placement of the UAV, beam pattern and transmit power. To address this problem, we first transform the non-convex problem into a total path loss minimization problem, and hence the optimal 3D placement of the UAV can be achieved via standard convex optimization techniques. Then, the multiobjective evolutionary algorithm based on decomposition (MOEA/D) based algorithm is presented for the shaped-beam pattern synthesis of an antenna array. Finally, by transforming the original problem into an optimal power allocation problem under the fixed 3D placement of the UAV and beam pattern, we derive the closed-form expression of transmit power based on Karush-Kuhn-Tucker (KKT) conditions. In addition, inspired by fraction programming (FP), we propose a FP-based suboptimal algorithm to achieve a near-optimal performance. Numerical results demonstrate that the proposed algorithm achieves a significant performance gain in terms of sum rate for all IoT devices, as compared with orthogonal frequency division multiple access (OFDMA) scheme. [ABSTRACT FROM AUTHOR]

An unmanned aerial vehicle (UAV)-aided secure communication system is conceived and investigated, where the UAV transmits legitimate information to a ground user in the presence of an eavesdropper (Eve). To guarantee the security, the UAV employs a power splitting approach, where its transmit power can be divided into two parts for transmitting confidential messages and artificial noise (AN), respectively. We aim to maximize the average secrecy rate by jointly optimizing the UAV’s trajectory, the transmit power levels and the corresponding power splitting ratios allocated to different time slots during the whole flight time, subject to both the maximum UAV speed constraint, the total mobility energy constraint, the total transmit power constraint, and other related constraints. To efficiently tackle this non-convex optimization problem, we propose an iterative algorithm by blending the benefits of the block coordinate descent (BCD) method, the concave-convex procedure (CCCP) and the alternating direction method of multipliers (ADMM). Specially, we show that the proposed algorithm exhibits very low computational complexity and each of its updating steps can be formulated in a nearly closed form. Besides, it can be easily extended to the case of three-dimensional (3D) trajectory design. Our simulation results validate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper considers a rotary-wing unmanned aerial vehicle (UAV)-enabled wireless power transfer system, where a UAV is dispatched as an energy transmitter (ET), transferring radio frequency (RF) signals to a set of energy receivers (ERs) periodically. We aim to maximize the energy harvested at all ERs by jointly optimizing the UAV's three-dimensional (3D) placement, beam pattern and charging time. However, the considered optimization problem taking into account the drone flight altitude and the wireless coverage performance is formulated as a non-convex problem. To tackle this problem, we propose a low-complexity iterative algorithm to decompose the original problem into four sub-problems in order to optimize the variables sequentially. In particular, we first use the sequential unconstrained convex minimization based algorithm to find the globally optimal UAV two-dimensional (2D) position. Subsequently, we can directly obtain the optimal UAV altitude as the objective function of problem is monotonic decreasing with respect to UAV altitude. Then, we propose the multiobjective evolutionary algorithm based on decomposition (MOEA/D) based algorithm to control the phase of antenna array elements, in order to achieve high steering performance of multi-beams. Finally, with the above solved variables, the original problem is reformulated as a single-variable optimization problem where charging time is the optimization variable, and can be solved using the standard convex optimization techniques. Furthermore, we use the branch and bound method to design the UAV trajectory which can be constructed as traveling salesman problem (TSP) to minimize flight distance. Numerical results validate the theoretical findings and demonstrate that significant performance gain in terms of sum received power of ERs can be achieved by the proposed algorithm in UAV-enabled wireless power transfer networks. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the unmanned aerial vehicle (UAV)-aided simultaneous uplink and downlink transmission networks, where one UAV acting as a disseminator is connected to multiple access points (AP), and the other UAV acting as a base station (BS) collects data from numerous sensor nodes (SNs). The goal of this paper is to maximize the system throughput by jointly optimizing the 3D UAV trajectory, communication scheduling, and UAV-AP/SN transmit power. We first consider a special case where the UAV-BS and UAV-AP trajectories are pre-determined. Although the resulting problem is an integer and non-convex optimization problem, a globally optimal solution is obtained by applying the polyblock outer approximation (POA) method based on the problem’s hidden monotonic structure. Subsequently, for the general case considering the 3D UAV trajectory optimization, an efficient iterative algorithm is proposed to alternately optimize the divided sub-problems based on the successive convex approximation (SCA) technique. Numerical results demonstrate that the proposed design is able to achieve significant system throughput gain over the benchmarks. In addition, the SCA-based method can achieve nearly the same performance as the POA-based method with much lower computational complexity. [ABSTRACT FROM AUTHOR]

To improve the autonomy and reliability of asteroid landings, an intelligent approach to fast and reliable generation of optimal landing trajectories is proposed. Unfortunately, the indirect methods require good initial guesses for shootings. To address this issue, deep neural networks (DNNs) are developed to approximate the costates of the indirect methods and supply good initial solutions to achieve high success rate of shootings. This article focuses on the following three contributions. First, the original asteroid landing problems are connected with two-dimensional (2-D) asteroid-free transfer problems using model continuation and state transformation techniques. Second, DNNs are developed and optimized to approximate the costates of the 2-D transfers with high accuracy. Third, a systematical solution for asteroid landing trajectory optimization is developed, wherein the DNNs provide good initial solutions, and the accurate solutions for landings are obtained through a solution continuation process. Additionally, an alternative solution supplying strategy based on error statistics of DNN approximation is presented to take over the solution supplying when the predictions of DNNs fail to converge to the optima. Evaluations of the DNNs for solution supplying and simulations of landings on 433 Eros and 101955 Bennu are given to substantiate the effectiveness of the proposed techniques and demonstrate the performance of the developed algorithm. [ABSTRACT FROM AUTHOR]

Bundling visually aggregates curves to reduce clutter and help finding important patterns in trail-sets or graph drawings. We propose a new approach to bundling based on functional decomposition of the underling dataset. We recover the functional nature of the curves by representing them as linear combinations of piecewise-polynomial basis functions with associated expansion coefficients. Next, we express all curves in a given cluster in terms of a centroid curve and a complementary term, via a set of so-called principal component functions. Based on the above, we propose a two-fold contribution: First, we use cluster centroids to design a new bundling method for 2D and 3D curve-sets. Secondly, we deform the cluster centroids and generate new curves along them, which enables us to modify the underlying data in a statistically-controlled way via its simplified (bundled) view. We demonstrate our method by applications on real-world 2D and 3D datasets for graph bundling, trajectory analysis, and vector field and tensor field visualization. [ABSTRACT FROM PUBLISHER]

Clustering of trajectories of moving objects by similarity is an important technique in movement analysis. Existing distance functions assess the similarity between trajectories based on properties of the trajectory points or segments. The properties may include the spatial positions, times, and thematic attributes. There may be a need to focus the analysis on certain parts of trajectories, i.e., points and segments that have particular properties. According to the analysis focus, the analyst may need to cluster trajectories by similarity of their relevant parts only. Throughout the analysis process, the focus may change, and different parts of trajectories may become relevant. We propose an analytical workflow in which interactive filtering tools are used to attach relevance flags to elements of trajectories, clustering is done using a distance function that ignores irrelevant elements, and the resulting clusters are summarized for further analysis. We demonstrate how this workflow can be useful for different analysis tasks in three case studies with real data from the domain of air traffic. We propose a suite of generic techniques and visualization guidelines to support movement data analysis by means of relevance-aware trajectory clustering. [ABSTRACT FROM PUBLISHER]

We present an approach for planning ensembles of channels, ribbons, within 3D printed implants for facilitating radiation therapy treatment of cancer. The ribbons are traced out by sweeping a constant width rigid body (cuboid) along spatial curves. We propose a method for planning multiple disjoint and mutually collision-free ribbons of finite thickness along curvature and torsion constrained curves in 3D space. This is equivalent to planning motions for the cross section of the ribbon along a spatial curve such that the cross section is oriented along the unit binormal to the curve defined according to the Frenet–Serret frame. We propose a two-stage planning approach. In the first stage, a customized sampling-based planner uses rapidly exploring random trees (RRTs) to generate feasible curvature and torsion constrained ribbons. In the second stage, the curvature and torsion along each ribbon is locally optimized using sequential quadratic programming (SQP). We use this approach to design curved radiation delivery channels inside custom 3D printed implants that allow temporary insertion of a high-dose radioactive source that is threaded through the channels using a wire and allowed to dwell for specified times to expose cancerous tumors for intracavitary brachytherapy treatment. Constraints on the curvature and torsion are required for 3D printing (to allow flushing of sacrificial material) and for smooth insertion of radioactive sources. In simulation experiments, this approach achieves an improvement of 46% in tumor coverage compared with a greedy approach that generates channels sequentially. [ABSTRACT FROM AUTHOR]