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Trajectory Design for Distributed Estimation in UAV ...

[ ] 11 May 2018 Trajectory Design for Distributed Estimation in UAV Enabled WirelessSensor NetworkCheng Zhan,Member, IEEE,Yong Zeng,Member, IEEE,and Rui Zhang,Fellow, IEEEA bstract In this paper, we study an unmanned aerial ve-hicle (UAV)-enabled wireless sensor network, where a UAV isdispatched to collect the sensed data from Distributed sensornodes (SNs) for estimating an unknown parameter. It is revealedthat in order to minimize the mean square error (MSE) for theestimation, the UAV should collect the data from as many SNs aspossible, based on which an optimization problem is formulatedto Design the UAV s Trajectory subject to its practical mobilityconstraints. Although the problem is non-convex and NP-hard, weshow that the optimal UAV Trajectory consists of connected linesegments only. With this simplification, an efficient suboptimalsolution is proposed by leveraging the classic traveling sales-man problem (TSP) method and applying convex optimizationtechniques.

arXiv:1805.04364v1 [cs.IT] 11 May 2018 Trajectory Design for Distributed Estimation in UAV Enabled Wireless Sensor Network Cheng Zhan, Member, IEEE, Yong Zeng, Member, IEEE, and Rui Zhang, Fellow, IEEE Abstract—In this paper, we study an unmanned aerial ve-

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Transcription of Trajectory Design for Distributed Estimation in UAV ...

1 [ ] 11 May 2018 Trajectory Design for Distributed Estimation in UAV Enabled WirelessSensor NetworkCheng Zhan,Member, IEEE,Yong Zeng,Member, IEEE,and Rui Zhang,Fellow, IEEEA bstract In this paper, we study an unmanned aerial ve-hicle (UAV)-enabled wireless sensor network, where a UAV isdispatched to collect the sensed data from Distributed sensornodes (SNs) for estimating an unknown parameter. It is revealedthat in order to minimize the mean square error (MSE) for theestimation, the UAV should collect the data from as many SNs aspossible, based on which an optimization problem is formulatedto Design the UAV s Trajectory subject to its practical mobilityconstraints. Although the problem is non-convex and NP-hard, weshow that the optimal UAV Trajectory consists of connected linesegments only. With this simplification, an efficient suboptimalsolution is proposed by leveraging the classic traveling sales-man problem (TSP) method and applying convex optimizationtechniques.

2 Simulation results show that the proposed trajectorydesign achieves significant performance gains in terms of thenumber of SNs whose data are successfully collected, as comparedto other benchmark Terms Unmanned aerial vehicle, Trajectory Design , Distributed Estimation , wireless sensor INTRODUCTIONThe last two decades have witnessed a dramatic advance-ment in the research and development of wireless sensornetwork (WSN) for applications in various fields. A WSNtypically consists of a large number of sensor nodes (SNs) thatare Distributed in a wide area of interest. SNs are typicallylow-cost and low-power devices, which are able to sense, process,store and transmit information. Although the SNs usuallyhave limited sensing, processing and transmission capabilitiesindividually, their collaborative Estimation /detectioncan behighly efficient and reliable [1], [2].One typical application of WSN is for the Estimation ofan unknown parameter (such as pressure, temperature, etc.)

3 In a given field based on noisy observations collected fromdistributed SNs. Specifically, each SN performs local sensingand signal quantization, then sends the quantized data to aFusion Center (FC), where the received data from all SNs arejointly processed to produce a final estimate of the unknownparameter. Prior research on Distributed Estimation in WSN(see, , [1], [2]) has mainly considered the static FC ata fixed location. As a result, SNs may require significantlydifferent transmission power to send their data reliably totheFC due to their near-far distances from it, which results ininhomogeneous energy consumption rates of the SNs and thuslimited lifetime of the overcome this issue, utilizing unmanned aerial vehicle(UAV) as a mobile data collector for WSN has been proposedC. Zhan is with the School of Computer and Information Science, South-west University, Chongqing 400715, China. (e-mail: Zeng and R. Zhang are with the Department of Electrical andComputerEngineering, National University of Singapore, Singapore117583 (e-mail:{elezeng, a promising solution [3] [5].))}

4 With on-board miniaturizedtransceivers that enable ground-to-air communications, UAV-enabled WSN has promising advantages, such as the ease ofon-demand and swift deployment, the flexibility with fully-controllable mobility, and the high probability of having line-of-sight (LoS) communication links with the ground SNs. Incontrast to fixed FCs, a UAV-enabled mobile data collector isable to fly sufficiently close to each SN to collect its senseddata more reliably, thus helping significantly reduce the SNs energy consumptions, yet in a more fair 61u 61u 61u 61u 61u 61u 61u 61u 61u Fig. 1. A UAV-enabled mobile data collector for wireless sensor fundamental problem in UAV-enabled WSN for dis-tributed Estimation is the Design of the UAV s Trajectory (seeFig. 1), which needs to take into account two importantconsiderations. Firstly, for an SN to send its data reliablyto the UAV, the UAV needs to fly sufficiently close to theSN (say, within a certain maximum distance assuming anLoS channel between them).

5 Secondly, given a finite flightduration, the UAV s Trajectory should be designed to cover (with respect to the given maximum distance) as many SNsas possible to optimize the Distributed Estimation performance( , minimizing the mean square error (MSE) for the esti-mated parameter). Notice that in our prior work [5], the SNs wakeup schedule and UAV s Trajectory were jointly optimizedto minimize the maximum energy consumption of all SNs,while ensuring that the required amount of data is collectedreliably from each SN. In contrast to [5] where the UAV needsto collect independent data from all SNs, this paper considersthat all SNs data contains noisy observations of a commonunknown parameter. As a result, their approaches for the UAVtrajectory Design are also fundamentally Trajectory Design for optimizing communication per-formance has received growing interests recently (see. ,[6] [10]). In [6], the UAV s Trajectory was jointly optimizedwith transmission power/rate for throughput maximizationin a UAV-enabled mobile relaying system, subject to prac-tical mobility constraints of the UAV.

6 The energy-efficientUAV communication via optimizing the UAV s trajectorywas studied in [7], which aims to strike an optimal balancebetween maximizing the communication rate and minimizingthe UAV s propulsion power consumption. The deploymentand movement of multiple UAVs, used as aerial base stationsto collect data from ground Internet of Things (IoT) devices,was investigated in [8]. The work in [9] maximized the min-imum throughput of a multi-UAV-enabled wireless networkby optimizing the multiuser communication scheduling jointlywith the UAVs Trajectory and power control. In [10], the UAVtrajectory was designed to minimize the mission completiontime for UAV-enabled multicasting. Different from the abovework, this paper investigates the UAV Trajectory Design undera new setup for Distributed Estimation in WSN. The maincontributions of this paper are summarized as follows: First, we show that for Distributed Estimation in an UAV-enabled WSN, minimizing the MSE is equivalent tomaximizing the number of SNs whose sensed data arereliably collected by the UAV; Second, with a given UAV flight duration, we formulatean optimization problem for designing the UAV s trajec-tory to maximize the number of covered SNs, subject tothe practical constraints on the initial and final locationsof the UAV as well as its maximum speed.

7 Althoughthe problem is NP-hard, we show that the optimal UAVtrajectory consists of connected line segments only; Third, with the above simplification, an efficient greedyalgorithm is proposed to obtain a high-quality suboptimaltrajectory solution by leveraging the classic travelingsalesman problem (TSP) method and applying convexoptimization techniques; Last, numerical results show that the proposed trajectorydesign achieves significant performance gains in termsof the number of SNs with successful data collection ascompared to benchmark SYSTEMMODEL ANDPROBLEMFORMULATIONAs shown in Fig. 1, we consider a WSN consisting ofNSNs arbitrarily located on the ground, denoted byU={u1, u2, .. , uN}. The horizontal coordinate of SNunisdenoted bywn R2 1,n= 1, , N. Each SN canobserve, quantize and transmit its observation for an unknownparameter to the FC, which estimates the parameter basedon the received Distributed EstimationEach SNuimakes a noisy observation on a deterministicparameter ( , temperature).

8 The real-value observationyiby SNuiis modeled asyi= +ni,(1)whereniis the observation noise that is assumed to bespatially uncorrelated for different SNs with zero mean andvariance 2i. We further assume that the noise variances forall SNs are identical, , 2i= 2, i. Denote by[ W, W]the signal range that the sensors can observe, whereWis aknown constant that is typically determined by the sensor sdynamic range. In other words,yi [ W, W].The local processing at SNuiconsists of the following:(i) an uniform quantizer with2 Siquantization levels, whereSidenotes the number of quantization bits and i=2W2Si 1represents the quantization step size; (ii) a modulator, whichmaps theSiquantization bits into a number of symbols basedon certain modulation scheme, such as binary phase shift key-ing (BPSK); and (iii) transmission of the modulated symbolsto the FC. It is shown in [11] that with uniform quantizer, thequantization noise variance foruican be obtained as 2i= a homogeneous sensor network with equal observationnoise power for all SNs, we assume that all SNs generate thesame number of quantization bits, ,Si=S, i[1].

9 TheFC then performs the linear Estimation based on the receiveddata from all SNs to recover using the Quasi Best LinearUnbiased Estimators (Quasi-BLUE) [2], and the correspondingMSE can be obtained asMSE=(K i=11 2i+ 2i) 1=1K( 2+W23(2S 1))),(2)whereK Nis the number of SNs whose sensed data arereliably expression in (2) shows that for the considered dis-tributed Estimation , the MSE is inversely proportional to thenumber of SNsKwhose data are reliably collected. Therefore,in order to minimize MSE for the Distributed Estimation , theFC should successfully collect data from as many SNs UAV Data CollectionFor the UAV-enabled WSN, a UAV is employed as a flyingdata collector/FC for a given time horizonT, which collectsthe quantized information from SNs and jointly estimates theparameter . It is assumed that the UAV flies at a fixed altitudeofHin meter (m) and the maximum speed is denoted asVmaxin meter/second (m/s). The initial and final UAV horizontallocations are pre-determined and denoted asq0,qF R2 1,respectively, wherekqF q0k VmaxTso that there existsat least one feasible Trajectory for the UAV to fly fromq0toqFin a straight line withinT.

10 The UAV s flying trajectoryprojected on the ground is denoted asq(t) R2 1,0 t assume that the transmit power for each SN is given(but can be different among SNs in general, depending oneach SN s energy availability). Thus, in order to satisfy theminimum required signal-to-noise ratio (SNR) at the UAV forreliable data collection from each SNun, the UAV locationprojected on the ground should lie within its communicationrange, which is denoted byrn. For each SNun, define thecoverage areaDn,{q R2 1| kq wnk rn}. Ingeneral, an SN with smaller transmit power has a smallerrngiven the sameSfor all SNs. As a result, the UAV can collectthe data reliably fromunas long as it is withinDn, as shownin Fig. 1. In the following, we refer to the event that the UAVenters intoDnasUAV visitsun. For example, in Fig. 1, theUAV has visited SNsu2,u6,u7andu8. Since the number ofquantization bits is typically small for practical applications( ,S= 10bits) [1], the required transmission time for thequantized information can be neglected compared to the UAVflight time.


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