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ICACT Transactions on Advanced Communications Technology (TACT) Vol. 8, Issue 2, March 2019

Volume. 8 Issue. 2

6J

1 Passive Geolocation with Unmanned Aerial Vehicles using AOA Measurement Processing

1193

Grigoriy Fokin** State University of Telecommunication, 22 Prospekt Bolshevikov, St. Petersburg, Russia

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ICACT Transactions on Advanced Communications Technology (TACT) Vol. 8, Issue 2, March 2019

1193

Passive Geolocation with Unmanned Aerial
Vehicles using AOA Measurement Processing
Grigoriy Fokin** State University of Telecommunication, 22 Prospekt Bolshevikov, St. Petersburg, Russia
grihafokin@gmail.com

Abstract—This paper considers 3 dimensional (3D) angle ofarrival (AOA) measurements processing model for positioning
a transmitter by cooperation of flying segment based onreceiver station aboard Unmanned Aerial Vehicle (UAV) withterrestrial segment including stationary ground receiver stationand confirms its practicability for handling Non-Line-Of-Sight(NLOS) problem. Positioning with UAVs is especially relevantin heterogeneous terrain with inherent reflections resulting inprimary measurements distortion. NLOS problem was wellinvestigated for 2D scenarios with ground receiver stations,however for 3D UAV based positioning this is a topic of ongoing
research. In this paper different measurement processing
techniques and results for UAV based location were analyzed to
explore advantages and shortcomings of AOA among others.
The contribution of the current research is the refinement ofmathematical and simulation models for positioning of radiotransmitter with one stationary ground and one flying UAV
based receiver station using AOA processing and its
performance evaluation with handling AOA noise. Resulting
estimates agree with known results for UAV based positioning
and validate its practicability to face NLOS problem, when
AOA deviation is less than 10 degrees.
Keyword — Cramer-Rao bounds, Direction-of-arrival
estimation, Position measurement, Radar signal processing,
Root mean square, Unmanned aerial vehicles

T

I. INTRODUCTIONHIS work presents geolocation application of actual
wireless networks which widely exploit joint
cooperation of flying segment based on transceiver stations
aboard Unmanned Aerial Vehicles (UAVs) with terrestrial
segment including stationary ground transceiver stations [1].
Geolocation tasks in such networks are essential for bothmilitary applications, for example, in tactical networks [3] orbattlefield environments [4], and civil applications, forinstance, in ground-aerial surveillance [5], search and rescue
operations [6], drone-equipped wireless control measurement[2] and flying sensor networks [1].
Positioning is implemented from passive measurements of———————————————————————
Manuscript received December 29, 2018. This work was sponsored by the
Ministry of Science and Education with Grant of the President of the RussianFederation for the state support of young Russian scientists №
MK-3468.2018.9, and a follow-up of the invited journal to the accepted &presented paper of the XXIth International Conference on Advanced
Communication Technology (ICACT2019).
Grigoriy Fokin is with the Bonch-Bruevich Saint-Petersburg State
University of Telecommunications (SUT), 22 Prospekt Bolshevikov, St.
Petersburg, Russia (corresponding author phone: 8 921 985 80 04; e-mail:grihafokin@gmail.com).

the arrival times, directions of arrival, or Doppler shifts ofelectromagnetic waves received at various sites [7].
UAV based positioning techniques had already got
considerable attention in the past years and can be subdivided
by primary measurements into Time Difference of Arrival(TDOA) [9]–[14], Frequency Difference of Arrival (FDOA)[15], Angle of Arrival (AOA) [16], [17] and Received Signal
Strength Indication (RSSI) [18], [19] positioning.
Every measurement processing technique based on
TDOA, FDOA, AOA or RSSI has its advantages andshortcomings. While TDOA technique could achieve highaccuracy in optimistic Line of Sight (LOS) conditions, it
requires precise receiver synchronization. In 3D at least four
receivers are required for TDOA. On the other hand, DOA
technique requires less number of receivers and neither
synchronization among them, however it needs an antenna
array for each receiver and resulting location accuracy ishighly dependent on the distance between the object oflocation and receivers. RSSI based localization is preferred inmany applications because of the simple implementation, but
its accuracy degrades in large scale environments [8] due toinherent variation of the received signal strength (RSS).
The use of UAVs as moving receiver in conjunction withstationary ground based receiver, reducing the number of
sensors required to obtain multiple TDOA measurements,
was presented in [9], [10]. Recursive location estimation of astationary and moving transmitter from a pair of UAVs using
TDOA was investigated for Kalman [11] and Gaussian [12]filtering techniques. Cooperation of flying segment based onreceiver station aboard UAV with terrestrial segment
including several stationary ground receivers using TDOA
was investigated in [13], [14] and achieved accuracy of 10 m.
Mobile emitter geolocation and tracking using TDOA andFDOA fusion is considered in [15].
Hierarchical DOA estimation and the fusion of DOAs andthe terrain map was proposed in [16] to reduce computational
complexity of the near-real-time monitoring system. In [17] aseries of both real-world flight testing and computer
simulated scenarios were conducted to study the feasibility ofa low-cost UAV DOA geolocation platform.
RSSI localization and tracking architecture, where a data
driven neural network model is used for estimating unknown
signal strength and extended Kalman filters are utilized for
eliminating RSS noise is presented in [18]. Localization of aradio frequency (RF) transmitter with intermittent
transmissions as quickly as possible via a group of UAVs
with omnidirectional RSS sensors is considered in [19].
Observed accuracy results are summarized in Table 1.
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ICACT Transactions on Advanced Communications Technology (TACT) Vol. 8, Issue 2, March 2019
TABLE I
ACCURACY RESULTS FOR UAV BASED POSITIONING
Assumptions
Ref.
[3]
[4]
[9],
[10]

Accuracybounds, m
21 – 100
16 – 99

3D, 1 UAV, LOS
3D, 1 UAV, LOS

500 – 2000

3D, 1 UAV, LOS[11]

10 – 1000[12]

100 – 1000

Layout2D, 2 UAVs, LOS, Kalmanfiltering
2D, 2 UAVs, LOS, Kalmanfiltering

[13],
[14]
[20]
[21]

10 – 20

3D, 1 UAV, 5 RxGR, LOS

20 – 5000
20 – 5000[15]

10 – 2000[16]

15 – 65[17]

20 – 200[18]

28 – 57[19]

30 – 200

3D, 1 UAV, 5 RxGR, NLOS
2D, 5 RxGR, NLOS
2D, 2 UAVs, LOS, Kalmanfiltering
3D, 2 UAVs, LOS, terrain
map
2D, 1 UAV, LOS
3D, 3 UAVs, LOS, Kalmanfiltering
2D, 2 UAVs, LOS

Primary
Measurements

TDOA

1194

II. AOA MEASUREMENTPROCESSING IN UAV BASED POSITIONING
Here we present UAV based positioning model, AOA
positioning geometry, measurement processing model andCramer-Rao lower bound (CRLB) computation.
A. UAV Based Positioning Model
UAV based positioning system under consideration,
including flying segment based on one receive sensor aboard
UAV with terrestrial segment including one stationary
ground receive sensor is shown in Figure 1.
UAV basedri sensor, i=1,…,N

GNSS
synchronization& self geolocation

Primarymeasurement
receiver

TDOA–FDOA
Primary measurement transmitter

AOA

bi

AOAi
RSSI

To validate AOA measurement processing for UAV based
positioning in heterogeneous terrain with NLOS conditions
let's analyze existing accuracy results for TDOA, FDOA,AOA techniques, shown in Table 1. Results are simulation
based, differ noticeably and depend on a plenty of factors,
including model setup and parameters. However, we canmake following conclusions. Firstly, more receiver stations
provide higher positioning accuracy. Secondly, transmitter
location accuracy in 2D is mainly higher than in 3D
scenarios. Thirdly, most results are valid for optimistic LOS
conditions and do not account for possible reflections inheterogeneous terrain. However, positioning with UAVs isespecially relevant in heterogeneous terrain, when primary
NLOS measurements, obtained after reflections, could leadto a significant Root Mean Square Error (RMSE) exceeding
103 m [20], [21]. Thus, the task of current investigation is torefine existing AOA measurement processing technique for
UAV based positioning model in [20], [21] and evaluate its
robustness in handling AOA variance encountering primarymeasurements disturbances after NLOS reflections.
AOA measurement processing technique for positioningof transmitter was already investigated in [22], [23] andpointed that it is not able to directly apply existing 2D AOA
models, because two angles have to be used jointly in theirrespective non-linear measurement equations in order todetermine the position of the source, however, it did not take
into account influence of moving receiver aboard UAV.
Thus, it is reasonable to refine models in [20], [21] with 3D
AOA measurement processing technique [22], [23] with joint
azimuth and the elevation angle measurement equations.
The material in the paper is organized in the following
order. Mathematical model for positioning of transmitterwith one stationary ground and one flying UAV based
receiver using AOA measurement processing is presented in
Section II. Developed simulation model, scenario of
positioning and numerical results for AOA positioning
accuracy performance evaluation are given in Section III.
Finally, we draw the conclusions in Section IV.

Transmittersource,x

Measurement processing unit
AOA
measurement
processing

Primarymeasurement
receiverEstimate x̂

AOA0

b0
Primary measurement transceiver
GNSS
synchronization& self geolocation

Primarymeasurement
receiverGround based r0 sensor

Fig. 1. UAV based positioning system.

Ground and UAV based receive sensors whose positions
are available with Global Navigation Satellite Systems(GNSS) carry out the task of receiving primary AOA
measurements from packets transmitted by radiating emittersource. Single passive sensor can record the time stamp anddirection of the received packet. Accurate time stamping ispossible since each sensors has a GNSS receiver for timesynchronization. Then, AOAs of each sensor are forwarded
to the measurement processing unit, which in turn using
known sensor locations and AOA measurement processing
 y,z  .
estimate radiating emitter coordinates x =  x,
If positioning is carried out by AOA in three-dimensional
space, flying UAV based receiver produces azimuth andelevation angles every time instant along UAV flight path asshown in Figure 2.
ri(xi,yi,zi)r2(x2,y2,z2)

AOA i

rN
(xN,yN,zN)

si

AOA N

s2

sN

AOA 2

s1

s0

r1
(x1,y1,z1)

AOA1

AOA0

r0
(x0,y0,z0)x(x,y,z)Fig. 2. Using of UAV as moving sensor with ground based sensor.

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ICACT Transactions on Advanced Communications Technology (TACT) Vol. 8, Issue 2, March 2019

B. UAV Based AOA Positioning Geometry
Denote receive sensors with available coordinatesri   x i , yi , z i  , where time intervals i  0,..., N correspondT

to synchronized timestamps, N – the number of primarymeasurements along UAV flight path, and transmitter withunknown coordinates x   x, y, z  , then from Figure 3Tx i  x  x i , y i  y  y i , z i  z  z i 



ri z

y

(xi,yi,zi)

z
ϕi
si
s0
ϕ0

r0
(x0,y0,z0)x(x,y,z)θi

1195

Denote vector a 2Di  sin i ,  cos i , 0 , then usingT

notations in (1) we can rewrite (8) asa T2Di x  a T2Di ri 

where a 2Di satisfies aT2Di si  0 and a 2Di 2  1 as in [24].
Expressions (5) represent error-free values of AOAs, noisy
measured AOAs can be rewritten as
 i  i  n i ,  i  i  n i , 

where n i and n i are white Gaussian with zero mean withvariables 2i and 2i , respectively. Then (9) can bexrewrittenTTa 2 Di x  a 2 Di ri  n 2 Di 

yTTwhere a 2Di  sin  i ,  cos  i , 0  and term n 2Di  a 2Di si .

θ0Relationship between elevation angle i and unknown
transmitter coordinates can be derived using manipulation[25] for (5), yielding tan i  zi sixy , orxFig. 3. Positioning geometry.

Relationship between x and ri is given by [24]sin i s ixy  cos i z i  0 

x  ri  s i 

where si is the noise-free bearing vector connecting ri to x .
Actual range between transmitter x and sensor ri is defined
as norm of bearing vector si  x  ri

Expressing sixy in (4) with notations in (6) yields
s ixy  x i x i

x i 2  y i 2  y i y i

x i 2  y i 2  x i cos i  y i sin i ,

and putting (13) in (12) we gets i  s i 2  x  ri 2  x i 2  y i 2  z i 2 

 x i sin i cos i  y i sin i sin i  z i cos  i  0 

where  2 – norm operator over a vector [26]. Projection of

Denote vector a3Di  sin i cos i ,sin i sin i ,  cos i  ,bearing vector si on x-y plane is defined bythen using notations in (4) we can rewrite (14) ass ixy  x i 2  y i 2 

Actual error-free bearing pair including azimuth i andelevation i AOAs from transmitter x to sensor ri is z  y 
i  arctg  i  , i  arctg  i  , s 
 x i  ixy Using following notations from Figure 3
cos i 

T

T
T
a 3Di
x  a 3Diri 

T
where a3Di satisfies a3Di
si  0 and a3Di 2  1 as in [24].

Using noisy measured AOAs, (15) can be rewritten [25]TTa 3Di x  a 3Di ri  n 3Di 

T
T
with a 3Di  sin  i cos  i ,sin  i sin  i ,  cos  i  , n 3Di  a 3Di si .

Concatenating (11) and (16) gives following system

s ixy
x i
y i
z
, sin i 
, cos i 
, sin i  i 
s ixy
s ixy
si
si

we can represent bearing vector si as
s i  s i  cos i cos i , cos i sin i , sin i  T

C. AOA Measurement Processing Model
Relationship between azimuth angle i and unknown
transmitter coordinates can be derived using manipulation[25] for (5), yielding tan i  yi x i , orsin i  x i  cos  i y i  0 

Ax  r  n 

where A   2 N 13 , r   2 N 11 , n   2 N 11 : a T2D 0 r 
 a T2D0 0 n 2D0 




  
  
  


 T

 T 
 n 2DN 
a 2DN rN 
a 2DN 
A   T , r   T
 , n   n  
 3D 0  a 3D0 r0  a 3D 0 
  
  
  






T
T
 n 3DN  a 3DN a 3DN

rN 




Copyright ⓒ 2019 GiRI (Global IT Research Institute)

ICACT Transactions on Advanced Communications Technology (TACT) Vol. 8, Issue 2, March 2019

D. CRLB for AOA Measurement Processing Model
Bearing pair bi  

21with i and i is represented bybi   i , i  , after N timestamps forms array B   2 N 11 ,T

defined by B  x    0 , ,  N , 0 , ,  N  . Jacobian matrixTJ  x   B  x  x   2N3 can be computed assin 0



s 0xy




sin
N
 

s Nxy
J x  
 cos 0 sin 0

s0




cos


N sin  N
sN
cos 0s 0xyIII. SIMULATION SCENARIO AND RESULTS
Simulation model described further include arrangement,
estimation and visualization subsystems, described in [20],[21]. Positioning was performed for scenario whentransmitter is at the point (5, 4, 1) km in an area with a size of(10 × 10 × 5) km, stationary ground receiver is at the origin
point (0, 0, 0) km, and UAV flies circumferentially over thearea at a constant altitude z = 4 km, as depicted in Figure 4.

0
cos  N
s Nxy





 

0 

 
cos 0 

s0 
 

cos  N 
s N 

1196

sin 0 sin 0s0sin  N sin  NsN

The key in producing the CRLB is to construct thecorresponding Fisher information matrix (FIM), computed attransmitter location x   x, y, z  . The diagonal elements ofFig. 4. Example NLOS simulation scenario with ground and UAV receiver.

T

the FIM inverse are the minimum achievable variance values:
CRLB  x   trace  FIM 1  x   

When the primary AOA measurements are zero-mean
Gaussian distributed, FIM  x  can be computed as [26]In Figure 4 we have illustrated scenario when moving
receiver aboard UAV produces NLOS measurements
because of mountain obstacle for a short time flight.
Resulting RMSE of current estimates in three axes according
to UAV flight is provided in Figure 5.

FIM  x   J T  x  C 1J  x  

where C   2 N 12 N 1 is AOA noise covariance matrix
C   AOA I 

where  AOA is AOA standard deviation for azimuth i andelevation i , and I   

2 N 1 2  N 1

is identity matrix.

Numerical search to solve (17) was the Gauss-Newton
least squares (LS) algorithm which solves for x byminimizing the LS cost function







  B x T B
  B  x  x  arg min BxT   0 , ,  N ,  , ,   is bearing measurement
where B
0Narray. The iterative GN algorithm procedure is       B  B  x  

x k 1  x k  J T x k J x k J T x kk where J x k is Jacobian matrix (19) computed at x k . Initialvalue for the iterative GN algorithm (24) is calculated as themean of the receiver positions ri along UAV flight path.
The RMSE of coordinates estimate of transmitter is [27]
RMSE= E  x  xˆ  +  y  yˆ    z  zˆ   
2

2

2

 y,z
   is transmitter GN location estimate.
where x =  x,Fig. 5. RMSE estimation for scenario in Fig 4.

From Figure 5 it can be seen that the RMSE considerablyincreases in the interval from 42 s to 60 s, which is illustrated
by reflected rays, when LOS between UAV and transmitter isabsent and NLOS measurement comes after reflection frommountain during the UAV flight behind the obstacle.
Figure 6 shows resulting location RMSE versus AOA
standard deviation σAOA for azimuth 2i and elevation 2i
angles, and it can be seen, that RMSE quickly degrades with
the increase of AOA noise and reaches the order of 103m,
when AOA deviation σAOA approaches 10 degrees.
RMSE order of 103m is considerably higher, than LOS[13], [14], but lower, than NLOS transmitter location error[20], [21]. Approach to identify and exclude NLOS error,
validated in [20], [21], utilizes RMSE threshold, whichshould be higher than LOS error for worst SNR values and, atthe same time, lower than location error for NLOS scenario.

Copyright ⓒ 2019 GiRI (Global IT Research Institute)

ICACT Transactions on Advanced Communications Technology (TACT) Vol. 8, Issue 2, March 2019

Fig. 6. Emitter location RMSE versus AOA standard deviation σAOA.

IV. CONCLUSION
In this paper we refined 3D AOA measurements
processing model for positioning a transmitter with one
stationary ground and one flying UAV based receiver station.
Performed simulation results validate possibility to handle
NLOS with just two stations, because even coarse AOA withσAOA<10° can contribute to NLOS measurements identifying.

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Ph. D. Grogoriy Fokin (M'18) is with the
Bonch-Bruevich Saint-Petersburg State University of
Telecommunications (SUT) as Associate Professor of
the Department of Radio Communications andbecame a Member (M) of IEEE in 2018.
He graduated SUT in 2005, then received Ph. D
there in 2009 and from 2010 till 2014 worked as
Senior Researcher in Radio Research andDevelopment Institute (NIIR).
Mr. Fokin is author of 61 scientific papers, 5 tutorials and winner of grantcompetition of the President of the Russian Federation for the state supportof young Russian scientists № MK-3468.2018.9.

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